Infinite reactions

Here is a summary of some of the comments I have received about the Horizon programme To Infinity and Beyond. Most of them, I’m glad to say, were very positive!

I must begin by disclaiming responsibility for the infinite universe(s) in the second half of the programme. My own view is that the observable universe is finite; anything else that might or might not exist has no effect on us, so speculation is pointless. But, although they asked me about that, they didn’t put my response in the programme.

First up was Neill who put a comment on his blog. He said,

… my very favourite moment came in the first five seconds.

DRAMATIC NARRATION: I’ve seen things you people wouldn’t believe. Things that would change the way you see this world. Enough… to drive men to madness.

CUT TO: Shot of my Dad sitting in his study, looking a bit confused.

Well yes, we have been here before … Did I tell you my Raj Persaud story?

A correspondent asks if there is a layperson’s book about infinity. I suggested John D. Barrow’s “The Infinite Book”, with a caveat that although he is a cosmologist I consider that what he says about the possibility of infinity in our actual universe to be a bit flawed. Incidentally, here is a quote I gleaned from the book (probably an old saw, but it was new to me):

[Infinity] is . . . the staple of the mystic contemplation of reality — “make me one with everything” as the mystic said to the hamburger vendor

Geoff Smith’s eleven-year-old “rebelled – quite reasonably – at” the idea that in an infinite universe, everything that can happen will happen infinitely often. The programme quoted David Spiegelhalter on the “monkeys and typewriters” argument. David said that he had explained his caveats (which didn’t make the programme) and had also pointed out that, when the experiment was actually tried, the monkey “just typed ‘s’ and used the keyboard as a toilet”, which sounds very reasonable and shoots down the argument quite effectively. See this BBC News report concluding that “the ‘infinite monkey’ theory is flawed” (according to the scientific officer at Paignton Zoo).

One of my colleagues pointed out that the title (which is also the title of a book by Eli Maor about infinity) is taken from the manual for a telescope: “the range of focus of your telescope is from 15 feet to infinity and beyond”.

Various correspondents have asked how the finite human brain can think about infinity, or indeed about such large finite numbers as Graham’s number. I tried to explain this on the programme; let me put it this way. If the US military spending is a trillion dollars, you can come to terms with this number (in a sense) without having to visualise, individually and simultaneously, all these dollar bills. You could think of them done up into bundles of a thousand, and then a 1000×1000×1000 haystack made of these bundles would contain a trillion dollars. But nobody suggests that the mint has actually to produce so many dollar bills in order to pay for the armed forces!

In the same way, if we conceptualise an infinite set like the set of natural numbers as a single object, we can think about it without having to think individually about each of the numbers in the set.