What follows after 0, 1, 2, … , once you’ve managed to list every counting number?
Around 1875, Georg Cantor created — or discovered if you like — the transfinite ordinals : the list continues 0, 1, 2, …, then ω , ω + 1, ω + 2, etc, for quite a long long way. John H. Conway tells us about his Surreal Numbers , which add in such gems as
1 / √ ω
Check out Knuth’s Surreal Numbers, Conway & Guy’s Book of Numbers , or for more advanced users, Conway’s On Numbers and Games.
Bill Poundstone, author of The Prisoner’s Dilemma, tells us some game theory lore, how to model an arms race, and lessons for the good life.
John. H. Conway, one of the young men pictured above, tells us about his fabulous and simple method for rapidly calculating the day of the week.
With just a little practice, you too can Impress your friends (or drive them away) with this stupendous ability!
Niclas Hedell gives his solution to the third tree puzzle he posed last week, and we ask a puzzle about sums of numbers.
Niclas Hedell, a listener, poses a problem from his days in the Swedish military: given two trees in the forest, and a rope twice as long as the distance between the trees, how do you find a third tree so that all three make a right triangle.
And we explain how the Stork can catch the Frog.
Lord Butler, Knight of the Garter, has never heard of the rule on last week’s show. But he notes he does move down the table each year…
When we posed this problem, we thought things would turn out a little differently, as we discuss here.
A contestant for our Million-Dollar-Give-Away sent in Rayo’s Number, hitherto the largest number ever used for any real purpose: to wit, winning the
Check out the article by Scot Aaronson that inspired them to duke it out! And this thread on the math forum is quite interesting as well.
We visit a giant model of a four-dimensional polyhedron, made of the fabulous Zome math construction toy. Paul Hildebrandt, president of Zome, weighs in!
Dennis Shasha answers his puzzle.
Dennis Shasha, author of the “Puzzler's Elusion” gives us a new puzzle.
Download a great math factor poster to print and share!
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