Wednesday, July 18, 2007
The Trouble With Infinity
Kronecker had no way of knowing the real trouble with infinity.
When he and Cantor were arguing about it, the geniuses who would make the first computers were still in their diapers, or nappies, or Windeln, or whatever they called them in their particular little slice in the space-time continuum.
Kronecker thought infinite sets were unnecessary. Possibly even damaging.
Well, that's putting it mildly for programmers.
The real trouble with infinity is that it's infinite. Which means that we can use it as a symbol (called incidentally, a lemniscate), but calculating anything that approaches infinity takes infinite time, memory, and processing power, which most of us lack.
If you've got an Aleph hidden somewhere under your stairs, maybe you don't care.
But I do.
Infinity sucks. ¶ 4:34 PM
When he and Cantor were arguing about it, the geniuses who would make the first computers were still in their diapers, or nappies, or Windeln, or whatever they called them in their particular little slice in the space-time continuum.
Kronecker thought infinite sets were unnecessary. Possibly even damaging.
Well, that's putting it mildly for programmers.
The real trouble with infinity is that it's infinite. Which means that we can use it as a symbol (called incidentally, a lemniscate), but calculating anything that approaches infinity takes infinite time, memory, and processing power, which most of us lack.
If you've got an Aleph hidden somewhere under your stairs, maybe you don't care.
But I do.
Infinity sucks. ¶ 4:34 PM
