"Continuity is the same kind of thing as is temperature." Continuity has a close "Conceptual Distance" to temperature in addition to a close compression distance and information distance.
Is temperature ever precisely computable (akin to k-complexity)? I think everything, even math, has to be conceptualized from a conceptualizer. One man's infinity is another man's finiteness dependent on resources expended in observation. Even for blatant infinity representation you are still bounded within the system in which it is represented. IMO infinity is just a handle to an unperformed calculation. John -----Original Message----- From: Charles Hixson [mailto:[email protected]] Sent: Tuesday, March 11, 2014 8:16 PM To: AGI Subject: Re: [agi] human brain implies P = NP On 02/25/2014 10:52 PM, Ben Goertzel wrote: > On Wed, Feb 26, 2014 at 2:45 PM, Mike Archbold <[email protected]> wrote: >> Partly it depends on how you define infinity and what the context is. >> I know there exists more than one definition for infinity. I tend >> toward philosophy. Hegel had both a qualitative and quantitative >> infinity, but in both cases it was really what he called "spurious >> infinity." Real infinity was the thought itself you had of >> uncountable numbers. Still, I think it sounds very strange to say >> something like you are going to count past infinity. > Sounded fine to Buzz Lightyear, one of my role models ;) > > http://whyirundisney.files.wordpress.com/2012/09/to-infinity-and-beyon > d.jpg?w=605 > > > ------------------------------------------- > AGI > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: > https://www.listbox.com/member/archive/rss/303/232072-58998042 > Modify Your Subscription: https://www.listbox.com/member/?&; Powered by > Listbox: http://www.listbox.com > Sorry to post so late to this thread, but: The question would be why you believe that either infinity or continuity are actual rather than theoretical simplifications. (Well, the simplify description, if not implementation.) I have seen no evidence that such is the case, and have doubts that it is possible. It seems much more likely that when things get quite small you encounter something similar to quantum indeterminacy, where you can't really tell just where you are, precisely. OTOH, my expectation would be that for say distance this would occur at around 10^-33 cm...i.e., where current theory has space-time dissolve into quantum foam. I also expect that the largest number that it is reasonable to consider is something like the powerset of the number of energy-states in the universe. A truly huge number, but finite (presuming that the universe is finite). Also that identical regions identical WRT all information that they contain within their light-cone are, in fact, identical, and thus don't require to be counted more than once. FWIW, even though I suspect that the multi-worlds interpretation of quantum theory is correct, I assert that this still yields a finite, though immensely large, number. N.B.: People tend to use the word "infinity" to describe something too extreme for them to contemplate. In such a usage it makes sense. It's the mathematical concept of the real number line that I feel to be basically incorrect. And the idea of painting a set of numbers red and another set blue is... well, it's a nice image, but it's not something that has any actual meaning. Numbers aren't physical objects, and if they were you couldn't paint an infinite number of them even one color. P.S.: Continuous is a useful concept as long as you are far enough away from the scale at which it breaks down. But every time we are able to look closely enough at something, continuity dissolves away. The "Milky Way" is stars, dust, and light. None of them are continuous under close examination, however continuous the looked before there were telescopes. The surfaces if crystals and metals are only approximately defined, but when you look closely enough the edge of the surface dissolves into atoms and electrons. Again, not continuous. Continuouity is the same kind of thing as is temperature. Useful when dealing with an unconsidered mass, but not an actual thing, but rather more of a abstract collective property to use where one doesn't have enough information, time, energy, or patience to deal with all the pieces. -- Charles Hixson ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
