Re: Wave Function of the Universe?
- From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
- Date: Fri, 3 Jun 2005 15:47:34 +0000 (UTC)
Seratend wrote:
Arnold Neumaier wrote:
Seratend wrote:
I prefer to say that deterministic and statistical description are just two equivalent ways of giving predictive results: I accept both. Decribing a function by its points or by its induced probability law is somewhat equivalent (2 point of views).
But there is a difference between asserting that the die shows a three and asserting that the probability of getting a three is 1/6.
The die is a random variable or a function if you prefer. We have the determinist results (e,f(e)), where e is a point of the trial space.
Of course I know the standard interpretations. I just wanted to point out that there is a difference between a random variable and a realization, and not two equivalent ways of expressing the same.
Well as I have a finite capacity brain, I just can understand/see dicrete and finite quantities (I have never handled an infinite quantity except in the math and physics models).
With your finite brain capacity, it is much easier to understand or see continuous quantities (such as a straight line) rather than highly discretized quantities (a long line of equispaced dots). Much of brain processing is indeed concerned with producing simple continuous models of a messy reality.
My brain does not understand what a line really is.
If it understands what a large number of discrete objects are it should also understand what a line is. The brain works on concepts, which are few-bit summaries of complex phenomena. Thus it finds much easier to remember a line than to remember 10 points. The line needs no infinite limit to be grasped, though the mathematical definition might need it.
Even if the fields are continuous, the observables, at least what we [can] measure is discrete.
By convention only. In fact what we can measure is fuzzy, not discrete. Borderline cases are simply forced into a Procrustean bed to make them fit a fixed scheme. In view of the inevitable measurement error this does not harm things, but in a quest for understanding (and that's what the foundations of QM are) one should not use the same Procrustean techniques. http://www.mythweb.com/encyc/entries/procrustes.html
By convention or simply due to the physical incapacity to really handle continuous variables?
By convention. Since the definition of a position, say, involves a coordinate system and yields real values, which we measure to some approximation.
However, I prefer to view the universe as finite and discrete (~epistemic/practical view): all the mathematical problems of infinities dissappear
... and together with it, all deep insights into physics, all differential equations basic to all sciences, the calculus that made Newton famous and physics the 'hard' science it is today.
This sort of magic is completely against my taste... Instead of solving the problems it provides a carpet of intractability under which to sweep every challenge that is left in the foundations.
Interesting, I force myself to consider the discrete models in order to remove the magic of the infinites in continuous models.
Well, I see that we'll not reach agreement here with such diametrally opposite views on this matter...
Arnold Neumaier
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