Dark Mind Posted August 10, 2005 Report Share Posted August 10, 2005 Now quit debating!! ;) Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted August 10, 2005 Report Share Posted August 10, 2005 Math has nothing to do with such trivia as the physical universe and what can fit in it. Anyway, sez hoo that 10^(10^100) can't "fit into" the universe????? Now quit debating!!I shall not quit!;) :Alien: :hihi: :eek: :eek: :eek:... Quote Link to comment Share on other sites More sharing options...
Boerseun Posted August 10, 2005 Report Share Posted August 10, 2005 A googleplex is exactly as far from infinity as zero is from infinity. Quote Link to comment Share on other sites More sharing options...
C1ay Posted August 10, 2005 Report Share Posted August 10, 2005 A googleplex is exactly as far from infinity as zero is from infinity.I'd say 0 < googolplex < infinity. It could also be said though that googolplex is infinitely smaller than infinity. Quote Link to comment Share on other sites More sharing options...
Tormod Posted August 10, 2005 Report Share Posted August 10, 2005 if infinity is so large that we cant express it by any of our means, how can a googolplex not be close to infinity if you can not possibly ever express it. Because as has been pointed out...a googolplex is quantifiable, whereas infinity is but a concept. But take your comparison to the number of atoms or particles in the universe. Now take that (incredibly large) number and count all the possible ways to configure those particles. Not even that is an infinite number, but it will most likely be larger than a googolplex. I think. :Alien: Quote Link to comment Share on other sites More sharing options...
sinewave Posted August 10, 2005 Report Share Posted August 10, 2005 Because as has been pointed out...a googolplex is quantifiable, whereas infinity is but a concept. Not a concept, concepts are limited whereas infinity is precisely what the limited isn't. Thus can not be conceptual. The actual is not concept, only thinking is concept. Quote Link to comment Share on other sites More sharing options...
CraigD Posted August 10, 2005 Report Share Posted August 10, 2005 I believe the “thought straining thought” that moved alexander to start this thread is an example of what a General Semanticists would call a “need for indexing” and slightly more recent philosophers would call a “category mistake”. In short, we’re actually considering 2 distinct things for which we’re using the same name – infinity. Let’s call the various numbers defined by expressions such as “1/x as X approaches 0” “mathematical infinity”, or “infm”. Let’s coin a new (to this thread) term for “the biggest number we’ll ever need to describe the physical universe”, or, closely related, “the biggest number we can represent with complete precision” as “practical infinity”, or “infp”. Making a big guess as to alexander’s meaning, “Is googolplex almost infinity?”, then, can be rephrased as “does infm = infp?” This is a formal statement, and can trivially be answered “no”. Various folk in this thread have provided informal explanations supporting this answer. I thing a less literal rephrasing is more rewarding, along the lines of “does infp exist? If so, approximately what is it?” I think the holographic_principle, a Physics conjecture that’s gained popularity in the last 10 years, shows promise of answering this question “Yes. At least 2^(10^100), (quoting Jacob Bekenstein, in italics), which could in principle be packed inside a sphere a tenth of a light-year across. Estimating the entropy of the universe is a difficult problem, however, and much larger numbers, requiring a sphere almost as big as the universe itself, are entirely plausible.” So googolplex (10^(10^100)) could actually be greater than infp, or perhaps much too small. In principle, though, if the holographic principle is true, it should be possible (and easy) to write an expression for a number larger than it using the form 10^(10^(10^…))… Tormod 1 Quote Link to comment Share on other sites More sharing options...
Tormod Posted August 10, 2005 Report Share Posted August 10, 2005 Not a concept, concepts are limited whereas infinity is precisely what the limited isn't. Thus can not be conceptual. Well, I went to a different school of semantics than you, apparently. Quote Link to comment Share on other sites More sharing options...
pgrmdave Posted August 10, 2005 Report Share Posted August 10, 2005 A slightly different question - is a googolplex closer to infinity than 1? Quote Link to comment Share on other sites More sharing options...
C1ay Posted August 10, 2005 Report Share Posted August 10, 2005 A slightly different question - is a googleplex closer to infinity than 1?No, there is only 1 googolplex between 1 and googolplex, there are infinitely many googolplex between googolplex and infinity. BTW posters, alex spelled googolplex correctly.... Dark Mind 1 Quote Link to comment Share on other sites More sharing options...
pgrmdave Posted August 10, 2005 Report Share Posted August 10, 2005 BTW posters, alex spelled googolplex correctly.... So did I :Alien: Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted August 10, 2005 Report Share Posted August 10, 2005 A googleplex is exactly as far from infinity as zero is from infinity.Nope. A googolplex is exactly a googolplex from zero, while it is infinitely far from infinity. Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted August 10, 2005 Report Share Posted August 10, 2005 C1ay,A slightly different question - is a googolplex closer to infinity than 1?I think this was meant in the sense of "closer to infinity than 1 is to infinity". Answer: Slightly! It's only (googolplex -1) closer to infinity than 1 is. Quote Link to comment Share on other sites More sharing options...
Dark Mind Posted August 10, 2005 Report Share Posted August 10, 2005 Math has nothing to do with such trivia as the physical universe and what can fit in it. Anyway, sez hoo that 10^(10^100) can't "fit into" the universe????? Five question marks.... I think I gotta take this one :hihi:. For your first sentence; that's not what I said or tried to imply. For the question; actually alex said that it is probably close enough to the number of molecules in our universe to be represented by every individual molecule in our universe. What I tried to say is that a googolplex is so large a number that all actual matter in our (on a molecular scale) cannot be used to accurately express it. (That's a pretty damn big number :Alien:) Infinity couldn't be expressed or shown if we used all actual matter and then an a$$ load of imaginary matter to fill up our existing universe with nothing but a gigantic block of molecules :eek: . This is assuming our universe has an "edge" or an end. Here's a question: If our universe is infinitely expansive, would an infinite amount of matter be enough to fill it up :eek:? Quote Link to comment Share on other sites More sharing options...
Dark Mind Posted August 10, 2005 Report Share Posted August 10, 2005 A googleplex is exactly as far from infinity as zero is from infinity.Nope. A googolplex is exactly a googolplex from zero, while it is infinitely far from infinity.I think you misread his post... Check it again :Alien:. Quote Link to comment Share on other sites More sharing options...
Dark Mind Posted August 10, 2005 Report Share Posted August 10, 2005 C1ay,I think this was meant in the sense of "closer to infinity than 1 is to infinity". Answer: Slightly! It's only (googolplex -1) closer to infinity than 1 is.:eek: :eek: :eek: I can't believe you just wrote that! Saying anything is or can be close to infinity implies it's quantifiable... IT'S A CONCEPT. Nothing is near infinity.... That's the whole idea of infinite :rant:. None of these numbers are even a million googolplex away from infinite! This number - 999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999 is just as far away from infinite as this one -0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ... Make sense? Quote Link to comment Share on other sites More sharing options...
pgrmdave Posted August 10, 2005 Report Share Posted August 10, 2005 I disagree. I think that each time we add 1 to a number, we get closer to infinity, even though we are still infinitely far. Quote Link to comment Share on other sites More sharing options...
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