Pi (update 3)

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

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!):

1. A theory has to be rooted in experimental data for it to be science, which ensures a large value for Pr(data).
2. 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)

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

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)

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

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

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.