Fibonacci numbers - The Fingerprint of God

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Yeah I KNOW, it seems all you need for atheists to scrutinize your holy book is to claim your god is perfect and infallible and he wrote it. Man!

I'm certainly not talking about the renunciation of beliefs. Rather, I am talking about the reconciliation of faith with science. If we accept that scripture is allegorical, then the existence of a divine creator can still be encompassed within our scientific knowledge.

at least untill you start extrapolating the various teachings.

some of them provide one thing, arguments that they in essence are non workable.

Is this related to "divine proportion"?

If you mean the "golden ratio" ( 1 + sqrt(5) / 2) yes.

ruveyn

For a theist (at least the flavor that I happen to be), God is the source of all truth and beauty. I probably wouldn't have put it as "the Fibonacci numbers are godly", but they are beautiful and true, so I think describing them as like 'fingerprints of God' (as in the thread title) is reasonable.


It has a society dedicated to it, and a mathematical journal that has been running since the 60's, and I've seen at least one book (although there are almost certainly quite a few). So, no, it really isn't mundane.


Assuming this is correct (I'm not familiar with linear recurrences in general), that's something nice about linear recurrences too.


I'm aware of the matrix formula for calculating Fibonacci numbers. It is computationally more expensive than the formulas for doubling the index. The matrix form tracks 3 numbers instead of 2, and in a 2x2 grid, so it duplicates one of the numbers once.

There is also a formula that lets you take 2 pairs of Fibonacci numbers and essentially add their indexes together, so you can use that together with the doubling formulas to get an O(log n) algorithm for calculating Fibonacci numbers.

If you still think they're mundane, consider this: if you have any recurrence like the Fibonacci sequence, where F(n) is the nth Fibonacci number and a(n) = a(n-1) + a(n-2), then a(n) = F(n)a(1) + F(n-1)a(0). For instance, the powers of phi (aka "the golden ratio") fit this format, so phi^n = F(n)phi^1 + F(n-1)phi^0 = F(n)*phi + F(n-1). You can't do that with just any sequence.

well if you take a look at the pyramid, they knew pi to like 1/1000 or something.

Soooo... leave the discussion, if you don't find it worthwhile; other people here obviously do.

The Ancient Egyptians estimated pi to be 3.16 which is off by 0.02 or 1/50.

Archimedes got it much closer. To about 5 or 6 decimal place equivalent.

ruven

The Fibonacci and Bernoulli numbers are computable. Ergo, they are no the true fingerprint of God. The Chaitin numbers, beginning with Chaitin's constant, are truly of divine origin as they are something that only God can know.

What about "Atlas Shrugged"?

Oh wait, Ayn Rand wrote that...

You can believe so. But this thread is more about claiming it to be proof of creationism and disturb evolution. That's sort of lame.

Specially because it is just the same old watchmaker's argument. "see? This is beautiful/complex/whatever" it must have been designed.

It is always ironic to see the watchmaker's argument to be used against evolution. When it was evolution which destroyed the watchmaker argument and made it invalid in regards to the complexity of nature. Darwin showed that simple natural laws can create this complexity and beauty. THAT's how it made science evolve. We no longer needed the watchmaker to explain things.




Tons of mundane things have societies dedicated to them and journals. Rocks are mundane and geologists are all over them.



The formula uses irrational square roots and thus it can't be computed accurately when n is large.




You can with any linear one, and there are infinite of them.

All this is true - I've created it myself in a computer simulation. Randomly placed particles in a screen-sized universe soon formed a circle (which I realised was the result of them following the second law of thermodynamics - they were collapsing into their lowest possible energy state, which meant all being equidistant from each other and from the centre of the screen).


I've never heard of any 'organic soup', not artificially formed, that would have a sufficient concentration of free RNA monomers for it to replicate very much - in any case, having oppositely charged hydrogen bonds line up with a molecule doesn't make it particularly more complex.


Yes, our bodies and DNA and everything that was being talked about is made out of atoms - nobody's debating that.


Non sequitur. The binding of ink to paper in a book and the reflection of light allowing my eyes to see it are all 'governed by simple rules of physics' too; the writing on the pages is also an emergent property, as is the whole collection of matter making the book - but none of that backs up the conclusion 'no author required'.

I suggest you look up emergent properties as you didn't mention that and it is key to the whole process of complex structures forming from less complex components. Highly complex arrangements of matter can naturally form as their component molecules and atoms fall to their lowest energy state as governed by the 2nd law of thermodynamics. It is actually things like hydrogen bonds and repulsion and attraction between molecular chains that is responsible for the formation of complex 3D protein structures from their component molecules and their subsequent emergent properties to do things like transport oxygen or the other myriad features found in living organisms. Similarly with the formation of lipid bilayers and their natural ability to house other molecules. I could go on and on but if you are interested there are thousands of books on physics, chemistry, biochemistry etc going into all this in incredible detail and I have neither the time nor inclination to educate you.

It would be a non sequitur to say that God was required in any of what I described. Whether there is such a creature as God is irrelevant to the whole thing. Complex structures and processes arise naturally without any external magic from hypothetical super-beings.

You can treat this thread as if it were about anything you want. I'm treating it as a good opportunity to talk about the Fibonacci numbers.


If you're trying to debunk the watchmaker's argument, why spend time trying to say the Fibonacci numbers aren't beautiful? All your arguments so far only try to shift the beauty from the Fibonacci numbers to somewhere else.

For someone trying to make the watchmaker's argument with the Fibonacci numbers to be able to get around that, all they have to do is point to the new location of the beauty. If you attack the watchmaker's argument itself, that won't help them.


From what little I know of them, rocks are fascinating. This says more about either your knowledge of rocks or your ability to be interested in them than it does about rocks themselves.


You're thinking of a different formula.

I'm thinking of a pair of formulas:
F(2n-1) = F(n)^2 + F(n-1)^2
F(2n) = F(n)^2 + 2F(n)F(n-1)

And there's one for combining:
F(n+m) = F(n)F(m+1) + F(n-1)F(m)

Using the matrix formula requires you to also calculate F(2n+1) each time you double it (or combine it), and if you're using someone else's generic matrix multiplication code, you have to calculate F(2n) twice each time as well. And there's enormously more work if you multiply each matrix individually, instead of squaring as much as you can.


You can do what I said with any sequence of the form a(n) = a(n-1) + a(n-2). (For people who don't like formulas: any sequence where you can get the next number by adding the previous two.) There are infinitely many of them, too.

I am not trying to debunk the watchmaker argument, it has been debunked by Darwin about a century ago.

I have read my posts in this thread and I never claim it not to be beautiful . but it is not godly and it is still mundane. A lot of mundane things are beautiful.







Well, the other half of what I am trying to say in this thread is this:

Fibonacci numbers are horribly overrated. Maths is full of strange numbers with strange properties that can be found in nature. All this hype about being god's signature is not deserved.

They are beautiful, but really, in maths beautiful is the norm.




That's exactly the same the same logic that is allowed to use the matrix multiplication algorithm Your claim of these formulas being more efficient than matrixes is kind of unfounded considering they are both doing the same :/