Re: Knowledge-proof arrogance


"Frank Krygowski" <frkrygow@xxxxxxxxx> wrote in message
news:349fd637-11ff-4f1f-886b-2e5fb631656f@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Jan 21, 8:16 pm, Michael Press <rub...@xxxxxxxxxxx> wrote:
In article <R4mdnfORnoxYI-rUnZ2dnUVZ_gSdn...@xxxxxxxxxxxxx>,
"Tom Kunich" <cyclintom@yahoo. com> wrote:



To be a surpassingly good engineer you need to be a surpassingly good
mathematician for sure. But just being a mathematicians makes you
nothing
but a mathematician.

I'll differ with Tom here. To be a surpassingly good engineer, you
need to be a decent mathematician. You certainly don't need as much
research-level theoretical math as the typical professional
mathematician!

Then these two early exercises from the foundations of
the differential and integral calculus will offer no difficulty.

1) There is a rational number between any two distinct real numbers.
Hint: Archimedean property of the real numbers.

2) Every sequence of real numbers has a monotone subsequence.

:-) This is kind of fun.

OK, the proper engineering answer to that is, "Who cares? Those don't
have anything to do with anything practical, and I work to get things
done. Besides, my project deadline is coming up."

An engineering type question. Let's have a mathematical solution.

3) A cube shaped box with the edge length 1 m stands against a wall.
A ladder of length 5 m leans against the wall, and just touches
the box at an edge. How high on the wall is the top of the ladder?

And the first engineering response is: "Why do you want to know?"
Not to be smart, but to settle the next question: "What's the
tolerance?" Because in the engineering world, there must always be
tolerance, and good enough is perfect.

After that, if the tolerance were less than a few centimeters, the
engineer asks "What are the detail dimensions of the ladder?"
Because, being practical, he knows the ladder's thickness and end
profile obviously matter.

When the questioner says it's really just a theoretical line - that
is, an infinitely thin "ladder," the engineer will say "Oh, this is
just an unimportant little puzzle."

He then may say "The answer is any distance at all between zero and 5
meters." Why? Because you didn't specify _which_ edge of the box the
"ladder" touches, nor which part of the ladder leans against the wall
Considering the bottom and vertical edges of the box, it could be
anywhere from laying on the floor to perfectly vertical. And the
engineer grins.

If the questioner says "No, no, no, I meant the theoretical "ladder"
leans in the usual way against the edge of the cube which is parallel
to the intersection of the wall and floor... and I really want an
answer, please," then the engineer sketches a couple similar triangles
on scratch paper, pops two equations into his equation solving
software, and says:

"4.83850116 meters high, and 1.26052 meters out from the wall. Do you
need it to be more exact than that?"

- Frank Krygowski

Frank,
How does the ladder's thickness obviously matter?
Thanks,
Kerry


.

Relevant Pages

  • Re: Knowledge-proof arrogance
    ... mathematician for sure. ... A ladder of length 5 m leans against the wall, ... is, an infinitely thin "ladder," the engineer will say "Oh, this is ...
    (rec.bicycles.tech)
  • Re: Knowledge-proof arrogance
    ... mathematician for sure. ... A cube shaped box with the edge length 1 m stands against a wall. ... A ladder of length 5 m leans against the wall, ... is, an infinitely thin "ladder," the engineer will say "Oh, this is ...
    (rec.bicycles.tech)
  • Re: Knowledge-proof arrogance
    ... mathematician for sure. ... To be a surpassingly good engineer, ... A cube shaped box with the edge length 1 m stands against a wall. ... A ladder of length 5 m leans against the wall, ...
    (rec.bicycles.tech)
  • Re: Knowledge-proof arrogance
    ... mathematician for sure. ... A cube shaped box with the edge length 1 m stands against a wall. ... A ladder of length 5 m leans against the wall, ... is, an infinitely thin "ladder," the engineer will say "Oh, this is ...
    (rec.bicycles.tech)
  • Re: Knowledge-proof arrogance
    ... "ladder" touches, nor which part of the ladder leans against the wall ... to the intersection of the wall and floor... ... answer, please," then the engineer sketches a couple similar triangles ...
    (rec.bicycles.tech)