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.

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The twenty-five members of the Royal Order of the Garter, founded in 1348, by King Edward III, dine once each year at Windsor Castle, about a round table. From time immemorial, there has been a rule that no two members may be seated next to one another more than once each decade. But can they do better?

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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

LARGE NUMBER CHAMPIONSHIP

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.

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Graham’s number, as huge as it is, can be “described” or “named” in a very few symbols. Several people sent us programs that (in principle!) calculate Graham’s number— you can think of any of these programs as notation for Graham’s number.

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Graham’s number is truly, absolutely staggering…

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We never did resolve the question of which grows faster:

In this corner we have
Sequence 1 n^^n
1, 2^2, 3^3^3, 4^4^4^4, and so on.

And over here we have Sequence 2, defined recursively by

In short, we can define the second sequence as s(1) = 1; s(n) = n, followed by s(n-1) factorial signs.

Which sequence grows faster than the other??

We have many conflicting answers, and no decisive resolution; here was one idea .

Our minds boggle as we continue our quest! This week we discuss the Knuth Arrow notation, for describing some really staggeringly large numbers. And yet we are still two weeks from talking about the largest number ever used for any real purpose!

We also discuss an April Fool’s paradox! Last week we said there were three errors on the Math Factor. But there were only two, so this announcement was one of the three errors! But then the announcement was correct! ETC.

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