Paul, could explain to me a non-mathematician why you say "Calculus
is Dead"? Feel free to over simplify. I quoted you and was
challenged to back up the statement. I said I thought it might have
something to do with "computer finite analysis" but that I did not
know the reasoning behind your comment. Be forewarned, your
comments may find their way to my friends old calculus professor at
Indiana University. :)
I explain further: while I was slapping shoes on a mean little
arab. we were talking about how the computer empowers non-
mathematicians/non engineers to attempt complex designs using CAD.
Another example is how (in my opinion) CAD has eliminated the need
for Trigonometry in the machine shop. Jerry
I am no mathematician either but as I understand it integral calculus
is all about computing the area or volume under certain mathematical
curves. It does this by slicing the area or volume into infinitely
thin slices,
calculating the area or volume of those slices and adding them up
to determine the total area or volume under the curve(s).
A computer can do this real easy and the curve(s) does/do not
have to have a mathematical definition such as y = x^2
to use a simple example. The curve(s) can have ANY shape.
All the computer needs is a set of coordinates for points
on the curve(s).
Way back before personal computers and electronic calculators
I was charged with calculating the speed attained as a function
of distance traveled for a land speed record car. Not being sharp
at all in calculus I opted to do it the long way.
I calculated the increase in speed and acceleration every .1
second knowing the driving wheel torque as a function of gear
ratio, engine RPM, car weight, aerodynamic down force, aerodynamic
drag, tire rolling resistance, coefficient of friction, the phase
of the moon and the distance the car traveled in that .1 second
and added them all up.
It took me a week to get to 400 MPH. I used a Friden mechanical
calculator that had a hundred buttons or more. See the attached
picture of the electro mechanical version. The one I used had a big
hand crank on the side of it. Second picture.
"Inventor: Frank Stephen Baldwin 1839-1925."
"Baldwin patented a pinwheel device that enabled carries in a compact
device. In 1900 he invented a method that allowed digits to be
entered by a single stroke."
"Each complete forward turn of the large crank on the right will add
the value set into the 8 x 10 keys into the bottom register of the
carriage. The main register on the carriage shows the result. The
smaller register above it counts the turns. Subtraction is achieved
by turning the crank in reverse. To multiply by more than one digit
the Repeat button is pressed and the crank turned as often as needed
for the low-order digit. Then the carriage is moved to the right
with the handle in front, so the next digit of the factor can be
cranked in."
http://www-db.stanford.edu/pub/voy/museum/pictures/display/1-
Calculators.htm
A computer can do that in about two or three ms after the
program is written. A few years later, after I had a computer
and the program, I used to astound my car magazine journalist
friends by predicting what their test car would do in the 1/4 mile
to the nearest .01 seconds. No need to actually test the car as long
as the manufacturer was not lying about the engine HP.
Paul Lamar ...No rotor no motor.
Hello, Paul,
I'm amplifying on your most interesting observation that
calculus is
dead.
As you may recall, I'm both an automotive journalist (engineering
editor, Road & Track) and also a mathematician (Ph.D., Case Western
Reserve, 1969).
Yep, computer algorithms have taken a lot of the grunt work out of
mathematical analysis. But, as you recognize better than most, the
computer needs to be programmed by someone, and that person uses the
underpinning of calculus, and often calculus per se, to compose these
programs.
What's more, a great many mathematical areas arise from calculus.
They and their core area calculus continue to flourish.
A curious word-origin aspect: The word "calculus" comes from the
Latin, "calculi," pebble, a little stone. Of course "calculate" has
the
same root, namely using little stones to keep track of things.
Though we rarely use pebbles, their basic function, counting, is
alive and well. And so is calculus.
All in good fun. Thanks for raising this interesting issue.
Dennis (Simanaitis)
What Dennis says is bizarre. I hired Dennis at R&T. He was (and is)
coldly calculating. I never saw him play with pebbles, but he was
frequently stoned. And the root of the word Calculus comes from Cal
(California) and the ending is us (for U.S.). The cul in the middle
of the word is obvious and intuitive.
jd
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