Fraser’s Spiral

The Fraser’s spiral illusion is an optical illusion that was first described by the British psychologist Sir James Fraser. The illusion is also known as the false spiral or by its original name, the twisted cord illusion. The overlapping black arc segments appear to form a spiral, but the arcs are in fact concentric circles. The visual distortion is produced by combining a regular line pattern (the black circles) with misaligned parts (the differently colored strands). It is like many other visual effects, in which a sequence of tilted elements cause the eye to perceive phantom twists and deviations. The illusion is augmented by the spiral components in the checkered background. It is a unique illusion, where the observer can verify the concentric strands manually. When the strands are colored differently, it becomes obvious to the observer that no spiral is present. So class, take out your Sharpie and outline one of these circles on your screen.

Infinitely many mathematicians walk into a bar. The first says, “I’ll have a beer.” The second says, “I’ll have half a beer.” The third says, “I’ll have a quarter of a beer.” The barman pulls out just two beers. The mathematicians are all like, “That’s all you’re giving us? How drunk do you expect us to get on that?” The bartender says, “Come on guys. Know your limits.”

G.H. Hardy, an Oxford and Cambridge mathematics professor, professed to be an atheist, but in dealing with providence, he bore in mind the possibility that life’s operation might, after all, be manipulated by God, with an understandably low opinion of Hardy. He also considered air travel dangerous. Once, shortly after Hardy had left on an overseas flight, a colleague found a note lying on his desk that read, “I have proven Fermat’s last theorem.” The news spread and by the time Hardy returned home all the world was agog to learn the proof. Hardy had to explain that he had not proved it—the note had been insurance. God, he said, had been forced to bring him back alive to show him up as an imposter.

How many mathematicians does it take to change a light bulb? One: she gives it to three physicists, thus reducing it to a problem that has already been solved.

Find x

Why’d the chicken cross the road? The answer is trivial & is left as an exercise.

Finally, I’ll leave you with Mathgen, an Internet toy that allows you to generate fake scientific papers. It is a program to randomly generate professional-looking mathematics papers, including theorems, proofs, equations, discussion, and references. Try it for yourself! Here is one of mine: Fermat’s Last Theorem, M. Regenaxe, T. Maxwell and V. Fermat. The results look realistic enough. Just don’t hang around so long that you are asked to explain them.