2015-10-13 14:26 GMT+02:00 Bruce Kellett <[email protected]>:
> On 13/10/2015 11:00 pm, Quentin Anciaux wrote: > > 2015-10-13 13:44 GMT+02:00 Bruce Kellett <[email protected]>: > >> A computer made of silicon can emulate a Turing machine. A brain made of >> wetware can be emulated by a silicon computer, or a Turing machine. The >> fact that a Turing machine can be define mathematically is entirely >> secondary. >> > > The fact that a computer made of matter can emulate a Turing machine is > because we have a definition of a turing machine which is a mathematical > concept... but if you reject the mathematical definition, I wonder how you > can say that a "computer" emulate a turing machine... You should first > define computation in terms of matter, and shows that the "mathematical" > game is coincidentally like it. > > > Who said I reject the mathematical definition of a Turing machine? > If you don't reject it, your explanation of computation is circular if you don't have a *definition* of what is a physical computation without using the mathematical definition. > A computer emulates a Turing machine in the sense that the silicon based > computer can do everything that an ideal Turing machine can do -- in fact, > the modern computer on your desk is a perfect universal Turing machine. I > don't have to *define* computation in terms of matter -- > You do have to, for not to be circular. > I simply have to compute the output from the given input. > > Also I wonder how you could justify with such theory the equivalence > between two computations... if not by using abstract computation theory to > justify it... > > Two computations are equivalent if they give the same answers. > > How do you justify it ? I can easily write an emulator of another machine > and justify the correct functionning by logic alone, no matter involve... > so if logic is just a game, and matter is the end point, algorithm *can't* > be used as justification of the correct working. > > > Who said matter was the end point? > > You... why do you insist on matter, if it is not primary and can be made > of something else ? > > > Who said matter was not primary? > Who said it was ? If it is not, then reality can be explained in terms of computations alone, and matter could be a product of computations... You dislike that idea, that somehow must mean matter is primary in your view... so IMO, you're saying matter is primary, don't you ? > > > I can justify the equivalence of two computations by pointing to the fact >> that they give the same numerical output. >> > > Then you say it only if you have achieved all possible outputs ? because > you can't use mathematical induction to justify they will on the same > domain. > > > A computation has one input and one output -- it is a mapping between the > input and the output. > Yes so to prove them equivalent, you have to prove the mapping between input and output for all input... how do you achieve that without mathematical induction ? > Different inputs may give different outputs, but then they are different > calculations. > > > Computations might be definable in terms of algorithms, but more than one >> algorithm can give the same computation -- give the same result for the >> given input. >> > > Yes, an infinity of them... but that's a mathematical result... no matter > is used in the reasoning . > > > That mathematical result can be instantiated by actually doing the same > calculation -- same output for the given input -- in a number of different > ways. I can do this without recourse to any mathematics at all. The > material world can be considered as a model instantiating the mathematical > result. This does not diminish either the physical or the mathematical -- > they ride on this together. > > Bruce > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- All those moments will be lost in time, like tears in rain. (Roy Batty/Rutger Hauer) -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
