Stathis Papaioannou wrote:
> Peter Jones writes:
>
>
>>Computer programmes contain conditional (if-then) statements. A given
>>run of
>>the programme will in genreal not explore every branch. yet the
>>unexplored
>>branches are part of the programme. A branch of an if-then statement
>>that is
>>not executed on a particular run of a programme will constitute a
>>counterfactual,
>>a situation that could have happened but didn't. Without
>>counterfactuals you
>>cannot tell which programme (algorithm) a process is implementing
>>because
>>two algorithms could be have the same execution path but different
>>unexecuted branches.
>
>
> Every physical system contains if-then statements. If the grooves on the record were different,
> then the sound coming out of the speakers would also be different.
That's not a statement contained in the physical system; it's a statement about other
similar physical systems that you consider possible. You could as well say, (print
"Hello world.") contains an if-then because if the characters in the string were
different the output would be different.
>>Finitism doesn't imply stasis. New frames could be popping into
>>existence
>>dynamically.
>>
>>
>>>If time is continuous then in a linear universe movement is the
>>>result of a series of static frames of infinitesimal duration.
>>
>>Likewise.
>>
>>
>>>There is no room for movement within
>>>a frame in either case -
>>
>>There is room within an infinitessimal frame. dx/dt is not necessarily
>>zero.
>
>
> No-one knows what dx/dt is. It is the smallest non-zero number, or the reciprocal of the
> largest finite number.
You must be thinking of dx or dt. The derivative dx/dt is well defined. There's no
more reason to treat velocity as mysterious than position. Per QM they are
complementary variables.
>If there is room for movement within an infinitesimal interval then
> it can by definition be divided up further - it isn't an infinitesimal interval.
Infinitesimal doesn't mean indivisble.
>However, this is
> straying from the original point I wanted to make, which is that whatever reasons there
> might be against block universe theories, continuity of consciousness is not one of them.
> Every digital computer has clock cycles during which nothing actually "happens", and it is
> the conjunction of these cycles which makes the program "flow". There is no way from
> within the program to know what the clock rate is, if there are pauses in the program, or
> if it is being run in several parallel processes. You might argue that it would not be possible
> to run the program at all without a causal connection between the steps, but the fact
> remains, discontinuous framesd during which nothing changes give the illusion of continuous
> motion.
No that's not quite right. If you see two frames, A and B, of a motion picture you
can't infer a time order. If you also see a third, C, you can probaly order them
and constrain the time order to be either ABC or CBA. This corresponds to making
the two delta-x/delta-t have the same sign. All continuity says is that if you make
delta-x small enough, you will be able to do this. No need to go to infinitesimals
in any particular case. Infinitesimals (and continuity) are just limits that are
convenient for reasoning because then you can avoid always having to repeat
conditions like "for delta-x small enough".
Brent Meeker
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Received on Mon Aug 21 2006 - 15:53:03 PDT