Re: Fun with C

["Nasser M. Abbasi" <nma@12000.org>]

On 4/24/2011 12:46 PM, Dmitry A. Kazakov wrote:
> On Sun, 24 Apr 2011 12:07:37 -0700, Nasser M. Abbasi wrote:
>
>> Do then you start teaching students nonlinear systems before
>> linear systems?
>
> If you are going to teach them pendulum, would it make much sense to
> pretend it linear? x is a pretty good approximation of sin(x) near 0.
>

It is not pretending, it is approximation. A good one, if the angle is
small.  Buildings, rockets, trains, advanced control systems are
designed based on linear system theory, and somehow they seem to
work just fine. My teacher kept telling us this all the time. He should
know :)

> BTW, there is an important difference between empirical and fundamental
> laws of nature.
>

And what makes you think GR is fundamental and classical mechanics
is not?  We do not know what the fundamental laws of nature are, if
we did, we would have a unified field theory, which we do not. GR works
well in large scale, but not too well at at the nano-scale, so it
can't be a fundamental law of nature.

Everything we learn can be viewed as approximation to how nature work.

>> Your point that we should start learning general relativity
>> before classical mechanics makes no sense to me.
>
> My point is that historic views need not to be taught.

My view is the opposite. I learn a subject better by learning how
it came about. I like to read old papers and books more than new ones,
because it gives me more insight into the subject. Even if the
old views are no longer the most accurate ones on the subject.

> Anyway, importance
> of classic mechanics looks overestimated. You cannot see planets when
> living in a large city, but do can the computer on your desk. Explain why
> it works using Newtonian mechanics.
>

Do not understand.
  
>> Then why not start with string theory first before general
>> relativity?
>

> String theory is not yet generally accepted.
>

It is tought at many schools allready. Any way, the point
is that, there are many models of nature, some are
more complicated than others. If a model works well for
what one wants to do, and the model is simpler, use that
mathematical model.

Telling a civil engineer they need to learn GR first in order
to design a building do not make any sense.

--Nasser