
Fibonacci Flim-Flam. - jamesbritt
http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm
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jgershen
Thanks for submitting this. After seeing the article that claimed the design
of the iCloud icon was brilliant because it included Fibonacci ratios, I
desperately wanted to nail this article to the (other) author's monitor.

Whenever I see that kind of unjustifiable Fibonacci-worship, I get the same
feeling I do when I read creation myths or just-so stories. It honestly hurt
the first time I read the truth, and realized I was taught many of the
outlandish claims this author points out as fact in grade school math classes.

~~~
cormullion
They were just fibbing.

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5hoom
The golden ratio, rule of thirds and other such formulas for creating
aesthetically pleasing images probably work because they cause the artist to
actually stop & think about composition, kind of like how feng-shui causes you
to think harder about the arrangement of your furniture than if you just put
it wherever. No mystical forces involved.

As for spirals, well they just look pretty. All swirly & hypnotic...

~~~
celoyd
As an occasional semi-pro photographer and graphic designer, I agree. And this
view can be extended to other things like religious and political beliefs. I
know plenty of people who hold ethical views I strongly disagree with, but who
act in an overall remarkably ethical way because holding their views strongly
forces them to keep an eye on ethics at all times.

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jpdoctor
This article soooo needed writing.

There are people building entire careers out of financial Fibonacci fakery.

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EGreg
I don't know about all that, but my math background does nudge me to point out
one thing:

The fibonacci sequence is such that a[n+2] = a[n+1] + a[n], and as a result,
we have

a[n+1] / a[n] -> a[n+2] / a[n+1]

that is to say, the sequence of ratios a[n+1] / a[n] tends to a limit, and
this limit is Phi

here is the cool thing: in spirals, there is a certain scale invariance going
on when it comes to fibonacci numbers. Consider a rectangle where its larger
side is Phi * its smaller side. If whatever process made the rectangle uneven
now operates with the larger side, it will make a rectangle whose larger side
is Phi * its smaller side (assuming the process is scale invariant). Of
course, in reality this would be much more of a continuous process. Put
another way, if a process has the following properties:

1) it is scale invariant 2) it is rotation invariant 3) its operation on the
larger structure overpowers its operation on the smaller structure

then this process would produce something akin to a golden ratio spiral. So I
would expect at least some things in nature to be like this, at least
theoretically.

EDIT: that said, passing the golden ratio thing off as fact when it's just a
coincidence is doing a big disservice to science, especially when done by
science teachers.

~~~
tripzilch
First of, Phi is the limit ratio of many sequences, not just the Fibonacci
sequence.

Now I don't quite follow your rectangle example, but this is the process of
how and why Phi occurs in nature:

<http://www.wolframscience.com/nksonline/page-410>

This is the mechanism for pinecones, sunflower seeds and tree branches. As far
as I'm aware, this mechanism is the _only_ place in nature where Phi, or
rather the angular ratio 137.5 : 222.5 degrees, occurs.

If you know of a significantly different mechanism in nature where Phi occurs,
I'd love to hear about it.

Please note that the Fibonacci sequence (as well as other less apparent
sequences) are a side effect of this angular ratio, if the specimen develops
flawlessly. Yet even if the specimen has flaws (due to external factors), it
will still grow and tend to return towards the 137.5:222.5 angular ratio, even
though it will never return to following the Fibonacci sequence numbers.

~~~
EGreg
I think this is the type of process I was talking about. And yes, it's Phi
that is important, and not the fibonacci sequence.

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Sniffnoy
Heh, I have to wonder who drew that diagram of the Platonic solids
corresponding to elements. (Kepler? Looking it up, apparently so.) What's
funny is not the mysticism of it, but that the mysticism has been done in a
blatantly arbitrary fashion -- if it's to be even slightly credible, obviously
the tetrahedron and the dodecahedron should be swapped, so that fire is dual
to water and so that the ether is self-dual!

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ggchappell
It is nice when someone points these things out. Good article.

However, it should be noted that not _all_ appearances of the Fibonacci
sequence are the result of misunderstandings & fakery. This is noted in the
article:

> Phylotaxis. .... This is one part of nature where the fibonacci sequence and
> related sequences seem to show up uncommonly often, and it's legitimate to
> inquire why. The interesting cases are seedheads in plants such as
> sunflowers, and the bract patterns of pinecones and pineapples.

~~~
tripzilch
the fibonacci sequence is a side effect of these patterns, not the other way
around. if they get disturbed, as they very often do in nature, they no longer
follow the fibonacci sequence. the angles between branches on a tree do often
tend to the golden ratio (137.5 degrees) and will continue to do so after a
disturbance.

fact of the matter is that only the perfect, flawless examples follow a
fibonacci sequence.

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thefool
Meh... what I've always gotten out of stuff about Fibonacci numbers is that
it's pretty amazing that a lot of disparate things in nature seem to arrive at
similar patterns because very different situations end up having similar sorts
of constraints.

The fact that the Fibonacci sequence doesn't explain the mechanism is kinda
the beauty of the thing.

Sure people take it too far, or misinterpret it and what not... but that
doesn't stop this article from being a little silly.

~~~
tripzilch
Except that if you look at what processes in nature _really_ arrive at Phi,
they are not that disparate at all.

Which is why it's important to point out that Phi does not occur in the spiral
of a nautilus shell or a galaxy or in fact any spiral.

But it _does_ occur in a very specific type of growth mechanism, in the form
of an angular ratio of 137.5:222.5 degrees.

And only there.

Which makes Phi just about as equally amazing as the exponential function,
squares of integers, triangular numbers, limited growth sigmoid function, the
Feigenbaum constant, spheres, circles, symmetry, lines or just about anything
else where something in Mathematics explains a tiny part of nature ;-)

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capex
I think the ratio is still magical. Watch Sal's video on this here:
[http://www.youtube.com/watch?v=5zosU6XTgSY&feature=playe...](http://www.youtube.com/watch?v=5zosU6XTgSY&feature=player_embedded)

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tripzilch
Awwww those 149 karma points could've been mine. I posted this link yesterday
in the iCloud icon thread.

Oh well, it's good the get this info out there nonetheless. And it's not like
I wrote the article or something, anyway.

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dextorious
Seems like the most common occurrence of the fibonacci series in nature is in
bad programming language benchmark code.

~~~
pmiller2
Actually, because 1 mile is about 1.609344 km, you can convert approximately
between miles and km using Fibonacci numbers. See
[http://www.catonmat.net/blog/using-fibonacci-numbers-to-
conv...](http://www.catonmat.net/blog/using-fibonacci-numbers-to-convert-from-
miles-to-kilometers/)

~~~
dextorious
And why use fibonacci numbers, instead of say, multiply by 1.6?

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ga2arch
Very interesting reading. thank you =)

