Two scientists with clipboards look through an observation window at a monkey and a typewriter. One scientist asks the other, "How long do you think it'll take him?" She responds with a shrug.
The monkey sits down at the typewriter, pushes a few keys, then tears the page off, walks over to the window and slaps the paper against the glass.
It reads, "Forever, you idiots. I've never read Shakespeare!"
If the universe isn't truly infinite, it may as well be. There's 93 billion light years of observable stuff. That's a large distance. Impossible to think about.
And that's just what we can see!
Space is so vast that pretty much everything you can imagine exists, somewhere.
But 93 billion is a number. It is finite. It has an end.
Comparing 93 billion, or even 93 quadrillion, to infinity is meaningless.
It's mathematically inaccurate to say, "Space is so vast that pretty much everything you can imagine exists, somewhere." A monkey typing on a typewriter (skypal?) won't write part of a Shakespeare play in 93 billion years. It doesn't work like that. Numbers don't scale gradually up to infinity.
If there was an immortal monkey and you sat him down in front of a typewriter, with an infinite amount of time, there is a certainty he will reproduce an exact replica of Romeo and Juliet. The experiment can't be done, but the math tells us something profound.
If the universe truly is infinite, everything you have ever imagined and haven't imagined must exist . . . somehow!
But everything imagined and not imagined must exist, if and only if the universe is infinite. Not nearly or almost infinite. There's no such thing as an almost infinite number, because infinity is not a number. Infinity transcends measurement.
What is π?
The radius of all circles is length one. The circumference of all circles is 2π or 6.28... radians. So the circumference divided by its radius is 2π. Here's some helpful gifs:
Another definition of the circumference of a circle is 3.14... times the diameter.
To 'roll out' a circle so that its circumference is expressed as line segments in a square is called "squaring the circle," but this can never be done perfectly because π is a transcendental number. It can't be expressed as an equation with rational numbers. An irrational number is one that can't be expressed as a fraction. π is also 'irrational.'
The circumference of a circle transcends measurement, so to describe it as a number with its own radius as the unit of measure produces an endless stream of digits that never repeat or fall into a permanent pattern.
It would take the rest of time to express π with 100% accuracy.
So what is π then, if not a number?
π = Circumference/diameter.
π is a comparison. π defines the immeasurable circumference of all circles with the measurable radius. It is a description by the finite of the infinite. If you try to express it as a number, it's never-ending, never-repeating.
This tells us that the circle literally doesn't exist in the material world. You can fool the eye with a compass, but due to the changing thickness of the pencil, the texture of the paper, the angle of the hands, etc., the circle will not be perfect. Zoom in and the pencil line is fuzzy and uneven.
Even on a computer, only so many digits can be calculated before the Sun explodes.
Philosophy of sacred geometry
Are pure geometric forms just things we imagine, like the boogeyman or healthy donuts?
The mineral world expresses pure volumetric geometry with the greatest clarity, but it is important to remember that these solids do not exist in nature. In their perfect form they exist only on a metaphysical plane, as pure, creative ideation, and can be represented, for the mind to grasp, only through geometry. ~Sacred Geometry Philosophy and Practice by Robert Lawlor
Pure geometric forms, like π, exist and don't exist.
Nature gravitates toward and oscillates around pure geometric form. Like how when the spiralling nautilus shell grows, its geometry approaches but never touches the golden mean (φ). The fibonacci spiral, created with a compass and ruler, approximates φ, converging and diverging but never touching φ.
"Music is liquid architecture; architecture is frozen music." ~JW Goethe[π]
What makes a song so catchy? The underlying architecture is mysteriously attractive geometry.
In other words, the arithmetic and harmonic means between the double geometric ratios are the numerical ratios which correspond to the tonal intervals of the perfect fourth and the perfect fifth, the basic consonances in nearly all musical scales. ~Sacred Geometry Philosophy and Practice
All energy follows the path of least resistance. That path is directed by the usually hidden, always underlying architecture. The architecture "can be represented, for the mind to grasp, only through geometry."
By drawing constants found in nature, mysteriously attractive forms are produced. In creating and calculating constants like π or φ, the brain is able to comprehend the infinite truth of universal harmony and order that underlies everything.
π is one of many transcendental forms, but π is primary because, in sacred geometry, everything starts with the infinite circle. Geometrically speaking, before anything can be created there must be a division of unity; there must be one from which all is born.
The scientists watch as the monkey pushes a few keys on a typewriter.
"How long do you think it'll take him?"
The monkey tears the page off, walks over to the window and slaps the paper against the glass.
It reads, "Forever . . ."
///
Sacred Geometry Philosophy and Practice by Robert Lawlor
JRE podcast #610 with Brian Cox
https://en.wikipedia.org/wiki/Pi
[π] http://www.goodreads.com/quotes/337462-music-is-liquid-architecture-architecture-is-frozen-music
Pics and gifs not owned by skypal link to sources.
The convergence/divergence image comes from the book Sacred Geometry Philosophy and Practice by Robert Lawlor, which skypal owns.
"squaring the circle with a piece of π on top" is an image created by skypal. The square's perimeter approximates the circles circumference more precisely than what is possible with a compass on paper, but still not 100% accurately.