# the golden mean

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So i was watching a program about the golden mean, (i dare not spell it lol), and its ratio is considered divine.

IMO assigning a "divine" title to a particular sequence that exhibits itself in the natural world is complete ignorance.

What i saw when i watched the various examples of the ratio, was that it was in fact just an optimized number. Nature has evolved to reach certain amounts of stuff that work better than others, and this number is evolutions example.

Thoughts?

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IMO assigning a "divine" title to a particular sequence that exhibits itself in the natural world is complete ignorance.

Yes and no. It is a sequence that turns up over and over, even sunflower seeds follow the pattern. In this respect it is like an underlying number in the Universe , like pi or e. That doesn't make it any more divine than pi is though. So from that perspective, yes it is arguing from ignorance. Bearing in mind that there are those who believe pi to be a divine number. Since it is an "ultimate" number that the Universe is based on, that makes it a sign of the Creator. (One way of looking at it, I suppose)

However, and what makes the ratio so fascinating is that when it is incorporated into the design of a building, the building is more "attractive" to the eye. The Parthenon uses the ratio extensvely IIRC. Somehow the ratio seems to cause our innate sense of "balance" and "beauty" to respond to it.

I have no idea why it does this it just does, and I've yet to see a really good explanation as to why.

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Or rather we are the product of Evolution and therefore have a predisposition to previously based sequences or numbers that are largely maximized for efficiency.

Suppose that the golden ratio was 4, would that mean that 4 is somehow divine? or is it just a quantity that is the essence of maximized efficiency that we have evolved to?

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Zolar, quite possible.

The school of thought I follow looks at it sort of this way.

There is a creative force, but not a "God" as such. The creative force caused the Universe to be the way it is. I personally view this as by kicking around various factors during the Big Bang.

The laws of the creator are written into the very fabric of time and space itself, represented by Pi, e, the Golden Mean and probably heaps of others that we haven't discovered yet. (Beats the hell out of a couple of stone tablets.) While these things don't tell us why the Universe was made but they give us an insight as to how it was done. "Why" is for the philosophers, "How" is for the scientists.

The thing is that the Golden Mean and others "resonate" (for want of a better word) with us because we recognise them as the signature of the creator. Just as the Golden Mean is a sign of the creator in the Universe, our response to the Mean is a sign of the creator in us.

I can't of course provide any proof to back up a single word of the above, but it is to me consistent with observations, and in no way compromises the beliefs of others, and it makes me pleased o consider it as a possibility, so I do.

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Or rather we are the product of Evolution and therefore have a predisposition to previously based sequences or numbers that are largely maximized for efficiency.

The big question is why is the Golden mean so efficient in so many places? Sure, we could evolve for maximum efficiency, and that adjusts ratios... but why does the ratio end up being the golden mean in so many cases?

That's why people ascribe it some special meaning.

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but why does the ratio end up being the golden mean in so many cases?

Because it is the current Peak of efficiency, it is the pinnacle of millions of years of evolution trying to be as efficient as possible. It's fundamental reason probably lays within the very fabric of physics, that is thermodynamics and the conservation of energy. It is chaos quantified, it is the middle ground between endo and exo.

At least that's what it seems to me.

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Because it is the current Peak of efficiency, it is the pinnacle of millions of years of evolution trying to be as efficient as possible.

Fair enough, but why is it also pleasing to the eye? Buildings designed in this ratio look "better" and more "balanced". Artwork using it is prettier. I take your point about why it occurs in nature as it simply makes sense. But why is it so esthetically pleasing as well? How is our sense of beauty attuned to it?

The questions are philosophical, but very interesting.

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Because it is the current Peak of efficiency, it is the pinnacle of millions of years of evolution trying to be as efficient as possible. It's fundamental reason probably lays within the very fabric of physics, that is thermodynamics and the conservation of energy. It is chaos quantified, it is the middle ground between endo and exo.

At least that's what it seems to me.

But why is it the peak of efficiency for so many completely different things?

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But why is it the peak of efficiency for so many completely different things?

Well there wouldn't be one single reason for it, just like there isn't one single reason that pi or e show up. And like pi or e, in most individual cases the reasons for it can be deduced - it's not as if it's some random number that shows up all over the place by sheer coincidence.

Also, a lot of the supposed examples of supposed golden ratios in nature (like mollusk shells) are not that at all, but rather just similar logarithmic progressions with a good deal of variation.

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Indeed. I'm trying to point at why some people would call it "divine." The fact that it pops up in so many disparate places leads some people to use that name.

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I suspect the reason it shows up in nature is due to on of the properties it has: if you have a rectangle who's sides are the golden mean ratio, and you remove a square, you end up with a smaller rectangle again with the sides the golden mean ratio (same with adding a square). This would seem to me an important property for growth, although I don't really see how it would be important for non-rectangular beings.

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But why is it the peak of efficiency for so many completely different things?

Well, it could be because it follows the rules of physics and therefore has very solid constricting bounds that it has to work within.

If we were to hypothesize what an alien would look like, we would likely draw conclusions about them based upon our knowledge of chemistry, physics, and biological evolution. They as previously discussed would not be so drastically different then what we are because they, as well as us, follow the same set of constricting bounds. Those bounds being fundamental laws of the universe: Physics and Chemistry.

So apply the same type of principle to why the "Golden Mean" is the peak efficiency for so many things, and it would seem that you get a rather logical answer.

Fair enough, but why is it also pleasing to the eye? Buildings designed in this ratio look "better" and more "balanced". Artwork using it is prettier. I take your point about why it occurs in nature as it simply makes sense. But why is it so esthetically pleasing as well? How is our sense of beauty attuned to it?

The questions are philosophical, but very interesting.

Don't objects of similar energetic quantities tend to have less conflict with objects of different energetic quantities?

IE the total energy of a system when completely balanced has less conflict then an energy system still trying to achieve balance?

Entropy/enthalpy?

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I just thought of this, but these ratios/golden numbers/pi/e and all others seem to signify the evolutionary pinnacle of Efficiency. However they follow those aforementioned constraints and we are left with multiple numbers. One can only infer that there are factors that differed in the evolutionary development of those numbers.

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Don't objects of similar energetic quantities tend to have less conflict with objects of different energetic quantities?

IE the total energy of a system when completely balanced has less conflict then an energy system still trying to achieve balance?

Entropy/enthalpy?

I don't know what you mean by this. "Conflict?" You mean flow of energy? Increase of entropy? What does this have to do with the golden ratio?

I just thought of this, but these ratios/golden numbers/pi/e and all others seem to signify the evolutionary pinnacle of Efficiency. However they follow those aforementioned constraints and we are left with multiple numbers. One can only infer that there are factors that differed in the evolutionary development of those numbers.

I don't know what this means, either. Evolutionary development of numbers?

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I don't know what you mean by this. "Conflict?" You mean flow of energy? Increase of entropy? What does this have to do with the golden ratio?

I don't know what this means, either. Evolutionary development of numbers?

Sorry for the randomness of the words, they were words that i couldn't remember for previous posts and are relevant to this one.

Entropy:

From what i understand the universe's entropy is trying to go from concentrated amounts of energy within space to evenly spread out energy within space. What i mean by this in regards to the objects looking pleasing to the eye, is that we are programmed to want the "evenly spread out energy" and so an object that has achieved the golden ratio would be more pleasing to the eye than an object that is of a different ratio because it is "evenly spread out energy".

The idea is that we like equilibrium and the golden ratio is close to it.

Evolutionary development of the numbers:

I mean that the golden ratio is the result of evolution trying to achieve equilibrium, and it is not the pinnacle but another step in the path to equilibrium. However just like evolution on the Galapagos islands where you have multiple types of finches that have evolved differently, So have the numbers. Why can't evolution only evolve the biological (genes and such) without the influence from the laws of physics? Shouldn't evolution evolve with the laws of physics, therefore giving us these sets and types of numbers that represent the entropy of the universe?

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What i mean by this in regards to the objects looking pleasing to the eye, is that we are programmed to want the "evenly spread out energy" and so an object that has achieved the golden ratio would be more pleasing to the eye than an object that is of a different ratio because it is "evenly spread out energy".

Fair enough, but the question remains "Why?" Why would entropy be pleasing to the eye? Fashions of beauty have changed many times over the millenia but AFAIK, this one has remained constant, almost by definition that makes it unusual. Why is it such a strong influence in what is a purely subjective area? We're moving the question from "What is pleasing to the eye?" to "Why is it pleasing to the eye?"

I don't have a good answer but I find the question interesting.

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Sorry for the randomness of the words, they were words that i couldn't remember for previous posts and are relevant to this one.

Entropy:

From what i understand the universe's entropy is trying to go from concentrated amounts of energy within space to evenly spread out energy within space. What i mean by this in regards to the objects looking pleasing to the eye, is that we are programmed to want the "evenly spread out energy" and so an object that has achieved the golden ratio would be more pleasing to the eye than an object that is of a different ratio because it is "evenly spread out energy".

Personally, I prefer patterns (less entropic) than random sprinkling of colors with no pattern (large entropy), or a homogeneous mixture of all component colors (maximum entropy). But I also do not like my art to consist of regions of colors grouped color by color (minimum entropy). For entropy, equilibrium occurs at maximum entropy.

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Sorry for the randomness of the words, they were words that i couldn't remember for previous posts and are relevant to this one.

Entropy:

From what i understand the universe's entropy is trying to go from concentrated amounts of energy within space to evenly spread out energy within space. What i mean by this in regards to the objects looking pleasing to the eye, is that we are programmed to want the "evenly spread out energy" and so an object that has achieved the golden ratio would be more pleasing to the eye than an object that is of a different ratio because it is "evenly spread out energy".

The idea is that we like equilibrium and the golden ratio is close to it.

Evolutionary development of the numbers:

I mean that the golden ratio is the result of evolution trying to achieve equilibrium, and it is not the pinnacle but another step in the path to equilibrium. However just like evolution on the Galapagos islands where you have multiple types of finches that have evolved differently, So have the numbers. Why can't evolution only evolve the biological (genes and such) without the influence from the laws of physics? Shouldn't evolution evolve with the laws of physics, therefore giving us these sets and types of numbers that represent the entropy of the universe?

Thank you, for clarifying, Zolar...I have been following this thread with some interest and was very confused from where you were coming from in your original Op. I have always been fascinated with the golden ratio but I am not quite so sure I agree with the premise that it is a peak of evolutionary efficiency. Before I continue, is that what you are saying?

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Thank you, for clarifying, Zolar...I have been following this thread with some interest and was very confused from where you were coming from in your original Op. I have always been fascinated with the golden ratio but I am not quite so sure I agree with the premise that it is a peak of evolutionary efficiency. Before I continue, is that what you are saying?

Not quite, What i am saying is that these ratios are the result of evolution and are also still evolving. I am baising my speculation on evolution, physics, entropy, and equilibrium.

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Not quite, What i am saying is that these ratios are the result of evolution and are also still evolving. I am baising my speculation on evolution, physics, entropy, and equilibrium.

Okay, I think that I am getting there with understanding. Are you saying that evolution is still happening to fit the golden ratio that already existed or that we humans have finally evolved to appreciate the golden ratio?

(I am for the latter, personally.)

Then I think maybe I can maybe make the jump to entropy and equilibrium. (Although I may need further information. Please bear with me.)

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Not quite, What i am saying is that these ratios are the result of evolution and are also still evolving. I am baising my speculation on evolution, physics, entropy, and equilibrium.

Hm, well could you tell me when the golden ratio becomes anything other than $\frac{1 + \sqrt{5}}{2}$? And why such a number would have anything to do with either any of the four things you mention?

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No,still not quite.

What i am saying is the Golden ratio is the product of evolution. The reason for it's general nature to many organisms is because of the bounds and constraints of physics. However the Golden ratio is not the end result, there is a more finite ratio that is better described, but has not been evolved yet.

BTW why do people believe evolution stopped? Cuz it hasn't.

Hm, well could you tell me when the golden ratio becomes anything other than $\frac{1 + \sqrt{5}}{2}$? And why such a number would have anything to do with either any of the four things you mention?

$\frac{1 + \sqrt{5}}{2}$ is the result of evolution operating within physics. The reason why you see it in so many things is because physics affects them all.

Personally, I prefer patterns (less entropic) than random sprinkling of colors with no pattern (large entropy), or a homogeneous mixture of all component colors (maximum entropy). But I also do not like my art to consist of regions of colors grouped color by color (minimum entropy). For entropy, equilibrium occurs at maximum entropy.

Why is a pattern less entropic? if you were to make a homogeneous mixture of all component colors aren't thier particles at a atomic level more or less in a pattern?

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