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In article <1144353593.735461.323000@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Han.deBruijn@xxxxxxxxxxxxxx wrote:
> Randy Poe wrote:
>
> > Everthing being constructed here is for the purpose of using
> > under an integral sign (or possibly as a differential term in
> > a differential equation). Nothing is intended to use without
> > integration.
>
> This debate becomes funnier on every turn. Now we're already talking
> about the "purpose" and "intention" of having an integral. Let's make
> a proposal for you. We shall talk about "Randy's Virtual Integration"
> every time an infinitesimal is encountered in physics. OK?
>
> > Incomplete. You haven't shown me how it's being used. I wager
> > that when doing an actual calculation, you will see an integral.
>
> Infinitesimals are unmeasurable by definition. So if somebody wants to
> compare his results with experiment, he must remove the infinitesimals.
> So far, you haven't said anything substantial. But what really worries
> me is how an "_actual calculation_" is defined here.
>
> > Because physics does not use rigorous mathematics, except
> > in very rare cases. Most physicists know quite well that what
> > they're doing isn't rigorous, but could be supported with a rigorous
> > argument. Usually. So there's no reason to put together an
> > argument which nobody else in physics cares about.
>
> Augh! That hurts!
>
> Are you saying that mathematics, with all of its rigour, isn't actually
> much relevant to physics?
The reason that physicists are abit causal about rigor is that they have
physical reality ready, willing and able to point out their errors.
Mathematics does not have the luxury of relying on such outside help,
but must be able to find and eliminate its errors internally.
> Are you saying that mathematics doesn't have
> to be rigorous in order to arrive at significant & trustworthy results
> in science?
Exactly the opposite, that mathematics absolutely needs rigor in its
derivations whereas physics and the other sciences that use mathematics
can, and do sometimes, rely on being corrected by nature.
Whew! So you finally admit that I am right?
Actually quite the opposite, but then HdB may have got into that sloppy
habit of allowing nature to point out the need for corrections.
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