Someone — it may have been Matt Parker — told the MathsJam conference last weekend there was now a terrifying number of monthly MathsJam meetups, and a murmur went around the room. It was just about the only audience in the world where more than a couple of people would have asked “how do you define a terrifying number?”
The problem is complicated by the fact that there isn’t a fixed number of MathsJams — it’s somewhere on the order of 30, but they pop in and out of existence like the arch-nemeses of ants. In the past, it’s been complicated by certain cities (I’m looking at you, Birmingham) sneakily pretending to be in both the north and the south, but a rearrangement of the menus has fixed that ambiguity, at least.
The first suggestion for a definition came from Pi Munchers, but Knuth up-arrow notation was quickly rebutted by Paul Crowley:
@pozorvlak @pimunchers Up-arrow notation? Molest me not with this pocket calculator stuff. scottaaronson.com/writings/bignu…
— Paul Crowley (@ciphergoth) November 17, 2012
… linking to some genuinely, terrifyingly big numbers ((I may have used the search term ‘molest calculator’ in the writing of this article.)).
Ewan Leeming suggested:
@mathsinthecity @icecolbeveridge for some reason I think of a terrifying number as looming over its neighbours to some degree
— Ewan Leeming (@champnav) November 19, 2012
… which we’ll come back to in a bit.
I searched the Online Encyclopedia of Integer Sequences to find the Sequence of Terror: number $n$ such that the first ten digits of $n^{1/5}$ contain each of the digits from 0 to 9. It’s called the Sequence of Terror because it starts with 911.
Christian Perfect wins a virtual (read, imaginary) prize for the best tweet on the subject:
@mathsinthecity @icecolbeveridge to paraphrase JFK, we have nothing to fear but vier itself, so 4 should be the sole terrifying number.
— Christian Perfect (@christianp) November 22, 2012
Although the results of Novemtory (MathsJam’s annual stock-take of where the meet-ups take place and how many people show up) aren’t yet in, I’m pretty sure there were more than four MathsJams taking place this month. Nor were there 911. To Miles’ credit, something of the order of $3 \uparrow \uparrow 2 = 27$ is a fair stab at a terrifying number of MathsJams.
However, I’m going to suggest that what Ewan meant was the numbers between twin primes — by definition, these terrifying numbers loom over their neighbours in terms of number of factors. Under this definition, 30 — another good guess for the number of MathsJams — would be a terrifying number.
And the question to life, the universe and everything could be, “what’s the next terrifying number?”