Rekna

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.

CoachAlan

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!

__________________
"If I cannot smoke cigars in heaven, I shall not go!"
- Mark Twain

Rekna

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.

Rekna

Phi is one H of a lot better than Pi!

(sorry had to throw in the math humor)

Halx

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.

__________________
You have found this post informative.
-The Administrator
[Don't Feed The Animals]

Rekna

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.

Halx

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.

__________________
You have found this post informative.
-The Administrator
[Don't Feed The Animals]

Rekna

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.

Rekna

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/

meepa

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

Halx

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

__________________
You have found this post informative.
-The Administrator
[Don't Feed The Animals]

anti fishstick

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..

__________________
And the day came when the risk to remain tight in a bud was more painful than the risk it took to blossom.
~Anais Nin

CoachAlan

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.

__________________
"If I cannot smoke cigars in heaven, I shall not go!"
- Mark Twain

stingc

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 . 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 .

Rekna

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).

Charlatan

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

__________________
"My hands are on fire. Hands are on fire. Ain't got no more time for all you charlatans and liars."
- Old Man Luedecke

Rekna

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

Sargeman

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 there are no facts, there is no truth, just data to be manipulated. I can get you any results you like, what's it worth to you.....

Stompy

...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.

__________________
I love lamp.

Halx

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?

__________________
You have found this post informative.
-The Administrator
[Don't Feed The Animals]

stingc

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).

CoachAlan

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.

__________________
"If I cannot smoke cigars in heaven, I shall not go!"
- Mark Twain

Rekna

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

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

Rekna

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.

hannukah harry

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.

__________________
shabbat shalom, mother fucker! - the hebrew hammer

Nafter

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

__________________
I must not fear. Fear is the mind-killer. Fear is the little-death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone past I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain."

Rekna

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?

CandleInTheDark

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.

__________________
Where there is doubt there is freedom.

TheKak

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

__________________
Roses are red, violets are blue, I'm a schizophrenic and so am I.

Halx

Bingo! Thank you!

__________________
You have found this post informative.
-The Administrator
[Don't Feed The Animals]

Rekna

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.

irateplatypus

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 you will not fight when your victory will be sure and not too costly, you may come to the moment when you will have to fight with all the odds against you and only a precarious chance for survival. There may even be a worse case. You may have to fight when there is no hope of victory, because it is better to perish than to live as slaves.

~ Winston Churchill

hannukah harry

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?

__________________
shabbat shalom, mother fucker! - the hebrew hammer

rukkyg

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?

Locobot

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.

whocarz

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

__________________
If there exists anything mightier than destiny, then it is the courage to face destiny unflinchingly. -Geibel

Despise not death, but welcome it, for nature wills it like all else. -Marcus Aurelius

Come on, you sons of bitches! Do you want to live forever? -GySgt. Daniel J. "Dan" Daly

MSD

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.

CSflim

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

__________________

CSflim

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)

__________________

Zdragva

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