Bruno Marchal wrote:
> On 20 Apr 2009, at 14:50, Brent Meeker wrote:
>
>   
>> Jason Resch wrote:
>>     
>>> I think in regards to conscious, you can't have one without the  
>>> other.
>>> Both information and computation are needed, as the computation
>>> imparts meaning to the information, and the information accumulates
>>> meaning making each computation and its result more meaningful.
>>>
>>> If I sent you an arbitrary binary string, it would have no meaning
>>> unless you either knew in advance how to interpret it or how it was
>>> produced.  Either interpretation or understanding of how it was
>>> produced can be described with computer programs, but without that
>>> foreknowledge the binary string is meaningless because there would be
>>> an infinite number of ways to interpret that string.
>>>
>>> To understand how information "accumulates" through successive a
>>> computations, consider how today's most common processors can only
>>> consider 32-bit numbers at a time, yet like any Turing machine they
>>> are nonetheless capable of performing any computation, including  
>>> those
>>> involving numbers much larger than can be expressed in 32-bits.
>>>
>>> Consider what the neurons do (at least artificial ones), essentially
>>> they only multiply and add (multiply the strength of a received  
>>> signal
>>> by the connection strength, then sum the received signals to  
>>> determine
>>> if they met the threshold to fire).  At a low level the additions
>>> might correspond to the intensity of one color for one pixel in a
>>> visual field, say the brightness of red.  Another neuron might then
>>> sum the intensities of red, green, and blue colors to arrive at a
>>> color for that pixel, while another one aggregates a collection of
>>> those results into a field of colors.  Finally this field of colors
>>> might be processed by an object identification part of the neural
>>> network to identify objects.  Whether or not an object is identified
>>> as a cat or a dog, might ultimately be determined by the firing of
>>> just one neuron, yet at every stage the same basic computation is  
>>> done
>>> (multiplication and addition).  The only difference is the  
>>> consequence
>>> of the computation at each stage; how it is ultimately interpreted by
>>> the next level.
>>>
>>> So the question comes down to where does the consciousness lie:  
>>> during
>>> the computation of information, the computed result, or in the
>>> computations upon the computed results.  Maybe it requires a loop of
>>> such hierarchies as Douglas Hofstadter suggests.  I don't have an
>>> answer but it is something I too wonder about.
>>>
>>> Jason
>>>
>>>       
>> I think "meaning" ultimately must be grounded in action.  That's why
>> it's hard to see where the meaning lies in a computation, something  
>> that
>> is just the manipulation of strings.  People tend to say the meaning  
>> is
>> in the interpretation, noting that the same string of 1s and 0s can  
>> have
>> different interpretations.  But what constitutes interpretation?  I
>> think it is interaction with the world.  If you say, "What's a cat?"
>> and I point and say, "That."  then I've interpreted "cat" (perhaps
>> wrongly if I point to a dog).
>>     
>
> A computation is a sequence of numbers (or of strings, or of  
> combinators, etc.) as resulting by an interpretation. For such an  
> interpretation, you don't need a "world", only an "interpreter" that  
> is a universal system, like elementary arithmetic for example. 

You put scare quotes around "interpreter".  I don't see how arithmetic 
is an interpreter - isn't it an interpretation (of Peano's axioms)? And 
how does arithmetic avoid the problem of arbitrarily many mappings, as 
raised by Stathis?

Brent



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