Date: Sat, 27 May 2000 22:07:46 +0000 From: Anatoly Vorobey <mellon@pobox.com> To: Rahul Siddharthan <rsidd@physics.iisc.ernet.in> Cc: chat@freebsd.org Subject: Re: Infinite quantities in nature! (was Re: The Ethics of Free Software) Message-ID: <20000527220746.A14516@happy.checkpoint.com> In-Reply-To: <20000526103343.A1459@physics.iisc.ernet.in>; from rsidd@physics.iisc.ernet.in on Fri, May 26, 2000 at 10:33:43AM %2B0530 References: <20000524205815.A79001@mad> <200005250137.SAA12207@usr05.primenet.com> <20000524222053.A80883@mad> <20000525230446.A89273@linkfast.net> <20000526103343.A1459@physics.iisc.ernet.in>
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On Fri, May 26, 2000 at 10:33:43AM +0530, Rahul Siddharthan wrote: > Wrong argument. For instance, the set of real numbers is infinite, > and "most" of them (a mathematician would say "almost all") are > irrational, but the rational numbers are also infinite in number. If > you only want to stick with countably infinite sets (like rational > numbers or integers), one could say the majority of integers (99% of > any random selection) are not divisible by 100, yet an infinite number > are. <nitpick> This is in fact incorrect, because there is no satisfactory definition of a random selection on integers: no probability space can be defined on the integers which could give an equal probability to every integer number. </nitpick> Defining precisely just how we can formalise the notion of "almost every" integer number being non-divisible by 100 is surprisingly difficult. Probably the easiest way would be to calculate the probability on segments [-n,n], and point out that the probability stays 99% in the limit n->infinity. This isn't as convincing as "real" random probability, but it's pretty convincing nevertheless. > Before talking about what infinite wealth means, one has to quantify > wealth. Is intellectual knowledge wealth? Certainly some people are > willing to pay for it. But the amount of undiscovered knowledge about > the universe is infinite. Is software wealth? The number of programs > that could be written is infinite. How much of that wealth is > realisable in the sense that you can keep writing software and people > will keep buying it and making you richer? Certainly not an infinite > amount, but probably "unlimited" which is different from "infinite" -- > you can't put an upper bound and say "the pie can grow so big but no > bigger". "Unlimited amount" is quite scary when you think of it. This is what the original question boils down to, anyway -- can the universe "encode" an unlimited number of bits of information? What I pointed out in an earlier message is an important fact that even if the number of particles in the universe has a permanent upper bound, encoding unlimited information is still possible by using ever-growing distances. One could probably design another way to do that with ever-growing time distances -- i.e. use two time sources and manipulate their phase differences; you can make it as large as you want and encode information in it. Your calculations will then also grow slower inevitably as the amount of information grows, just as in the encode-information-by-distance scenario. I wonder if this is a universal rule of some kind. -- Anatoly Vorobey, mellon@pobox.com http://pobox.com/~mellon/ "Angels can fly because they take themselves lightly" - G.K.Chesterton To Unsubscribe: send mail to majordomo@FreeBSD.org with "unsubscribe freebsd-chat" in the body of the message
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