Golden Ratio & The Fibonacci Sequence

[Pollux]

** A post moved from the: "Trees with “Crown Shyness” Mysteriously Avoid Touching Each Other"-thread,  since it was off-topic, and  I didn't wanna derail the thread**



But another interesting things about how plants,and animals are shaped in nature according to the Golden Ratioand/or the Fibonacci Sequence.

A heavily debated issue where some claim that the Golden Ratio/Fibonacci Sequence are a sort of basic building block of how the whole nature of existence is "ruled" after this formula. It does appear in nature in many ways how plants and animals are structured, and also the geometry of the human body. Further claims that it can be seen in art, architecture, and music, and all kinds of designs

I think is just the inherent way of how we humans perceive the world around us - intentionally or unintentionally (naturally). If we as humans have seen these patterns over and over in our whole evolution as humans in nature, it is rather logical that we impose this on everything we creates as humans, since it "harmonize with us" and our sense of our surroundings - as I mentioned; in art, architecture, and music, and all kinds of designs made by humans.

If it where any other sorts of mathematical sequence that we would see in most things in nature I would bet we would create, compose, construct "things" that would be in accordance with that - since it would feel "natural", and harmonizing, to us. But, why so many things are revolving around this Golden Ratio is interesting. But I guess it would be like to ask; why is there order in the universe/nature/physics instead of ever changing chaos?
Why is there order?

PS: On a side-note; the debate of the structure of snowflakes has always been an amazement to people, and the intricate structure of them - and how no snowflake are like the other. But some skeptics has seen it as a quest to debunk this issue, and claims it often "fails", and that most of the times we see asymmetrical "disfigured" snowflakes - and why some of the time we see symmetry is just the nature of ordinary physical properties of how things in nature are formed - molecules of water are controlled by the chemical and physics of hydrogen molecules etc. - or something of the like (I'm no physicist).
Read about it here>>

• https://www.its.caltech.edu/~atomic/snow.../alike.htm
  
• http://www.its.caltech.edu/~atomic/snowc.../myths.htm
  
• http://snowcrystals.com/
  

Regardless which; It is amazing.

Feel free to disagree.

Some videos on on the Golden Ratio and Fibonacci Sequence




 ( Edit: I saw that they, in the later part of this video below veered off into some conspiracy-theory on the subject, a bit like; The Sacred Geometry that are "hidden" from us by some Illuminate cabal, that hindered us "shleps" to know the "real truth"....  Yeah, well, I dont know about that. If you wanna learn about it, it is all out there...)




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[url=https://en.wikipedia.org/wiki/Fibonacci_number]




PS 2: a small sidenote on this one-of-a-third that we often see as harmony is when we take a picture of something. Most photographers knows that if you take a picture of someone there is a more sense of "harmony" if the person/object is in the 1/3 of the picture - also known as the; Rule Of Thirds   http://en.wikipedia.org/wiki/Rule_of_thirds instead of having the person/object in the dead-centre, which doesn't "harmonize" with us in the same way. All comes down to the Golden Ratio.

Like this:


[Image: rule-of-thirds-landscape.jpg]

[Image: rule-of-thirds-vertical.jpg]


[Image: fibonacci-and-thirds.jpg]

I must say personally, I tend towards the Fibonacci values appearing in nature as falling out of simply geometry in an orderly structure. An everyday example of such order (but not Fibonacci as such) is the difference between a random pile of bricks and a smooth wall made of the same bricks. Or the fact that crystals have flat sides, and in recognisable geometric form such as a cube.

Of course Pythagoras noted the appearance of simple mathematical ratios in the notes sounded by a string subdivided to give a harmonious sound.

The idea that the universe is built upon numbers is both an attractive and a useful one. However, it can be misused, for example there was an attempt in ancient cosmology to make the number of bodies in the Solar system be exactly 10, no more and no less. I think we should be wary of attaching too much mysticism to these ideas - unless one is a mathematician for whom the subject itself does express a kind of beauty.

PS 2: a small sidenote on this one-of-a-third that we often see as harmony is when we take a picture of something. Most photographers knows that if you take a picture of someone there is a more sense of "harmony" if the person/object is in the 1/3 of the picture - also known as the; Rule Of Thirds   http://en.wikipedia.org/wiki/Rule_of_thirds instead of having the person/object in the dead-centre, which doesn't "harmonize" with us in the same way. All comes down to the Golden Ratio.

I mus say I am very sympathetic to this point of view. I've been interested in both art and photography since childhood.

However, I've seen some hideously ugly pictures taken by beginners in photography where they have attempted to slavishly follow the so-called "rule of thirds", where the image would have been more pleasing with the subject placed at dead-centre. Nowadays, I tend towards the idea in artistic composition that it is often a good idea to place a main focus of attention somewhere away from the centre of the picture - but this can vary from anything from a slight nudge off-centre, to placing the focus near one edge. What makes for a satisfying image can be much more varied than either the rule-of-thirds or golden ratio would lead us.

My apologies to those who were wanting to talk about "Trees with Crown Shyness". I'll shut up now.

[Pollux]

I will get back to you later with a reply Typoz. Got some things to tend to now.

The Holotope

[Image: Holotope.jpg]

Explained

I was thinking of a thread on why is it that mathematics describes the physical universe. Is math an invention or inherent that then becomes 'discovered' by humans? Can science/technology be created without the use of mathematics? Oddly enough, I was reading some book on physics by some well known popularizer (I forget who) and in it was but forth the argument that indeed math was not necessary to do science.

Would an alien technologically advanced species possibly have a totally 'alien' physical 'explanation' of the universe in which to build a sort of science and technology paradigm? Would they even have an electronics based technology? Could their tech rely on some unfathomable form of atomic theory/particle physics? Would they even have a particle/quantum model of the universe but discovered some totally different theory that works for them?

Could it be so exotic as purely consciousness based? Thought forms materialize. Want to travel across a galaxy... just will it!

Would an alien technologically advanced species possibly have a totally 'alien' physical 'explanation' of the universe in which to build a sort of science and technology paradigm? Would they even have an electronics based technology? Could their tech rely on some unfathomable form of atomic theory/particle physics?  Would they even have a particle/quantum model of the universe but discovered some totally different theory that works for them?

Could it be so exotic as purely consciousness based? Thought forms materialize. Want to travel across a galaxy... just will it!

All of the above. This AND that.

"Want to travel across a galaxy... just will it!" Sorta.

One way we have been introduced to is an extremely important concept we have yet to grasp. Objects have a 'location variable' as part of their energetic equation. Change to variable, the object (ship) must instantaneously change to the new location.

A more detailed explanation is available.

[Pollux]

I mus say I am very sympathetic to this point of view. I've been interested in both art and photography since childhood.

However, I've seen some hideously ugly pictures taken by beginners in photography where they have attempted to slavishly follow the so-called "rule of thirds", where the image would have been more pleasing with the subject placed at dead-centre. Nowadays, I tend towards the idea in artistic composition that it is often a good idea to place a main focus of attention somewhere away from the centre of the picture - but this can vary from anything from a slight nudge off-centre, to placing the focus near one edge. What makes for a satisfying image can be much more varied than either the rule-of-thirds or golden ratio would lead us.

My apologies to those who were wanting to talk about "Trees with Crown Shyness". I'll shut up now.

I'm no photographer, and I dont think the "rule of third" always applies - and sometimes it feels quite obviously "forced" when amateurs does it. Photography is a quite delicate art, and a professional and an amateur can, with the same camera, and the same object, create quite different photographs. I can agree that some objects will look better "dead-center". Like a close-up of a persons face, or like a big giant tree, etc.



But I think that it has much to do qith the background also, if the "rule of third" should be applied, as in the pictures I posted in the OP. But symmetry and geometry is something we often "feel" is right. DaVinci's Vitruvian Man and the proportions is something most people "resonates" with - but it's not a "law".

Beauty is in the eyes of the beholder. A perfect example of that is the hideous `modern art´ that most of the time makes me motion-sick and wanna puke when I see it, but other people think it is the most beautiful thing they ever seen.