Phi

[greenfairy]

The Divine Proportion. The Golden Ratio.
Found in mathematics, nature, growth patterns, art and architecture, and the human body.
How awesome is it??

 

[greenfairy]

It's my current obsession.

 

[EJCC]

I'm a huge fan of it!!

Honestly, I see it as a miracle -- one of the only miracles I can think of in the world. (Being Episcopalian, I'm not too into miracles, generally.) Pi prompts a particular type of religious feeling in me, that this Einstein quote describes well:

“The scientist's religious feeling takes the form of a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is utterly insignificant reflection."

 

[sprinkles]

 

[entropie]

I'm a huge fan of it!!

Honestly, I see it as a miracle -- one of the only miracles I can think of in the world. (Being Episcopalian, I'm not too into miracles, generally.) Pi prompts a particular type of religious feeling in me, that this Einstein quote describes well:

“The scientist's religious feeling takes the form of a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is utterly insignificant reflection."

Phi and Pi tho are different. Pi would be the length of a rope which was formed into a circle of the diameter 1.

The golden ratio was kinda the first time when mankind tapped into natures collection of constants. Nowadays there are hundreds more constants and they have become big scale fundamental. Like the speed of light c or the Planck and Boltzman constants h and kb.

Somehow tho I cant agree with Einstein here. I like the possible symetrie of a universe as well and what it brings for mathematical equations but its a reflection of the "cold state" the universe is in nowadays. In the beginnings of the universe it was more chaos theory that applied, a mathematical model that predicts uncertain outcomes of a process tho the process is deterministic. An example would be the weather conditions on Earth. The dynamics of a growing storm for example are deterministic or in other words, they are predictable. Yet nobody can surely predict the outcome of the storm and that tho there are no random components. In other words that means it is a deterministic chaos. Of course that is no magic or mystery,the problem on a macroscopic level rather is the finding of the exact initial conditions to a system. But then again things like the uncertainity principle, which proposes that the place and the impulse of certain particles cant be measured simoultaneously, raises the question: is the universe meant to be symetrical ? Or is classical determinism and the symetry it brings with it the "divine beauty" of the universe or is the divine beauty the inmeasureable chaos or even mankind who could be a reflection of that chaos as a player in the big cosmic whole ?

I dunno, its a personal opinion of mine but symetry alone holds no beauty for me. Symetry and Chaos hand in hand I rather find intriguing following the princple of the butterfly effect, as in: "Can the flap of a wing of a butterfly in Europe cause a tornando in the States ?"

 

[sprinkles]

[MENTION=4109]entropie[/MENTION]

Yeah. Symmetry is quite interesting to wonder about.

What I'm really a fan of in that regard is chirality. I wonder why it is that 90% of all snails have a right handed shell? Why is it that a minority of snail species have a left handed shell? What causes mutations where a rare specimen occurs with the opposite chirality, like a left handed shell in a right handed species? Why is it that apparently left handed snails get eaten less by snakes?

 

[greenfairy]

Fascinating!

From what I've read, golden ratio and golden spirals can describe different types of spirals- good to know the details and the fact that some people label things incorrectly.

 

[greenfairy]

Phi and Pi tho are different. Pi would be the length of a rope which was formed into a circle of the diameter 1.

The golden ratio was kinda the first time when mankind tapped into natures collection of constants. Nowadays there are hundreds more constants and they have become big scale fundamental. Like the speed of light c or the Planck and Boltzman constants h and kb.

Somehow tho I cant agree with Einstein here. I like the possible symetrie of a universe as well and what it brings for mathematical equations but its a reflection of the "cold state" the universe is in nowadays. In the beginnings of the universe it was more chaos theory that applied, a mathematical model that predicts uncertain outcomes of a process tho the process is deterministic. An example would be the weather conditions on Earth. The dynamics of a growing storm for example are deterministic or in other words, they are predictable. Yet nobody can surely predict the outcome of the storm and that tho there are no random components. In other words that means it is a deterministic chaos. Of course that is no magic or mystery,the problem on a macroscopic level rather is the finding of the exact initial conditions to a system. But then again things like the uncertainity principle, which proposes that the place and the impulse of certain particles cant be measured simoultaneously, raises the question: is the universe meant to be symetrical ? Or is classical determinism and the symetry it brings with it the "divine beauty" of the universe or is the divine beauty the inmeasureable chaos or even mankind who could be a reflection of that chaos as a player in the big cosmic whole ?

I dunno, its a personal opinion of mine but symetry alone holds no beauty for me. Symetry and Chaos hand in hand I rather find intriguing following the princple of the butterfly effect, as in: "Can the flap of a wing of a butterfly in Europe cause a tornando in the States ?"

Good thoughts.

Symmetry + chaos. Yang + yin respecively. Very beautiful to me.

 

[greenfairy]

[MENTION=4109]entropie[/MENTION]

Yeah. Symmetry is quite interesting to wonder about.

What I'm really a fan of in that regard is chirality. I wonder why it is that 90% of all snails have a right handed shell? Why is it that a minority of snail species have a left handed shell? What causes mutations where a rare specimen occurs with the opposite chirality, like a left handed shell in a right handed species? Why is it that apparently left handed snails get eaten less by snakes?

How does a shell correspond to a hand?

 

[sprinkles]

How does a shell correspond to a hand?

The direction it twists is asymmetrical and not mirror superposable - just like hands.

The technical terms are actually sinistral and dextral but I find the casual terms to be more sensible.

On the left of the picture is a sinistral, or left handed shell
The right one is a dextral, or right handed shell.

See how the spiral is asymmetrical?

 

[Lady_X]

I'm not buying it! Still infp!

 

[greenfairy]

I'm not buying it! Still infp!

Haha. I really do love it though! I ain't frontin'. And I'm trying to incorporate it into a sacred geometry symbol I came up with.

 

[RaptorWizard]

I'm not buying it! Still infp!

There was an xNTP named Leonardo da Vinci who was absolutely obsessed with sacred geometry.
evidence:

 

[RaptorWizard]

more evidence:

 

[RaptorWizard]

the evidence continues:

 

[greenfairy]

The direction it twists is asymmetrical and not mirror superposable - just like hands.

The technical terms are actually sinistral and dextral but I find the casual terms to be more sensible.

On the left of the picture is a sinistral, or left handed shell
The right one is a dextral, or right handed shell.

See how the spiral is asymmetrical?

Do these have any pattern in location? Because I know that energy and weather patterns spiral in opposite ways in the hemispheres.

Haha. I really do love it though! I ain't frontin'. And I'm trying to incorporate it into a sacred geometry symbol I came up with.

Found it. The smaller circles correspond to the larger circles as they correspond to the largest ones, and it's all in a yin yang.

[MENTION=15371]RaptorWizard[/MENTION]: That's pretty cool. I love mandalas. And if you notice, at 1:36-8 in the second one, it looks like the Phi symbol!

I have a book which I'm reading called Divine Proportion Phi in Art, Nature, and Science (by Priya Hemenway) which I'm sure mentions Da Vinci. (I haven't gotten that far yet.) I was so excited when I got the book, I was inspired to create this thread. You all should check it out! I got it at a rare book store, but you might be able to find it.

Here's a quotation I love from page 12:
"As a language, mathematics lies somewhere between the worlds that can be translated to language and those that are described by art-a mysterious, harmonious, almost magical modality in which abstractions become realities and unknowns appear as solutions to practical puzzles."

Another, and one which expresses the philosophical meaning of the symbol:
"The most essential and universally fascinating attraction of the Divine Proportion comes from the ratio's subliminal reference to ourselves, for its most profound aspect is explicitly evoked when we put the human being into the equation and perceive the proportion as a relationship that includes ourselves. Contemplating our place in the equation, we will variously find that we are the whole, we are the larger, and we are the smaller of the parts- always in some perfectly balanced ratio of whole to larger and larger to smaller.
As a relationship of macrocosm and microcosm, the Divine Proportion describes the larger and the smaller in their most intimate relationship: They are not separate; they are related. The proportion links them in such a way that there is a mirroring effect that makes it possible to see the large in the small and the small in the large."

Like this!


And in my symbol, which is a map of the chakra system. We are a microcosm of the Earth and all the patterns in it.

 

[Salomé]

Symmetry + chaos. Yang + yin respecively. Very beautiful to me.

Beautiful Chaos...

 

[sprinkles]

Do these have any pattern in location? Because I know that energy and weather patterns spiral in opposite ways in the hemispheres.

Not really, since the vast majority of gastropods are dextral regardless of location. It's more similar to some people being left handed, or dextrocardia (people with heart on the right side instead of left)

It's a genetic thing that happens just because it happened to work out that way.

 

[Such Irony]

The direction it twists is asymmetrical and not mirror superposable - just like hands.

The technical terms are actually sinistral and dextral but I find the casual terms to be more sensible.

On the left of the picture is a sinistral, or left handed shell
The right one is a dextral, or right handed shell.

See how the spiral is asymmetrical?

Am I wrong in thinking that those shells are orgasmic in a sense?

 

[greenfairy]

Beautiful Chaos...

Omg. What a trip! Universes in universes. Totally brain bending. I'm going to have to watch all of these. I think I'm going to have to incorporate fractals into my study of philosophy and illustrations of reality.

But fractals aren't chaos; they are composed of patterns and mathematical equations. Or maybe chaos is too, and we just don't know it.

Am I wrong in thinking that those shells are orgasmic in a sense?

That's a weird and interesting idea. Quite possibly!

Not really, since the vast majority of gastropods are dextral regardless of location. It's more similar to some people being left handed, or dextrocardia (people with heart on the right side instead of left)

It's a genetic thing that happens just because it happened to work out that way.

Cool. They're the yin in the yang, or the other way around. Maybe.