5 ms·
Enormous Integers
- evincarofautumn 15y agoOn a tangentially related note, “Dark Integers”[1] is now perhaps the best short story I have ever read. [1] http://www.asimovs.com/_issue_0805/DarkINtegers.shtml http://www.asimovs.com/_issue_0805/DarkINtegers.shtml
- pavel_lishin 15y agoInstapapered it. Egan's novels always make my head hurt, and then make me want to read them again.
- polymatter 15y agoI just read it and enjoyed it immensely. Thanks for the recommendation.
- nsns 15y ago>> It’s like seeing a seasoned tiger hunter running through the jungle, yelling “Help! It’s a giant ant!” I don't think anyone can top this analogy in the near future :)
- losethos 15y agoGod says... thats_right freak youre_welcome petty hate rubbish end I_have_an_idea think_you_could_do_better Boo high_mucky_muck you_better_not
- michaelochurch 15y agoLarge integers are sometimes easier to think about in terms of infinities. Coming to mind is the extremely counterintuitive Goodstein's theorem, which becomes comprehensible when one uses (infinite) ordinal numbers: http://en.wikipedia.org/wiki/Goodsteins_theorem#Goodstein_sequences http://en.wikipedia.org/wiki/Goodsteins_theorem#Goodstein_se...
- evincarofautumn 15y agoI am not at all disturbed by heights, but very large numbers make me a bit uncomfortable.
- pavel_lishin 15y agoThe examples in that section made no sense to me at all.
- deleted 15y ago[deleted]
- hamidpalo 15y agoWhat about busy beaver numbers? http://en.wikipedia.org/wiki/Busy_beaver http://en.wikipedia.org/wiki/Busy_beaver
- ORioN63 15y agoAnyone else wondering about the problem with 26 letters?
- lotharbot 15y ago> "These higher levels of largeness blur, where one is unable to sense one level of largeness from another." IMO that's the really neat thing about enormous integers. They simply pass beyond our ability to reason about them in the same ways that we reason about numbers in our everyday life. We can conceive of two and three digit numbers simply by counting to them. We can conceive of millions and billions by imagining piles of material (a 2 foot cube of sand might be 1-2 billion grains). We can conceive of larger numbers by counting the number of digits, or equivalently, using logarithms -- often comparing them to the number of particles in the solar system or the known universe, or thinking in terms of how many bits are needed to store the number. At some point, though, we start dealing with numbers so big that Knuth's up-arrows or Conway Chained Arrow Notation become necessary. We reach a point where the numbers no longer correspond to objects, distances, or physical quantities. These sorts of large numbers are truly abstract -- the only way we have to measure them is with other ridiculously large numbers, which themselves are only understood as notation. See, for example, http://en.wikipedia.org/wiki/Large_numbers#Examples_of_numbers_in_numerical_order http://en.wikipedia.org/wiki/Large_numbers#Examples_of_numbe...