tag:blogger.com,1999:blog-6642011.post8547733056828753397..comments2023-10-29T10:32:36.914-04:00Comments on Philosophy, et cetera: Can something be bigger than everything?Richard Y Chappellhttp://www.blogger.com/profile/16725218276285291235noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6642011.post-12897102495822196382007-04-11T20:01:00.000-04:002007-04-11T20:01:00.000-04:00A - your point about information is a good one. I'...A - your point about information is a good one. I'd been thinking about that too, but I'm not sure I have a solid enough understanding of what "information" is, to apply it to the original case. Do fractals contain infinite information? Or, since it can be condensed down to a single equation, barely any info at all?<BR/><BR/>(Though, via an analogue of Timothy's argument, I guess it's trivial that the universe as a whole contains no less information than any part of it, including the fractal displayed on my computer screen.)Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-77250394843463658322007-04-11T17:29:00.000-04:002007-04-11T17:29:00.000-04:00Hmm ..quote " Cantor's theorem states that some ...Hmm ..quote " Cantor's theorem states that some infinite sets are larger than others. In particular, the power set of everything in an infinite universe would be larger than the universe itself."<BR/><BR/> then the infinite set is the new 'infinite' .. of which there can be a new power etc ..etc. <BR/> <BR/>If there CAN be a 'infinite' it is ... well ... infinite .<BR/><BR/>end of story ... by definition.<BR/> <BR/>unless of course, one is a philosopher it seems!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6642011.post-62132187045129933362007-04-11T08:22:00.000-04:002007-04-11T08:22:00.000-04:00Not sure the DOOM 3 example necessarily works with...Not sure the DOOM 3 example necessarily works without a very restricted definition of what you mean by size. In terms of "information" for example, (which is a "size" in some sense), the house clearly has more information than the game. <BR/><BR/>It seems to me that any discussion about the "size" of non-discrete objects will necessarily come to a discussion of the cardinality of infinite sets, as Alex demonstrated above.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6642011.post-59718138271477510362007-04-11T04:10:00.000-04:002007-04-11T04:10:00.000-04:00Paintist,I don't think so. Cantor's theorem state...Paintist,<BR/>I don't think so. Cantor's theorem states that some infinite sets are larger than others. In particular, the power set of everything in an infinite universe would be larger than the universe itself.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6642011.post-16462245177284247262007-04-11T03:02:00.000-04:002007-04-11T03:02:00.000-04:00"Clearly, the universe can contain representations..."Clearly, the universe can contain representations as of something bigger than the universe actually is..."<BR/><BR/>Unless, of course, the universe is actually infinitely large. Right?paintisthttps://www.blogger.com/profile/00443666588024095574noreply@blogger.comtag:blogger.com,1999:blog-6642011.post-54529934401198420392007-04-10T23:47:00.000-04:002007-04-10T23:47:00.000-04:00I think that if you start from two axioms:1- Any s...I think that if you start from two axioms:<BR/><BR/>1- Any size plus any other size equals a greater or equal size.<BR/>2- The size of any part is added to the whole <BR/><BR/>It's impossible to avoid the conclusion that the whole cannot be bigger than the parts. If one were false because there were somehow negative sizes it's easy to see how parts could be bigger than the whole but I cannot even begin to conceive of "negative size". I suppose one might also be false if there were incomensurable size quantities like imaginary size but I don't think that's got any bearing on the current puzzle. 2- Seems to me to be a matter of definition.<BR/><BR/>So I'd say it's pretty clear that any part or parts can never be bigger than the whole.Anonymousnoreply@blogger.com