[sdiy] OT ( was Re: Waveform analysis into non-sine components)

[Magnus Danielson]

On 04/11/2012 04:03 PM, Harry Bissell wrote:
> wow. I had a very similar experience. I was doing well up until differential calculus, when I encountered a professor who
> obviously flirted with failure before receiving his degree. Previous instructors has a firm grasp of both theoretical and real-world
> mathematics.
>
> example: He set up a problem to illustrate the concept of limits. A lighthouse has a beacon that is rotating at 1 RPM. The spot of light
> is case on a wall 1 meter away, that runs to infinity in each direction. He asked, what the the apparent velocity of the 'spot' of light
> as the angle of the beacon approaches 90 degrees (ie parallel to the wall).
>
> He looked absolutely SHOCKED when I put my hand up immediately... and said 186,000 miles per second, because once the angle becomes great
> enough, the spot of light is delayed in transit time and does not appear on the wall.
>
> Speed of light isn't just a good idea, its the LAW...
>
> I was also disappointed when he explained that the integral of (in effect) a square wave was a triangle wave, but we unable to connect that
> idea with the functional reality of the (familiar) electronic building block we call an "integrator" (opamp with capacitive feedback - y'all
> know what I mean :^)
>
> The ability to synthesize the connection between abstract and applied mathematics and convey ~that~ link to others is probably the most
> rare gift in academia...
>
> H^) harry (fortunately... ohms and kirchoff's laws are simple and almost universally applicable :^)

It is worth mentioning that for some math freaks, it's actually a beauty 
in itself that math does not apply to physical things. A fact that the 
joker Feynman reacted to (who seems to have selected his topic just to 
be able to call it Q.E.D.).

The point being, math folks tends to loose connectivity with the real 
world when presenting concepts, and thus also loose the opportunity to 
get more people along on the magic mystery tour of math.

There are many concepts which isn't all that hard to teach if you only 
bother to explain them. This is however where the issue lies, it takes 
more effort to explain them to a layman.

Concept like derivation is fairly easy to explain as the mathematicians 
tool to find the slope of a function, the integral just does the opposite.

Cheers,
Magnus