The Fibonacci sequence is reportedly making an appearance in nature in all sorts of weird places. I remember watching a video which was about the way the florets of a sunflower are arranged. Another video talked about how it's related to the so-called golden ratio.

My personal take on the Fibonacci sequence has to do with its geometric form - a spiral. A spiral for me is a wannabe circle. It has the motion required but the radius seems to be behaving oddly, increasing as the wannabe circle is being traced which effectively precludes the construction of a circle. All this reminds me of the phrase "spiralling out of control" and the only thoughts that spring to mind at the moment are cosmic inflation and entropy.

I suppose the Fibonacci spiral is an approximation of the universe. Take time as the radius, lengthening i.e. passing into, toward the future and the actual line that constitutes the spiral (it would've been the circumference if the circle could've been completed) representing matter and energy behaving cyclically. In essence, matter and energy would Big Bang and Big Crunch, the process repeating infinitely, but they would occur at distinct points in linear time. :chin:

Not having been a number theorist I had not thought about the Fibonacci sequence in a long while, recalling its definition, rabbit populations, and the relationship with the Golden Ratio, so I was surprised at the lengthy Wikipedia article about it.

If the Universe is like the Fibonacci sequence — Justin Peterson

I assume this is a metaphysical conjecture. Galaxy spirals, to my knowledge, aren't necessarily Fibonacci related. A logarithmic spiral might describe some of them. I don't know. A Golden Spiral is a special case of a log spiral, but I don't think there is evidence it predominates in galaxies. :cool:

It's funny that you mention entropy, I actually was talking about entropy in another discussion about the Big Bang with jgill at the beginning of this year. It's good to see you again!

I suppose the Fibonacci spiral is an approximation of the universe. Take time as the radius, lengthening i.e. passing into, toward the future and the actual line that constitutes the spiral (it would've been the circumference if the circle could've been completed) representing matter and energy behaving cyclically. In essence, matter and energy would Big Bang and Big Crunch, the process repeating infinitely, but they would occur at distinct points in linear time. — TheMadFool

Hmm, your idea is kind of hard to wrap my head around, but I think if I understand you correctly, I agree with everything you say. That is to say that there really is no beginning or end, that the Universe instead collapses upon itself in a never ended spiral of infinite proportions. My argument for why I don't use the Big Bang as an "event" is because I think it is instead a phenomenon. Take nothingness. If we live in a Universe it must exist, but in order for it to exist, it must have no properties. There mere fact that we exist either means that nothingness does not exist, or that nothingness is the same as everything.
that is to say that everything is nullified by an equal opposite. In this case, everything is both chaotic and still at the same time, therefore every "single" thing, or even a group of things that is less than the whole, is nothing more than pointing your finger to a point on the "spectrum" or the "spiral", or whatever you want to call the infinite source of possibilities.

I truly like your analogy though, "spinning out of control", it seems to make sense to me. The fibonaci sequence, if I understand it correctly, is just exponential growth, but what's interesting about it is that if you look at the pieces of nature you're referring to, the growth comes from the inside instead of from the outside of the object, the outside parts of the object only grow larger whereas the number of "units" increases from the inside.

Not having been a number theorist I had not thought about the Fibonacci sequence in a long while, recalling its definition, rabbit populations, and the relationship with the Golden Ratio, so I was surprised at the lengthy Wikipedia article about it. — jgill

It is something that has been becoming increasingly more popular. I'm not sure I've heard of any reference of it to rabbit populations, however. You are right, it does coincide with the Golden Ratio, basically, if you look at many objects in nature such as a pinecone, flowers, or even parts of outer space, you will see the patterns of the Fibonacci sequence in almost every supposedly "chaotic" occurrence of the Universe. Keep in mind that chaos does not necessarily mean unorganized, in fact it means just the opposite. Basically, it shows that the Universe is not completely random, and that there is in fact some kind of mathematical structure to how many things in the Universe are created, that is to say that they are formed from a "blueprint" or a "construct".

I assume this is a metaphysical conjecture. Galaxy spirals, to my knowledge, aren't necessarily Fibonacci related. A logarithmic spiral might describe some of them. I don't know. A Golden Spiral is a special case of a log spiral, but I don't think there is evidence it predominates in galaxies. — jgill

In reference to the galaxy spirals, I guess it depends on who you ask. It truly could be stated that non-geometrical structure could have some kind of resemblance to the Fibonacci sequence if you squint your eyes lol. I may be wrong here, but I'm pretty sure a logarithmic spiral is the same as the Fibonacci sequence, if not incredibly similar. Nevertheless, I agree that upon looking at some pictures of the galaxy, it is up to interpretation as to whether it resembles the Golden Spiral enough to be associated with it, but regardless you can find it in almost every form of consciousness, and that itself must be saying something.

Maybe...maybe...the Fibonacci sequence has something to do with optimizing. The sunflower video is about packing the most amount of florets in the available space and if one takes this idea but a step further we have, on our hands, the real possibility of using the Fibonacci numbers in problems of optimization; in layman's terms, getting the most out of something by expending the least amount of effort.

1, 1, 2, 3, 5, 8,...

If you had 2 dollars, you could get two items worth 1 dollar each.

If you had 3 dollars, you could get three items 1 dollar each but if you purchase two items, one 1 dollar and the other 2 dollars, you have something worth 2 dollars, something more valuable than any of the 1 dollar items you bought.

If you had 5 dollars, you could buy five items each 1 dollar each (not a good idea) or you could buy two items, one 1 dollar and the other 4 dollars but then you end up with an item you could've bought with 1 dollar. You must then buy two items, one which is 2 dollars and the other which is 3 dollars which would mean you would have an item you could've bought with 2 dollars and an item that has greater value, 3 dollars.

So and so on...

Optimizing on value seen in terms of price of items, a measure of quality. :chin: If you follow the Fibonacci sequence, you'll always land up buying the most number of quality items you can buy with your money provided the money you have is a Fibonacci number.

I'm not a mathematician so go easy on me.

Haha I'm no mathematician either! I see what you're saying though, but interestingly enough it goes to show that if what I'm saying about the Universe is true, then it is simply expanding by taking the path of least resistance just as you expressed! Curiously enough, that would imply that the Universe has some kind of resistance to its expansion does it not?

I'm pretty sure a logarithmic spiral is the same as the Fibonacci sequence, if not incredibly similar. — Justin Peterson

Close, but no cigar. :wink:

"The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (polar slope angle about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers. " (Wikipedia)