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-beyond.jpg?w=605
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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
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