The Mudcat Café TM
Thread #59418 Message #1953775
Posted By: Amos
31-Jan-07 - 02:42 PM
Thread Name: BS: The Mother of all BS threads
Subject: RE: BS: The Mother of all BS threads
In other news, I thought you might all be fascinated by the relationship between mathematics and the fundamental structure of reality. A brief overview from an essay called "Reality: The Grand Illusion", by one Peter Russell:
"...Numbers such as "pi", the ratio of the circumference of a circle to its diameter, or "e", the base of natural logarithms. They can be defined, but never written down exactly as a number for they go on forever, to an infinite number of decimal places. All this from the notion of distinction.
And there is more. Any positive number has a square root, the number that when multiplied by itself produces that number. The square root of one is one; of four it is two; and of eight it is 2.828... (another irrational number that goes on forever). But what, asked mathematicians of negative numbers, what multiplied by itself gives minus one? Nothing in the range so far discoveredÑany number, positive or negative when multiplied by itself results in a positive number. So they defined the square root of minus one to be a totally new number, an "imaginary" number, not part of the range or "real" numbers, and gave it the symbol "i". From this arose a new and even larger set of numbers, the so-called "complex" numbers, that were a combination of real and imaginary numbers. And these, it turned out were invaluable in helping mathematicians solve equations that had no solution in the realm of real numbers. Moreover the solutions applied to the real world.
Out of this panoply of numbers a most remarkable and intriguing relationship appeared. The irrational number "pi", the irrational number "e", and the imaginary number "i", come together in one of simplest equations ever; "e to the power of i times pi = -1".
Many mathematicians have eulogized over the significance and beauty of this equation. Out on the very edge of number theory a relationship is discovered that seems to show it is all in some way pre-ordained. Little wonder that some mathematicians feel that God is to be found in the beauty and perfection of mathematics.
That these three seemingly unconnected numbers should be related in such a simple way was startling enough; but even more was in store. This simple equation is the basic equation of any wave motion. Every wave from a wave on water, the air waves coming from a violin string, to light waves, can be expressed as a combination of simple equations of this form. It also expresses the orbits of the planets, the swing of a pendulum and the oscillation of an atom. In fact, every single motion in the cosmos can ultimately be reduced to an equation of this form. The whole of quantum physics depends upon it. If mathematicians had not discovered this most remarkable relationship, the strange story of the quantum would never have been told.
And all of this without a single empirical observation. No wonder then, that in the end all science comes down to mathematics. The very fact that it is not based upon phenomena, is why it is probably the best approximation to the underlying reality we have. ..."