Of course, doing this combinational calculation is really not all that
meaningful.... I'm not sure why we want to calculate unordered sets of
neural interconnections, when in fact temporal dynamics may be important to
the brain, so that in some cases the same set of synapses considered in a
different temporal order might "denote" different things (using the word
"denote" very loosely here).
Shane's 10^10 bits figure is very nice as it's just around a gigabyte, i.e.
the amount of RAM on a juiced-up contemporary PC. (Though, of course, to
emulate human thought in real-time one would need a lot of processors per
each gigabyte of RAM).
Based on a number of different calculations I've seen, my suspicion is that
this is off by at worst a couple orders of magnitude. This is why I believe
that, at present, AI is most probably less of a hardware problem (or a
software implementation problem) and more of a "create a workable design"
problem.
However, to make a side point, it's also the case that it requires more
resources to TEST and CREATE an AI than to run one. For our work on
Novamente, we run a lot of empirical tests to understand the behavior of
various system components, and to run tests on N copies of a Novamente
system obviously requires N times the resources one would need to simply run
a Novamente system.
This is similar to a well-known fact about text and image compression
research --- that doing this kind of research requires huge amounts of
memory on one's computers ;-) [even though what one is ultimately getting
at is *compression*] !
-- Ben
> > "Assuming there are n neurons in the brain, and on average
> > there are m connections between a given neuron and the rest of them, the
> > magnitude of the brain memory capacity can be expressed by the following
> > mathematical model, the human memory capacity model, as given below:
> >
> > n!/[m!(n-m)!]
> >
> > where n is the total number of neurons and m the number of average
> > partial connections between neurons.
> >
> > However, this is "extremely hard to calculate and is almost intractable
> > using a modern computer, because of the exponential complicity or the
> > recursive computational costs for such large n and m," so they did some
> > math tricks to estimate it.
>
> Well the standard way to estimate (sorry about reverting to LaTeX here
> for those of you who aren't mathematicians... ) this combination is
> to use the log from of Sterling's equation:
>
> \log_2 \binom{n}{m} = (n-m) \log_2 \frac{n}{n-m} + m \log_2 \frac{n}{m}
>
> here n = 10^9 (neurons in brain)
> and m = 10^4 (10,000 connections per neuron)
>
> These are my numbers, if they use slightly different ones it won't
> matter too much.
>
> This gives approx,
>
> 10^9 \log_2 10^5 + 10^4 \log_2 10^5
>
> which is about 10^10 bits which is about what I'd expect very roughly.
> They should have talked to a mathematician first. Estimating basic
> combinatorics like n!/[m!(n-m)!] is not hard.
>
> Shane
>
>
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