1.61803399 (Phi)
 

Let's talk about the number Phi (1.61803399), which is also known as the golden ratio.

Phi is a very special number, a number that makes Pi look insignificant in comparison. Yet many people have never even heard of Phi.

I first learned about Phi as an undergraduate doing a BS in mathematics. First let's calculate Phi. Many of you have probably heard of the Fibonacci sequence, a sequence where you add the previous two numbers of the sequence to get the next number.

The Fibonacci sequence that is the most well known is the following:

1,1,2,3,5,8,13,21,34,ect,ect

Now Phi is calculated by taking any number in the sequence divided by the previous. The farther you are in the sequence the closer to phi you are. That is the ratio of the sequence converges to Phi.

This chart illustrates this:

N F(N) Ratio
0 1 1
1 1 2
2 2 1.5
3 3 1.666666667
4 5 1.6
5 8 1.625
6 13 1.615384615
7 21 1.619047619
8 34 1.617647059
9 55 1.618181818
10 89 1.617977528
11 144 1.618055556
12 233 1.618025751
13 377 1.618037135
14 610 1.618032787
15 987 1.618034448
16 1597 1.618033813
17 2584 1.618034056
18 4181 1.618033963
19 6765 1.618033999
20 10946 ------------


So big deal right? Well it gets interesting if we change the starting numbers the ratio will still converge to Phi.

N F(N) Ratio
0 5 0.6
1 3 2.666666667
2 8 1.375
3 11 1.727272727
4 19 1.578947368
5 30 1.633333333
6 49 1.612244898
7 79 1.620253165
8 128 1.6171875
9 207 1.618357488
10 335 1.617910448
11 542 1.618081181
12 877 1.618015964
13 1419 1.618040874
14 2296 1.618031359
15 3715 1.618034993
16 6011 1.618033605
17 9726 1.618034135
18 15737 1.618033933
19 25463 1.61803401
20 41200 ------------

N F(N) Ratio
0 1 43
1 43 1.023255814
2 44 1.977272727
3 87 1.505747126
4 131 1.664122137
5 218 1.600917431
6 349 1.624641834
7 567 1.615520282
8 916 1.618995633
9 1483 1.617666891
10 2399 1.618174239
11 3882 1.617980422
12 6281 1.61805445
13 10163 1.618026173
14 16444 1.618036974
15 26607 1.618032848
16 43051 1.618034424
17 69658 1.618033822
18 112709 1.618034052
19 182367 1.618033964
20 295076 ------------

This alone is an oddity. But since we are using a pattern it can be easily explained. The fact any Fibonacci sequence converges to this ratio is not what makes it so significant. First this number turns up in mathematics all the time. This ratio appears everywhere, especially in many geometric shapes. I don’t want to go into to many details on this because again it is unimportant that it shows up in math.

What is truly amazing about Phi is how often it shows up in nature! Phi appears EVERYWHERE in nature. Animals from all over exhibit this ratio in their body. The following website illustrates some of the places this number appears in nature: http://evolutionoftruth.com/div/nature.htm . This number shows up in butterflies, dolphins, ants, sea shells, and more importantly people. Phi shows up all over the human body for example: (from http://students.bath.ac.uk/ma1cam/GRnat.html) “If you take the length of the last digit on one of your fingers and multiply it by Phi you get the length of the digit before it, this can be repeated for the next digit, and the bones in the hand.” The same is true with your arms, legs, ect. In fact Leonardo Divinchi used phi in his paintings to make his people look more realistic. I’m not kidding this number appears everywhere in nature. And it isn’t all biological either; it appears in galaxies, hurricanes, ect.

Here are some more links on Phi.

http://courses.ncssm.edu/compton/geo...erm/divine.htm
http://www.space.com/scienceastronom...ls_030917.html
http://www.championtrees.org/yarrow/phi/phi.htm

Ok so now comes why I posted this in this forum. There is clearly something non-random happening throughout everything in the universe. This number pops up far to often to be random. Because of how often it comes up and how impossible it would just a random coincidence this number is sometimes called the divine ratio.

So my question is how can something occur so frequently and so perfectly and not be caused by something? To me this is the single greatest fact pointing to a higher being, some sort of creator of the universe. I’d love to see someone explain Phi without acknowledging the very likely existence of a divine creator.

In addition to phi there is also Pi and e which tend to pop up a lot.

I recently read a book titled Mathematical Mysteries / the beauty and magic of numbers, by Calvin C. Clawson. It's ~300 pages of just these sort of oddities. While reading the chapter about the strange coincidences of phi, pi, and e, I was absolutely riveted.

I'm a mechanical engineering major, and I'm about to take calculus. Learning these kind of things about numbers really makes me want to take the high-end math the UNLV has to offer. I find it all incredibly fascinating.

Nice to find a kindred spirit, and thank you for the post!

One more oddity I just found out Phi (1.61803399) has a multiplicative inverse known as phi(.61803399). The strange thing is these are the only 2 numbers whose multiplicative inverses vary by exactly one.

Phi/phi are irrational numbers, that is they cannot be written as a fraction and their decimals go one forever without repeating. The fact that Phi's multiplicative inverse is exactly 1 less is amazing.

Phi is one H of a lot better than Pi!

(sorry had to throw in the math humor)

Too many Darren Aronofsky movies for you.

As Sol said: When your mind becomes obsessed with anything, you will filter everything else out and find that thing everywhere.

never even heard of him


How about you actually try to post a real response explaining how this number can be everywhere in the universe and be random.

My second line explained my stance on this subject quite well.

The movie is 'Pi' .. your observations have already been fully dispersed amongst the independant film crowd circa 1998.

I havn't seen pi, but pi and Phi are completely unreleated. This number has nothing to do with hollywood. There are a tun of reputable sources researching Phi.

Read the following webpage
http://mathworld.wolfram.com/GoldenRatio.html

Saying that people are finding Phi everywhere (in math, biology, astronomy, ect) is a result of obsession with the number is silly. First off defined irrational numbers are very rare. Then we have a sequence which converges to that number. Then we find that number in nature. Look at how many different ways Phi is defined on that mathworld page my favorites is the nested radical and continued fraction.

Here is a link to a very comprehensive site with Phi occuring throughout many things. Look around at some of the findings.

http://goldennumber.net/

In the spirit of Douglas Adams, I will now show how Phi indeed DISPROVES the existence of a deity!

Rekna, see the movie Pi and learn not to judge a book by it's cover (or a movie by it's title)

This math boggles me.
I come from an art perspective.
I first heard of Phi as the "golden ratio" and then the "divine ratio". I believe Polluck's paintings are accurate to the golden ratio. His seemingly "random" paint splatters actually come out to phi perfectly. I think the golden ratio is fascinating. And, not all human's are exactly accurate to the golden ratio. It is said that the more "beautiful" or aesthetically pleasing face possesses aspects of the golden ratio more than someone with an "ugly" face. It has to do with symmetry. How symmetrical are you? Is nature symmetrical? I'm not convinced that the recurring pattern's of phi prove a higher power or diety but I don't have any explanations as to why this number shows up so often other than symmetry. I do believe it shows that no matter how chaotic we think the world is, it is actually very structured. Chaos vs. order.. Asymmetry vs. symmetry. dischord vs. harmony/balance. Phi shows that there IS order, there IS symmetry and there IS balance..

You know, I didn't even see this when I first read your post. Apparently I was so happy to see a post about mathematical oddities that I just wanted to reply rather than finish reading.

Now that I am aware of it, I will have to disagree with your premise. I think that the commonality of phi is more than just coincidence, but not neccessarily indicitave of the existence of a Creator. There are many things about nature we do not understand, and mathematics is only in its infancy where it relates to modeling the real world. The more knowledgable we become, I think we will begin to understand better why we see phi so often.

Some people, after all, say that the architecture of the pyramids indicates a precise knowledge of pi. Others, however, say that the architecture of the pyramids indicates that they used a wheel to measure out their dimensions. Pi was simply a byproduct of that process.

As an agnostic, the jury's still out on the existence of God, but I'm not putting phi in to the evidence pile just yet.

I agree with Hal. It's an interesting number, but there's far too much hype about it. It has some geometric significance, so some of the things it applies to there will obviously carry over elsewhere.

"Defined irrational numbers" are not rare. Ones that have enough history for there to be an accepted symbol are rare, but that's history, not mathematics. Phi=(1+sqrt(5))/2. sqrt(2) is also irrational. Maybe I should call it upsilon. That's a rarely used Greek letter :D. I could come up with most of representations on mathworld for my new irrational number. I could even come up with a magical sequence that converged to it. There'd be a couple of things I couldn't reproduce, but Upsilon would have some neat properties that Phi lacks also.

Most of the biological things people point to are really just things that are "about 1.5," or they have an obvious geometric connection as I said above. I could also say that sqrt(3)=1.732.... is a special number. Its close enough that most things would work out. I'll leave out the religious sarcasm about 3's ;).

I love how many of you taut science as proff that god doesn't exist until it points to a good possibility of something else then all the sudden it is meaningless.

Realize it wasn't religious fanatics that found and pushed Phi it was hardcore mathematicians many of whom don't/didn't believe in god.

Just as you say if you are looking for something you will find it the reverse is true, if you avoid looking for something you won't see it (Holocaust anybody?).

It is true that not all human bodies perfectly use phi but instead use estimates that are about 1.6. But that doesn't change the fact that this number appears all over. Sunflowers use Phi for their seed arrangement. By using phi the sunflowers are using the most effiecent means to produce the greatest number of seeds.

And as for watching the movie pi, if I get a chance I will but i'd rather pull my knowledge of this subject from mathematical digests and periodicals than hollywood, I suggest you do the same (hollywood isn't the best source for information).

Pi wasn't made in Hollywood... it was a very independant film. But I get your point.

Thats right it is an indy but the the point stays the same ;)

For some strange and goofy reason, this actually intrigues me.
Explain this to me if you will.... about the sunflowers using this arrangement.

Oh, and think of me as a simple minded person, so maybe you could keep it to just plain english.

...because it's a number and numbers don't exactly prove the existence of a divine being? Maybe I'm not understanding, but I really see no significance of "fact" between reocurring numbers and a "divine creator".

Based off of this oddity, I would be inclined to believe that I actually live in the Matrix rather than "god does exist!"

It's just a portion of the pie.. a small variable in the overall flow of the universe. Of course there will be SOME numbers that are reoccurring.. there has to be. Otherwise everything would be chaos and random. Doesn't mean there's a god though.

Rekna, 'Pi's concepts are based off of documented philosophy that your post seems to mimic. The quote by Sol is not just a line out of a script, it describes a device in popular psychology that states when you train your mind on a certain shape or pattern, you begine to find it everywhere you look. This is the same device that convinces many people of the existence of Dog. You're idealizing a concept that you see repeated everywhere you look. Why don't I just build a shrine to the element Hydrogen?

I did not say that science proves or disproves god. It does neither. On a gut level, I actually tend to think that some things in science (physics actually) give evidence of a god, but I don't expect anyone else to believe that. It's not a rigorous argument. Anyways, a large part of science is being critical of the evidence you're given. It is not science per se to just present some measurements, even though they may be accurate.

Mathematicians (a long time ago) found Phi to be an interesting number *mathematically*. They did not push all of these things with biology. If you'll notice, the mathworld site made no mention of any amazing coincidences. It just quoted some cute formulae.

The sunflower connection has to do with the optimal way of packing seeds if I remember right. So a sunflower evolved an efficient configuration. Organisms are filled with optimizations. As I said in my previous post, some geometric optimizations automatically involve phi. This is nothing profound. If there is a good reason for something to be of an optimal shape in biology, it usually is.

If you have any experience with calculus, then you'll realize that finding optimal shapes is not that hard. With some computer programming experience, you'll find that it's also easy to do by biased chance (pick random things, and keep the ones that work better).

I agree with stingc, Rekna has the causality wrong. Sunflowers didn't "use" phi to produce the greatest number of seeds. Sunflowers naturally evolved to be more efficient, and phi happens to relate to the way that efficiency was achieved.

Read here it is pretty straighforward, if you need more i'll find more.

http://www.geocities.com/CapeCanaver...pineandsun.htm

Well it is not a proof of God it does suggest that our current model of evolution is incorrect. Also the fact that many things non-biological have phi in them; hurricanes, galaxies, planets, ect we can rule out that phi is only a result of it being optimal for evolution.

Let's look at evolution and the scientific process.

The scientific process is based on observing phenomena, formulating hypotheses that fit the phenomena, continue observing. When a new phenomenon is observed it either A. fits your hypotheses or B. doesn’t fit your hypotheses. If A is true then it strengthens your original hypotheses. If B is true then you have to either revise or reject your hypotheses to fit this new phenomenon.

Now Darwin’s theory of evolution and natural selection hinges on random mutations that give an edge to a creature over others. This edge allows this creature to survive better and reproduce. Eventually the random mutation propagates throughout the genes and becomes the norm.

Now if this theory were true you would expect things in nature to be fairly random. In the case of the sunflower it is possible that sunflowers randomly picked the optimal solution but it is unlikely, instead it is more likely that they would have a setting that was efficient but not optimal. In the case of animals and their proportions you would expect there to be an entire range of values for different species. You would hardly expect many of them to have the same proportions unless having those proportions provided some sort of advantage.

But it has been observed that this number occurs throughout nature a lot and in many circumstances this proportion provides no clear advantage. The reason the mathworld post does not go into biology is because it is focusing on the math side of phi only. There are entire mathematical digest dedicated to phi occurring in nature. These are peer reviewed articles and are not some random people posting on the internet. In addition these people writing these articles are meticulous scientists who do research for a living. This number is not so easy to just brush aside.

So we need to modify our theory of evolution to fit the new facts. Somehow there is a commonality between these organisms but why? What purpose does this ratio serve? And why is it occurring in non-biological environments also? What is the connection between the biological and non-biological occurrences? To me it seems that there is something greater at work than what science currently accepts. Maybe we are all in a matrix like a previous poster said but if that is the case we again have changed our look on evolution.

i'm not understanding why you think our theory on evolution has to be rethought. First off, you don't present any facts that need to be reconsidered. yes, phi may be present in lots of biologic and non-biologic systems. it could be that in biologic systems it was something a far back common ancestor adapted and was kept from that point on.

with your example of the sunflower, as it evolves it will constantly attmept to become more effecient through random mutation. it doesn't stop. when a more effience manner happens, that one propagates more then the others eventually out competing other varieties.

could it be possible that phi is common in hurricanes and planets because there is something about it that leads to better energy conduction/tranformance/whatever between particals in the swirling gases?

none of this points to a divine being. at best it points to a ratio that has proven to be very efficient within the natural world and therefor has become commonplace.

This is very interesting. I am in no way qualified to give a decent answer/debate on this as i have read very little about it, and i dont see any of the "other side" to the arguement as it were. Saying that, some thoughts, why does it have to be a divine being that is the cause of this, just because it is your only answer now, it was god, to anything we do not yet understand, as it has been in the past, back then it was god provides rain, god makes the plants grow or whatever, because we didnt know what was behind it. As scientific advances showed how these things could work without a divine presence, the awe was moved up a step, and as each thing was given a answer by science, another thing was brought up.
People seem to think that science is like a religion, that it has all the answers, but i think science is still young, so many things not explained, more theories put forward, its constantly changing and pushing what we know, but each step it takes seems to give us a lot more proof than religion ever gave us as that is the basis of science as you hint at with your scientific process. I think a arguement based on, isnt this amazing, only a omnipotent being could do this is always a poor one.
As Hal and others where saying also, if you look hard enough anywhere, you'll see patterns in everything. For instance, take a circle as a simple example, or pi that detirmines a circle. You see circles everywhere in nature, does this too mean that this is only gods doing, or is there something else behind it?

Its late here and ive babbled on, but i hope i got my thoughts accross

It is possible that a common anscestor caused phi but highly unlikely especially considering how varried the species that contain phi are. Also a common biological ascestor doesn't explain the use in non-biological systems. Look how often it comes up in our own solar system http://goldennumber.net/solarsys.htm. Especially interesting is how close phi is to the mean of the planets orbital distance compared to the planet closer than it. Common ansestory doesn't explain why it doesn't only turn up in physical aspects of life but also in behavioral aspects, ala reproduction, what is attractive, ect. People whose body more closely resembles phi are considered more attractive. TLC had a special on this exact topic where they measured lots of supermodels.

And since when do hurricanes/galaxies/planets have a mind which tells them to do what is the most effiecient?

Or perhaps Phi is simply a property of atomic or subatomic molecules. If the appearance of pi in the pyramids was due to use of a measuring wheel (assumption), then it may be possible that the appearance of Phi is due to a property of the most basic building block of the material universe?

A common ancestor is far more likely because of the diversification of the species using Phi. Behavior is intwined with of physical attriute becuse our genes, especially at the lowest forms of life, dtermine how life behaves.

Just because something is amazing and we don't understand it shouldn't be a reason to automatically start talking of a Creator or Devine being. That is what cavemen did, I thought we were past it :(

Bingo! Thank you!

I'm not calling this proof of God but saying it suggests that there is a possiblity of some creator or underlieing commonality. Common anscestors doesn't explain this because it turns up in to many things that aren't related to ascestory. For instance Phi turns up in both the works of Mozart and Beethoven. It is believed that this occured by accident because for some reason we find Phi pleasing. Now days art/photography classes teach you about this ratio so you can use it to make your work more appealing to people. Common ascestory doesn't explain why rabbits (and other animals) reproduce according to the fibinocci sequence.

my belief in God is unaffected by the amazing properties of phi, but i share much of rekna's wonder at its ubiquity.

to me, things like phi seem to convey that our current models of evolution and the big-bang are very crude. there is so much there beyond our simple models of reality. but, if at some point in eternity i learn that it is the fingerprint of God, it wouldn't surprise me.

if a pink unicorn can create the cosmos in 7 days while playing tiddley-winks with a hairless sasquatch, then they can have a mind.

/sarcasm

they don't have minds, neither do sunflowers. but galaxies are basically swirls of stars and planets, planets are made by a swirling clouds of interstellar gas and dust, and hurricane's are swirls of the molecules in the air.

have you ever noticed how if you take a glass of water and throw suger in it, it disolves and equalizes through out the glass? maybe the energy/matter in a galaxie/planet/hurricane inherently does something like involving phi because of the nature of energy/matter?

Because everything is quantum, it would stand to reason that there be a certain ratio that will come up more than others between adjacent or used quantum states. Planets can only orbit stars at specific distances. Energy is always released in quantum intervals. Perhaps this relates to the ratio in Phi somehow.
Has anyone read anything about how Phi relates to quantum mechanics?

I think this Phi thing is really the wrong direction, everyone knows that 23 is the number of mystical reoccurance.

Rekna-Darwin was writing 150 years ago, his ideas have been modified drastically. You present about a third of the current THEORY of evolution and then proceed to attack it unconvincingly.

If your religion doesn't have anything to compare to the glory that will be Valhalla don't bother trying to convert me.

Remember Locobot, if you don't die in combat you go to the coward's afterlife, Hel.

So far, this is the closest idea to the point that I was going to make. Everythign is broken down as far as quarks, since that's as small as we can see right now. The two quarks that are used in construction of matter are up and down. Up is smaller than down. I can't find any data on their relative sizes, but I'm willing to bet that the difference in size is (down=up*phi)

It is known that much of the universe exists in fractal states. If a fractal is built of a basic unit that fulfills the phi ratio, the whole thing will be full of dimensions that fulfill the phi ratio. I'll bet that if you broke down quarks into whatever they're made of, the size fo those particles would fulfill the phi ratio. Going in the other direction, something that's built of parts that fulill the phi ratio is probably going to fulfill that same ratio.

Rabbits don't actually reproduce according to the fibonacci sequence.

The relationship between mathematics and biology is indeed a fascinating one, even if it does get frequently attacked for being "reductionistic" (this is bad by the way).
If anyone is interested in reading up on this compelling subject, minus the hocus-pokus, I reccomend Life's Other Secret by Ian Stewart (popular) or The Origins of Order by Stuart Kaufman (technical)

Yes we'll id hate to burst any bubbles but it showing up in nature is hardly a surprise. If you deal with any kind of 'feedback' loop or a system that develops by either using or being changed by itself, i.e dna and air cuurents in tornadoes to name a few 'feedback' loops or self using systems, then ur going to get additions and subtractions of whatever into the over all system. Now i know that measuring air in a thunderstorm isnt practicle, but if u watch it build up ull notice that its simply a system of particular air currents plus all the other natural phenomena which go into making a thunderstorm that do appear. and not only that but we know some weather systems can ffed themselves into a massive frenzy before dying out, AND theyre very presence disturbs the surroundings they exist in. Im not at all surprised to find highly mathematical patterns and rules in the deepest workings of nature and the cosmos, i think its frankly wonderful that intellectual puzzles of such high beuaty on paper are intertwined into our deepest truths of existance. consider dna, to make anything the molecule copies parts of itself, at the very basic start of anything. Now i dont know how its done but if this phi effect was coded into the molecule in some way (Baaad science im sorry) then it would appear u would be born with perfectly proportioned fingures for a human being, which funnily enough most of us have. the fact that u get mathematical rules that govern very basic interactions both chemical bilogical and physical is only logical, after all ur hydrogen atoms in ur pepsin enzyme arnt blessed with brains, just a few set strength atomic particles going at determinable speeds around set paths obeying the basic rules we think we have discovered. To find that any mathematical rule such as PHI or indeed 1+1=2 applies anywhere u look is a bit disappointing really, yes its beautiful but its nothing fancy, if it exists it must abide by the rules our great parent in the sky set

BTW Mr SelfDestruct theres actually a thing called 'plancks constant' which actually prohibits anything smaller than a certain size existing, if it does it undergoes plenty of strange effects etc. but do read up a bit, our universe is fractal in nature but it is not A fractal, this means that although we can see signs of fractal patterns in it, it does not endlessly repeat forever in both directions as you imply. (If the universe was totally fractal then any massive object would be made up of infinate numbers of smaller massive objects and even the smallest mass times infinity leads to infinate mass, which is bad in our universe). Also the table for quarks and 'relatives' goes something like this:
Up quark - symbol u - (electron) charge +2/3 - Mass (GeV/c2) 0.33
Down quark - symbol d - charge -1/3 - Mass 0.33 (roughly)
charm quark- sybmol c - +2/3 - 1.58
strange - s - -1/3 - 0.47
top - t - +2/3- 180
bottom - b- -1/3- 4.58
This is the current list of all known and/or predicted quarks in existance, these however are but one group of a whole host of (seemingly) indivisble subatomic particles, including the electron but not the proton or neutron :D. +2/3 of an electron charge simply means the quark has 2/3rds of the opposite charge to an electron. and GeV/c2 is simply a way of working out mass (M) from E=MC2 and means 'Giga electron Volts divided by the speed of light squared'. the problems with breaking down quarks into 'whatever theyre made from' is that there doesnt appear to be enough energy in creation to crack that particular egg. The big bang itself is supposed to have gone thru a state of being a 'quark plasma' right after the singularity exploded. no one knows what these objects are, why they have these properties they have, or where they came from, only that they seem to be the smallest tangible objects in existance (and there are objects used in science today that 'technically' dont ever exist but still carry out functions, i.e gluons and gravitons). also it would seem that blowing them apart to see whats inside its a definate no as scientists agree that A there are the bottom of the pile of 'things' we call matter, and even if they wernt the kind of power needed is impossible, an if it wasnt impossible it would be fatal to our universe to use it.

Ha.

It's this aspect of theoretical science which always makes me laugh.

It's impossible because there is not enough energy and if there happened to be enough energy the universe wouldn't exist ... the smallest part cannot exist because the multiplicative of all the smallest parts would be infinite and therefore larger than the whole ... etc

Sounds an awful lot like saying "God is all powerful" with different words.

And if one more "scientist" tries to tell me that the universe is not infinte in size, I'm going postal.

I know what planck's constant is, but I've never seen it used as evidence that nothing smaller than a certain particle can exist. I know that the univers isn't a huger fractal, I realize now that I didn't word it very well. What I meant to say is that the universe contains many fractal structures, and therefore anyhting that is a fractal will repeat the patterns of its smallest unit. Even if the quark is the smallest unit, my argument remains the same, sans smaller particles. Your table gave the charge and mass of each quark, but not the relative size. That's where my theory was based. I've never heard it argued that gluons and gravitons don't technically exist, only that they are zero-mass particles. Your last sentence makes little sense, maybe you could explain why the amount of power necessary to split one of these particles would be fatal to the universe.

Most of the `science` being quoted here is not correct... I don't feel like writing out a long reply, but I'll just say that quarks do not have a size in any usual sense. Quantum "particles" have very little to do with the usual definition of "particle." They're the same in name only. This same thing could be said for most things in modern physics. It's really too hard to explain it without math, so everyone reading popular books ends up misunderstanding.

Right well first of all iv read that IF it was possible to split the quark :P then it would require that mankind can produce more energy than was produced in the big bang to overcome the quarks internal structure strengths (forces if there are any smaller particles) and split it. we're not talking about breaking atoms here, these particles are assumed to be the basis of all matter, now assuming is dangerous i agree, but if these particles are the first out of the big bang, show no signs of being able to exist alone, let alone to be split into compnent parts, and behave as if they are partly in another universe half the time then its going to be very difficult to get inside them, also gluons and gravitons are zero mass particles but the reason i say 'technically' they dont exist is because they are only means of exchanging forces, whether or not they do exist i suppose is up for debate but if they do we will never EVER get any DIRECT evidence for them due to quantum mechanics. As for stingc defining particles, fair enough if he wants a distinction thats up to him, when i think of particles i think of stationary if possible or at least low energy objects (objects meaning things not round balls) and they are pretty easy to describe etc. if they called particles, if you want to get into muliple paths, quantum wave forms or even (curse) subatomic string theory then go ahead. the science might not be correct but if you give me a break its not wrong either and ill be happy to debate long and hard 1v1 with u about current breakthroughs or developments in any area of physics large or small. and on a side note, letting off sources of energy not seen since the most violent event we know of is probably not wise, might not be fatal to the universe, is certainly impossible to let off more energy than exists anyway, there fore it kinda says these objects are the wall if its actually impossible to go any futhrar, supposing of course there is anything smaller, which is doubtful

I gota say some of those examples are just pathetic. All they do is pick random parts of an object or animal, in any order, measure it roughly from the horizontal and/or vertical plain then and this is supposed to show us Phi. Well I am convinced!

Lets do this on a person’s face they say. Okay lets pick some points:

- start with the bottom of the chin – obviously.
- somewhere in the middle of the chin.
- bellow the lower lip.
- slightly above the corner of her mouth.
- tip of her nose.
- tip of her eye brows.
- top of her hair.

Oh wow what a coincidence that we got the Fibonacci sequence out of these very specific spots. I am sure if some one else was to pick major reference points on a human face, picking the middle of the chin or slightly above the corner of the mouth would be the first points they would choose.

My favorite is the human body example.

Start with the top of a persons head and just place the first few points at random along the forehead. Then the next one is somewhere between the eyebrows and the eyes. Shouldn’t the point be right on the person’s eyes they ask? Nah. Next point would be somewhere on the nose. After that it would be on the Adam’s apple, then the middle of the chest, somewhere on the abdomen, middle of the thigh, and finally the feet. The wonders of Phi seem to appear everywhere!


Sorry, but it was fun to write :p

To assume that something is created would mean were a science subject at the least, perhaps a toy, those don't fit me well. However to answer your question you require us to find proof against something that we may/may not believe in.

Personally I feel that this shows that there is something out there, what I can't say, however its just as likely to have nothing out there.

At any rate, if there is a divine being he sure is cruel. He puts Phi and makes us like it for a ratio nothing more. Just to sum up my feelings on a perfect god is a quote from Catch-22

"And don't tell me God works in mysterious ways... There's nothing so mysterious about it. He's not working at all. He's playing. Or else He's forgotten all about us. That's the kind of God you people talk about - a country bumpkin, a clumsy, bungling, brainless, conceited, uncouth hayseed. Good God, how much reverence can you have for a Supreme Being who finds it necessary to include such phenomena as phlegm and tooth decay in His divine system of creation? What in the world was running through that warped, evil, scatological mind of His when He robbed old people of the power to control their bowel movements? Why in the world did He ever create pain?"

This is getting off-topic, but I'll respond to some of the quark stuff anyways.

Under current ideas, quarks cannot be split. I think you are referring to separating one quark from another. Our best theories say that this can't be done. It is understood, though, that those ideas break down long before you could throw the "energy of the big bang" into the problem. So if that's what you read, the author just made it up. It makes no sense at all on many levels.

I'm not sure why you think gluons are less "real" than quarks. Neither is observed directly. Yet both of them have consequences that have been confirmed many times over by now. The point I was trying to make in my previous post was that these things are just labels of specific mathematical objects in a specific theory. To say that there is evidence for quarks means that we have confirmed the consequences of a certain theory which contains mathematical objects Gell-Mann decided to call quarks (the ideas have evolved a bit since then without changing names, but my point is the same). Add more interpretation at your own risk.

Gravitons, by the way, are not a part of any accepted theory of physics. They are a hypothesis made by analogy with the other forces (even though gravity is very very different). String theory has them, but that is very far from being a coherent set of ideas, yet alone an accepted one.

I think it's safe to say that Phi is a real and prevalent constant. That does not, however, necessarily extend to mystical possibilities. It means that a successfully structured universe will have a common element, a common number. Planets that can sustain life will have certain common elements as well. Does that mean God exists?

I can find Pi in a hell of a lot more things than Phi, but somehow Phi gets all the attention. Perhaps precisely because it exists above our ability to visibly calculate and thereby "hides" right under our noses.

Order suggests divinity, but it is not evidence.

Yeesh, a bit late to the game, but...

A god that is all powerful and all knowing would be hard pressed to make, say, a married bachelor, or a rock so heavy that he could not lift it. He can't make 2 plus 2 equal 5. Even if the earth and all within was the result of a creator with intent, the abstract concept of the number 2 is, I contend, independent of any deity.

This applies to the Fibbonaci sequence, and the golden ratio. God or not, these numbers are on a level of abstractness that is independent of anything tangible, or intangible:

Exactly!

If you measure the diameter of the iris of your eye, and then measure the circumference of the iris, you will find that they are in an exact ratio of 1:pi!
Do we need to ask "what is the evolutionary value of having a ratio of 3.14159...?" Do our genes code for pi? Is this evidence for God?

No! Of course not. The fact is that in creating a circle, pi must logically fall out of it. You get your pi for free.

Similarly when you create a spiral that turns at a constant rate and grows with a constant acceleration (e.g. sea shells) you will get a logarithmic spiral, and phi falls out of this naturally.

I was going to post something to this effect, but you hit the nail on the head

good job.

You know even the great Einstein, an atheist, once said that the universe was so perfectly random that something had to create it.

By the way for oddities in numbers, I found one for 8. No other number can do this.

You take 8 multiply it by anything. Then add the numbers together and multiply 8 by the next number in sequence add the resulting # together and the end product becomes 1 less that the number before.

Example:
8x5=40 4+0=4
8x6=48 4+8=12 1+2=3
8x7=56 5+6=11 1+1 =2
8x8=64 6+4=10 1+0=1
then it starts over
8x9=72 7+2= 9

It continues this process forever. I was driving home from school and it just occurred to me one evening, don't know if there is a true mathematical theorem or word for this phenom but to me it was extremely intriguing and time consuming for the ride home.

pan,

9 also does something similar. multiply 9 times any number, and then add combine those numbers until it's only a 1 digit number and you'll always get 9.

9x1 = 9
9*2 = 18,1+8=9
9*3 = 27, 2+7=9
9*4= 36, 3+6=9
...
9*10=90, 9+0 = 9
9*11=99, 9+9=18, 8+1=9
9*12=108, 1+0+8=9
...
9*63=567, 5+6+7=18, 1+8=9

and on and on...

That I knew, learned in grade school that's how you know if 3,6,or 9 are divisible into a #. If the number ends and it is a 3,6,or 9 then 3 goes into it, even 6 would and if it adds to 9, 9 would. 4 is always the same last 2 digits like 1024. 2 always even, 5 = 5 or 0 end digit in number,

The thing with the 8 tho is perfectly unique, no other number does it. 7 doesn't follow a pattern, no other number follows a perfectly descending pattern in such a way, at least not that I know of. It's just an oddity that like I said I played with one night on my drive home and found it amazing.

I don't think this is any more significant than the fact that an object's acceleration is a derivative of its velocity which is a derivative of its position in a coordinate plane. Or any more significant than the fact that gravity exists. There is limitiless supply of things to point at and wonder, "Why the fuck is that like that?". When it comes down to it, there are many things that humans will never be able to explain with anything more than, "because that is the way it is". Besides, if one is going to marvel at the natural world, there are many things way more compelling in the argument for the existence of a diety than the golden ratio.

The simplest answer to the mystery of Phi can be summed up by something Prot said in K-Pax. He said that species on a given planet take the form that most effeciently uses the resources available. Therefore, he resembled a human on Earth so as to most effeciently take in oxygen, walk, etc. If you really think about it, there are thousands of factors that act upon all beings on earth. There is atmospheric pressure, a constant equilibrium vapor pressure, photons from the sun, nitrogen-rich atmospheric conditions, to name a few. The logical result of these constants would be evolution in favor of organisms that deal best with them. Of course, it is the human system of math that makes this commonality a number, but if numerals were not even applied here, there would still exist a natural common property amongst all beings that was the direct influence of their atmospheric constants.

As a religious person, I would say that no scientific oddity is any proof of the existence of a deity- it is simply proof that we do not yet know everything there is to know, not by a long shot. What we ponder over today will be child's play tomorrow.


Consider the thoughts of the first "doctor" to realize that bloodletting was NOT an effective means of curing what ailed people, and that sneezing will NOT encourage demonic possession (*achoo!* bless you.) Hell, there are still MANY places on this planet where the people from it would shit themselves if they ever saw a TV, or a picture of themselves. Some groups still believe that a picture taken of you steals your soul. Bow before your new God, my Olympus D-360 digital camera!!

Loved that movie... great soundtrack too!!!!!! :thumbsup:

Well said, Zdragva.

I'm a little sick of people looking at X or Y and saying "This is evidence of a Divine Creator". I might as well say, "This is evidence of the Great Alien Phi Conspiracy". But I seem to be discredited in the popular discourse, so I guess I'm wrong :p

Well i wasnt referring to parting quarks from others i was refering to splitting a quark into its component parts. Now i dont know all things about all areas of physics but there is a way physicists can 'factor up' if u will, he amount of energy required to split it, its something to do with the amount of energy it contains or the energy required to split apart an object orders of magnitude lighter or less energetic or whatever im not sure. basiclly to get an object of any mass to high enough a velocity to split a quark would require crazy amounts of energy, again im not sure on the exact details but better mathematicians than I (infact mathameticians considered the best there is) have speculated it would require a larger input of energy than exists. as for quarks not being able to exist alone this is true, however... proton-proton collisions at a large enough velocity have shown that after the collision u get 2 protons out, momentum is NOT conserved but a new particle appears, after doing all the sums all the mass/energy balances and no laws are actually broken, what is THEORIZED to happen is that 'whatever' makes up one proton collides with part of whatever makes up another proton, this mystery object is flung out of one proton, something happens and the original proton regains this mystery object and a new object appear (look up pi meson or other strange objects) ill now explain in detail, ASSUMIG quarks do exist, what happens. 3 quarks are flung towards 3 other quarks, one quark from each proton collides, one quark gets flung out of a proton, as it travels furthar and furthar the strong force between the quark and its old companions gains energy and forms what is called a flux tube, a region of high energy/large force whatever, this flux tube continues to gain strength and be streched (now im not good enough to explain the science on the next bit) the flux tube 'breaks' and forms a quark-anti quark pair. the new quark from the flux tube returns to the proton and all is well with it, the anti quark pairs with the originally flung quark and forms a very short lived meson. which then decays or rather annihilates into energy. i do not have the material at hand to describe HOW the meson is observed ill leave that to you guys to accept ur scientists arnt lying. this shows that protons arnt fundamental and are in fact made up of smaller objects. Points here are A: one of the protons travells close to lightspeed before collision (how fast must something travel to split a quark????) B: quarks are observed just not alone but as part of a particle anti particle pair for a short time. C: although momentum appear to not be conserved amongst the protons they arnt fundamental and therefore once ALL things are considered laws arnt brken. As for qluons, well they dont form particles, they are at best fluctuations of the strong forcei gluons are to the strong force what photons are to light. light can travel, well forever technically, given enough time infinate distances, strong force acts over a distance smaller than an atomic nucleus, its the reason that ur positive protons dont fly away from each other due to electrostactic repulsion (ever wonder about that?) without the strong force (which appears to apply only to quarks) there would be NO nuclei. the fact we exist is evidence for objects smaller than protons (scientists call them quarks) objects like these dont have a 'size' size is irrelevent they are quantum sizes, i gather a quark is at the planck length. btw if the planck length is the absolute smallest anything can be im puzzled to see how u can get anything smaller. an object at planck scale has no size, its the starting point for all larger sizes to be measured. its a bit like asking what is smaller than the smallest possible division of time. heres another point about objects at these sizes, recent research has said that objects of a certain type (dont give me grief im not arguing im stating what iv heard/read) like single atoms can be placed in a single quantum wavelength, i.e in the space taken up by a single atom u can place infinate numbers of the same atom, in the space reserved in the universe for usually one object u can put infinate numbers as long as they are unable to be distinguished. this is something i read not some thing i know to be a fact but its interesting, quantum wavelength sized blackholes someone said, but we as a species arnt close to that. yet :)

"Going in and occupying Iraq, thus unilaterally exceeding the U.N.'s mandate, would have destroyed the precedent of international response to aggression we hoped to establish. Had we gone the invasion route, the U.S. could conceivably still be an occupying power in a bitterly hostile land. It would have been a dramatically different--and perhaps barren--outcome."
-George Bush Sr.
-Brent Snowcroft
Filtherton funny how u can say that after Saddam used the nukes on the west he would have sold to al-quaida had Iraq been invaded. Weird how any americans can speak after the 3rd world war, which occured due to the fact no one acted fast enough, and now USA is a barren land and europe is now at war with the uprisen masses of asia and africa after decades of doing nothing.

dude there is no proof of WMD, so there never was any? if i was Saddam and i knew i couldnt win the stalemate and keep power and i had any weapons id give them to the ppl most likely to use them after i was deposed. Is it going to take a nuclear weapon going off in ur back yard before u can say, 'ah maybe we just couldnt find them'

also if i was persuing a 'Jihad' i would do my best to win as its by holy determination we have to win. How can a group of terrorists hope to destory western society with a few terrorist acts? no dude. These guys arnt stupid. If i was al-quaida main dude, or if i was trying to bring about the end of the most powerful group of nation ever i would wait until it was possible to win before starting my main attack. These attacks in Spain etc. are nothing more than shows to any western haters that there is still something in the works, i would wait untill my enemy was at its weakest before launching my main assault. The war on terror has started, it is not over, it is a real war. who know if invading iraq is the right thing to do? he was a merciless brutal murderer, he was hoping to make horrific weapons at the very least. many people, not just those in the middle east want the end of the current way of the world. Because nothing of any size has been found if i was President id take the view this means someone else has them, to think otherwise is dangerous, if u think they dont exist and they do that is far worse than thinking they do exist when they dont. Point is western media wants to sell scandal, that is all, when u turn on the tv and see PM ridiculed over WMD that just means they have found something else to rave about its NEVER the truth. Use ur own eyes ur own ears and think, these terrorists face the most unwinnable fight in the history of mankind, and they think there god has told them to win, there going to read every war book, dude ffs these guys are crazy, we all know that, yet most of the west is more concerned about tearing their own governments to shred, if these WMD do exist then WE, me and you, are the targets, dont forget that when u laugh at bush or you rage about the unfairness of the war.

If Phi is a number generated from a sequence of addition, then any system that builds itself from many particles operating under rules of interaction, will unavoidably generate the ratio you describe (which is probably just another way of saying what Zdragva said at the end of page 1). Hence galaxies, hurricanes, life the universe and everything.

This is fascinating, beautiful, awe-inspiring and deeply meaningful, however, I'd use this argument in order to help *disprove* the intervention of any higher concience. You see, this bootstrapping model totally removes the need for any designer because the pieces self assemble (and it is the self-assembly that produces the ratio you describe)

I second that- Exactly!

Just because we've mathematically ascribed a numerical ratio to things that we can observe; that is - devised a measurement device that returns a somewhat unexpected and seemingly fascinating result, doesn't any more prove the existence of a 'divine being' or some unexplainable 'order' in the universe any more than me declaring that I'm God...unless of course you contest that math is divine.

From your point of view Phi is evidence of the divine. So to quote from the common religious medium of the Bible it is said that we are "created in his image". Now this is a God that is held to be perfect. You are either perfect or you aren't there is no inbetween, now waivering, no flaws, nothing. If this was the image or link to a perfect creator you would think that it would be a single number and not about 1.6 to 1.7.

There's likely some link between physical (i.e. in physics, not biological) forces' interaction and the way the ratio falls. It is by no means an argument for a creator. Rather, it would seem to demonstrate the universal nature of physical force.

But, I am not a physicist, so I am not going to bother outlining (incorrectly) how that would work.

Nevertheless, I'd advise you to take your inquisition not to religion, but to some of the recent 'theories of everything.' It'd likely be more fruitful.

Eh, that's absurd and tendetious. "Perfection" is in no way necessarily an interger.

But, for that matter, "divinity" is in no way phi.

I find the number 1 to have just as many "divine" qualities. Take ANY NUMBER, divide it by itself, and you ALWAYS get ONE! Such beautiful consistency in nature clearly points to a higher being. I'm sure that if you got out the measuring tape you could find lots of 1:1 ratios on plants and animals.

Mathematics, in all its beauty, is an abstraction. Without man, there are no ratios.

I wasn't saying it was, I was actually refuting the idea that phi was evidence of such.

Don't be stupid, everyone knows that 42, not phi, is the answer to life, the universe and everything.

Math is teh suck.

No, it is a necessary consequence of the way Phi is defined:

http://www.mcs.surrey.ac.uk/Personal...html#simpledef

One definition of Phi (the golden section number) is that to square it you just add 1, or, in mathematics: Phi^2 = Phi + 1


Phi is also defined geometrically, but this definition is mathematically equivalent to the above:


http://www.dace.co.uk/proportion_child.htm

Phi is defined as the proportion that results when a line is divided into two unequal parts, such that the ratio between the whole and the larger part is equal to the ratio between the larger and the smaller part.


Visually, this definition can be represented thus:

A---------B-----C

Where the line AB is 1 unit, and where where AC/AB = AB/BC, and both ratios equal Phi:

Phi = AC/AB = AB/BC

Since AB is 1, and BC is AC-AB, we can rewrite this as

Phi = AC/1 = 1/(AC-1)

and then since Phi = AC/1 we can substitute Phi for AC and get

Phi = 1/(Phi-1)

Multiplying everything by (Phi-1) and rearranging terms quickly gives

Phi^2 = Phi + 1

Which says exactly that "Phi is the number which, when squared, equals itself plus one." The long and the short of it is that there is absolutely nothing even remotely amazing or surprising about the fact that Phi squared is Phi +1, or that 1/Phi is Phi-1; that's what Phi means.


Judging by your interest in Phi, you would love the movie pi - you just have to understand that the people who made it are idiots, and have no idea that what they are actually talking about throughout the entire film is Phi, not pi. The characters are always making Fib. spirals out of Go beads and whatnot, so while you're watching it, every time someone says "pi," just translate it into "Phi."


I do think God probably exists, but your argument is spurious, Rekna. That constants such as Phi or e do exist in nature doesn't necessarily mean that God put them there. It is interesting to speculate as to why they are there, but just because we have no definitive naturalistic explanation doesn't mean there is no naturalistic explanation. This line of argument...

"X is unexplained. Therefore, X must be caused by God"

...is relatively easy to refute - there were many unexplained things in the past which have now been explained, such as the appearance of bacteria in sealed containers or the existence of live on earth, and their explanations do not invoke God. If God didn't cause previously unexplained things, why should we think that God caused presently unexplained things?

That stated, there are mathematical arguments out there which do suggest the existence of a God, and I worked out one of them myself at this page:

http://www.childrenofmillennium.org/philosophy.htm --> Math & God

That seems like the kind of argument you would enjoy, Rekna.


Ahhhh. Agnostics see things so clearly. :)


No - there could just as easily be dozens of set ratios that come up more often than others (and, in fact, there are).


Oh ho ho mistar smaertym an thinsk he si too smaert for teh mahtematics!!111 Shtu up fag0t yuo aer too stpuid to talks abuot maht yuoo probaly spedn all yuor tiem playing Quaek I LOL so in concluison GO FUKC A BAN DSAW!!!!1


--Mark

I see dead people! :D

-joke removed, just in case :( -

The answer to Life, the Universe and Everything is 42.

As for Phi... well, there's a problem with the randomness of the "divine ratio". Let's take, for instance, the number 2.

Most animals have 2 eyes, 2 ears and two nostrils. Bipedal creatures each have 2 arms and 2 legs. Most male mammals have two testes. Birds have two wings, many fish have two gills. Humans are born with two lungs.

If I take a pie, and slice it in half, there are 2 pieces. If I slice it in half the other way, each of the 2 original pieces now have 2 pieces.

Reproduction requires male and female counterparts... two creatures in all (in most cases, of course).

2 is the "number of opposites". Night and Day, Good and Evil, Tall and Short, Wise and Ignorant, Wide and Narrow, White and Black, Here and There.

Stereo requires exactly 2 sounds sources. And since stereo sounds better than mono, perhaps 2 is the "audiophile number" as well.


I'm sure I could go on for a great length. Phi is just haphazard luck in most mathemeticians books.

I like this thread, and I'm bumping it.

Hey guys. I recently found out a wonderful thing called the Color Red. The color red occurs around the 600-700nm range of the electromagnetic spectrum.

What's incredible about Red is that it appears everywhere!!

Red is everywhere in Nature. Animals and plants use it to warn of dangerous toxins. There are Stars that give off Red light. Heck, even Mars looks Red!

People also use the Color Red. We use it to paint cars, dye our clothing. Even our blood is Red!

Wow guys! Look at how pervasive the Color Red is in the Universe! This can't possibly be a coincidence! I personally think that the Color Red indicates that there's something else out there. After all, this is simply too much of a coincidence to be random!

Considering the geometric determination involves dividing a length Z into two sections X and Y, such that Y=X+n, n=1 and the ratio of X:Y::Y:Z. This "strange thing" you're pointing out is that X and X+n differ by exactly one when n=1. Oooooooh.

Furthermore, the Fibonacci sequence is basically a integral math implementation of the geometric proof for proportionally larger values of Z and n (I.E. when you divide the system by n, thereby returning to n=1, you get a progressively closer approximation of the golden ratio for larger values of Z). The math is kinda cool, but there's nothing mystical about it.

While I agree with everything else in your post (having written it myself earlier in the thread), this does not follow. This is similar to the atheist's argument which says "Thomas Aquinas' arguments in favor of God are false. Therefore, God does not exist." Just because Aquinas' arguments were spurious does not mean there is no God; by the same token, the fact that Phi^2 = Phi+1 is just a consequence of the definition of Phi doesn't mean that "there's nothing mystical about it." As a matter of fact, there are defenite curiosities related to Phi, and the most noteworthy of these is the underlying relationship between Phi and human aesthetics.

For instance, our wallets are designed to accomodate credit cards shaped like golden rectangles. Several famous buildings, including the Parthenon and Notre Dame cathedral, were designed based on Phi. And as you may be aware, our music is Phi-based; the musical scale is based on a Fibonacci progression. The question is, why do human beings find this so universally apealing?

Before dismissing this as merely a spurious product of human culture, consider this article:


Neanderthal Flute

For randomness to produce such an object as was actually found, to match a possible do-re-mi-fa flute, the probability would be only about 1 chance in 7 million.


In other words, the best information at my disposal tells me that the Neanderthals were playing Phi-based music. This is not a consequence of the way Phi is defined, and while it is far indeed from proving God's existence, it definitely provides us with a mystery.


--Mark

I've had no luck finding a specific page I remember (and you'll see why if you search for "phi harmonic") but there are some very straightforward reasons why harmonic systems based on Phi outperform non-harmonic systems or systems based on some other harmonic. It's turtles all the way down. That X and X+1 differ by 1 is no more interesting than more stable systems remaining stable longer than less stable systems.

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

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.

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?

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

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

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.

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. :thumbsup:

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.

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.

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.

:lol: 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.

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

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?

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

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