Why are both Pi and Phi so unique?

[Bishadi]

Phi..... or 1.618....

and Pi.... 3.14 ..................

Why are these so important to nature and the sciences of the circle?

[Eclectic Mystic]

They are whatre called irrational numbers meaning they don't have a ratio. 3.5 has a ratio of 7:2 for example. But there are no two numbers one can use to create a ratio for phi or pi. Yet pi is defined as the ratio of circumfrence over diameter.

One thing this implies is that things can be broken down infinitesimally. Consider the atom. It was sometimes thought that an atom is the smallest unit of matter and indestructable/ indivisable. This would mean that larger pieces of matter (consisting of many atoms) would still have a rational relationship with the single atom. But when irrational numbers are looked at, this all gets thrown out the window.

[cyberpi]

In the imagination of math within any range of numbers: (# of irrational numbers / # of rational numbers) = Infinity

In the real world, for any collection of numbers: (# of irrational numbers / # of rational numbers) = 0

Why?

[seattlegal]

Originally Posted by cyberpi

In the imagination of math within any range of numbers: (# of irrational numbers / # of rational numbers) = Infinity

In the real world, for any collection of numbers: (# of irrational numbers / # of rational numbers) = 0

Why?

Because you cannot 'capture' or collect an irrational number; except as a concept.

[cyberpi]

Originally Posted by seattlegal

Because you cannot 'capture' or collect an irrational number; except as a concept.

Is that like: I can not 'capture' or simultaneously know both the momentum and position of a particle; except as a concept? Or more like: I can not 'capture' or collect Santa Claus and his flying reindeers; except as a concept?

Is that like: I can not 'capture' or know the real history here? Or more like: I can not 'capture' or know the exact name of an alien bug allegedly living on another planet?

Not only can I not capture or know the exact ratio of circumference to diameter of a perfect circle except as a concept... neither can I see one or ever make one wherein the exact ratio of circumference to diameter would be an irrational number. The true perfection is not in the alleged perfection.

If I 'imagine' that someone somewhere knows the true story, the true history, the exact precise origin of the concept of Santa Claus and his flying reindeers, and knows the exact precise momentum and position of every particle simultaneously... he would still not know an irrational number as being the exact ratio of circumference to diameter of an alleged perfect circle because this universe was not designed to ever allow one. In order to be perfect that circle must have no quantum elements. The space that it occupies must be continuous without quantum distances. The thickness of the circumference of the circle itself must be zero. If a person shows me where in this Universe there is a perfect circle with an irrational ratio of circumference to diameter then I can show them where they made the error of believing a mathemagician.

[seattlegal]

Originally Posted by seattlegal

Because you cannot 'capture' or collect an irrational number; except as a concept.

Originally Posted by cyberpi

Is that like: I can not 'capture' or simultaneously know both the momentum and position of a particle; except as a concept? Or more like: I can not 'capture' or collect Santa Claus and his flying reindeers; except as a concept?

Is that like: I can not 'capture' or know the real history here? Or more like: I can not 'capture' or know the exact name of an alien bug allegedly living on another planet?

Not only can I not capture or know the exact ratio of circumference to diameter of a perfect circle except as a concept... neither can I see one or ever make one wherein the exact ratio of circumference to diameter would be an irrational number. The true perfection is not in the alleged perfection.

If I 'imagine' that someone somewhere knows the true story, the true history, the exact precise origin of the concept of Santa Claus and his flying reindeers, and knows the exact precise momentum and position of every particle simultaneously... he would still not know an irrational number as being the exact ratio of circumference to diameter of an alleged perfect circle because this universe was not designed to ever allow one. In order to be perfect that circle must have no quantum elements. The space that it occupies must be continuous without quantum distances. The thickness of the circumference of the circle itself must be zero. If a person shows me where in this Universe there is a perfect circle with an irrational ratio of circumference to diameter then I can show them where they made the error of believing a mathemagician.

...and yet nature keeps trying....

[cyberpi]

Originally Posted by seattlegal

...and yet nature keeps trying....

Does it? Can you provide an example where nature is trying?

[Eclectic Mystic]

Originally Posted by cyberpi

In the real world, for any collection of numbers: (# of irrational numbers / # of rational numbers) = 0

Hi

Can you explain what you mean by this?

[Bishadi]

Originally Posted by Bishadi

Phi..... or 1.618....

and Pi.... 3.14 ..................

Why are these so important to nature and the sciences of the circle?

Maybe because they are ratio's of observed phenomenon.

[wil]

Originally Posted by Bishadi

Maybe because they are ratio's of observed phenomenon.

Are they unique? Are they unique among other constants? What would they be if we were to use base 12 or base 6 instead of base 10. What are they to a computer using binary?

What would be more important, Phi, Pi or gravitational velocity or who cares about the math when you just fell out of a plane?

[Tao_Equus]

Originally Posted by cyberpi

....... If a person shows me where in this Universe there is a perfect circle with an irrational ratio of circumference to diameter then I can show them where they made the error of believing a mathemagician.

Mathemagician. I think thats maybe where you go wrong cyber buddy. You have a bee in your bonnet about logical hypotheticals being used as the working basis for calculations. Even using whole numbers, if you use the pedantic reasoning you display, we discover that to measure two wholes of anything down to the quantum level and they will never be exactly equal. So in fact there is no such thing as a rational number. But you dont need such pedantry to make calculations that hold true in observable phenomena. More often than not approximations are perfectly adequate for both prediction and observation. The beauty of the irrational numbers we discuss is how they keep cropping up in nature, not just in circles, and that no matter how far into them we look no set or predictable pattern emerges. I am no mathematician but a random toy with my calculator shows me it is not that easy to divide one number by another and get an apparently infinite unpredictability. Usually some pattern emerges quite quickly. That we find this infinite unpredictability in a ratio that crops up throughout nature is the curiosity and reminds us that some puzzles are infinite and will never be answered. Just as mysterious to me as why anyone could believe in supernatural all seeing beings or santa claus

tao

[Bishadi]

Originally Posted by wil

Are they unique? Are they unique among other constants? What would they be if we were to use base 12 or base 6 instead of base 10. What are they to a computer using binary?

Binary is man created, constants are sought, and the ratio is simply existing in nature.

Can't fib what is all over the universe.

What would be more important, Phi, Pi or gravitational velocity or who cares about the math when you just fell out of a plane?

you answered your own question...... if the fall is evident, who cares?

[wil]

Originally Posted by Bishadi

Binary is man created, constants are sought, and the ratio is simply existing in nature.

The ratio is existing in nature?? Only in a base 10 system, only when using our current mathematics (adding subtracting multiplying dividing) it is all man made. Nature has no reason to determine area or circumference mathematically.

[seattlegal]

Originally Posted by wil

The ratio is existing in nature?? Only in a base 10 system, only when using our current mathematics (adding subtracting multiplying dividing) it is all man made. Nature has no reason to determine area or circumference mathematically.

Actually, wil, neither pi nor phi cannot be expressed as a simple fraction (ratio,) so it would not matter whether you were using a base 10 system, a base 2 system, a base 12 system, or any other base system, they would both still be irrational numbers.

[Tao_Equus]

Originally Posted by wil

The ratio is existing in nature?? Only in a base 10 system, only when using our current mathematics (adding subtracting multiplying dividing) it is all man made. Nature has no reason to determine area or circumference mathematically.

How so? A ratio between the two numbers diameter/circumference remains the same no matter which base you use. Oui/non, Ya/nein, Yes/no, Tak/nie, different languages but the relationship between the two always consistent.

Tao