On Tuesday, July 14, 2015 , Brent wrote:
> > > > Just ask yourself how you grasp the notion of infinity. I don't have a visceral grasp of the true immensity of infinity. Do you? On Mon, Jul 13, 2015 at 9:26 PM, Pierz <[email protected]> wrote: > > Sure. It's a concept even very young children can understand > Have you actually tried this experiment? I think if you ask a very young child for the largest number there is he will say something like a million zillion, if you counter with a million zillion +1 he will look puzzled for a second and then with a note of triumph in his voice will say a million zillion +2 and it will take some time to convince him that still isn't quite right. > > > Computers just iterate until told or forced to stop, they cannot reason > about their own iterative processes. > Actually they can. The computer program M athematica uses iteration to calculate the numerical value of PI, if you tell it to calculate the first 500 digits to the right of the decimal point it can do it in about half a second, if you tell it to calculate the first 10,000 digits to the right of the decimal point it can do it in about 3 second s, but if you ask it to calculate an infinite number of digits to the right of the decimal point it won't even start the iteration procedure, instead it will tell you that is an impossible task and you're being a idiot for asking it to do such a thing. Well OK,... the program is more polite than that and its language more diplomatic but I have a hunch that's what it's thinking. > > infinity and zero are about equally easy mathematical concepts to grasp - > historically both appeared in Indian mathematics around the same time. > And yet the idea that there was more than one sort of infinity and some infinite things were bigger than others wasn't discovered until about 1880, not because the proof was so technically difficult it isn't (the ancient Greeks could have discovered it), but because before Georg Cantor nobody had even tried; before Cantor everybody thought it was obvious that nothing could be larger than infinity and that was that. Everybody thought they understood infinity but they did not. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
