Almost everyone will agree that literacy is essential - everyone should be able to read and write. In a modern society, basic math and science skills are just as important! This page offers a few resources and links in this area...

Math puzzles for kids

Here is a selection of math problems and logic puzzles, to supplement homework for mathematically talented children. And here are a few more (in German), aimed at kids around 5th grade.

Patterns in primes

People of mathematical bent like to play with primes. Me too! Patterns in Primes: Enhancement to the Seive of Eratosthenes.

Feathers and Birds - Neurons and Nervous Systems

This is an excerpt of a paper (PSY/237/MK/Oct 67) written by Matthew Kabrisky from the Air Force Institute of Technology. In the full version of this paper, Kabrisky speculates that learning about the capability of individual neurons may shed very little light on how to build effective neural networks. Although the scientific content of this paper is long outdated, his closing story poses a more general question: how to we, as researchers, ensure that our experiments actually have something to do with the principles we are trying to investigate? This is his closing story.

The importance of doing the right experiment is pointed out by the report of a missionary team returning from two years in the Brazilian jungle in the early 1950's. During World War II, an Army Air Corps C-47 transport on a flight from Panama to Rio de Janeiro was blown off course in a storm and the crew, fearing that they did not have sufficient fuel to reach an alternate airport, elected to bail out over a small Amazon River town. Since the aircraft had been trimmed for level flight and set on the autopilot, it continued on after the crew bailed out and remained unreported for nearly a decade.

As luck would have it, the aircraft landed virtually intact on a river bank in plain view of an entire village during a festival. Although the village members had never had any contact with any other human beings, they had a fairly advanced culture and realized that the strange flying device might be important to them if they could only exploit some of the unique principles it so obviously possessed.

A research team set up to investigate the plane was charged with the responsibility of seeing how it could fly since its wings couldn't flap. This was perhaps the most maddening thing about the device; there was no doubt that it could fly, everyone had seen that, but it obviously violated the most important rules of flight. Another sticky point at first was the fact that it wasn't covered with feathers; the group leader quickly noticed though that the basic shape in plan and cross section of the wing was a fair approximation to that of a bird and it was assumed that this was an effective, albeit crude, imitation of that key portion of the flying problem.

After several fruitless days of investigation, the team discovered a remarkable characteristic of the wing: if a person put his ear down on it at one wing tip, the slightest tapping or scratching at the other end could easily be heard. There seemed little doubt that this was an important clue to the solution of the problem; after all, where else did such a phenomenon ever occur? Although a few discounted this, the rest of the team began a research effort which was still in full pitch when the missionaries arrived. By this time, the team had categorized innumerable sound sources as to quality of transmission both singly and in every possible combination, effects of every conceivable pattern of frond and skin wrapping on the wing during every possible type of sound transmission, etc., and there didn't seem to be any end to the experiments because each one suggested a dozen more. Nonetheless, each novel idea for an experiment renewed the team spirit and none of them had any doubt that before long the pieces would fall into place and that the enormous body of data they had gathered would soon produce the answer.

Not everyone agreed with the team, however, and one of the dissidents had fastened his attention on the peculiar substance which covered not only the wings, but the entire plane. Several square yards of it had been torn off in a shower of sparks when the C-47 landed and he began a series of experiments with the stuff since it was obvious that its widespread distribution on the plane proved that it must be extremely important to flight. He discovered that it could be bent, shaped, polished, melted, fatigued, and made into weapons, and was still testing it to try and find out what enabled it to fly when the missionaries arrived.

Several other minor efforts were underway; for instance, remembering the sparks on landing, one man was attempting to duplicate conditions to produce a similar display and another was still trying to deduce the significance of the three large movable flaps on the tail. But the only "useful" thing that the plane had produced had come from the emergency rescue kit, where following the pictorial instructions, several children had put the kite together and were still hoisting the antenna wire with it as a game when the missionaries arrived.

The missionaries had something more important to sell than aerodynamic theory and one can only surmise that the village is still working on their problem, although the kite has probably worn out by now.