Without wishing to go on and on
>>> . All you need is
>>> a infinite set of infinitely patient musicians.
>>
>> Current practical computational systems are finite. Perhaps you mean a finite but possibly large set of sufficiently patient musicians, where human bounds on activity without food, sleep, etc will be an interesting chief obstacle.
>
> Well for any given problem the set needed is finite. However, for
> every problem you can come up with I can name one that would be more
> complicated and need more musicians.
>
> To be Turning *complete* you then need a infinitely large set.
My understanding of the theory of computability (which probably needs a refresher course given I looked at the mathematics closely last in 1995) is that you can trade off space and time to an extent. I can use three humans as registers to enact any algorithm given enough time to do computation (though space for output and intermediate storage may be an issue). The original Turing machines had infinite tapes, and that's definitely the realm of the theoretical. Practical computers all have finite memory and finite instruction sets, registers et al. They are still general computational devices; we run them on and on and maybe our procedures eventually halt.
So 7 billion humans in the world should be enough for any algorithm you care to suggest, given enough time. Yet practically, even getting one human to be a computer component (in the old sense of the word) might be a challenge for any moderately boringly arcane mechanized procedure. There needs to be a further purpose, like religious conviction, wartime demand, wages, desire to 'win' a thread on a livecode mailing list etc
> It follows that your computer is not actually a "universal Turing
> machine" and merely would be if it had a infinite amount of memory.
>
> Consider for example the number X. X would be n+1 where n equals 2
> raised to the power of the number of the most elementary particles in
> the universe. Computationally it is possible to calculate this, in
> practice I don't think you could. Being "Turing complete" is a
> entirely theoretical concept.
>
> I would not lose any sleep over this; a symphonic orchestra should be
> enough computational power for anyone ;-)
I won't lose sleep since I only have a finite amount of hours left.
best
N
Received on Sun Jan 13 2013 - 17:05:55 GMT