Re: [ATM] Mathmatic's and Imagination

[Mark Holm <mdholm@telerama.com>]

I know this thread is sliding dangerously toward OT, but let me try to
add something perhaps a bit the other direction.

When it comes to math knowledge, I am definitely in the middle class,
lower middle really.  I got to where I could reasonably understand and
even make basic use of multi-variable calculus, vectors, a tiny bit of
linear algebra, etc.  I'm very rusty on the details now since I haven't
really used it since college.

Here is my point, amateur telescope making is bound to bring one up
against some level of math.  The trick is not to get math-phobic about
it.  We now have this wonderful tool called the Internet, plus the old
fashioned, but still very useful tools: books, clubs, mentors,
libraries, etc.  Ask questions!  If you don't follow some bit of math,
just come out and say so.  Those of us that do are quite often more than
willing to help.

Also, even if you are a severe math klutz, work hard to learn to read
graphs.  By graphs, I mean the x-y sort such as
http://www.atmsite.org/contrib/Holm/Plop_optimized_cells/design_space.html
Cartesian dualism may be a bunch of philosophical fertilizer, but
Cartesian coordinates (x-y graphs) are an even better invention than
sliced bread.  Ask yourself questions like,"what does it mean to be left
or right of that pink curve?, Is my mirror above or below that middle
straight line, and what does it mean?  A whole lot of science and
engineering is communicated via graphs.  If you can learn to be
comfortable with them, you can "get" a lot of concepts that remain
incomprehensible when written as equations.

Here is a really useful exercise.

1.  Go to whatever replaced your local five and dime, and buy a package
of graph paper.

2. Do a quantitative experiment.  It doesn't have to be profound, just
something that generates numbers.  Example.  Get a gallon milk jug, a
kitchen sink, a protractor and a watch.  Put the gallon jug under the
spout and open the tap some number of degrees.  Time how long it takes
to fill the jug.  Write down the number of degrees the tap was turned
and the time it took to fill the jug.  Empty the jug and do it again for
a different tap opening angle.  Repeat half a dozen times.

3. Draw an X and Y axis near the bottom and left sides of a sheet of
graph paper.  Make X be the number of degrees and Y be time in seconds.
 Pick numbers for the x and y axis that include your range of data, and
give convenient sized divisions.  It's nice if each square on the graph
paper represents some reasonably integral value such as 1, 2, 5, 10 or
even a fraction such as 1/2 or 1/4.  The scales on the x and y axes do
not need to be equal, in fact, outside of math classes, they usually are
not.

4. Plot your data points one at a time on your graph.

5. Look at the graph and ask yourself some questions.  Examples:  I took
data at 4 degrees and at 9 degrees: how long would it take to fill the
jug if I opened the tap 6 degrees?  Does the jug begin to fill at any
opening greater than zero or is there some minimum value of degrees of
opening before water begins to flow?  Does water flow increase
endlessly, or is there some maximum flow (minimum fill time) beyond
which the data does not go no matter how far I twist the tap?  If I
don't open the tap at all (and my faucet isn't leaky) how long would it
take to fill the jug, and how would I represent that on the graph?  Does
the data make a straight line, or does it make some sort of curve?

Does this sound like a stupid, pointless exercise to you?  Trust me,
this is exactly how quantitative science got started.  If you don't
believe it, then read up on Galileo.

(Extended exercise for the enthusiastic)

Get a nail and hammer.  Nail your graph to your bedroom wall.  Sit on
the bed and stare at the graph for at least 30 minutes, while allowing a
faint smile to play on your lips.  When your spouse asks, "What the *#!
are you doing?", just smile, point to the graph and say quietly, "Isn't
it wonderful?"  This will make it much easier to pry loose the money for
your next eyepiece.  I promise.

-- 
Mark Holm
mdholm@telerama.com

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