Re: Engineering and math

On 12 Oct 2006 06:48:30 -0700, alexshy@xxxxxxxxx wrote:

<snip>
To put it bluntly, the difficult math was done
by Steinmetz, Heaviside, Shannon, etc., the guys who came up with this.
They gave us the certainty that the methods work, and they had the
insight to use the right tools. Analysis using these methods is usually
routine, i.e. easy (albeit time consuming sometimes).
<snip>

I'll emphasize this with an easy example from history. The concept of
density is dead easy for us to conceive and apply, today. It is a
simple ratio between mass and volume, after all. Children learn the
idea easily.

Take a look at the history behind it. There were a lot of people with
a great deal of practical interest, yet it took rare people to disover
what our senses do not directly inform us about. Once someone does
discover the idea and explain it, it's child's play. But beforehand?

This doesn't address the "difficult math" you mention above, as
density isn't difficult math. But the discovery of Euler's e^i*w =
cos(w)+i*sin(w), or the discovery of rigorous application of
infinitesimals in differential variables or .... Well, we can all
apply these because we stand on the shoulders of those who discovered
the ideas and put them on rigorous footings.

Analysis using density is often child's play. But look how long it
took to discover as a useful principle. Natural philosophers were
debating the ideas of sharp and blunt as a principle for floating and
sinking, even in Galileo's day, for gosh sake. If someone told me
"density is obvious," and imagine that they are as creative,
imaginative, and smart as those who actually had to discover the idea,
I'd just smile and walk away shaking my head.

Jon
.

Relevant Pages

  • Re: Engineering and math
    ... took to discover as a useful principle. ... "density is obvious," and imagine that they are as creative, ... and you took the razor blade and kept slicing ...
    (sci.electronics.design)
  • Re: Just how does magic work?
    ... Because of the seeming existence of constances like pi I ... >> things that we've yet to discover I guess there ... But I think it can be argued that math is created. ...
    (alt.fan.harry-potter)
  • Re: Is the speed of light really constant ?
    ... I consider the math to be very important. ... >> to those who value ONLY the math part of physics, ... discover it all, ... the few areas that seems to escape this death trap is science. ...
    (sci.physics.relativity)
  • Re: When Did Mathmatics Come About
    ... then discover that, like any game with rules, you can do a lot more with ... but even more just grows out of other math. ... want to solve equations in radicals, and so you invent group theory and ... these are the cat's pajamas, ...
    (talk.origins)
  • Re: Engineering and math
    ... took to discover as a useful principle. ... and you took the razor blade and kept slicing ... figured it would spread out eventually, ...
    (sci.electronics.design)