Sunday, May 6, 2012

13 most important numbers and our perception of reality

Ever science I can remember I was fascinated by the idea that if an ant was to crawl around the inside of a clock – if it or its ancestors would ever understand the passage of time as we interrupt the it. Time tightly coupled with space and affected by relativistic factors. I guess I have overtime refined my thinking to consider whether man can ever really comprehend the complexity of the universe - everything.

1st Movement

We don't after all expect dogs or cats, to be able to figure out everything about the universe. And in the sweep of evolution, I doubt that we are the last word in intelligence. There might well be higher levels of intelligence later, which again, are unable to understand everything. Complexity may be logarithmic and approach infinity rendering it just un-understandable.

A proof for the 1637 theorem (Fermat’s last theorem) was finally published in 1995 despite the efforts of countless mathematicians during the 358 intervening years. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. And yet, Fermat's Last Theorem would fade in comparison to the infinitely complex and wondrous universe.

2nd Movement

Having said that it is amazing just how much we have gleaned about the universe from a tiny distant and largely insignificant vantage point. Which brings me to my next and related fascination.

That is - does the universe even exist if mankind isn’t there to perceive it? I know this type of a question has been asked in many forms over the centuries, including for example; If a tree falls in a forest and no one is around to hear it, does it make a sound – a philosophical thought experiment that raises questions regarding observation and knowledge of reality.

So without a conscious observer  [us] does the universe exist?
 Quantum physics has taught us that reality is not what it seems. Sub atomic particles for example are believed not to hold a position in space until they are observed.  Their location otherwise is governed by a probability wave. The more we discover about the location of an electron (say) the less we can know about its mass and speed. QED goes much much further.

Now this has some interesting implications that inspire all sorts of theories. One such theory is that everything that is possible does happen in one dimension or another simultaneously (parallel universe) which places "responsibility" on the observer to interpret which "reality" or "universe" is manifesting. A consistent theory of everything that ignores consciousness is probably (philosophically) impossible. You need an observer who looks at the universe. This includes of course universal constants or important numbers.

3rd Movement

Physics, in particular cosmology is full of physical constants or physical quantities that is generally believed to be both universal in nature and constant in time. Some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, Planck's constant h, the electric constant ε0, and the elementary charge.

So, once again, are these empirical truths that have been discovered or if it is simply invented by us to co-construct reality. The Classical Greek philosopher Plato was of the view that math was discoverable, and that it is what underlies the very structure of our universe. He believed that by following the intransient inbuilt logic of math, a person would discover the truths independent of human observation and free of the transient nature of physical reality.

So the question remains; if a mathematical theory goes undiscovered, does it truly exist? Maybe this will be the next “does a tree falling in the forest make any sound if no one is there to hear it?”

4th Movement

What follows is the 13 most important numbers in the Universe based on James D. Stein's Cosmic Numbers - Popular Mechanics. But the numbers on this list are of cosmic importance— they are the fundamental concepts that define our universe, that make the existence of life possible and that will decide the ultimate fate of the universe

1.    The Universal Gravitational Constant
2.    The Speed of Light
3.    The Ideal Gas Constant
4.    Absolute Zero
5.    Avogadro's Number
6.    The Relative Strength of Electricity and Gravity
7.    Boltzmann's Constant
8.    Planck's Constant
9.    The Schwarzschild Radius
10. The Efficiency of Hydrogen Fusion
11. The Chandrasekhar Limit
12. The Hubble Constant
13. Omega

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