On 8/16/2014 5:48 AM, Pierz wrote:
On Saturday, August 16, 2014 8:45:30 PM UTC+10, Liz R wrote:
On 16 August 2014 16:48, Pierz <[email protected] <javascript:>> wrote:
I assert this confidently on the basis of my intuitions as a
programmer, without
being able to rigorously prove it, but a short thought experiment
should get
halfway to proving it. Imagine a lookup table of all possible additions
of two
numbers up to some number n. First I calculate all the possible results
and put
them into a large n by n table. Now I'm asked what is the sum of say 10
and 70.
So I go across to row 10 and column 70 and read out the number 80. But
in doing
so, I've had to count to 10 and to 70! So I've added the two numbers
together
finding the correct value to look up! I'm sure the same equivalence
could be
proven to apply in all analogous situations.
But if your table gives the results of multiplying them, you get a slightly
free
lunch (actually I have a nasty feeling you have to perform a multiplication
to get
an answer from an NxN grid ... to get to row 70, column 10, don't you count
N x 70 +
10?)
So suppose your table gives the result of dividing them, I'm sure you're
getting at
least a cheap lunch now?
Sorry this is probably complete nitpicking. I can see that the humungous
L.T. needed
to speak Chinese would require astronomical calculations to find the right
answer,
which does probably prove the point.
Actually it's not nit-picking. My first thoughts on this were wrong. It's clear some
lookup tables aren't worth the computational cost of looking them up, e.g, a lookup
table of addition, whatever the precise computational cost (you can jump rows without
having to count through each cell, so I think the cost is still linear on the size of
the table). However, we can imagine a table of cubes or powers of 796.0584304 and see
that the lunch gets very cheap if you have the memory resources for it. It's a trade-off
of time versus space. Actually I think you can show that the LT saves work so long as
the program doesn't actually disregard any of the information passed to it and does some
real work on it. Why is this even interesting? Because if you can use lookup tables more
efficiently than doing the computations themselves, then maybe you can make a
philosophical zombie through the careful selection of recordings. However, I think you
can show this won't work. Firstly, the machine won't be a *complete* zombie because it
will have to work hard and therefore somewhat intelligently in selecting the correct
records, so then we have the situation of a "partial" zombie, which is absurd vie the
fading qualia argument.
But isn't this really how our brain works. There are things you learn so that you no
longer have to (consicously) think about them. In fact most sports are that way. If you
have to think about how to hit that tennis ball it means you haven't learned to play
tennis yet. The same with typing these sentences. It's not that qualia faded; it's that
they got pushed into the subconscious where they don't count as "qualia" even though they
are still input, and, within their domain, counterfactually correct.
Brent
But also, we have to recognise that to completely recreate the program/person, we can't
only record overt behavioural outputs, but also internally reportable states to cater
for the possibility of someone asking, "what are you thinking now?" etc. That means our
lookup table needs to record each step of each calculation, not only the outputs, and
that means no compression is achieved at all. To locate the machine's state, we can't
just look up a result from an input, but we have to go down the rabbit hole of the
computation itself, which will involve as many, and the same, computations as the
original program. Maybe it's possible that some compression could be achieved because
not all machine states can be interrogated. An "output" is after all merely an
accessible machine state. Inaccessible machine states could be compressed into a lookup
table or cache, but the interesting possibility here is that * maybe they already are*
and that is why they are unconscious and inaccessible. Perhaps we turn often repeated
computations into recordings and that is why they are unconscious, because no true
computation is being carried out any more. Ah gad, that's enough on that. I'm thinking
out loud more than anything else, sorry!
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