Bruno Marchal wrote:
> On 14 Jan 2009, at 18:52, Quentin Anciaux wrote:
>> Hi,
>> 2009/1/14 Brent Meeker < 
>> <>>
>>     Stathis Papaioannou wrote:
>>     > 2009/1/14 Brent Meeker <
>>     <>> wrote:
>>     >
>>     >> However a Turing machine is not just a set of states, it also
>>     requires a
>>     >> set of transition rules.  So in the same abstract way that the
>>     integers
>>     >> are ordered by "succession" the computational states of a
>>     Turing machine
>>     >> are ordered.  Whether just abstract rules, without
>>     implementation, are
>>     >> sufficient isn't clear to me.
>>     >
>>     > In an actual physical computer the transition rules are
>>     represented by
>>     > the causal links between the states, so that a particular input will
>>     > reliably give rise to a particular output. But I return to my
>>     question
>>     > about what would happen if there were a discontinuity in a
>>     sequence of
>>     > states, so that s1 to s10 on m1 are causally linked, s11 to s20
>>     on m2
>>     > are causally linked, but there is no link between m1 and m2, i.e. m2
>>     > just happens to start in s11 accidentally. Assuming that s1 to s20
>>     > occurring in a single machine results is a few moments of
>>     > consciousness (which is to say, assuming that computationalism is
>>     > true), what would happen if the sequence is broken in the way just
>>     > described?
>>     I suspect something is lost.  You are thinking of the states as
>>     abstract steps
>>     in a computer program.  But a computer program requires a computer
>>     to run and
>>     the computer implements distributed spatiotemporal links.  In
>>     general you cannot
>>     take even a digitial computer and freeze it in a instant of time,
>>     call that a
>>     state, and restart it without any effects. 
>> I do not see a problem with that... a program can be freezed any 
>> time... dump the memory to a file, on restart, load the dump file to 
>> memory, put the instruction pointer at the correct place and you're 
>> done. (well in practice it is a little more difficult, but you could 
>> do it for *any* program). In the situation that Stathis describe, 
>> causality is not broken in any way. S1->S10 run in computer 1, dump, 
>> reload on computer 2 S11->S20 run in computer 2, the causal link is 
>> given by the program that compute S1-S20 irrelevant on what physical 
>> device it is running on... the causal link is the program and a 
>> program is relative to a machine (abstract one). So a computation is 
>> the set of a program and the machine that runs it. A state doesn't 
>> exists by itself (state of what ?), and this is where Stathis is wrong 
>> I think.
> Stathis is not wrong but seems unclear on what a computation 
> mathematically is perhaps.
> Many miss Church thesis. The fact that there is a purely mathematical 
> notion of computation at all. 

I thought the Church's thesis was that all effectively computable functions 
in the lambda-calculus, but the "effectively" referred to intuitive ideas of 
what is physically realizable.  Later it was shown that the recursive functions 
and the Turing functions also defined the same set of effectively computable 
functions.  Turing was plainly motivated by considering physically implemented 


> Best,
> Bruno
>> Regards,
>> Quentin
>>      Switches are in intermediate states,
>>     EM waves are propagating, electrons are diffusing - it is not a
>>     static thing
>>     like a step in a program.
>>     In terms of Bruno's teleporter, one might say yes accepting that
>>     there would be
>>     a one-time gap in consciousness (ever had a concussion?), but one
>>     would probably
>>     hesitate if the there was to be a gap every 10ms.
>>     Brent
>> -- 
>> All those moments will be lost in time, like tears in rain.
> > 

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