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Fibonacci Flim Flam

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11–20 of 32 posts

Re: Fibonacci Flim Flam

#11
post #9
post #7

Earlier quoted context omitted.

> I'm no less interested in Fibonacci numbers, their occurrence (alongside other patterns) in nature Can you name an example of where it occurs?

...yes, of course. Are you saying that the article claims that there are no examples? Because it doesn't say that. > "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." Reducing seedhead patterns to "one…

He then spends the next few paragraphs going into detail about why seedheads actually DONT typically display Fibonacci patterns. The cases where they happen to look like Fibonacci spirals are coincidences. Those random coincidences then get cherry-picked by people who want to say that fibonacci patterns are found all the time in plants and other places and are some sort of mystical law of nature.

> The pattern of seeds seldom comes out perfectly matched to the golden ratio in the sunflower, but when it is very close, those are the seed heads that get photographed for "gee-whiz" articles about Fibonacci numbers.

Re: Fibonacci Flim Flam

#12
post #8

Earlier quoted context omitted.

The point was, I thought, that Fibonacci numbers don't appear in nature, and nor does the golden ratio. Spirals, yes; logarithmic growth patterns, yes; fixed ratios, yes; but Fibonacci... no, not specifically. Did you have an example in mind where you believe the Fibonacci sequence actually does crop up, naturally?

Really? It's like we're reading a different article. The author says several times that, sure, spirals that approximately but predictably implement the golden ratio exist, but so do others. As if that's supposed to convince the reader of something. I took this to be the thesis: > We have noted above that not all spirals in mathematics or in nature are golden spirals. Likewise, spirals can be produced by non-biologica…

The point of the article is that the fibonacci spiral isn't particularly more common than any other spiral. There is a whole range of spirals in nature, yet people worship fibonacci spirals as if it is something special.

Re: Fibonacci Flim Flam

#13
post #12
post #8

Earlier quoted context omitted.

Really? It's like we're reading a different article. The author says several times that, sure, spirals that approximately but predictably implement the golden ratio exist, but so do others. As if that's supposed to convince the reader of something. I took this to be the thesis: > We have noted above that not all spirals in mathematics or in nature are golden spirals. Likewise, spirals can be produced by non-biologica…

The point of the article is that the fibonacci spiral isn't particularly more common than any other spiral. There is a whole range of spirals in nature, yet people worship fibonacci spirals as if it is something special.

The fibonacci spirals _are_ something special. The simple continued fraction of the golden mean is [1;1,1,...], and its convergents (the sequence of fractions that best approximates it) is ratios of fibonacci numbers. In short, due to the 1,1,1,... nature of the golden mean's SCF, it is _the_ number that is hardest to approximate by any rational number. This is why anything that evolves to reduce "periodicity", they will try to approximate this number, and it is best approximated by ratios of fibonacci.

Re: Fibonacci Flim Flam

#14
post #13
post #12

Earlier quoted context omitted.

The point of the article is that the fibonacci spiral isn't particularly more common than any other spiral. There is a whole range of spirals in nature, yet people worship fibonacci spirals as if it is something special.

The fibonacci spirals _are_ something special. The simple continued fraction of the golden mean is [1;1,1,...], and its convergents (the sequence of fractions that best approximates it) is ratios of fibonacci numbers. In short, due to the 1,1,1,... nature of the golden mean's SCF, it is _the_ number that is hardest to approximate by any rational number. This is why anything that evolves to reduce "periodicity", they…

Why would something evolve in such a way that the ratio of two lengths of its body parts is hard to approximate by a rational number?

Re: Fibonacci Flim Flam

#15
post #5

I'm not sure what point the author is trying to make. That other patterns, aside from Fibonacci numbers, are found in nature? That washing machines obey laws of gravity and make spirals similar to some that are found in nature? That photoshop exists? That artists use 'rules' as guidelines only? That greedy people will use really stupid ways to trick people into buying things? This is written as if it's supposed to be…

It's not a judgment of Fibonacci numbers in general as Flim Flam, but rather the Flim Flam that surrounds them.

Re: Fibonacci Flim Flam

#16
post #12
post #8

Earlier quoted context omitted.

Really? It's like we're reading a different article. The author says several times that, sure, spirals that approximately but predictably implement the golden ratio exist, but so do others. As if that's supposed to convince the reader of something. I took this to be the thesis: > We have noted above that not all spirals in mathematics or in nature are golden spirals. Likewise, spirals can be produced by non-biologica…

The point of the article is that the fibonacci spiral isn't particularly more common than any other spiral. There is a whole range of spirals in nature, yet people worship fibonacci spirals as if it is something special.

The point is also that in fact the 'fibonacci spirals' which do show up in nature are crude approximations. There are no real perfect fibonacci spirals in nature, just a continuum of different spirals. People like to see fibonacci patterns where they dont exist.

Re: Fibonacci Flim Flam

#17
post #14
post #13

Earlier quoted context omitted.

The fibonacci spirals _are_ something special. The simple continued fraction of the golden mean is [1;1,1,...], and its convergents (the sequence of fractions that best approximates it) is ratios of fibonacci numbers. In short, due to the 1,1,1,... nature of the golden mean's SCF, it is _the_ number that is hardest to approximate by any rational number. This is why anything that evolves to reduce "periodicity", they…

Why would something evolve in such a way that the ratio of two lengths of its body parts is hard to approximate by a rational number?

I don't know about limbs, but it could explain sunflower seeds and branches of trees. If they are distributed with a period, every n'th time around they will shade for other seeds (or branches). Approximating \phi is then a good way to reduce such shading.

Re: Fibonacci Flim Flam

#18
post #5

I'm not sure what point the author is trying to make. That other patterns, aside from Fibonacci numbers, are found in nature? That washing machines obey laws of gravity and make spirals similar to some that are found in nature? That photoshop exists? That artists use 'rules' as guidelines only? That greedy people will use really stupid ways to trick people into buying things? This is written as if it's supposed to be…

>That other patterns, aside from Fibonacci numbers, are found in nature?

Yes, and that most patterns misidentified as Fibonacci are not Fibonacci actually.

Both of which make the Fibonacci nothing "special", in the sense of its usually touted ("it can be found everywhere in nature" etc.).

The same for the rest of stuff you mentioned. It's written as arguments against things people say about the fibonacci series.

You just enumerating it and dismissing them as "obvious" is missing the point completely.

Of course they are obvious. That's the whole idea: that the fibonacci claims are refuted by such obvious information.

>That washing machines obey laws of gravity and make spirals similar to some that are found in nature? That photoshop exists? That artists use 'rules' as guidelines only? That greedy people will use really stupid ways to trick people into buying things? This is written as if it's supposed to be an indictment of sorts, but after reading it, I'm no less interested in Fibonacci numbers, their occurrence (alongside other patterns) in nature, or the incredible contributions of a man who brought advanced Indian and Arabic math back home to white people who were still using Roman numerals.

Good for you. I, on the other hand, am.

Your comment seems more like a ill-spirited attack on the article than a valid critique of it, what with enumerating tons of arguments he gave as if they don't mean anything (kind of like saying: "so he says photoshop exists, big deal", "so he says artists use 'rules' as guidelines only, big deal", etc) when those are arguments he makes AGAINST commonly held beliefs about the Fibonacci series.

Re: Fibonacci Flim Flam

#19
post #17
post #14

Earlier quoted context omitted.

Why would something evolve in such a way that the ratio of two lengths of its body parts is hard to approximate by a rational number?

I don't know about limbs, but it could explain sunflower seeds and branches of trees. If they are distributed with a period, every n'th time around they will shade for other seeds (or branches). Approximating \phi is then a good way to reduce such shading.

That argument is too hand wavy to be convincing. Can you make it precise? How exactly are the seeds or branches being distributed in 2d/3d space, and how does that minimize shading? Why would sunflower seeds want to minimize shading in the first place?

There's also the trouble that sunflower seeds and branches of trees do not actually approximate phi in any meaningful way. Check out this picture: http://www.wingsdailynews.com/wp-content/uploads/2015/04/fib... No doubt it was cherry picked and the spiral placed in the best position, yet the match is abysmal (look at how far the center of the spiral is from the center of the flower). The seeds are just packed tightly together and this produces some patterns due to the seeds on the outside being more developed than those on the inside.

Re: Fibonacci Flim Flam

#20
post #19
post #17

Earlier quoted context omitted.

I don't know about limbs, but it could explain sunflower seeds and branches of trees. If they are distributed with a period, every n'th time around they will shade for other seeds (or branches). Approximating \phi is then a good way to reduce such shading.

That argument is too hand wavy to be convincing. Can you make it precise? How exactly are the seeds or branches being distributed in 2d/3d space, and how does that minimize shading? Why would sunflower seeds want to minimize shading in the first place? There's also the trouble that sunflower seeds and branches of trees do not actually approximate phi in any meaningful way. Check out this picture: http://www.wingsdail…

I only meant it as a possible explanation for why it wouldn't be unreasonable to think phi appears often in nature. I don't really have enough knowledge of nature to say if it's the case.

Distribute the seeds of a sunflower radially, placing one seed every 360*x degrees, gradually increasing radius. If x=a/b, after placing b seeds, you will be back to the initial position and the next b seeds will be (radially) shaded from the first b seeds (which I admit, might not be how shading works in practice). If x is irrational, but closely approximated by a/b, the seeds won't line up perfectly, but still enough to shade quite a bit. If x is phi, then they will shade as little as theoretically possible (I think.. This is by no means a proof, just some thoughts). IIRC, the "sunflower seed pattern" is actually achieved only if you simulate such a seed placing with x close to phi.

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