Re: Fun with C

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On Mon, 25 Apr 2011 23:58:37 -0700, Nasser M. Abbasi wrote:

> On 4/25/2011 11:18 PM, Dmitry A. Kazakov wrote:
>> On Mon, 25 Apr 2011 13:46:40 -0700 (PDT), Maciej Sobczak wrote:
>>
>>> On Apr 25, 9:09 am, "Dmitry A. Kazakov"<mail...@dmitry-kazakov.de>
>>> wrote:
>>>
>>>> No, it is a catastrophic approximation because linear system cannot
>>>> oscillate.
>>>
>>> What? A simple hanging spring can oscillate while being purely linear.
> 
>> That system is not linear.
> 
> One should really attribute linearity or not to the equations that
> describes the motion of the system.

> The pendulum itself is just the pendulum, and saying that
> the pendulum itself is not linear, I do not think is very exact,
> but I know you meant the equation of motion when you said that.
> 
> So, now lets talk then about the equation of motion.
> 
> Again, under small angle approximation, the equation of motion
> of the pendulum can be approximated to linear one.  When
> the angle is large, then the  approximation is not a good one,
> and one must use the non-linear equation of motion to make
> better prediction of its motion.
> 
> So, we back to square one.

I am not. The Ptolemy's system is a fair approximation of planet movement.
Moreover, it is asymptotically correct, and mathematically represents the
first ever example of harmonic analysis (a very important tool in
engineering). All that does not make it "right". The Copernican system,
which is plain numerically wrong, and also wrong from the relativity theory
point of view, is taught as a "truth". You cannot ignore the context.

> We make a mathematical model
> of the physical problem, and if the approximation we make
> to this model seems to give good results for our needs, then
> that is the model we should use.

Yes, except the cases where results cannot be verified, and discarding the
context makes anything unverifiable. Models you are talking about exist in
a larger context taken for granted. For example, you presume that laws do
not change with the time etc. Just consider models where time would be a
function of some system parameters. There is an infinite number of models
fitting given system. Among these only models consistent with more
fundamental laws and principles are considered. Empiric models are
subordinate. You can consider deploying such a model (like F=ma) only after
stating its conformance to a more fundamental theory (the relativity
theory). As an engineer you also must show the boundaries within your
empiric model can be used.

> Any way, this is how engineers look at things :)

You mean those programming in C? (:-))

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de