[Comp-neuro] Description versus understanding

Carson Chow ccchow at pitt.edu
Thu Aug 21 18:07:07 CEST 2008


Actually, I was only talking about whether or not there was a simpler 
model of the brain than the brain itself.  i.e. could you leave out some 
details.  I did not intend to  conflate description with understanding.  
I'm not sure what you mean by same class of complexity.  The KC in this 
usage is another means of expressing the information entropy of the 
brain, which is just some number of bits.  When people talk about 
complexity classes they usually mean computational complexity in the 
sense of how many steps it takes a Turing machine to solve a problem of 
size n.  By the Church-Turing thesis all computations are equivalent so 
that would include abstract Turing machines, evaluating a recursive 
function, or a Cell processor.  I've blogged recently on the debate of 
whether or not the brain is computable.  I argued that if you don't 
believe the brain is computable then you should also not accept that 
physics is computable.

It's good that you brought up the point of the genome because I was also 
going to write about that in my blog.   If you accept that the 
biophysics of genetic and cellular processes are computable then you 
could consider (some part of the) genome to be a code for the brain.  To 
be conservative then let's include the genomes of both the baby and the 
mother so we have something like 6 billion base pairs or 12 billion 
bits.  Then you could argue that inputs received during development are 
also important so if you assume we utilize 1000 bits of input per second 
then that works out to something like 20 billion bits per year of 
information.  So we can say that one estimate for the program size or 
entropy of the brain of a child say is on the order of 200 billion 
bits.  Obviously, if we use more of our inputs then the number is 
higher. (Some would argue that there are people that use very few of the 
input bits:)).   I'm not saying if this is an upper or a lower bound, 
it's just a completely uncontrolled estimate.


> I just wanted to point out that Kolmogorov complexity (KC) is  
> defined as
> the minimal length of a program that can generate a string and halt  
> on a
> Turing machine.  In this context, it would correspond to the minimal
> string length that could describe the brain, where the brain is coded
> into a bit string.  So if the brain were Kolmogorov complexity  
> complete
> (KCC) then the only description of the brain is the brain itself.  The

so does this mean all brains of a species are in the same class of  
complexity; and are genomes (as a description of systems that include  
brains) in the same class?

In this discussion 'description of the brain' and 'understanding the  
brain' seems to refer to the same idea. 'Description' (in the sense of  
turing machines) however, is a syntactical feature, and doesn't entail  
'understanding' (whatever that means).


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