The Fibonacci post has generated a longer comment thread than anything else I've written. I was just digging a little dirt and must have hit a power line. The question I tried to address, was "is there any physics in Fibonacci, or is it just a mathematician's curiosity?"

Here's the physics that came back:

a) AJ Meyer has looked at the galactic rotation curves, and pointed out that "rigid-body" rotation which is observed, can be obtained by having a mass which increases with radius. Now since we can look at galaxies from the side, and they don't get thicker with radius,  it would seem that this increase in mass must be due to something else. Gallo argues that it could be dust, or non-glowing "dark" matter. Meyer argues that a logarithmic spiral distribution, like the arms of spiral galaxies, would contribute more mass at larger radii, exactly as required to match the rotation curves. In other words, there is no "missing matter" in spiral galaxies, but precisely the rotation curve for being a spiral galaxy. Of course, Meyer has no explanation for why the stars are arranged in Fibonacci spirals.

b) Meyer also said that the Schroedinger equation which predicts wave behavior of electrons orbiting a proton, does have spots of zero probability, or "nodes" as they say in wave mechanics. The first two nodes of the "s-wave" solution give the "Golden Mean" which is also the ratio of two numbers in the Fibonacci series. His advisor, Perlmutter, thought it might be significant, but Meyer didn't publish what might be a simple coincidence.

c) Ultracold atoms can attract each other magnetically, and then "resonate" around some stable point, like a vibrating string. The first 2 resonating modes are the Golden Mean again.

d) Alan Newell thinks he may have a non-linear equation for which the energy minima lead to Fibonacci series in plants and pinecones. It's getting pretty messy out there, but perhaps future research will simplify it to a more general rule.

I still can't explain any of the physics, but the main response seemed to be "is there any ID in Fibonacci, or is it just math?"  Or to phrase it differently, "Does this Fibonacci series mean anything?"

I'm doing a thesis at Westminster seminary on the hermeneutical approach to meaning, where "meaning" falls into three categories: Authorial Intent, Reader Response, and Textual Speech Acts. So let's see if we can try to analyze the relationship between ID and Fibonacci using these categories.

Reader Response Theory:  ID ≠ Fibonacci.
On the one hand, ID is far more abstract, and would include Fibonacci if it were shown to be "intelligent". On the other hand, Fibonacci is both simple, and visually elegant. It evokes, if I can use the word, awe and worship, which ID rarely does. When I have seen good presentations on ID (such as Hill Roberts "Lord, I believe" extinct website) they use graphics from Fibonacci sites to make their point. So ID is the pointy-headed academic version of the graphic artist's Fibonacci.

Authorial Intent Theory: ID ∪ Fibonacci
Is there information hiding in the Fibonacci series, making it a subset of ID, or is it all coincidence, some sort of mathematical numerology? One web site says that sunflower whorls are merely an optimization for packing circles of increasing diameter. Another says that it arises from random sampling of periodic signals. Another says that nautilus shells are logarithmic spirals, but not Fibonacci spirals. These three detractors would say that Fibonacci occurs much less often than advertised, and is most frequently a "projection" of what the advocate wanted to see.

On the other hand, the first two zeroes of the Schroedinger equation that describes the hydrogen atom form the "golden mean", which is the ratio of Fibonacci numbers. Likewise, the frequencies of ultracold atoms are in a ratio of the golden mean. And galaxies have spiral arms that look amazingly like Fibonacci. None of these three observations can be explained by the detractors. There is no local optimization or projection that explains them. So it would appear that there is a hidden message in the series which does have physical significance, but physicists haven't yet decoded it.

And that is perhaps the significant difference between ID and Fibonacci. ID supposes that it can spot information and hypothesizes the author. Fibonacci supposes that it can spot the author, but hypothesizes the information. ID inductively works back from message to author, whereas Fibonacci tries to deductively go from author to message. ID provokes debate, Fibonacci provokes awe. ID promotes the people who have all this knowledge about God, Fibonacci promotes awe from the mystery. ID is Enlightenment rationality, Fibonacci is Medieval mystery.

Speech Act Theory: ID ⊂ Fibonacci
Sometimes it is neither the response of the listener, nor the content of the message that is important, but the mechanism of the pronouncement. Giving a promise, for example, establishes something that is more than persuasion, more than communication, but the establishment of a bond, a pledge, an independent entity. So what is it about Fibonacci or ID that has this quantity? To begin with, ID makes the hypothesis that we are here as a result of ID, so in some sense, the speech act is ID. But there is an additional sense that if we just understood Fibonacci, we would be participating in a global design, in a global objective. There's a sense that the golden mean is not meant just for our intellectual satisfaction, nor just for our awe-inspiring worship, but for a mysterious purpose in controlling the universe. It is as if we have been told to drive on the right-side of the road, but we haven't yet discovered cars.

I suppose someone might say this is the attraction to the Kabbalah, to the mysteries of numbers. And while many have warned me of its dire appeal, I also note how many famous scientists have spent decades in this study: Isaac Newton, P.A.M Dirac, Robert Dicke, George Gamow come immediately to mind, but Richard Feynman isn't completely exempt either. These men did not go crazy, nor did they denounce their days spent in numerology as a complete waste of time. So perhaps there is more to Fibonacci than meets the eye. Perhaps it provides, as John Forbes Nash said of his famous equilibrium, the hints that made them famous.

This strange attraction of numerology shows up in the comments in the Fibonacci (hijacked to Euler) thread:

#48 DiEb -- Frankly, I would be more impressed if the fraction 22/7 – or 355/113 popped up somewhere….

FYI, pi does show up in the Bible, but you have to make use of the Hebrew technique of assigning numbers to letters. Here's the story:

I'm about to graduate from UMd, and the physics dept snags a "nearly Nobel-prize" physicist (their price goes up after the award, and they migrate to Harvard) named Michael Fisher. So I sign up for his course in stat mech, and take my seat the first day with 55 other curious students. He opens his lecture by saying that the Bible thought π=3, which goes to show how ignorant Hebrews were, and the foolishness of considering the Bible divine. His quote was from 1 Kg 7:23, giving the diameter of Solomon's bronze basin as 10 cubits, and the circumference of the rim as 30 cubits. (My immediate hermeneutical objection, is that the basin could be shaped like a truncated sphere, so there's no cause for claiming stupidity or errancy.)

However, twenty years later I was given a book written by David Medved, an orthodox Jewish physicist, who explained that Kings and Chronicles tell the same story twice, and this verse is repeated in 2Chr 4:2. They are identical except for one word and one spelling. Blue Letter Bible gives that word:




Medved focusses on the spelling change in yellow. You will notice that the 1Kings7:23 version has no "dots" around it, which is to say, the Leningrad Codex from which my prof Al Groves at Westminster Seminary transcribed his Hebrew text and licensed it to Blue Letter Bible, didn't put in vowel points. Why not? Because it is misspelled, and the Masoretes, who put in the vowels when they copied the Bible in the 3rd-10th centuries, made a marginal note but otherwise left the consonants alone. The Masoretes, like David Medved and the Orthodox Jews today, believe that every consonant of the Scriptures was divinely inspired, and rather than change a single one, just put in marginal notes. (A practice that modern Biblical scholars should follow!) For technical reasons, the vertical line and double dots, the "waw-consecutive", which in English is a simple "and" but in Hebrew is combined with the following word, is not misspelled, but the remainder of the word highlighted is what is misspelled.

Blue Letter Bible has a handy lexicon that tells us what the correct spelling in 2Chr 4:2 means: -- a "line". The next word is "thirty", so this is translated into English as "circumference" or Latin for "a line drawn all around". So yes, this is the controversial ratio Fisher described, the ratio of circumference to diameter. Medved then goes on to argue that Hebrew used letters of the alphabet for numbers, which allows them to make "puns" with numbers. (And you thought puns in English were clever!) The process is called gematria and involves turning a word back into a number using the accepted conventions, conveniently tabulated by Wikipedia. The misspelled word has the values 100-6-5, whereas the correctly spelled word is merely 100-6.

Now mind you, devout Jews think every consonant is there for a reason, and even a misspelling is significant. (I have a paper on Jesus' use of this very principle in his defence of the resurrection.) So Medved, quoting the Vilna Gaon, converts the misspelled word and and its properly spelled word into numbers and takes their ratio. What does he get? 111/106 = ~π/3. Remember Fisher said the Jews thought π was 3? Nope, this ratio multiplied by the placeholder 3 in the text, will give π to 4 decimal places. Think of it as a correction factor, or as a pun, or as a very funny joke on Michael Fisher who is still waiting for his Nobel. And if that gives you shivers down your spine, buy the book off of Amazon and read the other chapters. Loads of fun.

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But do numbers themselves have meaning? Are they independently significant, separate from their meaning or their persuasion? The comments continue:

#77 Aleta -- Why does 1+1=2 depend on God?

Because we need something between 1 and ∞. We need something between Parmenides and Heraclitus. We need something between Hinduism and Islam, between Buddha and Allah. We need a rule of arithmetic that God uses, but doesn't abuse. When you ask "what is a rule?" or "what is truth?" , these other religions will either tell you "whatever you want it to be" or "whatever God wants it to be". The first answer gives relativism, the second answer gives arbitrary nominalism. To stand between these two antipodes that have swallowed mathematicians and empires, takes a belief in a special kind of God, a special kind of reality, a special kind of metaphysics. I can't take you through the foundations of number theory to illustrate these two pitfalls, but I refer you to a PhD in Math and New Testament, my advisor at seminary, Vern Poythress, who wrote on this topic.

Numbers are more than information, more than persuasion, they have independent existence because they are the speech acts of God.