Nachtwolf

Oh? Forgive my skepticism, but I can't think of any such straightforward reasons, and it seems rather obvious that if there were any, you'd have no trouble naming them. Please do, if you can; if not, then don't insist they are there.

You're an atheist, aren't you.


--Mark

John Henry

1) Numbers do not exist in nature, they exist in our heads. any numbers we see in nature are an artefacft of the seeing, not the nature. They are a simple way of describing relations between measurements we make.

2) As Zdragva points out, the set of operations that generate the Fibonacci sequence are so elementary that it would be far better evidence of the existence of God if Phi didn't turn up in our measurements (which to be dimensionless have to be taken as ratios) all over the place.

3) Douglas Adams, a noted atheist, cited earlier, inadvertantly provides us with a perfect example of how you can see whatever you want, wherever you look. FOLLOW THIS LINK to see how.

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"No one was behaving from very Buddhist motives. Then, thought Pigsy, he was hardly a Buddha, nor was he a monkey. Presently, he was a pig spirit changed into a little girl pretending to be a little boy to be offered to a water monster. It was all very simple to a pig spirit."

1010011010

It has to do with how the systems scale, and without the supporting math it sounds pretty much like mysticism. If you have two systems based on the same harmonic ratio, but at a different scale... in all probability the interactions between the systems where they overlap will be destructive. But when you overlay systems based on Phi (and sqrt(2) and e) you can end up with a third harmonic, also based on Phi (or sqrt(2) or e), in the overlapping region... because of the way that complex mathematical functions on these values are analogous to simpler functions. So the individual systems, and the combined systems remain coherent and stable... rather than fighting it out, each trying to overpower the resonance of the other system.

How clear is that?

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Simple Machines in Higher Dimensions

CSflim

That is a truely wonderful link. Thank you for posting it.

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Nachtwolf

Sorry, this is ridiculous. While the symbols we use for numbers are of purely human origin, the symbol is not the number, but rather a means of representing mathematical aspects of nature. Take a physics course.

I've completed one semester of Differential Equations, and while there is still much higher math for me to explore, I would be surprised if this were insufficient for the purposes of our discussion.

It's clear enough - but it's also clear from your explanation (assuming for the moment that it is true) that Phi is not the only possible "base" for a musical system. Yet the Neanderthals used it, the Chinese used it, the Greeks used it, and we use it, when to my knowledge no musical systems on earth have been based on either e or v2. Your claim was that "harmonic systems based on Phi outperform non-harmonic systems or systems based on some other harmonic," but here you write that both e and v2 could be used, when, to my knowledge, they never were. (It is interesting to speculate on what such music would sound like. I hypothesize that, even though the wave forms would combine appropriately, humans would still find them unappealing.)

Additionally, why do you think that Phi so appealing to humans on a purely visual level? Conflicting wavelengths of light are not an issue, here. Humans did not evolve alongside pentagrams and golden rectangles, after all; assuming that natural selection programmed this aesthetic into human beings, how do you believe that it did so? What is so interesting to me is that Phi seems to underlie human aesthetics in general, not merely the aesthetics of a single area. I'll expound on this further, but I want to see your response first.


--Mark

zen_tom

Mathematics is a limited way to describe nature - try counting a sub-atomic particle, it's impossible. It might be there, it might not - and as soon as you know whether it was there or not it's gone somewhere else (or has it?).

Physics and mathematics does a very good job of describing the universe in discrete terms that we understand - but we invented those terms, and chose how to define the boundaries between them. A feature of the universe is just that, a feature - something arbitrarily separated from the rest of nature by our minds. Mathematics help describe the relationships between those features we have deemed useful, but it's all invention piled on top of invention. It's real to us, but not necessarily so in the big scheme of things.

Why is the ratio aesthetically pleasing? It would help an animal distinguish the diseased from the healthy. A potential mate with limbs not fitting the Phi ratio may well be deformed and hence poor breeding material. It's not to much of a jump to guess that a system evolved to express such a preference might be implemented as a more general liking for things that posses similar proportions.

powerclown

While I myself have zero aptitude for numbers, I appreciate the deep interest and ability some show for Mathematics.

We very well might still be living in caves if it weren't for the enthusiasm and vision of Mathematicians and Engineers.

fckm

No Offense, but one semester of differential equations means nothing in the long run. I'm an engineering physics major. I've taken calculus, differential equations, linear algebra, complex analysis and group theory. Woohoo, big deal. Mathematics is far more than just one semester of diffential equations. How about number theory? Set theory?
Riddle me this. How do you know that human aesthetics is underlined by phi? Nono, I don't want a bunch of links, that's not my question. My question is this:
Phi is irrational. There are an infinite number of digits in phi. In order to prove that human aesthetics is underlined by phi, you would need to measure "aethetic" qualities (whatever that means) out to an infinite precision. In actuality, I would say that any measurement you make can be argued, and it's accuracy debated. Why do you measure from the fish's eye to it's tail. Where on the eye? The pupil? The center of the pupil? To where on the tail? What counts as the end of the tail? How exact are your measurements? Down to the centimeter? To the milimeter? To the nanometer?
It seems kind of ... irational, to me to say that phi exists in nature, when it is impossible to measure such things with the infinite precision necessary to prove the point. Maybe the ratios are acutally 1.61803398. Not a huge difference between that and Phi, but nonetheless, it isn't phi.
Because Phi is the convergence of a ratio of a geometric series. Cellular reproduction occurs by binary division. A geometric series. DNA replicates by binary division. I'm sure there are many possible explinations, but I'm no biologist. Phi may simply represent the most efficient (energy wise, time wise, or cell count wise) way of producing biological structures.
The human cochlea is shaped much like a conch shell. Perhaps the shape of the cochlea is also based on phi, so it makes sense that our music system may in some way also be based on phi.

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And if you say to me tomorrow, oh what fun it all would be.
Then what's to stop us, pretty baby. But What Is And What Should Never Be.

fckm

Here's an interesting point, from the original post:
I would venture to say that this is exactly why the ratio is significant. Think about it from a statistical point of view. That any system which is governed by Fibonacci ratios ultimately converges to Phi, regardless of which Fibonacci sequence is used. Imagine for a moment that the mechanics of life are based on Fibonacci sequences. That is, cell differentiation, protein production, cell division, etc. are all based on Fibonacci sequences. Then, it doesn't matter how many origial cell you start off with, or which cells differentiate first, after the system has reached steady state, any stuctures associated with such mechanisms would have ratios correlated to phi. Remember, also, that Phi is a ratio based on the Fibanocci sequence, whereas sqrt(2) and e are not ratios of common geometic sequences (at least, not that I know of. I'm no math major). Everything that people have been looking at are ratios.

__________________
And if you say to me tomorrow, oh what fun it all would be.
Then what's to stop us, pretty baby. But What Is And What Should Never Be.

1010011010

Well, if we agree about Phi-harmonic systems, then the recurrence of Phi everywhere is just an emergent property. There may or may not be a particularly good reason for it at progressively larger scales, but because it's Phi based on the lower levels, it's the default starting point.

As for why we'd use Phi based music rather than, say, e. Presumably, our ears are Phi based, so Phi based chords might set up nodes and standing waves at all the right places in our Phi based ears. e based music would also set up nodes and standing waves, they just wouldn't be in the right places, as far as out Phi based ears are concerned. It's a bit of a chicken and egg problem, honestly. And I don't actually know if Phi shows up in the structure of our ears.

As for "Why Phi?" It could have some empirical advantage over e or 2^0.5 (haven't a clue how to go about evaluating that) or it could just be Phi was the first out of the gate, and the others, if/when they finally showed up, never really caught on or couldn't compete in the Phi-based environment.

On to visual appeal... if we ignore the question of why Phi shows up in various biological ratios, and merely note that it does... Than a beautiful human, for example, one that was perfectly formed, would have Phi this and Phi that. So on some deep instinctual level Phi just looks right, because it means someone developed pretty healthily, has good genes, etc. And, being the smart apes we are, apply the same asthetic to our manufactured items.
It could also be simple ergonomics. If the ratio of your thigh to your shin is Phi, then the ratio of a comfortable chair's seat depth to its height will also be Phi.

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Simple Machines in Higher Dimensions

John Henry

roflmfao. I have a MASTERS DEGREE in physics, but thanks for the advice all the same.

While the symbols are not the number, the number is not the dimension and the dimension is not the object.

Consider a table upon which there is a bowl of water with a goldfish swimming in it.

How many objects are there on the table?

Is there one goldfish bowl, to show that there is only one God?

Or do we have a bowl of water with a fish in it to show how God relates to us?

No. Of course! There is a bowl, some water and a fish, to represent the Holy Trinity!

Feh!

My pleasure.

__________________
"No one was behaving from very Buddhist motives. Then, thought Pigsy, he was hardly a Buddha, nor was he a monkey. Presently, he was a pig spirit changed into a little girl pretending to be a little boy to be offered to a water monster. It was all very simple to a pig spirit."

Nachtwolf

This would be true if mathematics were the limited discipline it is generally considered to be. Statistics are excellent at dealing with these fuzzy areas, however - indeed, I tend to think of statistics as the single most useful mathematical discipline, because of the doors it opens to empirical study.

Sorry, I don't view nature as one giant holistic mass, and don't see that there is something "arbitrary" about the way one feature can be "separated" from unrelated features in an attempt it for us to understand it. I don't uncategorically reject this standpoint, but I'd like to know why you think this has to be true.

No, it's deduction, not invention; that's the way mathematics was developed.

This is close to my own view. I think that psychometric g (the statistical distillate of IQ tests, and an excellent proxy for what laymen mean when they use the word "intelligence") itself allows us to see ratios and patterns, even if only on a subconscious level, and that some other psychological system gives us a sense of pleasure whenever we come across these things. Unfortunately this is only a rather vague outline for what seems to be happening; how exactly does g allow us to detect Phi? Why do we prefer Phi to other constants such as e or Pi? What mechanism causes us to gravitate towards and "like" Phi in the first place? (Some other construct which differs from person to person, such as Psychometric O?)

Put my statement back into context and it means plenty: it explains what 1010011010 can and cannot easily discuss with me.

Not at all. To test whether Phi underlies human aesthetics, we need merely make a prediction based on this hypothesis and then carry out a psychological study to confirm or deny it. Again, this won't tell us with certainty that Phi does or does not underlie human aesthetics, but if acceptibly small p-values are achieved, even the staunchest skeptic would blush to claim "You still haven't proven anything!" Some such studies have been carried out, but since you don't want links, you won't get any.

Well, if you appreciated my earlier advice, I can give you more: You may want to consider taking a refresher course, because it is a very low level fact that every equation, formula, and constant in settled science is an empirically tested expression of empirical observations. You can assert all you like that Numbers do not exist in nature, they exist in our heads and then wander off on a tangent involving goldfish and the holy trinity, but that won't change the fact that science discovers what is and isn't there rather than dictating what is and isn't there like a revealed religion.

I keep seeing people write this way on this thread. It's frustrating; one of my strongest personal motivators is curiosity, and nothing for me is ever "just" or "merely." I always prefer to ask more questions, and in fact I consider this a moral obligation, but that's beyond the scope of this thread.

This is a creative explanation, but I don't think it's a very likely one. I don't think our ears are so precisely attuned to Phi; many things in nature approach Phi, just as many things in nature approach Pi (you are of course aware that no heavenly body is perfectly spherical).

Do we really live in an environment that is so Phi based? I'm not sure that Phi does have some empirical advantage - at least in mathematics, e and pi both figure far more prominently. Sine waves are also quite common in nature, but people don't gravitate towards sine waves.

...And e this and e that. And Pi this and Pi that. Do we see e and Pi everywhere in an attractive human body? The eye is the only place that really approximates pi, and as for e, I don't know of it being visible anywhere.

Truth be told, I think that sexual attraction and aesthetics are two functionally different things. I prefer bold, sharp corners, blacks, blues, and violets, and harsh contrasts in visual art, and the music I prefer (and compose) does not use lyrics. If aesthetics were merely sexual attraction, then I would prefer soft, round forms, pale peaches, magentas, and whites, and the sound of people talking to instrumental music. Why is music more aesthetically appealing to me than the sound of a woman's voice?

To the best of my knowledge, the mechanism underlying sexual attraction is the same mechanism for hunger, and it is based on health, but this is different from Phi. The mechanism underlying artistic appreciation is different, and I think it is a by-product of our developing intelligence; you can read This Essay for a more thorough explanation of my position.


--Mark

Zenir

While I do not doubt your prowess, there is a simple philosophy which I belive you can agree with. Descarte said one of the more famous philosophical quotes 'I think therefore I am' describing many things, however, it does say that reality is defined by perspective and of anyone here I would believe you would understand that. The relavation between relativistic physics and mechanic physics is just an arbitrary example, a poor one, but one. For the sake of simplicity I will answer your question as ochams razor would have us. There is one object on the table as the water is on the glass on the table. Or perhaps the fishbowl is merely considered a whole much like my favored spherical cow (refering to the simplification of extraneous variables for the sake of a more simplistic and closed system.) One a side note might I suggest someone use ochams' razor as part of their arguement against a higher being creating a sterile number 'phi'

I believe math to be everywhere as much as anything else is. The greeks and romans beleived that numbers were holy also and it prevented them (most often times) from exploring the extensions of mathematics. I am an Atheist I could care less if there was a god, for if there is one, he is natural and therefore not god to top it off if he is, he doesn't want us to know so it shouldn't relate to us eitehr way, if there isn't then it doesn't matter. Saying there is a god, it would make more sense that this is a blind study where he doesn't want us to act as if he's there. He wants us to act of our own voalition.

To be honest many of the worlds greatest mathematicians and physics professors were religious.

There is also a big difference between the scientific method and mathematical definitions. Math is not defined on what we see, merely on it's pre-ordained (or posibly soon revised) axioms. Then often times science can relate to math for help with verification. To be honest however I believe that it is entertaining that we are arguing the physical existence of Phi. There are many irrational numbers and often times they are found in very beautiful ways, this beauty though is not inherent, it is what we apply to it in trying to comprehend the idea of the value. Infinity is a difficult comprehension.

I would also like to argue that infinity is not impossible in reality. I do not recall who claimed that an infinite amount of particles in a particle which are infitely smaller is not infinite. While it leads to the relation of infinity/infinity it could also be looked at as a 'simple' irrational number, could it not?

__________________
Success is not the key to happiness. Happiness is the key to success.-Albert Schweitzer, philosopher, physician, musician, Nobel laureate
(1875-1965)

Nachtwolf

Oh, that's a shame; I let this sit for a few days, but there's been only one response.

I doubt this; can you cite a source? Considering the famous mathematical precocity of the ancient Greeks, they would have had to be preternaturally brilliant to have made the advances which they did even while acting under prohibitions. According to Arthur Jensen's The g Factor, Galton did estimate the Athenians to be two mental "grades" above the British norm (or roughly 120 IQ in more modern terms) but I believe he made this estimate on the basis of their accomplishments.

All too true; in fact the information at my disposal suggests that those majoring in math and science tend towards not only religious belief but fundamentalist styles of religious belief:

Religion, Science, and Rationality

Field / % Religious
Math-statistics 60%
Physical Sciences 55%
Life Sciences 55%
Social Sciences 45%
Economics 50%
Political Science 51%
Sociology 49%
Psychology 33%
Anthropology 29%

(For the full table and discussion, see the URL)


Fundamentalism and Liberalism:
towards an understanding of the dichotomy

There are also some similarities between what psychologists call the convergent style of thinking and fundamentalism while divergent thinking corresponds with liberalism. Convergent thinking focuses down from the general to the particular, dissecting and analysing. It prizes rational, deductive thought and aims towards certainty. It tends to be found among certain types of scientists and engineers in particular. Interestingly, we find that when scientists (especially from the physical sciences) and engineers become religious, they often tend towards fundamentalist religion.

I don't think you're an atheist, Zenir, because your position as stated here is more consistent with an Agnostic stance:

http://en.wikipedia.org/wiki/Agnosticism

Agnosticism is the philosophical and theological view that the existence of God, gods or deities is either unknown or inherently unknowable.

I am myself a proud Agnostic.


Yes, I was thinking that a problem distinguishing between these two things seems to underlie this thread. Mathematics is logical/deductive, whereas science is empirical/inductive. Things like "certainty," "exactitude," and "proof" do not exist within the realm of science.


Never have I understood why anyone should want to claim this. Finity is easily more difficult to comprehend, as it possesses a limit. Infinity by definition has no limit, and therefore has less to comprehend. Isn't it easier to understand nothing than it is to understand something?


--Mark

thedenden

why doesnt it always go back to the same # like Pi 3.14 it never changes or varies like Phi so in some sence wouldent Pi be more of a golden ratio