On 10/23/2014 1:56 PM, LizR wrote:
On 24 October 2014 09:09, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:On 10/23/2014 12:37 AM, LizR wrote:On 23 October 2014 15:29, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote: On 10/22/2014 7:12 PM, John Clark wrote:On Wed, Oct 22, 2014 at 1:30 AM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> > Quantum mechanics assumes real and complex numbers. Quantum mechanics works very well, but every time we've tested it with experiment the values we put into it and the values we measure after the experiment have only had values at best a dozen or so places to the right of the decimal point. Are we justified in extrapolating from that that it would work just as well if there were a infinite number if digits to the right of the decimal point? I honestly don't know.I think it's just a convenience for reasoning about rational numbers. But then I also think rational numbers are just part of our model of the world. That isn't too surprising. Anything we can think about is part of a model of the world.But you left out the "just".Yes, because if you're going to retreat to a "just a model of the world" viewpoint then you have to be prepared for the fact that it affects everything else. You're basically postmodernising the entire scientific enterprise.
No, I'm just pointing out we can't be sure that something that is part of our model of the world is part of reality; and this is exactly the same as being uncertain that there are real numbers. In spite of Kronecker, the integers are just as much a human invention as the reals. We shouldn't take our models to seriously. We may find a better one next week.
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