[Edu-sig] school physics/math courses

[Massimo Di Pierro]

On Oct 18, 2008, at 12:03 AM, Edward Cherlin wrote:
> 2008/10/17 michel paul <mpaul213 at gmail.com>:
>> "We should abandon the vision that physicists seek an ultimate  
>> mathematical
>> description of the universe since it is not obvious that it exists.
>
> I disagree with this attitude. We can seek an ultimate mathematical
> description, since it is not obvious that it does not exist. We should
> also be aware that we do not have one, and have some idea of the range
> of validity of our models. This will help us to avoid mathematical
> absurdities, particularly the infinities that result from calculations
> on unphysical point masses and point charges.

a consequence of the Godel theorem is that even if a complete  
mathematical description of the universe exists, and we find it, we  
cannot prove it is complete. We can only prove it works for those  
phenomena we have observed.

I say the goal if to seek a comprehensive effective theory that  
describes and explains observed phenomena.

>
>> The job
>> of the physicist is that of modeling phenomena within the physical  
>> scales of
>> observed events.
>
> True much of the time. Another part of the job is to model outside the
> scale of the observed, and go make the new observations needed, as in
> the case of General Relativity.

General relativity describes observed phenomena. It was so even at  
times of Einstein (orbit of planets)

>
>> For some systems, the modeling can be done more effectively
>> using algorithms."
>
> As a mathematician, I don't know what that means. Every algorithm can
> be represented by a system of equations in a number of ways, and every
> system of equations can be solved, at least approximately, by various
> algorithms.

Mathematical formulas described relations between quantities.  
Algorithms described a process (for example a process to solve a  
mathematical formula).
If you believe you can find a ultimate model for everything, it has  
to be described in mathematical terms. If you believe you cannot do  
better than explain known events observed with a finite precision,  
then numerical algorithms provide an efficient way to model the  
physics. I am not saying one can have one without the other. I am  
saying it is easier to teach Newton's gravity using Euler's  
approximate algorithm that it is to do it using symbolic integration.


> As a teacher, I know very well what it means. Some representations are
> easier to understand, or easier to work with, or easier to learn from.
> Various thinkers, including Babbage, Whitehead, and Iverson, have
> commented on the effects of the way we represent problems on our
> ability to think about them, and not only they but luminaries from
> Fibonacci to Einstein have labored to invent or teach new notations
> and representations.

I agree.

Massimo