St Luke's Church Eccleshill - Articles from "The Link"

An infinitely interesting job?

Dear Clergy In Bradford,

A reporter at the T&A is trying to write a feature on clergy who did interesting jobs before they were ordained. Please could you let me know if you fall into that category? Many thanks,

Alison Bogle

(Diocesan Press Officer)

Dear Alison,

How could a former research mathematician resist this invite?

It was a 19th-century mathematician, Georg Cantor, who first realized that you could have a "positive" definition of infinity. Up to that point people had known what a "finite" set was: you could count the objects and eventually you'd get to the end and you'd have counted them all. "Infinite" was simply "not finite". Cantor noticed that if you count a finite set of things in different ways, you always get the same answer: the "number" of things in the set stays the same, even if you rearrange them. But for an infinite set, you can rearrange the things and count them again and seem to get far more than there were before. So his big idea was: an infinite set is one where you can take some of the things away and you've still got the same number left as you started with. Or, more formally, a set which can be put into one-to-one correspondence with a subset of itself.

The next mathematical puzzle was this: are all "infinite" sets the same size, or are there different "sizes" of infinity? Can any two infinite sets always be matched up? Or are some infinite sets always "bigger" than some others, no matter which way you count them? The answer - there are different sizes of infinity, in fact (you guessed it!) infinitely many sizes of infinity.

The smallest size of infinite set is called "countably infinite", and an example of such a set is the set of natural numbers {0, 1, 2, 3, ....} . My research was to do with this question: what sorts of mathematical problems can be solved on a theoretical computing machine which can handle infinite amounts of information - but only the smallest size of infinity?

I would love to write more on this fascinating subject - but alas, parish magazines can hold only finitely many words. Do contact me and I'll explain much more. Not for nothing did theologians of the olden days try to speak about "how many points are there on a line?" - even though they used to express it in slightly odd ways, such as "how many angels (0-dimensional beings) can you fit on a razor (a 1-dimensional space)?"

Best wishes, yours sincerely - John Hartley

(The T&A did not take up this offer. We wonder why not?)

	*St Luke's Church, Eccleshill - The Link* magazine** The Link is published monthly at 40p (Senior Citizens 35p), and we deliver free within the parish and post copies (at the reader's expense) to those who request it. Please contact us if you would like a free copy for a trial period. August 2004, Page 2.
Home Page. Index of articles: by subject, by date. In this issue: (August 2004) Alpha, Infinite interest, General Synod, Bus clearway, Marry anywhere? Pray for the dead? Other articles on infinity.	An infinitely interesting job? Dear Clergy In Bradford, A reporter at the T&A is trying to write a feature on clergy who did interesting jobs before they were ordained. Please could you let me know if you fall into that category? Many thanks, Alison Bogle (Diocesan Press Officer) Dear Alison, How could a former research mathematician resist this invite? It was a 19th-century mathematician, Georg Cantor, who first realized that you could have a "positive" definition of infinity. Up to that point people had known what a "finite" set was: you could count the objects and eventually you'd get to the end and you'd have counted them all. "Infinite" was simply "not finite". Cantor noticed that if you count a finite set of things in different ways, you always get the same answer: the "number" of things in the set stays the same, even if you rearrange them. But for an infinite set, you can rearrange the things and count them again and seem to get far more than there were before. So his big idea was: an infinite set is one where you can take some of the things away and you've still got the same number left as you started with. Or, more formally, a set which can be put into one-to-one correspondence with a subset of itself. The next mathematical puzzle was this: are all "infinite" sets the same size, or are there different "sizes" of infinity? Can any two infinite sets always be matched up? Or are some infinite sets always "bigger" than some others, no matter which way you count them? The answer - there are different sizes of infinity, in fact (you guessed it!) infinitely many sizes of infinity. The smallest size of infinite set is called "countably infinite", and an example of such a set is the set of natural numbers {0, 1, 2, 3, ....} . My research was to do with this question: what sorts of mathematical problems can be solved on a theoretical computing machine which can handle infinite amounts of information - but only the smallest size of infinity? I would love to write more on this fascinating subject - but alas, parish magazines can hold only finitely many words. Do contact me and I'll explain much more. Not for nothing did theologians of the olden days try to speak about "how many points are there on a line?" - even though they used to express it in slightly odd ways, such as "how many angels (0-dimensional beings) can you fit on a razor (a 1-dimensional space)?" Best wishes, yours sincerely - John Hartley (The T&A did not take up this offer. We wonder why not?)
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