Fact and Fiction

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2007-08-25T20:34:00.000Z

Please go to The Spline for future blog postings.

Widescreen laptop computers

2007-02-25T16:26:00.000Z

My veteran laptop PC is a (less than 1 GHz) Pentium 3 powered Compaq Presario 1800, which has a mere 320MB of RAM and a 30GB hard disk, and it even needs an expansion card to enable it to talk to a wireless network. The real reason that I bought it around 5 years ago was the quality and size of its LCD screen; it has a 15 inch LCD screen which comfortably runs at 1400 by 1050 pixels (16 bits per pixel).

The LCD screen makes heavy duty technical wordprocessing relatively painless to do, especially as I use Publicon to do my technical writing. So, despite being an old and underpowered laptop PC, it creates worthwhile results because it is well-matched to the needs of the software that I run on it.

However, it would be nice to upgrade my laptop PC now that its processor is two generations out of date, having been overtaken by the Pentium 4 and the Core 2 Duo. A new laptop PC would also have a much larger RAM and hard disk, which would make the computer more generally useful to me.

So off I went to PC World to do some window-shopping, and I was really disappointed with what I discovered there (and at various other places that I also visited). Every laptop PC on display had a widescreen format. That would be fine if the height of the screen was as good as what I already have on my 5 year old laptop PC, and some extra width had been added to give it a widescreen format. However, none of the screens used the full height that was available in its clamshell lid housing. Instead, they had a thick plastic border area both above and below the screen to act a "filler" for a missing area of screen, so that the overall effect was to make the screen have a widescreen format (i.e. more like a letter box than a window).

It seems that the laptop PC manufacturers think that the aspect ratio of the screen itself is more important than fitting the largest possible screen in the clamshell lid housing, even in their top-of-the-range laptop PCs. The only reason that I can think for doing this is that it is fashionable to have a widescreen format LCD screen, and that the laptop PC will sell only if its LCD screen satisfies this criterion, even if there is room in the clamshell lid to fit a larger (i.e. higher) LCD screen.

I will never buy a laptop PC that doesn't allow me to do heavy duty technical wordprocessing with maximum facility. Currently, I have 1050 pixels of screen height on my 5 year old laptop PC, and I will not settle for fewer pixels than this. There was not a single laptop PC on display at PC World that satisfied this criterion; I also looked in various other places with a similar lack of success, so this comment is not a criticism of PC World. Later, I checked on-line and I found a few models of laptop PC that were OK for my purposes, but they were in a tiny minority.

Another thing I noticed at PC World was that all of the laptop PCs on display had highly reflective LCD screens, whereas I am used to using LCD screens that are not very reflective. I checked how easy it would be to use these LCD screens when there was a lot of light coming from behind me. My conclusion is that this sort of highly reflective LCD screen is unusable, unless the lighting conditions are of the sort that you would get in an ergonomically designed office. You certainly couldn't use it if there was a significant amount of light coming from behind you. Worse still, you certainly couldn't use it outdoors on a sunny day, especially if you were wearing a light-coloured shirt.

I'm glad that I went on my window-shopping expedition to PC World. My interest in upgrading my laptop PC has now definitely been put on hold until the manufacturers get the ergonomics of their laptop PC designs sorted out.

I didn't even try to put to serious use any of the laptop PCs that were on display; no doubt I would have found other things to moan about if I had tried them out. I'll leave it for 6 months before I do another window-shopping expedition, and hope that things have improved by then.

Update: 6 weeks have now passed by, and I could not resist trying out Windows Vista on some of the laptop PCs - the ones with 2 Gbyte of RAM. Superficially, there is a lot of "eye candy", but I hoped that I would find it was more interesting underneath. Sadly, I didn't get very far, because I was astounded at how slow Windows Vista is, even on a fairly powerful laptop PC (e.g. the ones costing around £1000 from Sony and HP). I deliberately booted from cold to see how long it took to start up, and I thought something had gone wrong because nothing seemed to happen for a long time. The whole booting process took at least a couple of minutes! This sluggishness was not limited to booting the PC; the whole user experience was that you were being held back by a PC that was unable to keep up with you. I now have even more reasons (see my complaints above about the latest types of LCD display) to stay with my old 2001 vintage 1GHz Pentium 3 laptop running Windows XP in a paltry 320MB of RAM.

Enigma variations

2007-02-09T23:09:00.000Z

Am I the only one, or has anyone else noticed how a lot of the New Scientist brainteasers (in the Enigma section) appear to have been constructed so that they can be solved by brute force? In fact, brute force makes it very easy to construct a "brain" teaser in the first place, because all you need to do is to describe a largish (but not too large) ensemble of potential solutions (e.g. all possible n-by-n grids of digits), then state a set of conditions that a unique member of the ensemble has to satisfy, then ask the reader to find that unique member, and submit it as their solution to the "brain" teaser.

Enigma 1428 in the most recent New Scientist appears to belong to this category of "brain" teaser. Here it is:

Foursight. Enigma No. 1428

If you place a 1, 2, 3 or 4 in each of the sixteen places in this grid, with no digit repeated in any row or column, then you end up with a “Latin square”. Then you can read eight four-figure numbers in the grid, namely across each of the four rows and down each of the four columns. Your task today is to construct such a Latin square in which those eight numbers are all different, none is a prime, no two are reverses of each other, and:

1st column X 3rd column
-------------------------------
2nd row X 3rd row

is greater than 4.

The relatively small size of this problem, and the fact that it looks numerically messy, immediately suggested to me that it was designed on computer, and that the quickest way to get the correct result was a brute force computer attack. I got out my trusty Mathematica and did the following steps (inputs in bold), where I made abolutely no attempt to streamline the code, I generated each input by copying/pasting/modifying earlier inputs, and the goal was to get to the answer as quickly as possible. The code is not really intended to be read except by masochists; it is a special write-only style that I use for problems like this.

How many candidate Latin squares with all digits different in each single row?

4!^4

331776

Construct all possible single rows.

perms = Permutations[{1, 2, 3, 4}]

{{1,2,3,4},{1,2,4,3},{1,3,2,4},{1,3,4,2},{1,4,2,3},{1,4,3,2},{2,1,3,4},{2,1,4,3},{2,3,1,4},{2,3,4,1},{2,4,1,3},{2,4,3,1},{3,1,2,4},{3,1,4,2},{3,2,1,4},{3,2,4,1},{3,4,1,2},{3,4,2,1},{4,1,2,3},{4,1,3,2},{4,2,1,3},{4,2,3,1},{4,3,1,2},{4,3,2,1}}

Join together in all possible ways to make all possible candidate Latin squares.

perms2 = Flatten[Table[{perms[[i]], perms[[j]], perms[[k]], perms[[l]]}, {i, 24}, {j, 24}, {k, 24}, {l, 24}], 3];
Length[perms2]

331776

Keep only the ones in which each single column has all digits different. The rows already satisfy this condition.

perms3=Select[perms2,Apply[And,Map[Length[Union[#]]==4&,Transpose[#]]]&];
Length[perms3]

576

Keep only the ones in which all 8 rows and columns are different numbers.

perms4=Select[perms3,Length[Union[Map[FromDigits,Join[#,Transpose[#]]&[#]]]]==8&];
Length[perms4]

480

Keep only the ones in which none of the 8 rows and columns is prime.

perms5=Select[perms4,!Apply[Or,Map[PrimeQ[FromDigits[#]]&,Join[#,Transpose[#]]&[#]]]&];
Length[perms5]

88

Keep only the ones in which none of the 8 rows and columns is the reverse of another.

perms6=Select[perms5,Length[Union[Map[FromDigits,Join[#,Transpose[#],Map[Reverse,#],Map[Reverse,Transpose[#]]&[#]]]]]==16&];
Length[perms6]

24

Keep only the ones in which col 1 * col 3 / (row 2 * row 3) > 4.

perms7=Select[perms6,#[[5]]#[[7]]/(#[[2]]#[[3]])>4&[Map[FromDigits,Join[#,Transpose[#]]&[#]]]&];
Length[perms7]

1

The unique answer.

perms7[[1]]

{{3,2,4,1},{1,4,3,2},{2,3,1,4},{4,1,2,3}}

Winter has come

2007-02-09T22:04:00.000Z

Here is a photo showing the view from my house this afternoon. On a clear day you would see hills/woods/fields in the middle distance of the photo. But yesterday and today the snow monster visited instead.

I live way up on the side of the Malvern Hills facing the prevailing weather, so I get more than my fair share of the weather when it comes. The depth of the snow is nearly twice what it is in regions neighbouring my microclimate.

I was going to go out for a snowy walk on the Malvern Hills, but decided not to when I saw how deep the snow was. So I have now spent a couple of days holed up in my house, because my car is notorously difficult to drive in snow (it is a heavy BMW with an automatic gearbox) and I would never get it back up the hill driving from work to home. I have put my time to good use creating some tutorial material to help people at my place of work understand all about the research that I have been doing for the past 20 years. Somehow I think the effort will not be as worthwhile as I had initially hoped it would be.

I must get out and play in the snow before it disappears, which the weather forecast says will happen over the weekend.

Bottom-up design of high energy physics theories

2007-02-04T11:11:00.000Z

In last week's New Scientist there was an article entitled The Large Hadron Collider: Bring it on! which discusses how physicists are going to set about interpreting the flood of data that will emerge from the Large Hadron Collider (LHC) at CERN. This grabbed my attention because the method of bottom-up construction of physical theories that is described in the article is closely related to how self-organising networks are designed.

The standard approach is to start with the various candidate theories about how particles interact when they hit each other inside the LHC, and then make predictions about what each of these theories expects to find in the products of such collisions. This allows you to discover which theory gives you predictions that correspond most accurately with what you actually observe in the LHC data, and if the correspondence is exact (or nearly so) then this thory becomes an accepted law of physics.

There are lots of other constraints that moderate this process. For instance, it is necessary but not sufficient that the newly accepted theory agrees with what is observed in the LHC data. It must also agree with everything else that we have observed or will observe, so the process of testing the theory goes on in perpetuity as repeated attempts to falsify it continue to be made.

Also it may turn out that none of the candidate theories fits the data, in which case you need to think up some new theories. Or it may turn out that more than one of the candidate theories fits the data, in which case you need to think up some new experiments that might discriminate between the remaining candidate theories.

That's the standard way of finding the right theory: the scientific method.

The article in New Scientist describes an interesting alternative approach to finding the right theory. It was introduced in a paper by Bruce Knuteson and Stephen Mrenna entitled Bard: Interpreting New Frontier Energy Collider Physics (www.arxiv.org/hep-th/0602101), which describes a way of building physical theories from scratch from the experimental data. Actually, the method described there is not an alternative to the scientific method, but rather it is an attempt to automate part of the scientific method.

The approach goes roughly like this. You start with a lot of raw experimental data, and based on what incoming and outgoing particles you see in each collision you hypothesise the existence of particle interactions that can give rise to the observed experimental data. That alone would not achieve very much because it just says that you see what you see. However, if you go further than this by imposing constraints on what sorts of particle interactions you allow yourself to use, then it is not usually possible to explain all of the experimental data directly, and you are forced to build composite interactions that consist of more than one of the allowed basic interactions joined together in various ways (i.e. you build Feynman diagrams out of elementary vertices joined together by propagators). The hope is that you can use fairly simple composite interactions to successfully explain each set of experimental data, and if you can't do this then you enlarge your allowed set of allowed basic interactions until you can explain the data.

In order for this bottom-up approach to designing physical theories (or models) from observed experimental data to work successfully you need to have strict rules to control what interactions you can add to your allowed set of basic interactions. In effect, you need to emulate the refined sense of judgement that theoretical physicists use when crafting new theories. This consists of a combination two rather different abilities: (1) the inspiration needed to invent a radically new class of models (this is hard to automate), (2) the patience and stamina to check out the individual members of a class of models (this is relatively easy to automate). The bottom-up approach can readily be applied to type-2 modelling, but it becomes progressively harder as you penetrate type-1 modelling territory. Nevertheless, provided you can write a "template" for each class of models, then it is possible in principle to automate the search over model space to find the candidate that is the best fit to the data.

A big advantage of the bottom-up approach is that it is relatively unprejudiced, because it treats each of the candidate models in an even-handed way, so there is no possibility of prejudice making you overlook a viable candidate. Nevertheless, the candidates are limited to only those classes of models for which templates have been defined at the outset, so there is a global form of prejudice hard-wired into the bottom-up approach.

What really caught my eye about this bottom-up approach to the design of physical theories is its "equivalence" to the data-driven design of self-organising networks. In both cases you try to "explain" the structure of the data by first of all attempting to fit the data with the allowed building blocks: basic interactions in physics, or links in networks. If (or usually, when) this fails to give an accurate fit to the data, you then move to a composite explanation in which you introduce another layer of explanation to explore a larger space of models, within which you hope that a good fit to the data can be found.

In physical theories this larger space of models would allow additional types of basic interaction, or it might be just a refined version of the basic interactions that you were already using (e.g. using more loops). In self-organising networks this larger space is usually (but not invariably) constructed by adding another layer of nodes to the network, which has the effect of introducing indirect links between the nodes in the previously existing network layer(s). In both physical theories and self-organising networks the effect of enlarging the space of models is essentially the same; progressively more indirect explanations of the data become candidates to be considered.

I wonder to what extent self-organising networks (of whatever type) might be used to automate the discovery of physical theories.

Bell Labs: Over and out

2007-02-03T17:49:00.000Z

In this week's New Scientist there is an article entitled Bell Labs: Over and out, which is about the decline and fall of Bell Labs. As the article puts it, Bell Labs was "formerly the world's premier industrial research laboratory". So, what went wrong?

The article says

What, then, was the key to its success? A large part of it was the way it encouraged its employees to strive for great ideas and tackle the toughest problems. The company trained technical managers to inspire staff, with ideas rather than meddle with details, and could afford to have multiple teams try different approaches at once. No doubt it also benefited from the security of working for a regulated monopoly insulated from the whims of the marketplace.

and also

Eventually Bell's success ended too. After years of litigation, AT&T spun off its regional telephone service as seven separate companies in 1984, ending the decades of cosy monopoly. A dozen years later, it spun off most of Bell Labs along with its equipment division as Lucent Technologies, which initially prospered but then stumbled badly, shrinking from a peak of 16o,ooo employees to 30,5oo before merging with Alcatel ... It will be missed - it already is. The greatest loss is not so much Bell's vaunted basic research, but its unique ability to marshal teams of top technologists to transform bright ideas into effective technology.

Bell Labs was a laboratory that did great research because it employed top-notch researchers, it was protected from the marketplace, and because its managers could operate in a hands-off mode rather than micromanage everything, which allowed its researchers to get on with doing basic (read "long term") research. When these preconditions (i.e. protection from the marketplace, and hands-off management) are removed the structure of the organisation begins to change irreversibly, e.g. basic research ceases to be done.

I'm not so sure that I agree that "the greatest loss is not so much Bell's vaunted basic research", because basic research provides the source material for future technology. Even if you employ the best people in the world for turning the results of basic research into usable technology, you can get away without doing basic research for only so long before the cellar full of fine wines laid down in earlier years runs dry.

I particularly liked the phrase "transform bright ideas into effective technology" that was used in the article, because it sounds like the sort of "mission statement" that could be used by any organisation that wanted to plunder its cellar to convert its past basic research results into technology.

Because I do a lot of basic research myself, I have an interest in freedom to do basic research being granted to individuals who have a flair for this sort of activity (not many people, in my experience); I have commented on this in an earlier posting here. It seems that wherever I look conditions are changing in ways that are hostile to this civilisation-creating activity; see here for my earlier posting on this.

Marvin Minsky bashes neuroscience

2007-01-30T18:18:00.000Z

From KurzweilAI.net I learn that Marvin Minsky has given an interview to Discover magazine here. Minsky is one of the pioneers of artificial intelligence, and he is a very articulate and outspoken character. In the interview he comments on the activities of neuroscientists.

Q (Discover). Neuroscientists' quest to understand consciousness is a hot topic right now, yet you often pose things via psychology, which seems to be taken less seriously. Are you behind the curve?

A (Minsky). I don't see neuroscience as serious. What they have are nutty little theories, and they do elaborate experiments to confirm them and don't know what to do if they don't work. This book [The Emotion Machine] presents a very elaborate theory of consciousness. Consciousness is a word that confuses possibly 16 different processes. Most neurologists think everything is either conscious or not. But even Freud had several grades of consciousness. When you talk to neuroscientists, they seem so unsophisticated; they major in biology and know about potassium and calcium channels, but they don't have sophisticated psychological ideas. Neuroscientists should be asking: What phenomenon should I try to explain? Can I make a theory of it? Then, can I design an experiment to see if one of those theories is better than the others? If you don't have two theories, then you can't do an experiment. And they usually don't even have one.

I'm sure the activities of neuroscientists are well-intentioned, as they adopt a reductionist approach to the analysis of a highly complex system (i.e. the brain) by working upwards from the detailed behaviour of individual neurons. However, neuroscientists' theorising about AI is bound to be wildly off-target, since AI lives at a much higher level than the relatively low level where they are working. Tracing the detailed neural circuitry of small parts of the brain (or even the entire brain) will not lead to AI; discovering the underlying principles of AI (whatever those turn out to be) will lead to AI, and it will not necessarily need biological neurons to "live" in.

In the early 1980's I jumped on the "neural network" bandwagon that had restarted around that time. There was a lot of hype back then that this was the rigorous answer to understanding how the brain worked, and it took me a few years to convince myself that this claim was rubbish; the "neural network" bandwagon was based solely on some neat mathematical tricks that emerged around that time (e.g. back-propagation for training multi-layer networks, etc), rather than better insight into information processing or even AI. My rather belated response was to "rebadge" my research programme by avoiding use of the phrase "neural networks", and instead using phrases like "adaptive networks" and the like; I wasn't alone in using this tactical response.

Q (Discover). So as you see it, artificial intelligence is the lens through which to look at the mind and unlock the secrets of how it works?

A (Minsky). Yes, through the lens of building a simulation. If a theory is very simple, you can use mathematics to predict what it'll do. If it's very complicated, you have to do a simulation. It seems to me that for anything as complicated as the mind or brain, the only way to test a theory is to simulate it and see what it does. One problem is that often researchers won't tell us what a simulation didn't do. Right now the most popular approach in artificial intelligence is making probabilistic models. The researchers say, "Oh, we got our machine to recognize handwritten characters with a reliability of 79 percent." They don't tell us what didn't work.

This caricature of the cargo-cult science that passes itself off as genuine science made me laugh. As it happens, I use (a variant of) the probabilistic models that Minsky alludes to, and I find the literature on the subject unbelievably frustrating to read. A typical paper will contain an introduction, some theory, a computer simulation to illustrate an application of the theory, and a pathetically inadequate interpretation of what it all means. The most important part of a paper (the "take home message", if you wish) is the interpretation of the results that it reports; this comprises the new conceptual tools that I want to take away with me to apply elsewhere. Unfortunately, the emphasis is usually on presenting results from a wide variety of computer simulations and comparisons with competing techniques, which certainly fills up the journal pages, but it doesn't do much to advance our understanding of what is going on.

Where are the conceptual tools? This is like doing "butterfly" collecting rather than doing science. We need some rigorous organisational principles to help us gain a better understanding of our large collection of "butterflies", rather than taking the easy option of simply catching more "butterflies".

It seems to me that the situation in AI is analogous to, but much more difficult than, the situation in high energy physics during the 1950's and 1960's, when the "zoo" of strongly interacting particles grew to alarming proportions, and we explained what was going on only when the eightfold way and the quark model of hadrons were proposed. I wonder if there are elementary degrees of freedom underlying AI that are analogous to the quark (and gluon) DOF in hadrons.

I'll bet that the "elementary" DOF of AI involve the complicated (strong?) mutual interaction of many neurons, just as the "elementary" DOF in strong interactions are not actually elementary quarks but are composite entities built out of quarks (and gluons). I'll also bet that we won't guess what the "elementary" DOF of AI are by observing the behaviour of individual neurons (or even small sets of neurons), but we will postdict (rather than predict) these DOF after someone (luckily) observes interesting information processing happening in the collective behavour of large sets of neurons, or if someone (even more luckily) has a deep insight into the theory of information processing in large networks of interacting processing units.

Who is in control?

2007-01-07T14:11:00.000Z

New Scientist ran a New Year competition in which you were invited to imagine that you were an alien who had recently arrived on Earth, and you had to send a short text message home describing what you found there. The winners have now been announced here, and my two favourites are:

Arr. Earth. Dominant species "car". Colourful exoskeleton and bizarre reproduction via slave biped species. Aggressive but predictable. Intelligence uncertain. (from David Armstrong)
Parallel evolution of intelligent life. One carbon based, one silicon based. Carbon form domesticated by silicon form to feed it with all its needs. (from Dennis Fox)

As you can see, my two winners have a common theme because they both ask "who is in control?".

I suspect that the message about the carbon/silicon hybrid is going to get a lot more serious as time goes on. There are people (such as Ray Kurzweil and Nick Bostrom) who make entire careers out of predicting where this sort of symbiotic man/machine hybrid will go.

Here is an entertaining little exercise, which I was told about many years ago so I don't know its origin, but I certainly have seen a science fiction film (title unknown) in which a spaceship full of troopers is subjected to this "experiment". Think about what happens if your biological brain cells (i.e. neurons) are replaced one at a time by functionally equivalent artificial brain cells. At the start of this process you have your original biological intelligence, and at the end you have a functionally equivalent artificial intelligence.

It is tempting to say that the AI version of you isn't really you; after all, it is only a load of silicon (or whatever). However, the AI version is reached by a series of infinitesimally small steps, where only one neuron at a time is transformed. What would your subjective feeling be as each neuron was transformed in this way? By definition, there should be no subjective change, because each biological neuron is replaced by a functionally equivalent artificial neuron, so whatever it is that each neuron does, it does the same thing before and after the transformation into an artificial neuron. Thus, artificial you = biological you.

Of course, I slipped an assumption past you in the above "proof"; I assumed that "you" and "brain" are one and the same thing. This is the assumption made in Francis Crick's book The Astonishing Hypothesis, in which Crick claims "You, your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behavior of a vast assembly of nerve cells and their associated molecules". I think that until we have actually done the biological-to-artificial transformation experiment (or something like it) we cannot know for sure that there is no subjective difference between our subjective biological and artificial intelligences.

I will not be offering myself for this experiment (even if we had the technology to do it), because there is too much to lose if (for some as yet unknown reason) our functionally equivalent artificial neurons are not actually functionally equivalent. Absence of evidence is not the same as evidence of absence, so just because we haven't observed something doesn't mean that that something does not exist. Neurons may (and probably do) communicate in ways that we do not yet suspect, and there may also be lots of things other than neurons involved in our "biological" intelligence. Mother Nature is always more imaginative than we are.

Anyway, none of that changes the truth contained in the message about the carbon/silicon hybrid. We are already carbon/silicon hybrids, because the everyday lives of a significant fraction of people on the planet depend on computer-based things going on in the background (and this relationship is reciprocal). This dependence is going to become more and more direct and intimate as time goes on.

Who is in control?

Indeed!

Who is in control?

Possible worlds

2006-12-26T22:34:00.000Z

I have just finished Richard Dawkins book The God Delusion, the last paragraph of which reads as follows:

How should we interpret Haldane's 'queerer than we can suppose'? Queerer than can, in principle, be supposed? Or just queerer than we can suppose, given the limitation of our brains' evolutionary apprenticeship in Middle World? Could we, by training and practice, emancipate ourselves from Middle World, tear off our black burka, and achieve some sort of intuitive - as well as just mathematical - understanding of the very small, the very large, and the very fast? I genuinely don't know the answer, but I am thrilled to be alive at a time when humanity is pushing against the limits of understanding. Even better, we may eventually discover that there are no limits.

Some of the above terminology needs to be explained by citing its earlier use in the last chapter of the book:

... the universe is not only queerer than we can suppose ...
... our brains ... evolved to help us survive in a world - I shall use the name Middle World - where the objects that mattered to our survival were neither very large nor very small ...
... I want to use the narrow slit in the veil [i.e. burka] as a symbol of something else. Our eyes see the world through a narrow slit in the electromagnetic spectrum ... The metaphor of the narrow window of light ... serves us in other areas of science ...

I had one of those eerie feelings of déjà vu when I read the paragraph quoted above. Its message is spookily similar to what I was saying in my earlier posting Demystifying hard subjects, which was itself based on thoughts that I had long before I read The God Delusion.

Anyway, my message to Richard Dawkins is we can "achieve some sort of intuitive - as well as just mathematical - understanding of the very small, the very large, and the very fast". The trick is to bang the right sort of mental rocks together.

Nikola Tesla portrait

2006-12-26T17:45:00.000Z

A while ago I received a gift of the pencil portrait below (drawn by Malcolm Victory):

This is a portrait of Nikola Tesla who was "the man who invented the 20th century". He looks as if he is in one of his more hectoring moods. Naturally, I have mixed feelings about receiving this gift!

Demystifying hard subjects

2006-12-25T22:15:00.000Z

Some subjects are called "hard" because you need years of training to understand and practice them. Examples of hard subjects are mathematics, physics, chemistry, etc, and examples of soft subjects are sociology, media studies, etc. Essentially, the difference between these two categories is that hard subjects are far from our everyday common sense so they are not intuitively accessible, whereas soft subjects are close to our everyday common sense so they are intuitively accessible.

It seems to me that the "hardness" of a subject is strongly correlated with the following two properties to do with reasoning about and sensing the world:

How mathematical/logical its formulation is; this property is to do with reasoning about the world. Anyone who does not have the appropriate mathematical/logical training is automatically excluded from the subject, which thus falls into the "hard" category.
How accessible it is to observation and verification by our senses; this property is to do with sensing the world. Any subject that relates to phenomena that are accessible only by using specially designed sensors falls into the "hard" category.

Either way, our common sense is limited by what our bodies can do unaided, whether it is sensing (e.g. using our eyes) or reasoning with our brains. To develop an enhanced common sense we need to enhance our sensors (e.g. use a microscope) and/or our enhance our ability to reason (e.g. attend further education classes).

Here I want to focus on the improvements to common sense that can be gained by enhancing our ability to reason, which are gained (often at great expense in time and money) by further education. Of course, I have a vested interest in this aspect because my own further education didn't finish until I was around 27 years old (or 1/3 of a typical lifetime), and it was heavily mathematical towards the end. However, I have a very ambivalent attitude to the type of enhancements to my common sense that I gained as a result of my lengthy education. I can do fancy maths to calculate results that are both correct and useful, and which thus can serve as enhancements to my prior common sense. But I can't do these calculations in real-time, because I have to do each calculation laboriously off-line rather than on-line, so they are rather slow enhancements to my common sense. It would be much better if these enhancements could be "compiled down" to become fast response (i.e. on-line rather than off-line) enhancements, which could then more justifiably (i.e. they now work in real-time) be called enhancements to my common sense reasoning ability.

All of this "compiling down" amounts to finding ways of short-circuiting mathematical calculations so that results can be seen directly without having to go through all the intermediate steps of the mathematical derivation. This possibility is called computational reducibility, and it is not guaranteed to even be possible, e.g. many simulations in NKS are strictly computationally irreducible. Where a calculation is computationally reducible it is because there is a higher level principle at work (whose inner details are implemented by the individual steps of the mathematical derivation) which allows us to take large strides forwards through a derivation rather than achieve the same thing by a large number of time consuming little steps. Generally speaking, the higher the level of the principles the greater the speed-up that can be achieved. Note (for physicists) that another way of viewing these high-level principles is that they bear the same relationship to the low-level mathematics as effective theories bear to underlying theories.

Here is a simple example. When I was about 10 years old I realised that the formula p=ρ.g.h for pressure p at a depth h in a medium of density ρ could be understood directly and intuitively; in effect I never memorised that formula (even when I was 10 years old) because I always rederive it in real-time every time that I need it. This early insight was a complete revelation to me, and it has influenced the way that I do science and mathematics ever since. I carry very little memorised information in my head, but I do carry a small number of principles that I use to quickly rederive whatever I need. Naturally, I have now gone far beyond p=ρ.g.h but the same general approach still applies. Very conveniently, this approach (i.e. rederive rather than memorise) served me very well in various school/university examinations!

So, how are computational reducibility, higher level principles, and enhanced common sense related? How is it possible to see results directly and intuitively? Here I will have to assume that what works for me also works for other people, so I will focus on the use of visual intuition where low-level mathematics become elementary operations for manipulating a visualised world, and then high-level principles emerge as composite operations on this visualisation. It should be clear that the amalgamation of many low-level operations into fewer high-level operations amounts to a form of visual intuition about the behaviour of this visualised world.

Let's discuss a concrete example to illustrate the strengths and weaknesses of visualisation. How about the simple p=ρ.g.h example given above? The medium can be visualised as a cloud of small blobs (atoms), where the average number of blobs per unit volume (number density) is n, the mass of each blob is m, so the average mass of blobs per unit volume (density) is ρ=n.m. Each unit area of whatever this cloud rests upon must supply an (upward) force that is equal to the (downward) weight of the blobs in the cloud resting on the unit area, otherwise the upward and downward forces would not be in balance. The thickness of the cloud (depth) is h, so the average mass of blobs per unit area is ρ.h. Finally, the (downward) acceleration due to gravity g causes this mass per unit area ρ.h to have a (downward) weight g.ρ.h. Gathering it all together, the (downward) weight per unit area is ρ.g.h, which must be equal to the (upward) force per unit area, which is one and the same thing as the pressure p at the base of the cloud of blobs, so p=ρ.g.h.

Whew! Written out like that the derivation of p=ρ.g.h is incredibly verbose. However, I am not suggesting that you actually write things out in this way, but that you create a visualisation whose properties are described by the various sentences in the above paragraph. With exercise this process of visualisation becomes semi-automatic, and the whole of the above paragraph can be quickly "simulated" in your head. This simulation then becomes a virtual derivation (written in visual symbols) of the formula p=ρ.g.h, which can be converted into a real derivation (written in standard algebraic notation) as necessary. This example illustrates the relationship between the visual and the algebraic approaches to doing mathematics.

Of course, p=ρ.g.h is a very simple example where the visual representation is so easy to create from the algebraic representation that you might assume that you could always start from the algebra and derive the visualisation from it, rather than the other way around. However, almost everything else is more complicated than p=ρ.g.h, and although the algebraic approach always works correctly, it rapidly becomes so complicated that its results can no longer be obtained directly and intuitively, which is where the alternative visual approach allows you to take intuitive visual shortcuts to quickly derive qualitative results.

For an example of a more substantial use of a visualisation type of approach have a look at my Spooky action at a distance? posting where I discuss the so-called EPR paradox in quantum mechanics. In fact there is no paradox there, but only confused thinking caused by a failure to use the mathematics of QM consistently, i.e. assuming that "observers" somehow exist outside the QM system that they are "observing". I was taught QM using this inconsistent approach, which was fine for passing physics exams, but started me off with a hopelessly confused point of view when I eventually had time to sit down and really think about QM. It took me a while, and several false starts, before I finally realised that "observers" have no special status, and should therefore be lumped in with the system that they are observing, which led inevitably to me rediscovering what I later learnt was the Everett interpretation of QM (see the The Everett FAQ) which I wrote about in State vector collapse? Anyway, I now have a visual language (e.g. Spooky action at a distance?) that enhances my everyday common sense so that I can intuitively and directly obtain qualitative QM results. Why can't this type of approach be taught in QM courses?

Of course, I can't prove that it will always be possible to find intuitive visual representations of complicated mathematics, but I certainly feel that I understand the mathematics much better if I can find such a representation, and use it to intuitively and directly derive qualitative results. I have heard it claimed that some fields of work lie outside the realm of direct intuitive comprehension (e.g. when a simple result seems to magically pop out of an enormously complicated piece of mathematics), but I hope that this claim is the result of a lack of imagination rather than there being a fundamental limitation to what we can visualise using appropriate techniques.

The visual approach described above can be used to enhance your everyday common sense, so that it becomes able to intuitively reason about what are normally viewed as "hard" subjects. In effect, "hard" subjects become "soft" subjects, when addressed using a common sense that has been enhanced by use of visualisation techniques.

We don't really know what string theory is

2006-12-17T11:42:00.000Z

I learn from Not Even Wrong that Steven Weinberg has said:

The critics are right. We have no single prediction of string theory that is verified by observation. Even worse, we don’t know how to use string theory to make predictions. Even worse than that, we don’t really know what string theory is.

I have deep respect for Steven Weinberg's views on physics, not merely because he is a Nobel laureate but because he is deeply thoughtful about what he says, so his damning comment on string theory carries a lot of weight with me.

The situation with string theory always reminds me of the brilliant quotation by Richard Feynman:

Physics is to math what sex is to masturbation.

It seems that I had a narrow escape when I left physics for even sexier research back in the early 1980's, because I suspect that had I stayed I would have been enticed into working on string theory, and would have thus unwittingly tossed away my entire research career.

Four preconditions for civilisation

2006-12-15T22:36:00.000Z

A propos my previous posting It pays to keep a little craziness, here are the four intellectual processes underlying human achievement, as listed on the back cover of the book Pioneering Research: A Risk Worth Taking by Donald W Braben that I discussed a few months ago here.

Ask questions not on the agenda
Explore ideas wherever they lead
Pursue goals because they are important
Create options not yet perceived

Here are the sorts of questions (numbered as above) that "bureaucracy" asks which strangle these processes:

Does your proposal directly address the issues outlined in the invitation for tender?
What is the breakdown of your proposed project into work packages and deliverables?
What's the business case for your proposed line of research?
Does your proposal directly address the issues outlined in the invitation for tender?

I am regularly asked all of these questions, and, yes, they do have the predicted strangling effect. All of this is to satisfy those people who like to reduce everything to a bunch of spreadsheet cells, so that they can control things. It seems that the admin-geeks (see here for more details) now rule the world.

What could be done to avoid these control freaks? Hmm ... tricky problem.

It pays to keep a little craziness

2006-12-09T15:17:00.000Z

This week's New Scientist has an editorial entitled It pays to keep a little craziness, which makes a case for supporting a small number of maverick scientists. The entire editorial is reproduced here:

Time was when all scientists were outsiders. Self-funded or backed by a rich benefactor, they pursued their often wild ideas in home-built labs with no one to answer to but themselves. From Nicolaus Copernicus to Charles Darwin, they were so successful that it's hard to imagine what modern science would be like without them.

Their isolated, largely unaccountable ways now seem the antithesis of modern science, with consensus and peer review at its very heart. Yet the "outsider" tradition persists. Think of Alfred Wegener, the father of plate tectonics and, more controversially, of Gaia theorist james Lovelock. Both pursued their theories in the face of strong opposition from their peers.

Such mavericks can be crucial to progress, but are they a dying breed? Beyond young disciplines such as neurobiology, where the territory is largely uncharted, or esoteric areas like quantum theory, where it's hard to prove anything, the consensual nature of science can make it hard for lone voices to thrive.

This may be inevitable. Peer review is inherently conservative, and increasingly only proposals that fit the research framework get funding. The sheer number of ideas in circulation means we need tough, sometimes crude ways of sorting geniuses from crackpots.

The principle that new ideas should be verified and reinforced by an intellectual community is one of the pillars of scientific endeavour, but it comes at a cost. We shouldn't allow it to freeze out individuals who are courageous, brilliant or foolhardy enough to go it alone.

Why does this issue grab my attention? It's because it strikes very close to "home" for me, because throughout my research career I have marched to the beat of a differerent drum. Except for very early on (e.g. during my PhD years) I have never been attracted to the idea of doing "fashionable" research, i.e. of a sort that would gain the approval of my peers, lead to lots of publications in high profile journals, and lots of recognition generally. Surely, this list of potential rewards is enough to make the decision about what sort of research to do a no-brainer? For most researchers this is indeed the case, but for a small subset of researchers the mere idea of running with the herd is deeply repulsive.

My rate of publishing in respectable journals has reduced as my research work has advanced, because I have gradually moved away from the accepted mainstream of research in information processing. I have a magnificent collection of rejection letters and referee's reports that I have collected over the years, which clearly demonstrate how conservative and cliquey the peer review process can be. Oh well, I will have to find other publication channels to disseminate my ideas, and with some imagination it isn't too hard to find unconventional ways to publish one's work. Wouldn't it be fun at some point in the future for mainstream researchers to ascend a hitherto unscaled peak, only to find an old flag with the monogram "SPL" already planted there?
Is it just a dream? Who knows? It all depends on whether I am courageous, brilliant or foolhardy (to quote from the above editorial).

Update: In Richard Dawkins book The God Delusion I found this very relevant passage (on page 196 in my 2006 edition):

As with genes in the gene pool, the memes that prevail will be the ones that are good at getting themselves copied. This may be because they have direct appeal ... or it may be because they flourish in the presence of other memes that have already become numerous in the meme pool.

So, to get your paper published it has to either stand all by itself as a self-contained body of work, or it has to dovetail neatly with the papers that have already been published. So what happens to papers that depend on other papers that have not been published? Memetics is a harsh midwife, methinks.

What's done is done, or is it?

2006-10-01T10:56:00.000Z

There is an article by Patrick Barry entitled What's done is done, or is it? in this week's New Scientist, in which he discusses whether quantum mechanics allows the future to change the past.

Ho hum! Here we go again.

I debunked this whole class of phenomena (or, at least, the wrong interpretation(s) of them) in an earlier posting of mine called Spooky action at a distance?, where I showed exactly how QM explains the instantaneous communication that seems to occur between separated particles. Of course, there is no such instantaneous communication; any correlations between separated particles are explained entirely by the fact that they were in close contact at an earlier point in their history, together with the fact that the full QM description of the real physical state of the particles and the "observers" is a superposition of all of their allowed alternative states. For a detailed explanation of this see Spooky action at a distance?.

People love to imagine that QM is mysterious (remarkably, that includes the vast majority of physicists), and journalists take advantage of this weakness by writing articles like What's done is done, or is it?. I would prefer that we didn't encourage this sort of folk science, because it makes our thinking muddled, which makes it impossible to develop a correct shared understanding of QM.

If that sounds haughty, then I apologise, but this torrent of articles about "mysterious this" and "spooky that" tests my patience. Maybe I should write a popular science book to share my understanding of QM with others.

Update: That rant of mine seems to have scared you all off! Surely, I am not alone in feeling this way about the "reverential" treatment of QM in the popular press? As long as we insist on calling QM "spooky" and "mysterious" we will hold ourselves back from really understanding it.

Fly by light

2006-09-09T15:46:00.000Z

This week's New Scientist has a cover story entitled Fly by Light by Justin Mullins. This article describes a device invented by Roger Shawyer that is so obviously a "perpetual motion machine" that I am amazed that New Scientist had the cheek/ignorance to publish the article. In fact, the article is perfect source material for this Fact and Fiction blog.

Here is a quote from the article to start us off:

Take a standard copper waveguide and close off both ends. Now create microwaves using a magnetron, a device found in every microwave oven. If you inject these microwaves into the cavity, the microwaves will bounce from one end of the cavity to the other. According to the principles outlined by Maxwell, this will produce a tiny force on the end walls.

All is OK so far. But then the article goes on to say:

You might think that the forces on the end walls will cancel each other out, but Shawyer worked out that with a suitably shaped resonant cavity, wider at one end than the other, the radiation pressure exerted by the microwaves at the wide end would be higher than at the narrow one.

and also:

Shawyer calculates the microwaves striking the end wall at the narrow end of his cavity will transfer less momentum to the cavity than those striking the wider end [this is supported by a diagram showing a tapered cavity with sloping sides and parallel end walls]. The result is a net force that pushes the cavity in one direction. And that's it, Shawyer says.

This is backed up by a lot of pseudo-scientific hocus-pocus, and it also mentions how "relativity and the strange nature of light come in". You couldn't invent this stuff! Sorry, unfortunately someone has, and I am reading it.

Shawyer's calculation evidently omits contributions to the overall force on the cavity from microwaves striking the sloping side walls of the cavity, where the local contribution to the force is perpendicular to the local patch of side wall. Note that this perpendicularity assumption is a good approximation for the high-Q cavities discussed in the article, where the walls of the cavity act as mirrors. Overall, the net force due to striking the side walls points towards the tapered end of the cavity. If Shawyer had taken this into account then he would have found that the net force due to striking the side walls is equal and opposite to the net force due to striking the end walls.

This result does not depend on the detailed shape of the closed cavity; the forces always cancel out when they are all taken into account. That means that there is no net force on the cavity, so it will not accelerate off in one direction. You certainly won't be powering spaceships using this type of drive, as is suggested in the article's title "Fly by Light".

This "Fly by Light" article belongs in a 1st April edition of New Scientist.

Update: Roger Shawyer has now written a letter to New Scientist (see here) to defend his position against all of the criticism he has received following the publishing of the article discussed above. Here is a copy of his letter with my comments inserted in square brackets:

The momentum exchange is between the electromagnetic wave and the engine, which is attached to the spacecraft. As the engine accelerates, momentum is lost by the electromagnetic wave and gained by the spacecraft, thus satisfying the conservation of momentum. In this process, energy is lost within the resonator, thus satisfying the conservation of energy. [This is a correct description of energy and momentum conservation by the individual interactions between photons in the EM wave and electrons in the engine, but you can't build up the claimed acceleration in this way because there are interactions all over the inside wall of the engine, and these balance out on average.]

The emdrive concept is clearly difficult to comprehend without a rigorous study of the theory paper, which is available via emdrive. corn or the New Scientist website (http://tinyurl.com/npxv8). This paper, which has been subjected to a long and detailed review process by industry and government experts, derives two equations: the static thrust equation and the dynamic thrust equation. [The analysis in the cited paper is unnecessarily complicated, so one can't see the wood for the trees, which is why mistakes were made. The simplest way to see that the claims are false is to consider the energy/momentum conserving individual photon-electron interactions, as described in my comment immediately above. QED.]

The law of the conservation of momentum is the basis of the static thrust equation, the law of the conservation of energy is the basis of the dynamic thrust equation. Provided these two fundamental laws of physics are satisfied, there is no reason why the forces inside the resonator should sum to zero. [Force is built out of the impluses due to the momentum exchanges that occur during all of the individual photon-electron interactions, which are momentum conserving so that equal and opposite momenta are exchanged during each interaction. The system is closed, so the total force must be zero.]

The equations used to calculate the guide wavelengths in the static thrust equation are very nonlinear. This is exploited in the design of the resonator to maximise the ratio of end plate forces, while minimising the axial component of the side wall force. This results in a net force that produces motion in accordance with Newton's laws. [Non-linearity is irrelevant. Think in terms of the individual photon-electron interactions to avoid unnecessary complications.]

We are now in the process of negotiating a trial flight programme. [Good luck! You'll need it!]

ACEnetica is where I blog about my research

2006-09-01T20:20:00.000Z

I try to separate my blog postings into two categories: those related to my research, and the rest. It is not always possible to draw a clear-cut distinction, but this blog Fact and Fiction tends to contain all of the frivolous material plus an admixture of a few more serious postings, whereas my ACEnetica blog is where I write about my professional research.

If you are looking for material about my research on self-organising networks then you should visit ACEnetica. I notice that the physics aggregator Mixed States gets a feed from this blog Fact and Fiction, which must puzzle a lot of people because I would have thought that it should get its feed from ACEnetica.

Photo quiz

2006-08-15T19:02:00.000Z

Here are 3 photos that I took whilst in the Land's End area of Cornwall:

How are these photos related? Give details to justify your answer.

Holiday

2006-07-23T18:50:00.000Z

I will be on holiday in the south-west of England for the next 2 weeks, and I won't be able to access the internet, so any comments will remain unanswered until I return.

Update: I extended my holiday to 3 weeks because I couldn't face going back to this! Unfortunately, the weather didn't arrange a similar extension. I spent a lot of time in the West Penwith area of Cornwall, with a brief interlude at the Big Green Gathering at Fernhill Farm in Somerset. Due to the walking/cycling that I did whilst away I now weigh several pounds less than before my holiday, and I even look slightly healthy due to the sun/wind tan that I acquired. The peace and tranquillity once you are off the beaten track in parts of West Penwith is very relaxing, and I can recommend the area for "chilling out", but I won't tell you precisely where I stayed.

Pioneering research - a risk worth taking

2006-07-21T22:15:00.000Z

I have just received another batch of books from Amazon, and I have started to read Pioneering Research: A Risk Worth Taking by Donald Braben. Here is a choice quote that appears in the introduction:

"To summarise my story therefore: The greatest long-term risks facing humanity will not come from such apocalyptic threats as terrible weapons of mass destruction, prolonged global war, devastating disease or famine or extinction by a huge wayward meteor. Rather they will come from the debilitating attrition caused by the rising tides of bureaucracy and control. These trends are steadily strangling human ingenuity and undermining our very ability to cope."

What a hook! Now I have to read the rest of the book (NB: I haven't yet done so). This description of bureaucracy as a "strangler" succinctly describes my own experience of bureaucracy, so I can't resist making some comments about it here.

It seems to me that the spread of cheap computers and powerful software has had an unfortunate side-effect, where bureaucrats are now able to do much more than they could before the advent of computers. There are people with a certain type of mentality who love using computers. Whilst cheap computers were limited in their capabilities such people were limited to really geeky types (tech-geeks), who loved to control their little "computer universe" with very clever computer programs. Now the same amount of money buys you a computer that can effortlessly run Microsoft Office, so we have a new type of geek (admin-geek) who wears a suit, but who has basically the same mentality as the earlier tech-geeks. Meanwhile tech-geeks have become über-tech-geeks, but that's another story.

The admin-geeks love their spreadsheets, and they feel ever so good when they "capture data" to "populate the spreadsheet". They recognise (correctly) that they can create order out of chaos by building business models out of various MS Office documents, and they might even discover how to link these documents together so that they update each other automatically without data having to be reentered time and time again. Actually, my experience is that they rarely get this last bit right.

The problem is that these simplistic business models are to real-world businesses as simple Gaussian probabilities are to real-world statistical processes. In both cases the model is well-intentioned but naive. If you use a simple Gaussian probability model when the real-world actually has a longer-tailed distribution, then your model is going to be badly wrong out in the tails of the distribution. If you use a simplistic business model when the real-world business wants to behave in ways that differ from the model, then there is going to be dissent between the bureaucracy and those whom they seek to control.

It is easiest to build a business model that describes a tightly controlled business, which consists of "if this condition holds then do that action else do that other action" clauses mutually interacting with each other. You can readily imagine the admin-geeks gleefully constructing a business model along these lines.

Back to the main theme of pioneering research. This particular activity does not easily fit into the "if-then-else" approach to business modelling. Unfortunately, the effect of this simplistic approach to business modelling has the effect of strangling the very thing that is needed to make pioneering research flourish, i.e. the freedom to follow your investigations wherever they lead you. The continual desire by bureaucrats to measure what you are doing, so that they can keep track of it in their business model, causes interference that damages the very thing that they are trying to measure in the first place.

Are there any simple fixes to this problem? I think that the admin-geeks lack basic trust and respect for the people who they are measuring/controlling. All they appear to see are the cells in their spreadsheets, and the relationships between these cells, but they appear to forget that these cells have real-world counterparts. Exactly the same problem happens with tech-geeks who get their noses buried so deeply in their computer programs that they can't relate what they are doing to the real-world. So the fix to the problem (in both the admin-geek and tech-geek cases) is to not only look at the real-world indirectly through the distorting lens of a computer program, but also to try to interface directly with the real-world, and to develop a direct intuitive appreciation for what is going on. Unfortunately, this requires some effort from everyone, which seems unlikely because using a computer to do your thinking for you is (or seems to be) so easy.

I wonder what Pioneering Research: A Risk Worth Taking says about this. I must finish the book.

Update: I have now read the book, and everything it says is consistent with my own unpleasant experiences with bureaucrats who micro-manage research. There were places where the phraseology used in the book corresponds exactly to the ways that I have described various situations to my technical colleagues at work. I have therefore lent it onto one such coworker in order to spread the word, which will thus delay any further discussion about the book here.

Everyone uses prior probabilities

2006-07-20T20:20:00.000Z

There is a lot of rubbish about the Bayesian approach to inference being written in various blogs; to spare peoples' blushes I will not cite those blogs here. As I see it, the main error that people make is to assume that the Bayesian approach is guilty of being subjective because it uses prior probabilities, which seemingly have to be plucked out of thin air (i.e. subjectively).

Fortunately, or unfortunately, depending on your point of view, the Bayesian approach is not the only one that is subjective according to these criteria.

Bayes theorem allows joint probabilities to be split up into products of conditional probabilities and marginal probabilities. The simplest statement of Bayes theorem is

Pr(x, y) = Pr(x) Pr(y│x) = Pr(y) Pr(x│y)

where the marginal probabilities are defined as

Pr(x) ≡ Σ_yPr(x, y) and Pr(y) ≡ Σ_xPr(x, y)

This allows us to write the conditional probability Pr(x│y) as

Pr(x│y) = Pr(x)Pr(y│x) / (Σ_xPr(x)Pr(y│x)) = Pr(x) Pr(y│x) / Pr(y)

where the dummy x that is used inside the summation is different from the free x that occurs elsewhere.

So, in order to determine x given that you know y (i.e. Pr(x│y)), all you need to know is how to determine y given that you know x (i.e. Pr(y│x)) together with the prior probability of x (i.e. Pr(x)).

The criticism that the Bayesian approach is subjective arises from the Pr(x) term. Why should drawing an inference about x given y depend on this apparently subjective factor? If x is the value of a physical constant, and y is an experimental measurement of it, then why should the interpretation (i.e. Pr(x│y)) of this measurement apparently be subjective?

Firstly, there is an extreme case that we must dispose of. If the experimental data actually measures the quantity of interest with zero error (e.g. y = x) then the choice of Pr(x) has no effect. I am not talking about this extreme case. I am talking about the more realistic case where the data contains only partial information about the quantity of interest, because it is subject to noise, or maybe because it is a lower-dimensional projection of a higher-dimensional quantity.

Do some dimensional analysis (this is valid whether x and y are continuous or discrete):

Pr(x) and Pr(x│y) both have the dimensionality of 1/x.
Pr(y) and Pr(y│x) both have the dimensionality of 1/y.

Thus in Pr(x│y) = Pr(x) Pr(y│x) / Pr(y) the 1/x dimensionality of Pr(x│y) derives entirely from Pr(x), because Pr(y│x) / Pr(y) is dimensionless.

You have to use something like the dimensional Pr(x) factor in order to construct Pr(x│y). If this factor is not actually Pr(x) itself, perhaps because you don’t like to use apparently subjective quantities, then what else could it be? Because it has inverse linear dimensions it has to be physically like a density. What densities do we have lying around ready for use? If we imagine that x-space is composed of infinitesimally small x-cells, then the density of such cells has the required properties. How do we decide what a good choice for these cells might be? Do we make them all the same size when viewed in x-space, or exp(x)-space, or what? There is no uniquely obvious choice!

The problem of choosing a space in which to define the cell size, so that a density can be defined in order to give Pr(x│y) its dimensions, is the same as the problem of defining the Bayesian prior Pr(x). This is the reason why the Bayesian approach is not the only one in which you define a prior probability. Actually, in all approaches you have to define a prior probability, but only Bayesians use the term "prior probability", so they are totally honest about what they are actually doing.

You could define a density-like quantity in terms of the frequency of visits to each point in the space, which gives a number-per-unit-cell (i.e. a density). If you have an underlying model for generating points in x-space, then in principle it is easy to generate this type of density, and this would indeed be an objective way of defining a density. However, this ducks the issue of where the underlying model came from in the first place. There is a bootstrapping process, where you need to impose a density-like quantities on spaces that have never been visited before, and for which there is no agreed upon underlying model.

In short, everyone faces the problem of defining prior probabilities, but only Bayesians call them prior probabilities. It is disingenuous to use prior probabilities as a stick to beat Bayesians with. Unless, of course, you are a masochist, because everyone uses prior probabilities.

In memoriam Syd Barrett, madcap genius

2006-07-11T18:08:00.000Z

So. Farewell
Then Syd
Barrett.

You were
Famous for
Your big hit
Bike,
You can ride
It if you
Like.

Shine on
You crazy
Diamond.

A new kind of science - questions

2006-06-10T08:20:00.000Z

The NKS2006 (New Kind of Science) conference is announced here, where a large number of questions are posed that ask what can be done with NKS (essentially, NKS is science based on elementary algorithms, rather than based on elementary mathematical functions as is usually the case).

Here is the list (copied from here), with each question highlighted in bold, and with my comments appended. Note that my comments do not imply that I am keen to see things happen the way that is predicted in various places below (e.g. Ray Kurzweil's imagined future).

Will algorithm mining revolutionize software development? You need a way to detect when an algorithm is doing something useful, which requires a meta-algorithm for observing the algorithm under study. For instance, development via the process of Darwinian evolution uses a meta-algorithm (i.e. survival of the fittest) that has demonstrably led to some truly revolutionary developments. If we do simulated evolution (e.g. genetic programming) then we can guide the developments, but we have to be careful not to guide too closely otherwise we will miss the revolutionary developments.
Is there a core computational architecture in biological cells? It is difficult to see how Darwinian evolution could work without reusing standard building blocks developed during earlier stages of evolution. If you don't allow this sort of reuse then you end up with the naive argument-against-evolution, which reasons that the chance of everything working together in exactly the right way is so vanishingly small that things must have been deliberately designed by an external agency.
Will generative content revolutionize the entertainment industry? Virtual reality will rival and surpass real reality. The quality of the rendering is currently limited by computer power rather than by lack of algorithms, although improvements in both would be welcome. Ray Kurzweil suggests that nanobots could connect up directly to our nervous systems to provide a vivid virtual reality. Now that would be amazing, but rather invasive.
How will computer experiments change the face of mathematics? Experimental mathematics allows us to escape from focussing only on computationally extremely-reducible problems which are amenable to analysis based on properties of elementary mathematical functions. Experimental mathematics allows possible solutions to be explored much faster, whether or not they are computationally reducible. I find a good research strategy is to use experimental mathematics to do a numerical search to find potentially interesting relationships/patterns/etc, which I then attempt to prove (if the result is computationally reducible) by more conventional means.
Are there business structures founded on computation universality? I don't know the answer to this one, but I do have experience of the failure of computation universality. In my own narrow experience of business structures they attenuate the propagation of information, so the right hand doesn't know what left hand is doing. There are certain types of computation that simply cannot be done in the types of business structure that I have been exposed to. For instance, top-down dogma is frequently used to override bottom-up information (e.g. that's what led to the Challenger shuttle disaster).
What would an operating system for a swarm of microbots be like? Each single time step causes the invocation of a number of elementary update operations, and the elapse of multiple time steps causes the emergence of collective phenomena. The design of a suitable set of elementary update operations to lead to a required set of emergent phenomena is a hard problem. Simulated evolution is a way of developing such systems.
What kinds of artificial physics can support quantum mechanics? Multiway systems allow the parallel branching behaviour that you need to implement QM. Any artifical physics that allows this type of multiway branching has a QM-like flavour.
Will artificial life arise spontaneously within the internet? With some help from us to start it off, then the answer is yes. Ray Kurzweil's prediction of where evolution is taking us is probably how it will happen. He suggests that you will have biological humans who are enhanced by machine-like add-ons, and that eventually the add-ons will become so fancy that the biological part becomes irrelevant and unnecessary.
Can one map the space of all possible economic systems? I don't know.
Will the next core computer architecture be discovered by search? Not the next one, but one further down the line. Massive fine-grain parallelism (e.g. networks that are as large as a human brain, in terms of nodes and connectivity) can be developed by a combination of simulated evolution (to develop network structures) and self-organisation (to allow the plasticity in each such network to adapt to the environment).
Can we enumerate the morphologies of possible biological organisms? If there is a "core computational architecture in biological cells" (see earlier) then the answer is "yes".
What pattern recognition algorithms can molecules implement? Indirectly they can do very clever pattern recognition (e.g. DNA controls the construction of brains which then do pattern recognition). Directly they do only elementary pattern recognition (e.g. sensing signals), and if the molecules can communicate with each other then they can do some simple signal processing (e.g. smoothing, differentiation, etc). It is hard to see how molecules can themselves do cleverer things than this directly, so if you want to do fancy pattern recognition you have to use the molecules indirectly as a program (e.g. DNA) to construct the pattern recognition engine (e.g. a brain-like processor).
What does computational irreducibility mean for supercomputing? You can't simplify a computationally irreducible problem, so the fastest way of solving it is to use a programmable architecture to create a special purpose super-computer for running your computationally irreducible problem. The software for solving a computationally irreducible problem would effectively be a blueprint for constructing the corresponding special purpose architecture.
Is there an algorithm for telling if an object was designed? We know that computationally irreducible processes lead to structures that have arbitrary complexity, and that look as if they have been "designed". Can one look at a structure and reverse-engineer the underlying rules (if they exist) that led to it? This is a computationally hard problem, so there is no algorithm that will always work.
Will the most important nanomaterials be intrinsically random? Important materials will "design" themselves (i.e. self-organise). Such self-organisation is computationally irreducible because you have to go through all the intermediate steps to get to the result. The results can therefore be apparently random.
Can a single rule design the complete structure of a building? No. Unless you are a mollusc, that is.
Is there an absolute measure of elegance for programming languages? "Elegance" = "Brevity". That's one reason why I like Mathematica.
What is the network analog of a recursive function? Nested propagation loops in a network do a recursive computation, where the meaning of "recursive" has been broadened somewhat. This is analogous to computing a multi-loop perturbative expansion in quantum field theory, where the exact result of the computation is a recursively "dressed" version of the leading order approximation to the result.
Can we find the simplest undecidable problem in number theory? I don't know.
What would prove the Principle of Computational Equivalence? I don't know.
What will happen if kids learn cellular automata before algebra? A lot more copies of Mathematica will be sold. There will be a move away from the "classical" approach using toy models that are usually selected for their analytic tractability (i.e. computational reducibility), and a move towards simple models with useful emergent phenomena (a.k.a. "effective theories") that are computationally irreducible.
What will be the first major industry created by mining the computational universe? Human-level (and better) artificial intelligence. Simulated evolution will be used to search the space of simple algorithms for ones that lead to emergent properties that have "useful" properties. Very large scale brain-like processors will probably be developed in this way.

The failure of string theory

2006-06-02T19:28:00.000Z

Excellent! Physicists have in their midst the seeds of a revolution. The new book by Peter Woit entitled "Not Even Wrong: The Failure of String Theory And the Search for Unity in Physical Law" (see Amazon here) sets out to expose String Theory as an example of The Emperor's New Clothes. It's about time too. By the usual standards of science, where you demand that any theory must make predictions whose experimental verification can potentially falsify the theory, String Theory is not even science. String Theory is a very interesting piece of mathematics, but it doesn't have any impact on the real world that real scientists inhabit. As far as I can tell, from the perspective of scientists, the claim that String Theory is relevant to the real world belongs in the realm of philosophy; it is an interesting assertion, and one that we could debate at length, but one that is not anchored in the real world. Is String Theory the sort of ingenious philosophical construction that scientists construct when they are starved of real-world input from experiments? Is the pseudo-religious bigotry of some proponents of String Theory a sign that they are finally realising that they don't have any real scientific arguments to defend themselves, but that all they have is a rather beautiful mathematical construction that they merely claim is a model of the real-world.

I might be accused of indulging in "social commentary" here. Yes! That's exactly what I am doing, because the situation in String Theory seems to be driven by social dynamics rather than scientific dynamics.

Life begins at N=40

2006-04-02T11:36:00.000Z

In this week's New Scientist there is an article by Marcus du Sautoy entitled Life begins at N=40, in which he ridicules the idea that if you are a mathematician then "after 40 you're past your best and will never make any worthwhile discoveries", which is reinforced by the fact that the award of the Fields Medal (the Nobel prize of mathematics, sort of) has a cut-off age of 40. As a counterexample he cites the case of Lennart Carleson who was productive into his later years. I agree with everything in his article, and I want to generalise what he says.

The assumption that people "will never make any worthwhile discoveries" past a certain age is not limited to mathematics, and is also profoundly misleading in fields of work where it takes many years to become proficient. It is true that a 20-something has reserves of stamina that enable them to focus their activities in ways that are impossible for a 40-something. But it is also true that a 40-something has much more experience and insight than a 20-something, and can finesse problems in ways that are not possible for the less experienced worker. There is a trade-off here: one's stamina declines with age, yet one's experience increases with age. There are other factors to consider, such as the lack of mental baggage that is carried by a 20-something (this is good), and the general decline of mental abilities with age (this is bad), but I believe that the stamina/experience trade-off is the key thing.

In my own experience, when I was a 20-something I used to do a prodigious amount of mathematical work almost none of which became a permanent part of my subsequent work, but I now do much less mathematical work of which a much higher proportion is incorporated into my subsequent work. I now don't follow up lines of work that I can intuitively see are going nowhere, whereas in my earlier work I followed up all lines of enquiry in detail. Basically, I now work much more efficiently than I used to.

There is another effect that I have observed, which has to do with the relationship between younger and older researchers. I distinctly recall that when I was a 20-something I used to think that older researchers didn't know what they were talking about, and that they should thus be ignored. My perceptions were only partially true, because older researchers carry a lot of baggage that gets in the way of clear thinking, but they do know what they are talking about. What I did not anticipate was that the same argument would be applied to me when I became an older researcher myself! There are vast tracts of knowledge that I see being reinvented from scratch (or, more usually, being ignored because they are considered to be "too difficult") by the next generation of researchers, because they assume that they are so clever that they are the first people to ever think about these problems. This is a waste of resources.

One way in which this "generation gap" between researchers manifests itself is in the analytic/numerical trade-off. People who were educated before computers were widely available find analytic calculations much easier to do than those who were educated after computers became widely available. Older researchers tend to calculate, whereas younger researchers tend to compute. There is a group of people who straddle the advent of computers who can freely and productively mix analytic calculation and numerical compution; I am one of these people. We need to encourage researchers to be "bilingual", so that they can mix numerical computation with analytic calculation.

How can this harmonious mix of analytic calculation and numerical computation be achieved? We need a single tool that seamlessly unifies the two approaches. In my own work I have found that Mathematica is the ideal tool for this, because with it I can do everything that I ever used to do (i.e. numerical and analytic work) and lots more besides. I have found that this way of working has completely upset the stamina/experience trade-off that I mentioned earlier, because now Mathematica provides the stamina and I provide the experience. It just gets better with time, and I look forward to being a highly productive 80-something.

Neolithic string theory

2006-04-01T10:25:00.000Z

A radical new interpretation has been made of a neolithic site in West Cornwall in the UK. The photo below shows this site

which has thus far had various interpretations, including suggestions that the O is a singularity through which you might pass in the quest for eternal health and fitness, provided that you accumulated the correct winding number known only to a few initiates.

Theoretical physicists have now been forced to reveal that this is an advanced string theory calculation done all the way back in neolithic times. Hitherto, this knowledge had been suppressed because of its potentially negative effect on the success of grant proposals for similar theoretical work being done in modern times. The outlook for string theory is not good, because it is now the oldest theory of everything by thousands of years, which makes its lack of concrete predictions all the worse than had been assumed thus far.

Bertie

2006-04-01T08:10:00.000Z

By now you know me well for my analysis of Kate Bush's song π (Greek letter p) on her new album Aerial. Here is a foolish one from another song called Bertie on the same album.

The chorus of Bertie goes like this:

Sweet kisses
Three wishes
Lovely Bertie

Now let's highlight the characters:

Sweet kisses
Three wishes
Lovely Bertie

We know who KB is, but who is SL?

Pi (update 4)

2006-03-19T13:07:00.000Z

I have now added a lot more material to my A Great Big Circle web site, detailing what I have found hidden in Kate Bush's song π (Greek letter p) on her new album Aerial. My previous posts on this topic can be found (in reverse chronological order) here, here, here, and here.

I recently went on a field trip down to the Land's End area of Cornwall; this region features extensively in the hidden information in π. Whilst I was there I visited various places to check out some ideas that I had about what might be hidden in π, and this reinforced my confidence that this hidden information is the result of intelligent design by the composer (i.e. KB), rather than self-delusion by the listener (i.e. me).

People love to deride A Great Big Circle, and basically accuse me of "doing a John Nash". That's an understandable criticism, which I deal with by showing whereabouts in π there are some highly specific pieces of hidden information, which could not possibly be the result of random chance. According to good scientific practice, this can be verified by anyone else who cares to look in detail at π.

To whet your appetites, here are 2 pieces of hidden information:

I predict here the precise location (a 1 metre square patch of ground) of what turned out to be an artefact built out of stones to resemble a steam locomotive. The locomotive theme is part of an extended metaphor that runs throughout π, consisting of tunnels, columns, chimneys, mine shafts, and generally anything and everything to do with sex.
I predict by two independent chains of logic here and here the location (a 100 metre square patch of ground) of an object (a tin mine) that unifies many other features that one finds in π.

Back in December 2005 when I first noticed some unusual structure in π, if I had been told that there was all of this material hidden in π, I would definitely not have believed it. However, over the months I have gradually acclimatised myself, and now I start from a default position where I immediately look closely at any unusual structure in any song on Kate Bush's new album Aerial. This has been immense fun, and it has reaped amazing dividends!

The end of the Darwinian interlude

2006-02-12T11:20:00.000Z

Freeman Dyson has written a fascinating article in this week's New Scientist entitled Make me a hipporoo. The theme of the article is that Darwinian evolution is merely an interlude, that was preceded and will be be followed by a different style of evolution.

Darwinian evolution operates on species. Each species has its own set of genes that carry the biochemical processing "wisdom" that has been accumulated by that species. These genes are not shared between species, so tricks that are discovered by one species cannot be shared across different species, which means that there is a lot of reinvention going on.

An alternative type of evolution, that is akin to the sharing of open source software, occurs in systems where the interspecies boundaries are dissolved. Such a situation held before cells evolved to hold small packets of biochemical processing separately from the surrounding soup, and thus prevented the free sharing of tricks that were discovered by evolution. Free sharing leads to very rapid evolution, in the same way that open source software leads to rapid software development.

When the equipment to sequence genes and to synthesise genes becomes small and cheap, and when the knowledge of how to effectively operate this type of equipment becomes widespread, the boundaries between species will dissolve away. This will lead to the end of the Darwinian interlude. This has already occurred to a limited extent with the (sometimes controversial) transfer of useful genes between species that is currently done. This requires substantial resources to implement, and it is not yet what would be called a "table top" activity, but this limitation will not hold for much longer.

Freeman Dyson is very optimistic about the possibilities for the post-Darwinian era. I wish I could convince myself that he is right. As with all technologies there is the potential for good and bad applications. With nuclear weapons technology you can't produce a weapon in your garage without a lot of outside help, but with "table top" genetic engineering a single individual could conceivably cause havoc. The scenario in the book White Plague by Frank Herbert is a frightening realisation of what could happen.

The cosmic landscape: chapter 2

2006-02-09T20:04:00.000Z

This is my interpretation of chapter 2 of Leonard Susskind's book The Cosmic Landscape: String Theory and the Illusion of Intelligent Design.

Susskind uses this chapter to introduce the problem that physics has with correctly predicting the value of the cosmological constant. What we naively call the "vacuum" actually contains a seething mass of virtual particles (or vacuum energy), because that is what is implied by our most fundamental theory of how physics operates (i.e. quantum field theory). This mass will affect the gravitational field and thus have observable consequences.

Unfortunately, our fundamental physics theory predicts an infinite (or, at least, very large) vacuum energy, which is not what we observe experimentally. The discrepency is about 120 orders of magnitude!

Susskind then describes the cosmology that was introduced by Einstein (i.e. a static universe governed by the equations of general relativity), by introducing the analogy that space is like the surface of a balloon, where the tension in the ballon is analogous to a gravitational attraction that causes all objects in space (e.g. galaxies) to attract one another. Thus an additional repulsive force is needed to hold the galaxies apart from each other. Einstein noticed this problem, and introduced a suitable term into his equations to provide the necessary repulsive force; this was his famous cosmological constant.

It turned out that Einstein's cosmology was wrong, because the astronomer Edwin Hubble observed that galaxies actually recede from each other, so the universe was not static, so Einstein had no need for a non-zero cosmological constant.

Now, Einstein's cosmological constant is physically the same thing as the vacuum energy mentioned above, so we know that it is non-zero, and in fact we predict (by adding up the effects of all of the virtual particles) that it has a value that is enormously too large. We know the value is too large because this vacuum energy implies the existence of a gravitational field that is not actually observed.

Even calculating this vacuum energy is fraught with problems because a naive calculation gives an infinite result, so we have to make some adjustments to the calculation in order to eliminate the infinity in a "natural" way. The method used is to ignore the contributions from all virtual particles that are so energetic that they would form a black hole if they collided.

One possible way of predicting a zero vacuum energy is to notice that virtual bosons (e.g. photons) have positive vacuum energy, whereas virtual fermions (e.g. electrons) have a negative vacuum energy, so there is the possibility that they produce cancelling effects. Unfortunately, such a cancellation does not materialise for the known types of bosons and fermions. However, if the universe were such that bosons and fermions existed in matched pairs (which they don't!), then cancellation would occur; this is what happens in the so-called supersymmetric theories.

Finally, Susskind points out:

Cosmologists regard the cosmological constant as something with a small non-zero value that needs to be measured.
Physicists (especially string theorists) regard it as something with an exactly zero value that is produced by an as-yet-not-understood cancellation in their theory.

However, there is a Third Way! It is called the Anthropic Principle: some property of the universe must be the way it is, because if it wasn't then we wouldn't be here to observe it. Can this approach be used to explain the values that fundamental physical constants? Should this approach be used, or is it not even science?

Generally, physicists hate the Anthropic Principle for various reasons:

It abandons their cherished hope of deriving everything from first principles. It questions the very root of what science is, and if it turns out to be true it would certainly be a "new kind of science". This possibility cannot be discounted.
It smells suspiciously like an "intelligent design" argument, where the properties of the universe are tuned so that we can exist. In fact, this suspicion is ill-founded, because it fails to recognise the difference between the weak and strong forms of the Anthropic Principle (see the last paragraph below). This possibility is based on a misunderstanding, and can thus be discounted.

Steven Weinberg has looked closely at the Anthropic Principle, and he concluded that a value that is not much larger than the observed upper bound would prevent galaxies, stars and planets from forming from the original very small density fluctuations that existed in the matter distributed throughout the universe. These sorts of arguments can also be used to place a bound on how negative the cosmological constant can be, and again its magnitude has to be extremely small.

Steven Weinberg has thus used the Anthropic Principle to place bounds on the magnitude of the cosmological constant that are consistent with observations. This work has been largely ignored because physicists mistakenly assume that it is necessarily based on an "intelligent design" argument. This is not the case if there is an ensemble of universes each with its own laws of physics, one of which is the fortuitously tuned version that we observe around us

Susskind then describes a thought experiment in which he rediscovers the "natural" (i.e. Planck) units of length, time and mass. These units turn out to be fundamentally important in the unification of quantum theory and Einstein's general theory of relativity, because they tell us where the naive picture of space as being analogous to a smooth rubber sheet breaks down (i.e. Einstein's gravity) to be replaced by a deeply wrinkled and knotted surface (quantum gravity).

The most important thing to understand in this chapter is the Anthropic Principle, which is not an "intelligent design" argument. None of Susskind's book will make sense until it is appreciated that Susskind is using the weak form of the Anthropic Principle, in which there is no prior tuning of the laws of physics, but rather there is an ensemble of universes each with its own laws of physics, one of which is the fortuitously tuned version that we observe around us.

A war on science

2006-01-26T20:58:00.000Z

The latest Horizon programme on BBC2 was entitled A war on science, and it covered the debate between evolution and intelligent design.

As usual, Horizon did an excellent job, leading the audience deep behind the intelligent design frontier, before destroying them from within by using the all-powerful biological weapon known as Richard Dawkins, backed up by David Attenborough.

I relished this Horizon programme. There was a beautiful statement by Richard Dawkins, which was something like (quoting from memory) "The only people who are convinced by the proponents of intelligent design are people who know nothing". Go for it, Richard!

Both Richard Dawkins and David Attenborough pointed out that intelligent design explains precisely nothing, because the "explanation" is as complicated as what it purports to explain, and it isn't even verifiable, so it isn't science despite its claims to be science.

The cosmic landscape: chapter 1

2006-01-23T20:38:00.000Z

This is my interpretation of chapter 1 of Leonard Susskind's book The Cosmic Landscape: String Theory and the Illusion of Intelligent Design.

He introduces evolution as the origin of modern cosmological ideas, which prepares the intellectual ground for the arguments that I suspect he will use later on in the book. He then goes on to say that cosmology must use universal rules that have nothing to do with our existence, citing by analogy Richard Dawkins' "blind watchmaker".

Up until now the science of cosmology has assumed that the same laws of nature hold everywhere in the universe, but the new cosmology has the universe embedded in a landscape of alternative universes (which Susskind calls a megaverse), where the "constants" of nature depend on which universe you inhabit in the megaverse.

He then notes the "coincidence" that the laws of nature are consistent with our existence, which is called the anthropic principle. At this point he does not mention the important distinction between the weak and strong versions of the anthropic principle.

I found this rather disconcerting, because it could mislead some readers into thinking that he is about to embark on an "intelligent design" argument for our existence, which would be the strong anthropic principle in which the laws of nature are selected a priori to be hospitable for our existence. Fortunately, he actually uses the weak anthropic principle, in which the laws of nature are selected a posteriori conditioned on our existence, as is detailed below.

He points out that the theory of inflation implies a megaverse, and that there is experimental evidence to support the theory of inflation. He also points out that string theory implies a landscape of alternative universes; this is where the "frontier" of string theory is currently to be found. He notes that the extremely small observed value of the cosmological constant is not predicted by theory, but this value could be "explained away" by the anthropic principle, where we inhabit a part of the megaverse in which the cosmological constant happens to have the observed value, whose smallness is a prerequisite for our existence.

He then gives a fairly detailed and conventional summary of particle physics:

Clockwork Newtonian physics is replaced by intrinsically uncertain quantum physics, giving the uncertainty principle, where measuring something with greater precision causes the sytem to be disturbed more.
The smaller the wavelength of a photon the larger its energy, so big accelerators are needed to probe small objects. Use this to discover that protons and neutrons are made of quarks.
Quantum mechanics implies zero point energy, where confining particles causes them to have "quantum jitters". Conjugate quantities which are subject to the uncertainty principle are position and velocity, energy and time, and electric and magnetic fields; this last example is what gives rise to the vacuum energy all around us.
QM implies discreteness, where energy comes in packets.
QM implies interference, as famously exemplified by the two slit experiment, where very low light intensity still gives rise to interference effects, even though there is only one photon at a time passing through the apparatus. Therefore photons must be both particles and waves at the same time. There is no point trying to understand this using everyday intuition; it is a property of the universe that lies outside our everyday common sense.
Nature seems to be organised hierarchically, in which you break large objects down into smaller pieces, and so on. This is called "reductionism". Thus far in experiments we have followed down the hierarchy as far as elementary particles, which are described by quantum field theory, and intuitively visualised using Feynman diagrams to describe interactions between the particles.
He then summarises quantum electrodynamics (QED), the nucleus, Feynman diagrams (propagators, vertices, coupling constants), antimatter, fine structure constant, quantum chromodynamics (QCD), weak interactions, and that all of physics is derived from simple underlying particle creation and annihilation events.
The use of reductionism in physics has truly been a success story. Note that neither I nor Susskind assert that the reductionist approach should a priori be assumed to work in all cases.

He then goes on to make observations and ask questions that prepare the ground for later on:

He notes that there are 3 generations of elementary particles, and that the extra generations of particles appear to be unnecessary. Thus he says that elementary particle physics is not simple and elegant, despite what particle physicists would try to tell you; it is messy and it is more like zoology or botany. To be fair, particle physics is in much better shape now than it ever was before, but Susskind makes a valid point about the "spin" that particle physicists put on the elegance of their subject.
He points out that the "standard model" describes properties with incredible precision, but it needs around 30 experimentally measured constants of nature to achieve these results; this is too many constants for a fundamental theory. We have no theory that says why the standard model is right and not some other model.
Are there deeper laws that govern the standard model?

That final question is the focus of Susskind's book.

Wi-fi network

2006-01-17T08:44:00.000Z

I have finally bought a wireless router for home use, plus a wireless network card for my rather old laptop PC (a Pentium 3 - remember those?). This wi-fi network has transformed the way that I use my laptop PC (I used to use a rickety and unreliable Bluetooth link). Yes, I know that this upgrade is rather belated, but I have a policy of following the "trailing edge" of technology, because it saves me from wasting a lot of money on the hectic race to always have the latest and the best kit.

What I really want to do is to banish the large computer-related boxes with their whirring fans away from the living area of my house, and to use a wi-fi network to link them to my laptop PC. I can't do that yet, at least not as a cheap upgrade from where I am at the moment, but technology does seem to be moving in the right direction.

Now all I need to do is to wait for that brief moment known as British Summertime, so I can use my new wi-fi network to work outside in my garden.

The cosmic landscape: preface

2006-01-17T08:18:00.000Z

This is my interpretation of the preface to Leonard Susskind's book The Cosmic Landscape: String Theory and the Illusion of Intelligent Design.

How is it that the universe appears to be so well designed for our existence? Here are two possibilities:

The laws-of-nature are unique, so that a priori it is a lucky accident that the universe is hospitable for our existence.
There is an ensemble of many possible laws-of-nature, within which one can find laws-of-nature that happen to be hospitable for our existence.

Historically, physicists have assumed that (1) is the case, even though it would appear to be a stroke of luck that this could lead to our existence. It is an open research question whether (1) is how the universe works, but it may eventually turn out that (1) is indeed true. However, in the meantime, recent results (i.e. an ensemble or landscape of alternative laws-of-nature) from research into string theory open up the possibility that (2) might be the case.

The fact that (2) is now being considered as a realistic possibility has annoyed many physicists who have assumed (1) all along. However, this book describes an interesting type of science (i.e. (2)) that needs to be understood more widely, so that more people can enter into informed discussion about it.

If (2) is true then the ultimate "theory of everything" will have far less predictive power than if (1) is true. There is a sliding scale of possibilities ranging all the way from (1) to (2), and we should not make strong prior judgements about where the universe lies on this scale.

The laws-of-nature appear to be fine-tuned in such a way that they are consistent with the fact of our own existence. This is called the "anthropic principle".

The direction in which one chooses to use the anthropic principle is very important:

The laws-of-nature are fine-tuned a priori so that we can exist. This is the strong anthropic principle, which is also known as "intelligent design".
The universe is such that there is an ensemble of many possible laws-of-nature, amongst which we find one that happens to be fine-tuned a posteriori by the fact of our existence. This is the weak anthropic principle.

Susskind's book uses the weak version of the anthropic principle, as (potentially) applied to the rich landscape of laws-of-nature that emerges from string theory. His aim is to show that there is no need for the strong version of the anthropic principle, so "intelligent design" in superfluous.

In fact Susskind makes his intentions clear with this quotation from Laplace at the front of the book:

Your Highness, I have no need of this hypothesis.

Laplace said this to Napolean in response to being asked why he didn't mention God in his book on the System of the World.

The cosmic landscape: string theory and the illusion of intelligent design

2006-01-13T17:21:00.000Z

Finally, my copy of Leonard Susskind's new book The Cosmic Landscape: String Theory and the Illusion of Intelligent Design has arrived.

I posted some comments earlier (see here) about the weak form (i.e. not driven by an external goal-seeking agency) of the anthropic principle and its relationship to Bayes theorem, and made some generally disparaging remarks about the hostile attitude of some physicists to the weak anthropic principle. There was some misplaced criticism of Bayesian methods posted here, but I don't know whether this was related in any way to my earlier comments on Bayes theorem and the anthropic principle. However, I do know that it prompted me to reinforce my statement about Bayesian methods here, which led to this spectacular response, and my own response to that here. I will not comment further on that exchange; I leave it for you to read for yourselves.

Anyway, now I actually have Susskind's book, I can focus more on the particular details of his arguments, rather than my own favourite argument based on Bayes theorem. What I plan to do is to work through the book in stages, and to report back here at each stage to explain the material that I have read, and to interpret it in my own particular way.

For the record, I have no prior prejudice about whether the cosmic landscape (i.e. the possibility of choosing between multiple alternative laws of physics) exists or not, but I do care about following up all credible avenues of enquiry, until they can be shown to be wrong because they are inconsistent theoretically or experimentally. In a nutshell, that is the scientific method. So we have to view the cosmic landscape as a valid possibility for now.

Bayesian probability (update)

2006-01-06T15:11:00.000Z

Blimey! Look ye here! The lady doth protest too much, methinks. I will try to respond succinctly.

I will continue to write in a fairly informal style in this blog, and to point to the relevant literature for the more discerning readers. I made this decision to embrace a wider readership at the cost of annoying a few readers. I can see why one might uncharitably compare this style of writing to that of postmodern literature criticism, but I will just have to live with that. I have a more "scholarly" (in places) blog here, but the blog is currently dormant because of problems with uploading images.

My main interest here is how we do inference about complicated systems consisting of many interacting parts. Note that there are two levels here: the system's behaviour itself (e.g. physics) and the reasoning about the system (e.g. inference). I am mainly talking about the second of these two levels. Note that this second level is where we all operate when we reason about "the world", because all we are doing is manipulating knowledge about things, rather than manipulating the things themselves.

The above paragraph must sound rather postmodern, but it's not! See the next paragraph.

Let's start by citing the literature yet again: Cox R T, "Probability, frequency and reasonable expectation", Am. J. Phys., 1946, 14(1), 1-13. This paper gives a neat derivation of the Bayesian approach to inference, by deriving everything from some elementary axioms which demand that the inference process must be internally consistent. Loosely speaking, if x is the state of a system, and Pr(x) is the joint probability of the components of x, then all inferences can be done by Bayesian manipulations of Pr(x) not x.

Bayesian inference is about manipulating joint probabilities (i.e. inference) rather than about defining joint probabilities in the first place (i.e. prior probabilities). These prior probabilities can be constructed in any way that you please, as long as they satisfy the usual properties (i.e. non-negativity, summing to unity), and then the Bayesian inference machinery can make use of them.

The freedom to choose a prior probability is an advantage, not a disadvantage, because it allows you freedom in your choice of model (or ensemble of alternative models). Bayesian inference then uses any relevant data to convert this prior probability into a posterior probability, which effectively updates the model (or ensemble of alternative models) in the light of the data.

Here is my original posting on the anthropic principle and Bayesian inference, so you can see for yourself how it has been selectively quoted here. In particular, check out the penultimate paragraph (the one starting "If the properties of the universe are correctly described by string theory (this may indeed be the case)...") for what I say about science, philosophy, and string theorists.

One can aspire to relate one's conjectured scientific theory to the real world, but the longer you are unable to demonstrate a strong connection between the two, the more your activity can be credibly labelled as "philosophy" rather than "science". I too would like to see the laws of physics derived from first principles, but I would not go so far as to assert that the laws of physics had to be derivable in this way. Whether we like it or not, the landscape is still a logical possibility, and we should at least be aware of what science would look like in that type of universe.

I also live dangerously in my own research activities, where I follow up some fairly wild ideas for long periods of time, but I always have "bread and butter" threads of research running alongside, where I dive for cover when the going gets tough. I never put all of my eggs in one basket no matter how elegant (or even how promising) it looks.

Why bother playing guitar?

2006-01-05T22:28:00.000Z

My local musical instrument shop (see www.music47.co.uk) has changed over the past ten years or so, from one that used to be mainly classical instruments and sheet music, to one that is now mainly electric guitars and sheet music. The shop now has a specialist guitar section (see www.onlineguitars.uk.com) that seems to dominate the floor of the high street shop.

OK, so electric guitars have become more popular in the British popular music scene, and now it seems that every teenager (and 20-something) wants to play electric guitar. This is not quite as bad as everyone wanting to be a sound engineer, because at least there are quite a few young bands around each of which could absorb two (and a bit) electric guitar players, but there are very few sound engineering jobs.

I would have thought that (other things being equal) if you wanted to enhance your value as a musician you should learn to play something other than a guitar. Maybe you should forget the electric guitar altogether, and learn the electric violin instead.

I know this would tax the musical talent of most would-be guitarists, because there are no frets on a violin, so you would have to actually listen to what you are playing in order to get the intonation as you want it. Also that damn violin bow thingy can be so difficult to control if you have no muscular discipline.

However, the up-side is that if you can play electric violin even half decently, using a bit of reverb to fill in the holes in the music, then you are almost guaranteed a high-profile position in a band, and you can compete on equal terms with an electric guitar because the violin bow gives you a fantastic sustain.

Bayesian probability

2006-01-05T18:13:00.000Z

I recently blogged about The cosmic landscape, where I made some remarks about the relationship between Bayes theorem, the anthropic principle, and the cosmic landscape. I pointed out that the anthropic principle is a consequence of Bayes theorem applied to systems of interacting parts (e.g. observers and the observed). Thus our existence as observers is always part of the overall set of experimental observations that should be taken into account when constructing candidates for the "laws of physics". I would have thought that this much was obvious!

Not so, apparently. Such is the strength of conviction by some people that the anthropic principle is pseudo-scientific (e.g. many postings here!) that they choose to criticise the Bayesian approach, presumably because it is a rigorous approach to drawing inferences, which is thus justifiably perceived as a credible threat to their anti-anthropic stance. To assert that the Bayesian approach or the anthropic principle is pseudo-scientific (or a "dangerous idea", or whatever) won't make them go away, because they are more rigorous than some people appear to realise.

A particularly "fine" example of such misplaced criticism is by Luboš Motl here, because it appears to be based on an undergraduate level of understanding of the Bayesian approach, including all of the philosophical mumbo-jumbo that gets taught about the frequentist versus the Bayesian versions of probability. I too went through a frequentist versus Bayesian stage of my learning, mostly due to the influence of the otherwise excellent MaxEnt series of workshops . A good paper to read that uses an "axiomatic" approach to understanding all of this is: Cox R T, "Probability, frequency and reasonable expectation", Am. J. Phys., 1946, 14(1), 1-13.

It is such a pity when an intelligent scientist (e.g. Luboš Motl) chooses to criticise something by making apparently sage pronouncements too far outside their own area of expertise. Yes, you might read a text book one evening and then pass an exam the next day, but this limits you to what is in the text book, doesn't it? Experienced researchers know that the real expertise is not recorded as simple bite-sized entries in text books, but is accumulated over years of careful reflection about a subject.

Or maybe I have fallen for a troll, where Luboš Motl tricks me into mentioning his name (more than once!) in my blog, thus helping him on towards world domination.

Pi (update 3)

2005-12-30T21:54:00.000Z

When I haven't been filling myself with mince pies and mulled wine, I have been writing up my analysis of Kate Bush's song π (Greek letter p) which I described earlier here, here, and here.

There is quite a lot of material, so I have organised it as a web site called A Great Big Circle.

I have actually got quite a bit further with decoding this song than I have described on the web site, but I will need to do some "field work" to sanity-check the various ideas that I have had. Conveniently, the field work can be combined with a holiday in a very nice area of the country (i.e. the Land's End area, Cornwall).

With what I have discovered thus far, I know for certain that Kate lavishes attention on every detail of her published music, and that even things that appear to be sloppy errors (e.g. out-of-tune notes, or clumsy lyrics) are actually deliberate.

Constructive versus principled theories

2005-12-13T19:11:00.000Z

In this week's New Scientist there is an article entitled Power of the mind in which the relative merits of two types of scientific theory are discussed: constructive versus principled theories.

The article points out that Einstein stressed the distinction between these two types of theory, where the constructive approach aims to describe phenomena by working backwards from known experimental observations to induce what the underlying models might be, whereas the principled approach aims to do the same by starting from a set of underlying principles and then deducing what the experimental observations should be. Einstein's own approach was typically principled theories.

The article also points out that Martin Rees (President of the Royal Society) has criticised Einstein's favoured approach as being "armchair physics", which should make way for an approach based more in rigorous experimentation. I wonder if he is taking a swipe at string theory!

This all seems to be rather black and white to me. Sure, there are the polar extremes of top-down theories (inducing a model from data, or the so-called constructive approach) and bottom-up theories (deducing data from a model, or the so-called principled approach), but these are definitely not mutually exclusive.

To see what I mean, you need look no further than Bayes theorem, which says that you can break up a joint probability Pr(model, data) in the following two ways:

Pr(model, data) = Pr(model│data) Pr(data)

and

Pr(model, data) = Pr(data│model) Pr(model)

where every term that appears on the the right hand sides can be deduced from Pr(model, data) alone.

This means that Bayes theorem treats the model and the data symmetrically, so it must be wrong to claim that either the bottom-up (principled) or the top-down (constructive) approach is somehow fundamentally superior to the other approach.

Bayes theorem has the following quantitative consequences (expressed very informally, pace Bayesians!):

A theory has to be rooted in experimental data for it to be science, which ensures a large value for Pr(data).
A theory has to be principled for it to have a large value of Pr(model). The theories that have a simple internal structure (i.e. satisfy Occam's Razor) tend to have a large Pr(model).

The Bayesian approach gives you the means of computing a quantitative measure of how good your theory is irrespective of how you arrived at it, whether through artistic inspiration, or through the sweat and labour of inspecting experimental data, or a combination of both of these approaches. The Bayesian approach is impartial in this respect.

The best sort of theory will thus combine both the bottom-up (principled) and the top-down (constructive) approaches. When I work on a new theory I am aware of being influenced both by Occam's Razor (i.e. a sense of elegance and beauty) and by the experimental data (i.e. hard-nosed pragmatism), which together create a very interesting "tension" that I have to resolve. This part of my scientific work is really satisfying, in the same way that composing music or painting is satisfying.

So, constructive versus principled theories? No! It is not a matter of either/or, it is both please.

Pi (update 2)

2005-12-11T15:16:00.000Z

To continue the analysis of Kate Bush's song π (Greek letter p) from the previous update, I took this photo yesterday. As you can see, it is a woodland location, and there is an ancient-looking and apparently mysterious ivy-covered object in the picture. The object is a set of stones that have been carefully placed by hand, so this isn't the sort of random ivy-covered object that you typically find in a wood.

The reason I think you should be interested in this photo is that I deduced the precise location of the artefact from the song π. I very carefully triangulated the position of the artefact with respect to some known positions, and it is located to within a metre of the position that I had deduced before I arrived to take the photo.

I believe that this is convincing evidence that Kate Bush has indeed encoded a secret message in her song π, and that the message contains a puzzle for us to solve. I don't have any idea what the ultimate goal of solving this puzzle is, but if anyone puts an imaginative puzzle before me then I'm sure to bite on it. From what I have discovered thus far the puzzle is encoded in a layered way, so you have to solve it in stages.

My only slight concern is that (an abbreviation of) some of the lines in the song reads as "His numbers run him in a great big circle". One could imagine digging down through the layers of the puzzle, only to arrive back where you started after having invested a lot of effort. Oh well, that is how most of my research ends up, back at the starting point but much wiser.

Whither π? In locating this artefact, I have "used up" only part of the structure that I have found in π, so there is more to solve in this puzzle.

If/when anyone else visits the artefact please be careful, because I noticed that despite taking care I left some traces of my visit. Fortunately, the wood is a living growing being so it will heal itself.

Update: I just had someone (away from this blog) cast doubt on my sanity, because I am making these observations on the information that is secretly embedded in π. Well, all I can say is that the data is there for everyone to analyse, so this is a completely open exercise. What I don't want to do is to reveal prematurely what I have discovered, and thus to spoil the puzzle. That is the reason for the photo (which establishes that I visited a particular location), and the anagram "Heavy-hearted, contrary warmth" in the previous posting (which also identifies a relevant location). These two items do not give the game away, and they are proof-in-retrospect that I solved a particular part of the puzzle.

The cosmic landscape

2005-12-08T19:04:00.000Z

Peter Woit has blogged (and no doubt many others will also blog) about Leonard Susskind's new book The Cosmic Landscape: String Theory and the Illusion of Intelligent Design. Before I go any further I must confess that I have not yet read Susskind's book, so I will confine my comments to standard background material, and I will write later on about the specific details that Susskind includes in his book.

To summarise, Susskind says that string theory does not make a useful number of testable predictions, but it does predict a mind-bogglingly large number of vacua (each of which has its own laws of physics) so by random chance it can give rise to a universe in which the laws of physics are indeed as observed.

This last property is called the "cosmic landscape", because there is a landscape of alternative vacua, which allows the weak form of the anthropic principle to bear fruit. What this means is that we observe the universe to be exquisitely fine-tuned for our existence, because it is one of the mind-bogglingly large number of alternative vacua that happens to allow the development of observers like us. So there should be no big surprise that this fine-tuning is observed by us, because otherwise we would not be around to make the observations. The only universes that can be observed by their occupants are precisely the ones that are tuned in such a way that observer-occupants can exist in them, and for which the universe must therefore appear to be fine-tuned from their own point of view.

Note that the anthropic principle is not circular reasoning, because any system that can make measurements of its own behaviour (i.e. which has dynamics which allows its various parts to interact) must necessarily have certain correlations between its measuring parts (A) and its measured parts (B), so A will express "surprise" that B (i.e. what A observes) has certain properties that are (seemingly unexpectedly) related to the properties of A. This is a generalisation of what the phrase "fine tuning" means.

Another way of looking at this is using Bayes theorem, which provides a uniquely rigorous and consistent way of calculating what correlated entities "know" about each other. If the properties of the observer-occupants (A) are correlated with the laws of physics (B), then it follows using Bayes theorem that each can make predictions about the other. However, B => A is uncontroversial, whereas A => B is the weak anthropic principle. People who like B => A but not A => B are implicitly denying Bayes theorem, which means they are happy to reason inconsistently. Enough said?

Despite the logical consistency of the weak anthropic principle many physicists hate it, and denounce it as unscientific. Susskind is not one of these people; he accepts the "landscape" as a fact, and follows up its logical consequences where it is a physical framework for invoking the anthropic principle. However, he attracts the venom of those who hate the anthropic principle, because they perceive it as pulling the rug out from underneath science. This is because if the particular point which you occupy on the "landscape" has to be determined by experimental observation, rather than by theoretical prediction, then they claim that science has no predictive power, because the laws of physics are fixed by experiment rather than predicted by theory.

Just how arrogant can they get? Of course the laws of physics fixed by experiment rather than predicted by theory! That is what science is about, after all. The role of theory is to interrelate the results of experiments where these results are correlated with each other. That is still possible in a universe whose laws of physics are determined by experiment, which is how scientists have been working all along. The problem is that the goal (dream?) of string theorists is to assign a much larger role to theory than to experiment, so only a few basic properties (or perhaps no properties at all!) need to be determined by experiment, and then string theory is used to fill in the rest of the details. It is tough luck if the properties of the universe are such that that the predictive power of theory is smaller than string theorists would like it to be.

If the properties of the universe are correctly described by string theory (this may indeed be the case), and string theory predicts a whole "landscape" of alternative laws of physics, then the string theorists have to work with that, and they will have to measure what they cannot calculate. There is nothing wrong with that. It is called doing science, rather than doing philosophy. It seems to me that the string theory zeolots who do not like the "landscape", and who pour scorn on the weak anthropic principle, are trying to start a new type of philosophy that prefers only (or mainly) to calculate rather than to observe and calculate.

String theorists should get out more, and they should do science rather than philosophy. The weak version of the anthropic principle is science, but asserting that the laws of physics have to be derivable from first principles is philosophy.

Pi (update)

2005-12-05T19:48:00.000Z

I wrote a blog posting a few weeks ago about the song π (Greek letter p) on the new album Aerial by Kate Bush, where I said the following:

She recites π to a large number of decimal places. Actually, she doesn't recite the precise digits of π, and even omits a large block of digits, as has been noticed by many people. Now I don't believe for a minute that KB would make careless mistakes, because she has the reputation for being a bit of a perfectionist. That means that the "mistakes" in the digits are deliberate. How intriguing! This has just got to be a number puzzle that KB has set us to solve.

I have now had a close look at this song, and my impression that it contains a number puzzle has been strongly reinforced by what I have now found in the song. I am not going to tell you what I have found, but I will stake a claim on having found it first (eat your heart out GCHQ!) by quoting the anagram

"Heavy-hearted, contrary warmth"

(comma and hyphen are unimportant)

which is designed to be checkable by whoever created the puzzle in the first place (i.e. Kate Bush) or by anyone who solves the puzzle, but will confound everyone else unless I decide to explain exactly how it was generated. I may or may not decide to explain the anagram, depending on what other details I can decode from the song. However, I will say that the anagram is derived by a logical chain of reasoning, starting from information that is encoded in the song, and also including information that is referenced by the song, to generate 3-ish words that were then mangled into the above anagram.

Conveniently, there are several "parity checks" that my decoding of the song is correct, otherwise I wouldn't bother you with this anagram. I should add that I have not used any special knowledge to obtain this decoding, and I assume that there is lots more in the song that I have yet to decode.

If you think that you can unmangle the anagram, then I suggest that it would be quicker to attempt to decode the song itself, because solving the anagram is more difficult than deducing the code that is used in the song.

Nuke Florida

2005-12-03T17:46:00.000Z

I found this blog posting entitled What to do... on the potential problem of climate change causing the Gulf Stream to alter, so that Western Europe gets colder and the Atlantic hurricane season gets stronger. The solution is to remove Florida. Well, nuke Florida actually, because it's so much quicker. You know it makes sense.

It's a cracking read.

Mind your scientific language

2005-12-03T16:14:00.000Z

Lawrence Krauss writes an article entitled Mind your scientific language in the Comment and analysis section of this week's New Scientist, where he highlights various differences in the scientific and common lay use of words that have led to unfortunate misunderstandings.

For instance Krauss writes:

A scientific theory is a logically coherent and predictive system that has been tested against experiment or observation. It explains observable phenomena and makes falsifiable predictions about them.

and later on adds:

A key part of the argument made by those who wish to introduce religion into science classes is that evolution is "just a theory". By "theory" these individuals are referring to the common lay usage of the word, meaning a hunch or a guess, and not the more restrictive sense in which the term is normally discussed in science.

It is a fundamental requirement of meaningful communication that the participants have to agree on their use of terminology prior to engaging in any discussion. I have found that virtually all arguments that I have ever had can be traced to unfortunate differences in the use of terminology. When you have hot-headed combatants it is very tempting for them to go straight to all-out warfare, without going through the diplomatic preliminaries of checking whether they are actually in disagreement about anything.

Of course, the illusion that religion (read "intelligent design") is somehow to be put into the same category as evolution is caused entirely by a category error, which is traceable to the conflict between two different meanings of the word "theory". Evolution is a scientific theory, and is not a hunch or a guess.

Because the scientific and common lay meanings of words are frequently different, scientists have to be very careful to "put on the appropriate hat" (or "change gear", or any other of countless metaphors) according to whom they are speaking. This is a talent that needs a lot of practice, so if you are the sort of dedicated scientist who mainly communicates with like-minded people, then prepare yourself for arguments when you discuss science with non-scientists. At the very least you have to be able to think like the person you are talking to, no matter how crazy their worldview seems to you. If you can do that, then their different use of terminology is much easier to understand.

Krauss goes on to write:

Eugenie Scott of the National Center for Science Education, a US organisation that defends the teaching of evolution in schools, has argued that we should train ourselves to not use the term "believe" in a scientific context because it blurs the distinction between science and religion.

I couldn't agree more. The word "believe" has been used by many people in conversations with me as a linguistic device to trap me into making errors. The first time someone did this they "won" the argument, because although they had introduced the word, I foolishly did not request that it was replaced by another word such as "know", or "experimentally measure", or whatever. Of course, this use of the word "believe" worked only once on me, because my conversational countermeasures quickly evolved to include anti-"believe" clauses.

Like I said earlier, if you want to engage in meaningful communication, you have to put yourself firmly in the mind of whoever you are talking to. And I don't mean just passive nodding in sympathy with whatever they are saying, I mean making lots of effort to engage with their thought processes. Most conversations I have with scientists about non-scientists show that scientists look down on non-scientists, so no wonder they don't bother to understand how non-scientists think. News groups and blogs have many extreme examples of this phenomenon, though I would expect such sources to be a biassed sample.

So, mind your scientific language.

Blair says nuclear choice needed

2005-11-29T19:33:00.000Z

A BBC news item entitled Blair says nuclear choice needed reports that

Tony Blair says "controversial and difficult" decisions will have to be taken over the need for nuclear power to tackle the UK energy crisis.

The prime minister told the Liaison Committee, made up of the 31 MPs who chair Commons committees, any decision will be taken in the national interest.

That raises much hollow laughter in those who subscribe to the conspiracy theory of life.

The message is clear that the decision has already been taken to build new nuclear power stations. This much is obvious from the stark fact that most of the current generation of nuclear power stations is nearing the end of its life, and we are also committed to reducing CO2 emissions (which nuclear power stations can do), and we have not made sufficient effort to invest in renewable energy sources such as wind and solar energy (which also reduce CO2 emissions), aaand we have a nuclear weapons programme that we want to support.

On the nuclear weapons issue, I'll bet Trident isn't the last generation of such weapons, because as long as someone can throw a nuke at us we will retain the ability to throw one back at them. That's the logic, and I don't see another credible way out of the dilemma.

All of this points towards the absolute necessity for keeping a large nuclear industry going on for the forseeable future.

Frankly, I am amazed at the pretence and games that Blair and his acolytes play, when it is so transparently obvious what is really going on.

Nuclear power? Unfortunately, we've got no other choices left open to us!

SETI won't work

2005-11-26T21:02:00.000Z

The search for extra-terrestrial intelligence (SETI) is running a long term programme that searches through radio telescope data for signals that could have been produced by extra-terrestrial intelligent sources (little green men, if you want). You can participate in this search by going to the SETI at home site, and downloading the software there. A few years ago I began to run this SETI software as a screen saver on my PC, but I never found any extra-terrestrial intelligence, and nor has anyone else.

After staring at this screen saver for longer than most sane people would consider healthy, it became obvious that the search strategy that SETI uses is totally naive, and it is bound to fail in its goal. In a nutshell, what SETI looks for are transmissions that resemble carrier signals, which are the signals that are sent out by transmitters which you "tune into" when you twiddle the dial on your radio (or press the auto-search button). Actually, SETI is rather cleverer than that, because a transmitter is likely to be moving on a curved path (e.g. it is on a planet orbiting about a star) which will make the frequency of its carrier signal vary with time, so the search takes account of the variations in the carrier frequency that this causes.

Why is searching for carrier signals a naive strategy for SETI to use?

The answer is that an intelligent transmitter would not use such an inefficient way of transmitting signals. Also, they might not want anyone to eavesdrop on their signals, so they would use a more stealthy means of communication. The most obvious alternative possibility is something that we humans already do; it is called spread spectrum transmission, which was (surprisingly!) invented by the actress Hedi Lamarr. The trick is to not use one carrier frequency, but to use a random sequence of many carrier frequencies, thus spreading the transmitted signal over the frequency spectrum in a way that makes it very difficult to receive if you don't know the random sequence used. If you combine this with appropriate "whitening" of the transmitted signal, then the spread spectrum signal is indistinguishable from background noise, and it is actually impossible to receive if you don't know the random sequence and the whitening method used. Generally, a transmitter is at its most efficient in terms of both bandwidth and stealth when its transmissions look like white noise, and the means used to achieve this could be much more sophisticated than merely being simple variations of the frequency hopping approach described above.

If we are already using spread spectrum techniques ourselves, then it is likely that an extra-terrestrial civilisation would be doing something that is at least as clever, and probably far cleverer. This is why SETI won't work.

In this week's New Scientist there is an article Looking for alien intelligence in the computational universe in which Stephen Wolfram makes the same criticism of the SETI search strategy. He then proposes that we do a search of the universe of all possible algorithms (i.e. the computational universe) for ones that have behaviours that are a cyber-version of an extra-terrestrial civilisation. This is an application of A new kind of science. Wolfram's proposal is that a cyber-version of an extra-terrestrial civilisation is as good as the real thing. This is complete rubbish, and I am surprised that he offers this as a serious proposal. It is like saying that virtual reality is the same as real reality. They might seem to be the same but they are not actually the same.

I think that the computational universe is a very worthwhile place to harvest, because there will be algorithms out there that do very interesting and useful things, and which could be used as the basis for whole new technologies. This is why A new kind of science is a very good thing that more people should pay attention to. However, this has nothing whatsoever to do with SETI.

I will caveat that last remark. There is the possibility that there are algorithms out there in the computational universe that might be used as a sophisticated way of encoding/decoding transmissions, and which extra-terrestrial civilisations might already be using. All we need to do is to find these algorithms, and we can then eavesdrop on the extra-terrestrial conversation, assuming there are no other gotchas standing in the way, such as the very interesting scenario that is described in Piers Anthony's book Macroscope; read the book, especially if your IQ is 150+.

SETI should focus on reality and not create a virtual simulacrum of reality. Remember that science is about connecting with experimental results; computational simulations are very interesting in the same way that pure maths is interesting, but without an anchor in reality they are not actually science. This distinction is the same as the difference between natural philosophy (now discredited) and natural science.

SETI should also extend their search strategy to look beyond communication using mere carrier waves, otherwise they are going to waste an awful lot of computer time hunting through the radio telescope data.

Super-computer trounced by human brain

2005-11-21T22:09:00.000Z

IBM's Blue Gene super-computer has performed a record 280.6 trillion operations per second on the industry standard LINPACK benchmark. That is more than 10^14 operations per second.

The human brain contains around 10^11 brain cells, so Blue Gene could in principle deploy about 10^3 operations per second on simulating each brain cell in a simulation of the whole brain.

However, each brain cell has a lot of biological computing machinery associated with it (e.g. its large number of synapses, the dendritic tree that connects the synapses to the cell body, the cell membrane, etc), and the time scale for brain cell dynamics is around a millisecond, so the 10^3 operations per brain cell per second that Blue Gene gives you isn't anywhere near enough compute power for a real-time simulation of the brain.

If each brain cell (including all of its biological computing machinery) needs around 10^9 operations per second (1 per millisecond, times a conservative 10^6 to account for all the large number of synapses and the dendritic tree) , then the total number of operations per second that are needed for the whole brain is around 10^20 (10^9 operations per brain cell, times 10^11 brain cells).

Thus, conservatively 10^20 operations per second are needed for a real-time simulation of the human brain, but Blue Gene can supply only 10^14 operations per second. There is rather a large shortfall.

Clearly, we are nowhere near being able to simulate all of the neurons in the human brain in real time. Even if Blue Gene was fast enough, it would still lose out in terms of processing power per cubic millimetre. Blue Gene occupies a very large room (think "supermarket", or have a look at the photo here), whereas the human brain occupies a cranium.

And don't even think about comparing the relative energy requirements of Blue Gene and the human brain.

Blue Gene achieves its speed by connecting together a large number of conventional microcomputers, each of which uses a variant of a more-or-less standard computer architecture (the so-called von Neumann architecture). In the other hand, the human brain does not use anything remotely like this approach to the problem of doing computations. In effect, it uses special purpose biological hardware for each and every processing node (i.e. each brain cell plus its associated machinery), and this biological hardware operates as a fine-grained parallel computer.

To compete with a human brain, a remote descendent of Blue Gene will have to operate in a similarly fine-grained parallel way, and will thus have to be built using a much less clunky technology than tens of thousands of interconnected microcomputers.

I believe that the solution to this problem will emerge from nanotechnology, and it will use something analogous to artificial DNA to orchestrate the building of fine-grained parallel computers.

Endless projects

2005-11-16T20:23:00.000Z

When I was very young, and I was just becoming aware of a thing called "science", I thought that I could do something really worthwhile if I dedicated my professional life to doing research into fusion power. Even back then (around the time Neil Armstrong was making his "one small step") the prediction was that it would take several decades to get to the point where we could build a commercial nuclear fusion power station. That suited me because it meant that I would be involved in the main phase of the work, and I would retire at about the time these power stations came on line, and they would then keep me nice and warm in my retirement. The idea of infinitely extensible project time scales did not occur to me when I was very young.

Now I read the article Dream machine in the latest issue of New Scientist that the projected year for operation of the first commercial power plant is around 2050, and that is an optimistic projection. 2050 is almost certainly after I am dead. I am so glad that I didn't follow up my idealistic childhood dream of doing fusion research.

I feel much the same way about where I could have ended up after doing my PhD on QCD. I would probably have eventually been seduced by the beauty of string theory, which had a resurgence at about the time that I finished my PhD, and I would have ended up doing research on a long road to ... well, it might be somewhere, but it also might be nowhere (see Peter Woit's blog for lots on this). Ha! I couldn't resist a gratuitous swipe at string theory!

I like the sort of research that can be done successfully using simple equipment (e.g. a standard PC running Mathematica), that achieves useful results with the investment of only days or weeks of my time. The information processing research that I currently do admirably satisfies these criteria.

Endless projects? Not for impatient me.

Blacklight Power

2005-11-16T19:40:00.000Z

Amazingly, Blacklight Power will not go away. This organisation claims to have something to do with science, and that they can extract energy from hydrogen atoms as follows (quotation taken from here) :

... energy is released as the electrons of hydrogen atoms are induced by a catalyst to transition to lower-energy levels (i.e. drop to lower base orbits around each atom's nucleus) corresponding to fractional quantum numbers ...

Oh wow! I can see how a pseudo-scientist with a poor grasp of quantum mechanics might dream up this idea by noodling around with the algebra of the QM of a hydrogen atom. Fractional quantum numbers? Why not? If we do that then we can get energy levels lower than the previously accepted ground state energy. Fantastic! We can access a new source of energy. Hey, man, pass the bong.

There is a teeny little problem with this fractional quantum number idea. The wavefunction has to be multi-valued or has to diverge at infinity to accommodate this sort of quantum number, and since the wavefunction is the projection of the state vector onto a set of orthogonal basis states, this means that this projection would have to be multi-valued (or have to diverge). What is that supposed to mean? It means you have got it wrong.

Unfortunately, many intelligent people who are not formally trained in science fall for this sort of hocus pocus because of the Parrot Effect. Even if you are only slightly gullible, then provided that you hear about something from either a single apparently respectable source, or from a large number of unreliable sources, then you are likely to believe it.

Blacklight Power? I hope you haven't bought shares in it.

How to be invisible

2005-11-13T15:23:00.000Z

Continuing with the "Aerial" album by Kate Bush, there is an absolutely fascinating song called "How to be invisible", in which she explains how it is that she manages to seemingly vanish when she is not wearing her public KB persona.

The chorus of "How to be invisible" is

Eye of Braille
Hem of anorak
Stem of wallflower
Hair of doormat

I assume that this is a description of KB when she is wearing her alter ego. But this is clearly a description of a gypsy/traveller person. Such people often wear anoraks (i.e. hem of anorak) and have thickly matted hair (i.e. hair of doormat). If such a person kept a low profile (i.e. stem of wallflower) then they would effectively be invisible (i.e. eye of Braille).

What a revelation! Now I understand. Thank you to KB for sharing this with us.

Pi

2005-11-13T12:51:00.000Z

The new album "Aerial" by Kate Bush has a song called π (Greek letter p), which is about

Sweet and gentle and sensitive man
With an obsessive nature and deep fascination for numbers
And a complete infatuation with the calculation of π...

;-)

She recites π to a large number of decimal places. Actually, she doesn't recite the precise digits of π, and even omits a large block of digits, as has been noticed by many people. Now I don't believe for a minute that KB would make careless mistakes, because she has the reputation for being a bit of a perfectionist. That means that the "mistakes" in the digits are deliberate. How intriguing! This has just got to be a number puzzle that KB has set us to solve.

I don't have a solution to this puzzle. All I have done so far is to listen closely to what KB sings and how she sings it, and I have listed what I hear below.

I break up the digits into groups the same way that KB does (actually there is more structure in the way she sings the digits than I show below), I use bold font to denote digits that she particularly stresses, I put square brackets around digits that depart from the true π sequence, I use "BV" to show a contribution from the backing vocals, and I use "?" to show where I am not sure what I hear.

3.14159
26535897932
3846264
3383279
[BV chorus]
50288419
716939937510[101?]
582[31]97[10?]49
[BV mini chorus]
44
59
2307816406286208[22 digits omitted]8214
8[BV 0?]
865132
[BV chorus]
8230[BV 0?]664709384460955058223

I have had lots of ideas on how to crack this one, but I'm not so obsessed with numbers that I am going to waste a sunny Sunday sitting at a computer working on the problem. This one gets solved in "slow time".

Has anyone got any ideas on solving this number puzzle? One idea that I reject out of hand is the suggestion that there isn't a number puzzle here!

Bad apples in science

2005-11-07T22:43:00.000Z

In science you occasionally get bad apples, i.e. scientists who fabricate results. Fortunately, science is a self-correcting activity in which results have to be reproducible to be accepted, and theories have to be falsifiable in order to count as science. If nobody else can reproduce a result that is obtained by only one scientist then it is erroneous, no matter how talented that scientist is. A theory that makes no predictions about things that we can measure is not science, no matter how elegant or philosophically deep that theory is.

There are some famous recent examples of bad apples in science, such as J Hendrik Schön and Luk Van Parijs, both of whom lost their jobs and no doubt their careers as a result of their reckless dishonesty. The self-correcting nature of science worked for us by exposing these rogues, but the fall-out is that people trust scientists a bit less than they did beforehand. I wonder how many more as yet undiscovered cases of fraud there are out there.

What I don't yet understand is why would any scientist think that they could get away with fabricating results? They must know that other scientists will be attempting to reproduce their results. They must know that they won't receive any long-lasting recognition until other scientists actually do reproduce their results. No Nobel prizes have ever been rashly awarded because someone suddenly produced a surprisingly impressive result.

Is it possible that some scientists can so completely delude themselves that they really believe their faked results? I know self-delusion can easily happen, but usually a good night's sleep and a pause for reflection cures the problem. Maybe some people can't reset themselves in this way.

Is it possible that the demand for a continuous stream of publications forces some scientists into grey areas where they publish what they think their results would be if only they had the time to do the work? I am very familiar with this pressure to publish according to a schedule that is determined by "bean counters", and it isn't nice.

Trick or treat - no thanks

2005-11-01T19:13:00.000Z

When I was a child "trick or treat" was an American tradition. Now I am an adult it has migrated to the UK as well. The problem is that the kids expect a treat (i.e. cash) in return for doing nothing whatsoever, not even fancy make-up and an imaginative costume.

Last year my local newspaper published a picture that you could post in your window to say "no thanks" to trick-or-treaters. I decided that with a few modifications the picture would not only say "no thanks", but that it would also enter more positively into the spirit of Halloween.

Here it is (and it works as well!):

What do you care what other people think?

2005-10-30T11:33:00.000Z

In this week's New Scientist there is Creativity special: Looking for inspiration which discusses the issue of how creativity emerges in the human brain, and why some individuals have so much more of it than others.

The last word was given to various luminaries. One comment caught my eye because it was so close to my own viewpoint:

Lee Smolin (theoretical physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario): "The main ingredients in science are intensive immersion in a problem, fanatical desire to solve it (big problems are rarely solved by accident), familiarity with previous attempts leading to an original critique of where they went wrong, reckless disregard for what other experts think, and the courage to overcome your own doubts and hesitations, which are much scarier than anything anyone else can say because you know best how vulnerable your new idea is."

I think the most important point made above is to have a "reckless disregard for what other experts think". Too much respect for other people's ideas causes you to do their research for them, rather than doing your own research for yourself. You must follow your own nose, but remember to be honest with yourself so you don't fool yourself into thinking that things are going well when they are not.

Lastly, my apologies to Richard Feynman for stealing his book title for this posting.

Quantum computers can't be backed-up

2005-10-30T09:52:00.000Z

In this week's New Scientist there is an article entitled Attack of the quantum worms in which the problem of defending a quantum computer against malicious software attack is discussed. Even the leading quantum computer theorist David Deutsch says that he hadn't anticipated this problem. Frankly, I am amazed that he hadn't forseen this possibility; maybe he has never suffered an attack on his computer.

One of the key parts of your defence strategy is backing up your software, so that if something gets corrupted by an attack then it can be repaired afterwards. This is where quantum mechanics is not very helpful to you, because it is fundamentally impossible to make an independent copy of a QM state, so you can't do a safe backup. This is such an important property of QM that it has been elevated to the status of being called the No-cloning theorem.

This sounds crazy! How is it possible that QM should prevent you from making backups?

I have already discussed in an earlier posting Quantum mechanics is not weird the reason why many people think that QM seems to be crazy. It all boils down to people insisting that the everyday intuition that they have built up through exposure to the world through their senses will also work in situations where their senses are blind. One such example is QM, which exercises its effects in places that we don't directly see with our senses.

This problem of everyday intuition being inappropriately applied also gets in the way of understanding why QM prevents backups from being made. It is tempting to imagine that you can just grab the data and make a copy of it to keep somewhere else. The problem here is that in QM the implementation of the words "data", "grab", and "copy" have to be defined precisely. I already did something like this in my earlier posting Spooky action at a distance?, but the situation is much simpler here.

Suppose that a quantum computer contains only one particle (1 qubit), which is represented as A↑ (spin pointing up) or A↓ (spin pointing down). The power of a quantum computer comes from the fact that its state can simultaneously hold A↑ and A↓, so it can do truly parallel computations. In the intuitively comprehensible classical (i.e. non-quantum) computer these states are mutually exclusive possibilities, so classical computers can do only one computation at a time. It is this reality of doing parallel computations in quantum computers that gives them their enormous (a factor of 2^N for an N-particle quantum computer) speed advantage over classical computers.

Assume that the backup store is also a single particle, which is part of a QM backup system that denoted as U. The spin-up and spin-down states of the backup particle in U will be denoted as U↑ and U↓, respectively.

The initial state of the quantum computer and backup store is then U (a A↑ + b A↓), where a and b are the amplitudes of the two possible states of the quantum computer.
The state of the quantum computer and backup store after an attempt has been made to do a backup is then a U↑ A↑ + b U↓ A↓. Arrows have now been attached to U because interactions have occurred between A and U that cause the backup particle in U to become correlated with the state of the quantum computer.

OK, so that's it. We have apparently done a backup; A↑ has been copied as U↑, and A↓ has been copied as U↓. However, U is not a safe backup of A, because in QM the A and U particles are still connected to each other. A malicious software attack on A will thus propagate to U, and will thus be an attack on both A and U.

This is exactly the same effect that appeared in Spooky action at a distance?, where separating the particles does not destroy the connection between them. That means that if you start with a U↑ A↑ + b U↓ A↓, and then you separate the A and U particles you get something that can be represented as a U↑ ••• A↑ + b U↓ ••• A↓, where the ••• remind us of the fact that the QM connection between the particles is unchanged by separating them. This means that A and U behave as if they were the same particle, which was what Einstein called "Spooky action at a distance".

It is this sameness that destroys any pretence that U can be a safe backup of A, because effectively U is A, rather than U is a copy of A.

So the No-cloning theorem prevents backups from being made in a quantum computer. The only defence against attacks by malicious software is to ensure that the connection between the quantum computer and the outside world is switched on for only a negligible fraction of the time, and a further countermeasure is to choose the on-times randomly. This slows down the communication between the quantum computer and the outside world by a fixed fraction, but it does not affect the internal speed of quantum computation.

If intelligent design is science then so is astrology

2005-10-30T09:15:00.000Z

I have posted before on End of the Enlightenment, and I can't resist returning to the theme. In this week's New Scientist editorial the focus is on the court case on whether Intelligent Design pseudo-science should be taught alongside evolution science in the classroom. The leading article God goes to court in all but name contains a gem on how science is defined, which I quote (who is on which side is clear from the context):

The packed courtroom came alive for Behe's cross-examination. Eric Rothschild, an attorney for the plaintiffs, sparked a heated debate about the definition of a scientific theory. The National Academy of Sciences says it is, "a well-substantiated explanation of some aspect of the natural world that can incorporate facts, laws, inferences, and tested hypotheses".

In court Behe accepted that ID fails to pass muster, but argued that in practice scientists use the word more broadly. He offered an alternative: "A scientific theory is a proposed explanation which points to physical data and logical inferences. "

Rothschild saw his opportunity to move in for the kill. "But you are clear, under your definition, the definition that sweeps in intelligent design, astrology is also a scientific theory, correct?"

"Yes, that's correct," Behe said, as the court erupted in laughter.

"You've got to admire the guy," comments Robert Slade, a local retiree and science enthusiast. "It's Daniel in the lions' den."

As I read it, the distinction that is being drawn here is between the following two different definitions of "science":

NAS definition: "well-substantiated explanation".
ID definition: "proposed explanation".

The key point about the NAS definition is that your explanation must be backed up by experimental observations, whereas this is isn't the case with the ID definition.

This distinction was discussed at length in the excellent book The Fellowship by John Gribbin, where he describes the dawn of western science, where "natural philosophy" (i.e. explanations unsupported by experiments) was replaced by "natural science" (i.e. explanations supported by experiments).

Quantum mechanics is not weird

2005-10-27T19:01:00.000Z

In my two previous postings State vector collapse? and Spooky action at a distance? I have talked (ranted?) at some length about commonplace misunderstandings of quantum mechanics. I find the awe in which QM is held to be quite annoying. It is described using words like "spooky" or "weird" or "mysterious", which are used by journalists and scientists alike. Remember the parrot cartoon? Yes, this is another example that is very aptly described by that cartoon.

QM has been around since 1925. How long does it have to be around before people accept it as is? Why should anything about the universe be called "weird"? The only explanation for this behaviour is that we start with a prior prejudice that those phenomena that are directly accessible to us via our senses are representative of all phenomena in the universe. When we unearth something that is not directly accessible to our senses, we therefore register surprise if it does not fit into our "standard" intuitive understanding that serves us so well for those phenomena that are directly accessible to our senses.

One of the benefits of a scientific education is that it extends one's standard intuition into areas that were not previously accessible. QM is just one example where one's intuition needs to be built up from almost no prior intuitive understanding of QM. At first, QM will seem weird because it behaves in ways that are very dfferent from standard intuition. But once one has understood that one's standard intuition must be limited in scope, it is easy to open one's mind up to the novel features of QM, and thus to achieve an "extended" (i.e. "standard" plus the extra bits needed to incorporate QM) intuition.

Of course, there are also people who love things that don't fit into their standard intuition, because they are then things to be worshipped rather than to be understood. QM is a perfect candidate for these people, because they see QM as having a mystical favour that eludes direct comprehension. Certainly QM eludes standard intuition, but that doesn't mean that QM is mystical.

So, QM is not weird, provided that you are humble enough to acknowledge that the standard intuition (e.g. common sense) that you develop using your standard senses (e.g. eyes, ears, etc) is necessarily limited to the sorts of phenomena that they can sense. You need to use entended sensing apparatus (e.g. laboratory apparatus) in order to build an extended intuition (e.g. feeling for QM).

The artilect war

2005-10-23T18:00:00.001Z

I posted before on Human life: The next generation by Ray Kurzweil, which suggests that the rate of technological advance is such that it won't be long before we significantly upgrade humans to a better model. I disagree with that prediction, or at least I think that the time scale for things of that sort to happen will be quite long (i.e. many human lifetimes, at least).

In this week's New Scientist there is a letter Cosy Kurzweil whose author Hugo de Garis paints a far less rosy picture of our technological future than Kurzweil. de Garis has written a book The Artilect War (precis), about ARTIficial intelLECTs that have massive intellectual powers, which could reasonably be expected to be created (or create themselves from earlier prototypes?) sometime during the 21st century. [Update on 30 December 2008: The links in this paragraph are now dead. A PDF of The Artilect War is here. Hugo de Garis has a web page here.]

I strongly urge you to read The Artilect War. I find myself in a similar quandary to de Garis, who is working on building artifical brains yet he is worried about the possible consequences of his research.

One course of action that would be incredibly naive to take would be to unilaterally abandon research in the area of artifical brains. That would be as stupid as to unilaterally abandon defence research, where it wouldn't be long before your vulnerability to the hostile actions of others would soon be your undoing. Similarly, in artificial brain research, you at least have to understand what the potentialities of the technology are in order to protect yourself against hostile actions using such technology against you. The only moral course of action is to continue the research.

Here is a worst case, and a best case:

Worst case: Building artilects may turn out to be just another step in evolution, and that ultimately we (i.e. humans) would then be "viewed" (or whatever artilects do when they are "thinking") as just a stepping stone along their prior evolutionary path. In this scenario, the human species (as we know it) does not ultimately survive the appearance of artilects. Naturally, being humans, we don't exactly relish this prospect.
Best case: An artilect would be an artificial brain-like prosthesis that would greatly enhance the abilities of its human "wearer". To use a present-day analogy, imagine what it would be like to have direct brain access to the internet, rather than having to type with your fingers at a keyboard and receive results through your eyes. Assuming the interface was designed so that you could use it efficiently just by thinking, then you would be phenomenally knowledgeable. Now imagine upgrading this direct brain-internet access to include the ability to do massively more intelligent thinking (let's call it a "brain graft"), to add to the massively greater amount of information that you already had from your brain-internet access. What if you were able to program this "brain graft" just by thinking about it, so that you could offload some of the more tedious things that you now do laboriously with your existing biological brain (e.g. a trivial example would be mental arithmetic)? The possibilities of what you can do with a "brain graft" are endless.

Naturally, my vision is for a future that is something like the second case above, provided that the technology is used sympathetically. None of us wants to be like the Borg.

However, like de Garis, I am not optimistic about how different groups of people, using different levels of artilect technology, would smoothly interact with each other. This will be a big problem, which is discussed by de Garis as the "Terrans" versus "Cosmists" issue in The Artilect War. For instance, if they wished, groups of people could opt to not use this technology, much as some people people currently opt to live low-technology lives in tipis, but the tipi dwellers don't always have a smooth time with their technology-using neighbours. This type of problem could be exacerbated by many orders of magnitude by an artilect-based technology.

What do we do to get from where we now are to the vision of the good future described above? The only sensible course of action is to continue research in the area of artifical brains, and to ensure that whatever technology is created is integrated sympathetically into our human framework. We have to always be on the look-out for potential instabilities, where small groups of people can create dangerous versions of the technology, and to protect ourselves against this. A contemporary example of this problem (on a trivial scale compared to artilect technology) would be the fight against writers of assorted malware (e.g. software viruses, etc). The "arms escalation" that exists between the "good" and the "bad" guys ends up making the good guys much stronger, provided that they recognise early on that they are in a fight for survival.

Spooky action at a distance?

2005-10-23T10:03:00.000Z

Einstein said of quantum mechanics that it had a "spooky action at a distance". He wrote a scientific paper with two colleagues (Podolksy and Rosen) on what has become known as the EPR paradox. E, P & R genuinely believed that they had discovered something paradoxical in QM (that's why they wrote the paper), and that therefore QM had to be wrong. What they had actually done (although they didn't realise it) was to show that the universe behaves in stranger ways than they were prepared to believe.

What EPR had stumbled on was one of the consequences of what we now call "quantum entanglement". This entanglement is an obvious consequence of QM, assuming you have an Everett-like interpretation of QM, which I discussed in my earlier posting State vector collapse?.

So, why does EPR annoy me? It because EPR has become a wrong part of QM folklore. Some people think that EPR were right, and not that they were wrong. This manifests itself in various ways, one of which is that people believe that QM somehow allows faster-than-light (or even instantaneous) communication.

This is complete rubbish. Let me tell you why. This description is quite long and detailed, but it has a very simple logic.

I will describe the basics of EPR from the correct point of view, rather than the incorrect point of view that EPR themselves used in their EPR paradox paper. I want to do it this way because I see no point in perpetuating a misunderstanding by presenting the wrong argument first. This means that I change lots of details in order to tell the story the way I want to. Note that I am not going to discuss technical issues relating to particle statistics, because they don't affect the basic "quantum entanglement" result.

Here is the correct version of EPR:

Create a pair of identical particles (call them A and B) in such a way that their spins in the up/down direction point in opposite directions. This physical state is represented as A↑ B↓ + A↓ B↑, where the spin-arrows ↑ and ↓ are used to denote the direction of spin. Because the particles are identical, both ways of assigning spin to the particles (i.e. A↑ B↓ and A↓ B↑) are equally valid, and both possibilities actually and simultaneously occur in practice, so the real physical situation is correctly represented as the sum A↑ B↓ + A↓ B↑, rather than only one or other of the pieces A↑ B↓ and A↓ B↑.
Pull the particles apart until they are separated by an enormous distance, but make sure that you don't mess up their spin directions whilst separating them. You could represent this physical state as A↑ ••• B↓ + A↓ ••• B↑, where the ••• indicate the physical separation between A and B.
Introduce two observers U and V who are tasked with observing A and observing B, respectively. The real physical situation is now represented as U (A↑ ••• B↓ + A↓ ••• B↑) V, where I have placed U at the left and V at the right to indicate where they are located (i.e. near to A and near to B, respectively).
The two observers U and V now observe A and B to see what their spins are. The word "observe" here means that an observer interacts with a particle, in such a way that the state of their brain becomes correlated with the state of the particle (this will become clearer below). There are two possible outcomes of this experiment. The brains of U and V become correlated with A↑ ••• B↓ to create the state U↑ A↑ ••• B↓ V↓, or become correlated with A↓ ••• B↑ to create the state U↓ A↓ ••• B↑ V↑ (a spin-arrow ↑ or ↓ written next to U or V means that the observer's brain has observed the corresponding spin). The real physical situation is the sum of these two, which is U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑.
The net effect of the observation above is to transform the state from U (A↑ ••• B↓ + A↓ ••• B↑) V to U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑. The process that leads to this transformation is defined in detail by the dynamical equations of QM. Any other conjectured transformation must bring in assumptions from outside the dynamical equations of QM.
These results show that either (U observes A↑ and V observes B↓) or (U observes A↓ and V observes B↑), which means that what U observes and what V observes are deterministically associated with each other. Even though the particles are separated by an enormous distance when they are observed, they nevertheless produce observations in which A↑ is associated with B↓, and A↓ is associated with B↑.
This is the bit that Einstein said was "spooky action at a distance" because he maintained a distinction between the particles being observed, and the observers themselves. He would not accept that the observers were also a part of the whole QM state, so he never accepted that U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑ described a real physical situation. His view was (in a QM style of notation) that the real physical situation was described by (U↑ A↑ or U↓ A↓) and (B↑ V↑ or B↓ V↓), where (X or Y) allows only one of X or Y to occur (this is actually an exclusive-or), and (X and Y) requires that both of X and Y occur. This prescription (i.e. figmant of Einstein's imagination, if you want) is an example of a conjecture that is brought in from outside QM, as described in step 5 above.
Thus Einstein thought that the outcome of observing A was a random result that was either A↑ or A↓, and similarly the outcome of observing B was an independent random result that was either B↑ or B↓. He therefore thought that there was no reason why the results for A and B should be correlated with each other, provided that A and B were so far apart that there was no possibility of some other means of communication between them that might cause the results of the observations to be correlated.

In summary, we have an advantage over Einstein, because we know that after the observations have been made the (correct) real physical situation is actually described by U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑, whereas Einstein simply refused to believe that this was what reality was doing, and insisted that the (incorrect) real physical situation was described by (U↑ A↑ or U↓ A↓) and (B↑ V↑ or B↓ V↓). The correct description of reality makes it obvious that the QM associations were set up when the particles were originally close together, and were then preserved as the particles were pulled apart. The incorrect description of reality has been plucked from thin air, based on a prior prejudice about how the universe works, rather than being derived scientifically from QM. No wonder Einstein wrongly thought that QM was paradoxical.

The diagram below summarises the steps in the above argument.

A: Initial state of the particles A↑ B↓ + A↓ B↑.
B: State of the particles after being pulled apart A↑ ••• B↓ + A↓ ••• B↑.
C: Show the observers tasked with observing A and B as yellow squares, which together with the particles describes the state U (A↑ ••• B↓ + A↓ ••• B↑) V before the observations have been made.
D: Show the observers and the particles after the observations have been made. This describes the state U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑.

Can we do faster than light (or instantaneous) communication between the A and B particles (which are separated by an enormous distance) in the above description?

If you think like Einstein (who never accepted the reality of states like U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑ in QM) you would say "yes", because you would have no other way of understanding how the observations of A and B came to be deterministically interrelated, and therefore arrive at a paradox (assuming you believe that faster than light travel is paradoxical!), so you would deduce that QM must be wrong because it is what is allowing this faster than light communication to occur.
If you do accept the reality of states like U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑ in QM then you have no problem in saying that the communication between A and B occurred whilst they were still close together, and that the consequences of this communication are preserved as the particles are pulled apart, and are then "observed" (i.e. correlated with the brain states of U and V).

I used the suggestive "•••" notation to indicate the separation between A and B, because it also suggests that A and B are linked together no matter how apart they are. This linking is also called "quantum entanglement".

Spooky action at a distance? No way!

State vector collapse?

2005-10-22T12:53:00.000Z

This is a story of setbacks and revelations along my route to understanding quantum mechanics properly. The lesson that I have learnt along this route (and elsewhere) is never to accept what people tell you without first checking it all for yourself. If you don't have the resources to do these checks, then you must "label" the information as being potentially unsound.

Why did my undergraduate physics teachers insist that QM states collapse when you observe them? They did it because that's what they were taught themselves. They then went on to describe "paradoxes" in QM, with whimsical names like Schrödinger's Cat, Wigner's Friend, etc. Of course, as an innocent physics undergraduate I ignored the "paradoxes" and concentrated on doing QM calculations so that I could get the answers to come out right. As Richard Feynman said "Shut up and calculate" (or maybe it wasn't Feynman - see here), so that's what I did, and it worked pretty well for me.

The trouble came later when I had more time to think about QM. By then I had forgotten about the "paradoxes", but nevertheless on deep reflection I realised that something was not quite right about QM. I turned it over in my head for most of the time that I was doing my PhD on quantum chromodynamics, and eventually came to the conclusion that some of what my QM teachers had been teaching me was rubbish. What they had taught me was an "effective theory" (i.e. something that works, but which you shouldn't look at too closely) and not a "fundamental theory" of QM, yet they had given me (and everyone else, including themselves) the impression that they were teaching a fundamental theory of QM.

If you are told that something is fundamental then you tend to attribute to it an exalted status, where you are supposed to be able to derive everything from it. It takes on the role that axioms have for mathematicians; fundamental and immutable (actually, nothing is immutable in science). Unfortunately, just as you can write down contradictory axioms, you can also write down contradictory QM. What is the evidence for this? The above mentioned QM "paradoxes", of course!

How do we fix this problem of the QM "paradoxes"? In my musings during my PhD I rebuilt my understanding of what QM was about (this took a long time with many false starts), and the one part that didn't fit naturally was the so-called state vector collapse, where observing a physical system caused its state to collapse from a linear combination of alternatives into a single one of the alternative physically permitted possibilities. The QM equations simply didn't specify how this collapse occurred (or even that it occurred at all), so why were we taught that it did occur? I came to the conclusion that it was mainly for calculational convenience (i.e. an effective theory), and that it simply did not happen that way in practice. In fact, I found out later on that the interpretation of QM that I had derived for myself was already well-known as the Everett interpretation of QM (see the The Everett FAQ), but because I had been conducting my QM musings in secret (at the physics laboratory where I did my PhD it was thought to be distinctly unsound to be questioning the foundations of QM) I knew nothing of this prior work. Later on, as I mused deeper and deeper about QM, I refined my viewpoint further, but it still has a distinctly Everett-like flavour. The details are too technical to be repeated here.

It took a long time for me to flush out the errors that my QM teachers had taught me. All attempts at discussion about this with other physicists met with blank stares and uneasy behaviour. The implication was that they thought that I was a crackpot, which didn't form a good basis for building confidence in the correctness of my ideas. Anyway, over the following years it gradually became clear that I had been right all along. For instance, I took instantly to quantum computation, which was so self-evident to me (given my Everett-like view of QM) that I wondered what all the fuss was about. A very good exponent of these quantum computation ideas is David Deutsch, who has written an excellent book on the subject called The Fabric of Reality.

Of course, I can't say that state vectors do not collapse, but just that it is not necessary to assume that they do, and there is nothing at all in the QM equations of motion that says anything about collapse. If there is ever any experimental evidence for collapse, I would be interested to see how the underlying dynamics of collapse is then added into the QM equations of motion.

Unfortunately, QM still appears to be taught in the same way that I was taught it, producing hordes of people who "shut up and calculate". There will be a few of them who will go through the same rediscovery process that I went through. I hope it is easier for them than it was for me.

State vector collapse? No way!

The beauty of branes

2005-10-19T00:17:00.000Z

This month Scientific American has an article on The Beauty of Branes, which describes what Lisa Randall has been doing on the theoretical physics of higher dimensions, and all that sort of thing.

What I find amazing is what is written on her blackboard in the photo that accompanies the article. Actually, what is more to the point is what is not written on the blackboard. The blackboard is totally clean apart from one fragment of maths, which looks like a bit of standard Dirac algebra when I look at it through my magnifying glass.

This is totally unprecedented for a theoretical physicist!

What right does Lisa Randall have to call herself a card-carrying theoretical physicist if she doesn't even have the appropriate blackboard credentials? At the very least, I would expect to have to solve a complicated inverse problem (of the type that geologists regularly solve) just to deinterleave the various layers of equations that had been deposited on the blackboard over time.

Lisa! Please get a grip!

Update: I just noticed that the photo in the contents section of the print edition of Scientific American shows Lisa Randall standing in front of a blackboard that is suitably encrusted with chalky equations. So that's alright then!

Why time keeps going forwards

2005-10-16T17:02:00.000Z

This week New Scientist has an article entitled Why time keeps going forwards, in which the reason why time flows in one direction (i.e. from past to future) is explained.

Why is this a puzzle? The problem is that the basic laws of physics, which are so successful at explaining experimental results, are written in a way that makes no distinction between time going forwards and time going backwards.

What does that mean? It means that if the laws of physics allow something to occur, then they also allow the the time-reversed version of that "something" to occur (technically it's a bit more complicated than just time-reversal, but the essence is right).

But that's crazy! If a tea cup falls on the floor then it breaks, but we never see the reverse chain of events occurring. So the laws of physics must be wrong.

Not so! The key point to realise is that the following two items are not the same thing:

Equations that describe how things behave in general.
Solutions of those equations that describe specific instances of how things behave.

The solutions must be consistent with the equations, and they must also be consistent with any additional conditions that are imposed on them.

In the case of the flow of time, the asymmetry between the forwards and backwards flow directions is caused by the imposition of an initial condition, in which the universe initially has a highly ordered state. Of all the possible solutions to the equations of the whole universe, only an extremely small number of solutions that respect the highly ordered initial condition are allowed. These are exactly the solutions that we (i.e. our brains) interpret as having a forwards flow of time.

The phrase "flow of time" is a subjective quantity that we can use to summarise the asymmetric behaviour of systems generally. At the level of the whole universe the flow of time is a reliable quantity that goes on and on seemingly for ever, because human time scales are much shorter than the age of the universe. At the level of a small system that we prepare ourselves in a highly ordered initial state and then allow it to evolve (i.e. rather like a mini universe), such as gas atoms in a box with an initial condition that they are all in one corner of the box, there is a clear flow in one direction away from the initial condition as the gas atoms spread out inside the box. However, the small system behaves differently from the whole universe, because very soon the gas atoms come into equilibrium and uniformly fill the box, after which the gas behaves the same way whether you look at it running forwards or running backwards in time, so the flow of time as defined by the behaviour of the gas atoms no longer has a clearly defined direction. From the point of view of a gas atom there is no flow of time when the gas is in equilibrium; that is why "flow of time" is subjective.

Flying spaghetti monster relics discovered

2005-10-16T16:36:00.000Z

The deity known as the Flying Spaghetti Monster has consolidated his hold over the minds of his worshippers by guiding a few of his disciples (the "chosen ones") to discover some of his ancient relics.

This week New Scientist reports that:

Ancient noodle rewrites history

Who invented the noodle is a hotly contested topic - with the Chinese, Italians and Arabs all staking a claim.

But the discovery of a pot of thin yellow noodles preserved for 4000 years in Yellow river silt may have tipped the bowl in China's favour. It suggests that people were eating noodles at least 1000 years earlier than previously thought, and many centuries before such dishes were documented in Europe.

"These are undoubtedly the oldest noodles ever found," says Houyuan Lu at China's Institute of Geology and Geophysics in Beijing. His team found the noodles buried 3 metres deep in flood-plain sediment at Lajia in northeastern China after lifting out an upturned bowl. The "spaghetti-like" noodles, up to 50 centimetres long, sat atop a mound of silt which had sealed them in the bowl following a major earthquake and flood.

Lu's team report in Nature (vol 437, p 967) that the noodles came from two species of millet grass grown in north-eastern China at that time. They identified the species by examining starch grains in the noodles and phytoliths, silica particles formed in seed husks while plants are alive but which survive as fossils.

They believe the noodles were made by pulling dough into long strands before boiling.

Naturally, being religious relics, I don't expect this noodly experimental result to be reproducible.

Kate Bush video

2005-10-16T16:22:00.000Z

Channel 4 screened a "video exclusive" last night, in which we saw the new video for "King of the Mountain" by Kate Bush (I already mentioned KOTM here). The video was intriguing (to say the least!), and caused lots of puzzlement amongst her many fans on the main KB news forum (see here).

The video features Kate dressed in what looks like a trench coat, singing whilst swaying back and forth to the music, whilst being filmed from a point somewhere above her. A theme that runs through the whole video is Elvis Presley's clothes (minus Elvis himself) moving around (walking, flying, etc). Elvis is the target of the song's lyrics (see here). However, because this is all coming from the mind of Kate, it will have a deeply layered meaning, and maybe Elvis is a metaphor for someone else. Nothing KB does is as it superficially seems, and we can all have lots of fun trying to guess what the truth is.

Update: Judging by the Opinions on video thread on the Kate Bush discussion group her fans don't know what to make of the KOTM video. There is a lot of drivel written by people who have watched the video only once; that's a big mistake with KB material. Equally, there are overly protective people who want to silence the critics, whilst fondly imagining that KB is reading their postings. I think KB is doing nothing of the sort; her long-time track record is to ignore trends and opinions.

Ig Nobel prize

2005-10-16T15:43:00.000Z

The Ig Nobel prizes are awarded each year for "achievements that cannot or should not be reproduced" (see here). They are an accidental by-product of the self-questioning system known as "science", because when you allow any question to be asked, then inevitably some very silly questions get asked. These questions lead to experiments being done in order to obtain the answers to the questions, and the results are duly reported in the scientific literature.

Science, by its very nature, encourages repeated asking of the same question, the aim of which is to reproduce the experimental results in order to increase confidence in the correctness of the results. The Ig Nobel prize specifically suggests that this rule should be waived for certain "achievements that cannot or should not be reproduced".

To get an idea of what this is about here is an example of a prize-winning study:

The 2005 winner in the Fluid Dynamics section is Pressures produced when penguins pooh - calculations on avian defaecation (270kB PDF file), Polar Biology, vol. 27, 2003, pp. 56-8.

Heisenberg's uncertainty principle

2005-10-09T16:24:00.000Z

I keep seeing Heisenberg's uncertainty principle described in popular journalese as allowing a temporary violation of the law of energy conservation (or of the law of momentum conservation). The argument goes that HUP allows you to lend or borrow energy as long as settlement is made very soon, and that this arrangement represents a temporary violation of the law of energy conservation.

The truth is that there is no violation of the law of energy conservation.

The lending or borrowing of energy (and momentum) is done in a way that always respects energy (and momentum) conservation. How can this be? Just as with financial transactions where you lend to someone or borrow from someone, with energy transactions you lend to something or borrow from something. What is that something? The details depend on the precise circumstances, but I can illustrate one of the possibilities with the diagrams below.

Walk through these diagrams:

A: This shows a particle going along all by itself conserving energy (and momentum) as per usual.
B: This shows a particle that goes along as in A, but then it emits another type of particle (shown as the dashed line), after which the energy (and momentum) of the original particle have changed. Call these particles of type 1 (solid line) and type 2 (dashed line).
C: This shows particles of types 1 and 2 going along, but then the type 2 particle is absorbed by the type 1 particle, after which the energy (and momentum) of the type 1 particle have changed.
D: This shows diagrams B and C combined. The type 1 particle goes along all by itself, emits a type 2 particle, later on it reabsorbs the type 2 particle, and then goes along all by itself again.

That is the basic structure of how particles behave in physics. Energy (and momentum) conservation are always respected, so moving along each of the lines in the above diagrams each particle conserves its energy (and momentum), and at each of the vertices where a particle is emitted or absorbed the sum of the energies (or momenta) over all particles coming into the vertex is the same as the sum going out of the vertex.

Thus in diagram B the incoming type 1 particle's energy (and momentum) are shared between the outgoing type 1 and type 2 particles. This sharing between the type 1 and type 2 particles has to respect only the fact that the sum of the energies (or momenta) have to add up to the energy (or momentum) of the incoming type 1 particle. That means that one of the particles can have a negative energy and the other a positive energy, as long as the sum has the correct value.

The notion of a negative energy is counterintuitive. What does it mean? The physicist's definition of "energy" is the "frequency of oscillation" of the wave that is associated with the particle. Frequency can have any value (positive or negative) just as the rate of advance of a clock can be anything (forwards or backwards), so analogously energy can have any value.

Conservation of energy and momentum at the vertex where a particle is emitted or absorbed means that the particles don't have complete freedom to choose whatever energy and momentum they want to have, because their sum is constrained to be the same as whatever it was at the start. When a particle is going along all by itself (as in diagram A) there is a definite relationship between its energy and its momentum. After the particle has emitted another particle (as in diagram B), although the total energy and momentum are conserved the individual particles have energy and momentum that do not have the harmonious relationship that exists when the particle is going along all by itself. The physical consequence of this conflict in each particle is that they cannot not travel very far before they have to get their energy and momentum back into a harmonious relationship, and this requires the further emission or absorbtion of a second particle (as in diagram C). Diagram D brings it all together, where energy (and momentum) are conserved everywhere in the diagram (i.e. along each line, and passing through each vertex), and the conflict between each particle's energy and momentum in the "loop" part of the diagram means that the loop cannot be very large.

I think that this conflict between the energy and momentum of each particle, which is caused by the exact energy (and momentum) conservation everywhere in diagram D, is what is wrongly referred to (in popular journalese) as a temporary violation of energy (and momentum) conservation.

The relationship between the size of the conflict between each particle's energy and momentum and extent of the loop in diagram D is given by Heisenberg's uncertainty principle. The greater the conflict the smaller the loop. A particle going along all by itself has perfect consistency between its energy and momentum, so it is not part of a finite-sized loop.

End of the Enlightenment

2005-10-09T00:28:00.000Z

New Scientist has a rather worrying article titled End of the Enlightenment, which has the tagline "Why is so much of the world bent on rejecting reason, tolerance and freedom of thought?". It discusses the relationship between religious fundamentalism and secularisation. Should we build our understanding of the world based on empirical evidence from experiments or should we base it on faith and the reading of scriptures? The worrying part about the article is that religious fundamentalism appears to be gaining in popularity, thus risking everything that has been gained during the age of Enlightenment.

These two approaches can be summarised as follows:

The "Enlightenment" (or science) is an intellectual revolutiom that consists of asking questions about how the world works (i.e doing experiments), and based on that asking more questions, and so on. Gradually this accumulates to lead to a consistent understanding of the way the world works. This framework is open to revision in the light of new experimental observations.
Religion offers a stable framework based on sources called "scriptures". The stability of religious fundamentalism creates a consistent framework within which people can live their lives in relation to the world. This framework is not open to revision, although in non-fundamentalist religions the scriptures are frequently reinterpreted in the light of unforseen circumstances.

A nasty problem arises when people try to apply the above two "principles" to the same area of life. This is a big mistake. "Religion" is a set of rules that can be used to help people to live in harmony, and "science" is a set of rules can be used to help people to understand how the world around them works. These two rule systems have completely different areas of application.

The words "science" and "religion" frequently manifest themselves informally as follows :

Science commonly makes an appearance as "know-how", which is the general common sense that is used by intelligent people who have not been exposed to science. This does not involve the study of science as practiced by professional scientists.
Religion commonly makes an appearance as a "moral code", which is the general common sense that is used by intelligent people who have not been exposed to religion. This does not involve any fundamentalist reading of scriptures.

The above informal type of practitioner of science and/or religion is usually a well-adjusted individual who is pleasant to know.

Why should some people feel threatened (as the New Scientist article observes) by secularisation? In essence, the aim of science is only to provide a concise framework for inter-relating the meter readings that you get in different experiments. Despite pronouncements by various "scientific" luminaries, science does not make specific assertions about the way the world actually works. The most it can say is that things seem to behave this or that way, because we can't find any counter-examples that show otherwise. This doesn't sound very threatening to me.

Now back to the tagline "Why is so much of the world bent on rejecting reason, tolerance and freedom of thought?". I presume that it is because some people prefer the security of a stable religious framework to the ever changing face of a self-questioning scientific framework, and they wrongly think that the two frameworks are competing for the same territory so they must be in conflict.

Mobile phone radiation

2005-10-07T22:35:00.000Z

Is the electromagnetic radiation from mobile phones and mobile phone transmitters damaging to your health?

Uncontrolled experiments on myself reveal a tingling sensation in the general area of the ear to which I am pressing the mobile phone. Is this an effect caused by mobile phone radiation? Is it because I am getting cramp from clutching my phone too tightly? Or it is merely my over-fertile imagination? That's what controlled experiments are supposed to disentangle, so you know which effects occur because of which causes. Nevertheless, the tingling sensation is sufficiently strong that I now always use an earpiece for long calls on my moble phone.

I also hear about electromagnetic standing waves on the wire leading to the earpiece, but I ignore these stories, which has thus created an impregnable defence against any ill effects that such waves might have on my brain.

I would have thought that any form of electromagnetic radiation could potentially have bad (or good) effects on us, simply because everything in our body acts as an electrolyte which can therefore respond to electromagnetic radiation.

The frequencies used by mobile phones are in the 1-2 GHz range, which correspnds to a wavelength range 15-30 cm. This is in the same ballpark as the size of a human head, so surely it is possible for some sort of resonance to occur?

The mobile phone vested interests are strong. I know someone who has lost around £500k unsuccessfully fighting a court case to have a mobile phone transmitter mast removed from their building.

A key problem is that in science you can't prove a negative. Absence of evidence is not evidence of absence. No-one can prove that an effect does not exist, because people can always claim that the effect in fact does exist, but people were just looking for it in the wrong places. So when people claim that mobile phone radiation is not a problem they are being economical with the truth. What they mean to say is that they haven't yet seen evidence that it is a problem. Usually that means that they have turned a blind eye to things that might be positive evidence, just so they can say they haven't seen any such evidence. I'm being cynical? No, I don't think so.

Human life: The next generation

2005-10-07T21:11:00.000Z

New Scientist has an article entitled Human life: The next generation by Ray Kurzweil, which suggests that the rate of technological advance is such that it won't be long before we significantly upgrade humans to a better model.

The key to Kurzweil's argument is Kurzweil's Law (aka "the law of accelerating returns"), which says that future advances will give us an exponential growth of technology, rather than merely linear growth. Potentially, that could mean enormous advances over a human lifetime. Past experience shows that this may indeed be true.

The problem is to predict in what direction technological growth will occur. You know that the technology is going to be mind-bogglingly more advanced than current technology, but you don't know where these advances are going to manifest themselves.

Kurzweil says that:

"...information technologies will grow at an explosive rate. And information technology is the technology that we need to consider. Ultimately everything of value will become an information technology: our biology, our thoughts and thinking processes, manufacturing nd many other fields..."

I agree with all of that.

We are way past the stage where owning a steam engine was a good way of investing your money. Useful engines move bits nowadays.

Kurzweil also says that:

"...By the 2020s, nanotechnology will enable us to create almost any physical product we want from inexpensive materials, using information processes."

That is mostly rubbish.

It is certainly true that nanotechnology holds the potential for doing this. However, the design of a nanotechnological "factory" may require far more information than we can accumulate in the few years between now and 2020.

An example is manufacturing a human being, or a fish, or an ant or whatever. Assuming you start from nothing I don't think you will be able to manufacture any of these by 2020. We can already make a virus starting from nothing, but the process is rather hands-on.

Surely, Kurzweil is not suggesting that the same hands-on approach can be used for making more complicated objects? I assume not.

The production process has to be automated somehow. The obvious way is to first of all design a set of simple "tools", that then take over to do the next stage of designing more complex "tools", and so on up the scale of complexity, until you arrive at the object you wanted to manufacture in the first place. This sounds very much like the sort of solution that evolution discovered over a rather long period of random shuffling about and selection by the environment for "fitness".

How exactly is this evolutionary type of process going to be compressed into the time remaining between now and 2020? Er ... it's not. The reason is that Kurzweil assumes an exponential growth rate that is far too fast if his Kurzweil's Law is to achieve everything it needs to between now and 2020.

Nevertheless, Kurzweil's Law is probably broadly correct, and we will be able to drive evolution forwards at an increasing rate, so his future with nanotechnological "factories" making almost anything we want is much closer than we think it is. The trick will be not to specify in advance which particular complex objects should be made, but to wait and see which complex objects are feasible to make, and then to try to match these objects up with applications that we find useful.

Having said that, we'll still have some really cool technology in 2020, and some of it will be built by nanotechnological "factories".

Update: There is an interesting book called Accelerando that follows up the consequences of Kurzweil's Law. This was pointed out by John Baez here.

Kate Bush returns to planet Earth

2005-09-29T07:15:00.000Z

So finally she has returned from her long break who knows where. Welcome back Kate Bush! She has just released a single called King of the Mountain from her forthcoming album Aerial.

Here are the lyrics:

King of the Mountain

Could you see the aisles of women?/Could you see them screaming and weeping?/Could you see the storm rising?/Could you see the guy who was driving?/Could you climb higher and higher?/Could you climb right over the top?/Why does a multi-millionaire/Fill up his home with priceless junk?

The wind is whistling/The wind is whistling/Through the house

Elvis are you out there somewhere/Looking like a happy man?/In the snow with Rosebud/And king of the mountain

Another Hollywood waitress/Is telling us she´s having your baby/And there´s a rumour that you´re on ice/And you will rise again someday/And that there´s a photograph/Where you´re dancing on your grave

The wind is whistling/The wind is whistling/Through the house

Elvis are you out there somewhere/Looking like a happy man?/In the snow with Rosebud/And king of the mountain

The wind it blows/The wind it blows the door closed

KOTM is a dark and mysterious song which rewards repeated listening. It starts very quietly with indistinct singing by KB, then the mist clears and she is soaring with the clarity that we all know and love. The KTian sound is exactly as we remember. The BVs don't have much to do, but guitar and percussion have lots of fun.

Kate's lyrics are always deeper than you think they are. Her music is the same - it is deeply layered. KOTM appears to be about an ambitious and self-obsessed high-flyer who has not really got the hang of life. How many people like that do you know?!

I wonder what the "Aerial" album will bring. As for the name "Aerial", I suspect that it describes the impression that an artiste receives their ideas via a mental "aerial" that is picking up ideas that are floating "out there". Some people's aerials are definitely a lot better than other's! Kate's aerial is what the techies call ultra-wideband; it picks up everything.

Update: The news of KB's return has appeared here in a physics blog.

Fact and fiction

2005-09-28T11:48:00.000Z

This blog will be where I comment on what's going on in the world. Why "Fact and Fiction"? Well, do you take everything at face value? The cartoon (which I have shamelessly copied from an old copy of Private Eye) says it better than I ever can.

I also have a "scholarly" blog about self-organising networks at ACEnetica. I keep this material in a separate blog because I find reading interleaved "scholarly" and "informal" material really irritating.