I think JC resoinded to Brent: *"I don't have a visceral grasp of the true immensity of infinity. Do you?" *
I wonder if 'immensity' means - B I G - ? in which case I cannot refrain from thinking about the* infinite SMALL* as well. Just like I may think for 'eternal' as being momentary and timeless. We like to imagine meanings for concepts as we like. JM On Wed, Jul 15, 2015 at 4:26 AM, Bruno Marchal <[email protected]> wrote: > > On 14 Jul 2015, at 20:25, [email protected] wrote: > > >> >> >> On 07/14/15, John Clark wrote: >> >> >> >> >> 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? >> >> >> >> No, I don't, which was more or less my point. What we think of as our >> "grasp of infinity" is an ability to consistently manipulate and use some >> symbol that just means "bigger than anything else we're concerned with". >> In mathematics it mostly comes up in proofs by induction. There's an >> interesting book available online, >> http://www.cs.utexas.edu/users/moore/publications/moore-wirth-2014a.pdf >> which describes one somewhat successful effort to have a computer do >> automatic proof by induction; which is what I would regard as one kind of >> 'grasping infinity'. >> > > Another one is a theorem prover for a formal and effective (the theorems > are recursively enumerable) set theory. It has the axiom that there is an > infinite set, but soon or later the theorem prover will prove Cantor > theorem that all sets have a smaller cardinal than their power set. This is > proved by diagonalization instead of induction. In fact diagonalization is > very often effective or computable, and that is why machine can be aware of > their own limitation. > > Bruno > > > > > >> Brent >> 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 Mathematica >> 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. >> >> >> -- >> 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. >> > > http://iridia.ulb.ac.be/~marchal/ > > > > > -- > 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. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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