From: Anders Sandberg (asa@nada.kth.se)
Date: Sat Jul 06 2002 - 14:49:51 MDT
A very interesting and thought-provoking post.
Of course, using an analogy to reason about reasoning is always somewhat
risky. We should not imagine that we have exactly three levels of our
cognition, the lines are likely far more blurred and there might be
tricky loops in there. But still the analogy seems fruitful, since it
makes the multimetalevel (ouch, what a horrible neologism! :-)
predictions of the brain more clear.
On Sat, Jul 06, 2002 at 01:22:23AM -0600, marc_geddes wrote:
>
> a square. Now note that we can actually draw rough representations of
> higher
> dimensional objects, even though a piece of paper is only 2 dimensional. To
> draw the equivalent of a square in 3-dimensions, we simply duplicate the
> square, and draw connecting lines between the 'edges' again - we end up with
> a
> drawing of a cube. We can even gain an insight into what a 4-D object would
> look like, even though we as human beings can only see in 3-dimensions. To
> draw the 4-D equivalent of a cube we simply duplicate the cube, then draw
> connecting lines between the edges again. (The result is a drawing of a
> hyper-cube). So: if we have an x-dimensional object and we wish to
> represent
> its equivalent in x-y dimensions this turns out to be a simple recursive
> procedure.
Some would likely claim that our intelligence in many ways is sufficient
to reason about higher forms of cognition, just as we can reason about a
4D object from looking at a lower-dimensional projection of it. But it
will be a reasoning from an analogy, and some properties will not be
represented accurately. In many ways each new layer of cognition is a
more efficient way of handling the lower layers; by abstracting things
to a new level invariances can be exploited with less overhead. So even
if our intelligence in principle could calculate the same results as a
more powerful and abstract intelligence, it would likely take far more
mental resources. In large problem domains the amount of extra resources
might suffer a combinatorial explosion, so that it would simply not be
possible to do anything useful with lower level thinking.
> Recall that super-human intelligence would be the 4th dimension of mental
> experience. Thus it should consist of ‘predictions about predictions
> about predictions about predictions’ of our future physical states.
> Positive ‘super human thoughts’ would act as signals guiding the
> lower level thoughts (to accurate chains of reasoning). Similarly negative
> ‘super human thoughts’ would act as signals warning of invalid
> lower level thoughts (useless chains of reasoning).
It would also be predictions about what chains of thoughts would in the
end benefit us - i.e. the selection of what to think of, what problems
to concentrate one's efforts on. This is what I would call 'wisdom'.
Since we only can use our "3D" thinking, wisdom is currently acquired
mainly by trial and error and slow deduction, which explains why it is
so rare and often ascribed only to the elderly - they have had the time
to gather at least some data. A being that starts out with a "4D"
cognitive system would be wise from the start.
On the other hand: training extra dimensions takes more and more time.
It is trivial to design a neural net that can link stimulus with action
or learn such links contingent on reward. Making a neural net that can
link a stimulus with a series of actions that will in the long run
produce a reward is trickier, and requires far more training than the
stimulus-action network. Making a neural net (or other learning system)
that can successfully generalize already present information into
predictions about rewards is even harder. For each level the amount of
training necessary to produce a good performance increases a lot, since
the number of degrees of freedom increases. A 4D mind might need a far
longer childhood than a 3D mind.
Maybe posthuman superintelligences will have enormously long
"childhoods"; there is no reason to assume the amount of training
examples/experience necessary to enable a new dimension of thinking is
merely linear. If we look at 1D creatures (like insects), they have
"childhoods" that are essentially instant (physical maturation takes
longer than mental); lets say they take a day to mature (10^0 days). 2D
creatures like simple mammals have childhoods on the order of weeks
(~10^2 days). Humans (presumably high 3D) have maturations on the order
of a decade or more (~10^3-10^4 days). If that progression holds, a 4D
mind might take 10^5-10^6 days to mature - centuries or millennia!
Yet another reason to pursue life extension :-) Existing as a fast
informorph will of course speed things up a great deal, but it seems
likely speedups can not be arbitrarily large. If we assume a 10^3
speedup, the 4D intelligences will still take a year to a decade to
mature. And becoming 5D would still take a long time.
> In order words: When a post-human was utilising the 4th dimension of
> intelligence, this would yield automatic knowledge of abstract outcomes
> which to us are only obtainable by trail and error. But this is precisely
> equivalent to the dictionary definition of precognition! Thus: we can
> conclude that if there is a 4th dimension of intelligence, to us ordinary
> humans stuck with 3 dimensional reasoning , this 4th dimension would be
> indistinguishable from precognition. Post-humans would appear to us
> ordinary
> humans as beings which could predict the future in ways which would be
> inexplicable to us. We should label post-humans as ‘Pre-Cogs’
:-) Yes, they would likely seem precognitive to us. After all, we appear
precognitive to many of our companion animals, which in turn are
precognitive to the ant.
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
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