On 13 Jul 2015, at 18:08, [email protected] wrote:
Just ask yourself how you grasp the notion of infinity. It's not by
dividing by zero. It's by using "and then..." There's no obstacle
in principle to having a computer reason about the consequences of
having an axiom of succession. It doesn't need to have an infinite
memory capacity to do so (anymore than you do).
OK. Although there is infinitely more to say.
Also, may be "infinity" is simpler for human and animal which
instinctively bet on "and then" all the time. It might be harder to
believe in finiteness and mortality than in infinity and immortality.
Now which one is the illusion? The math shows that, for self-
referentially correct machine, it depends on the point of view.
On the general problem of grounding symbols, I think they must be
grounded thru interaction with the world
I can be OK. Just that the world is only a statistical appearance due
to our self first person dispersion in the universal dovetailing (or
the sigma_1 truth).
and the things symbolized. A computer depends on human beings to
interpret and ground the symbols.
Not entirely. My computer does not bug when I do some shopping
outside. Of course my computer does not care if I add euros or
dollars, and I can sometimes envy him for that. Grounding looks like
brainwashing, sometimes.
Only a robot can ground the symbols itself, e.g. a Mars rover
grounds they symbols for it's location, for the local terrrain, for
the charge in its batteries,...
The grounding is always relative to either one (mainly) universal
number (above the subst level, the classical world, say) or an
infinity of one below (plausibly the quantum reality). If our brain
are classical, we do not exploit that basic comp parallelism (the fact
that there is an infinity of machine competing to continue ourselves,
in arithmetic).
As far as we are correct scientists we cannot prove the existence of a
world satisfying our scientific beliefs, as that would be equivalent
to a proof of our own consistency, which is impossible for correct
machines/entities.
Also, grounding is actually even harder to use for infinity, because,
as Pierz pointed to, infinity cannot be shown ostensibly, except
through image (perspective) or poetry and art.
Bruno
Brent
On 07/13/15, Pierz wrote:
Here's something that bothers me when I try to think of the brain
too much as a computer. How would I teach a computer the notion of
infinity? In simple terms, how can I represent infinity in a
computer program? All a computer knows about infinity is 'stack
overflow' (or simply integer overflow), an inability to continue a
calculation due to lack of computational resources. Yet obviously
such a state has nothing to do with infinity, and the halting
problem shows that no computer can "grasp" the notion of infinity
through some algorithmic method. I could program in an infinity
symbol and under certain circumstances teach the computer to spew
out this symbol, such as when asked to divide by zero, but that's
like teaching a monkey to press a button that causes a recording of
Hamlet's soliloquy to be played whenever the monkey is asked, "How
do you feel about your life?" The understanding of the connection
between input and output is all external to the system. I'm curious
to know - how could one even in principle write a program that would
produce an output that could plausibly be regarded as a
representation of infinity, generated by the machine? How, for
example, could one get it to "work out" that a number divided by
zero gives an infinite or undefined result, without simply
programming that response? This is just another variant on the
symbol grounding problem of course, but it seems a telling one,
because infinity is a mathematical concept, and in its way almost as
important as zero.
I'm not advancing this exactly as an argument against
computationalism, but I am curious to know if anyone has a better
answer to it than simply something like "it will emerge at higher
levels" or something - which to me just begs the question of how.
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