There might be something to the fact that 57 year old Henry John Stephen Smith died in February of 1883 the same year his set theory became a 38 year old German mathematician's dust theory. This could be the real story but there isn't time to research it now, I have to get back to FaceBook and make some new friends.
I always hated math, but if teachers told me about Georg Cantor and his Dust, I might have paid more attention. Here is the way Georg explains his conundrum or perhaps how he explains Smith's conundrum:
{C * (n-1)} /3 * (U) *( 2/3 + {C times (n-1)} /3)*infinity
And there you have it.
That is the equation, here is the theory which is much more accessible.
Assume you have a yard stick, and you divide it into three one foot segments. You remove the middle section and you have two, one foot segments. You can divide those two sections into three equal segments, take out the middles and have four equal length segments. You repeat that action with the four segments, you get eight, then sixteen, etc. In fact you can repeat this action into infinity. Eventually you will have yourself an infinite number of very small segments that can be divided an infinite number of times again. So what do you call the little particles you get after you have gotten tired of dividing for infinity? Well, this set of infinitum is called "Cantor's Dust." It's all over your living room furniture at this very moment and there is nothing anyone can do about it.
So here is the conundrum, you eventually have an infinite number of these segments although you keep discarding a third of them along the way. But this infinity only equals 36 inches. So... thirty six inches is an eternity. And you thought size didn't matter.
How can the infinite be contained in the finite? Or how can a finite contain the infinite?
Make of this what you will. I chose to think of it like this:
If the television remote control is even three feet away from my hand it is infinitely too far away for me to get it so, "Would you get that remote for me, Darlin' ?"
As you were,
Jay
1 comment:
The fault is in the word 'eventually'. It would take an infinite amount of time to reach the state, sure there would be an infinite number of, er, things but they would be infinitely small.
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