13 October 1998

Notes taken by Alex Junievicz

**Alex Junievicz [CPS Substitute]**

He was upset by an ISPP presentation that used video tape to analyze an experiment used 30 frames a second, but the video gave a vertical rate of 60 cycles per second. Video has 60 raster interlaced; thus it is 30 full frames per second. 1/2 inch video tape units typically have 2 video heads, and they are offset in azimuth as a scheme to conserve tape and enhance performance in slow motion. Thus the 30 per second rate was displayed. This applied to only certain dual head video tape recorders, and in certain others the 60 cps rate would apply. Actually video has a mathematical phase relationship of 15 frames per second. This is due to the color sub-carrier. This is why there are noise cancellations, and provides the basis for the fact that comb filters work.

**Tynnetta Stanley [Home Schooling Mother]**

She simulated lungs by putting balloons in a bottle. She and her assistant tried to blow up the balloon inside a bottle until the balloon filled the bottle. It was easier to blow up a balloon inside a large bottle than a small bottle.

**Bill Shanks [Joliet Central H.S., retired]**

Walmart [or, more precisely, Sam's Club, for members only] has a laser for $15.00. Bill suggested that we prepare a "laundry list" of experiments one could do with a laser, such as looking into an ice cube, looking into a light bulb, reflecting off the gradations on a ruler to see fringes, etc.

**Betty Roombos [Gordon Technical H.S.]**

She is fortunate to have a student who has a digital Camera, and showed pictures of physics activities taken by the digital Camera, and printed on her color printer. It was impressive how well they looked while printed by a Hewlett-Packard 722C ink-jet printer, and on regular paper.

**Al Tobecksen [Richards Vocational H.S.]**

He showed the solution to the rope puzzle of the last meeting. The trick is to put a loop in the rope, and then feed it through the rope around one the hand of the other person. You either become free in the process, or else become more tightly enmeshed in the process.

**Roy Coleman [Morgan Park H.S.]**

He announced that there were some changes and new items on the **SMILE**
web page. The URL link is
http://www.iit.edu/~smile/ .

**Larry Alofs [Kenwood H.S.]**

He talked about cow magnets [obtained from the farm store in Kewaunee] and sold them for $2.50 each. They have a variety of uses, including those on the farm.

**Porter Johnson [IIT]**

He talked about a Geometry problem where twins drove 3 nails at random into
a table and formed a triangle. If the nails happened to lie along a
straight line, there would be no triangle [or else a very skinny triangle
with no interior!]. The probabilities of a new nail lying on the right or
left of the line are each 50%, and for a triangle there are three lines,
and you have to lie "left" "left" and "left" as you circulate around the
boundary [counterclockwise]. By this simple argument, you might expect the
probability of being inside as being 1/8 = 0.125. However, in the historic
words of the 20th Century Physicist Wolfgang Pauli, **"nicht Einfach; aber
Falsch"**---it isn't simple but it is wrong!

It is convenient to use vectors to decide whether a point is inside a triangle. Let us choose one vertex as special, call the vectors from it to the other vertices r1 and r2, and call the vector from it to the point in question r. Then the criterion for being inside the triangle is

r = a r_{1} + b r_{2} .

where a and b are both positive, with a + b < 1.

To gain insight, he employed a pseudo-random number generator and applied
the *****Monte-Carlo** technique. In a run of 10 million shots there was
a computer crash because one of the sets of points was accidentally linear.
He modified the program and then safely ran to 100,000,000 shots, without
incident [it took several hours on the 80 MHz 486PC], obtaining 7,637,924
hits. The corresponding hit probability is thus .076379 +/= .000100,
which is consistent with the number 11/144 = .076388888888... , and lots of
other more complicated numbers, as well. However, no clever soul has yet
appeared with the solution. A copy of the FORTRAN program was passed out,
along with a pseudo-random number generator touted by Liam Coffey [Physics
Faculty Member and Computational Physics guru], just in case you also want
to waste vast amounts of time on this problem or put your lazy computers
to work.

Roy Coleman commented that some pseudo-random number generators are not very successful in producing "random" numbers, as you can see from plotting them in pairs. The "safest" random number sequences involve tabulations of radioactive decay times, but they are difficult to use. The two pseudo-random number generators used here gave similar results.

*******Much of twentieth century science involves Monte-Carlo
simulations of actual experiments, theoretical models, hypothetical
problems, and even "useless and insignificant puzzles". The inventor of
the idea was the mathematician **Stanislaw Ulam**, who was involved in the
development of the atomic and hydrogen bombs. Ulam became ill after the
war, and spent a lot of time in hospital playing the card game Solitaire.
He realized that it is more straightforward to play a few games to
"estimate" the probability of winning the game, rather than to try to
calculate the odds of winning directly. Ulam realized that many problems
too difficult to be solved analytically could be resolved by this technique
using fast computers. This story, along with many others, appears in his
autobiography, __Adventures of a Mathematician__ [ISBN 0-520-07154-9].