I have just started a new fortnightly column for Mint, titled "A Matter of Numbers". This is a place where I hope to explore the wonders of mathematics and science. It will be a challenge to write, but a challenge I thoroughly look forward to. It should be a whole lot of fun.
The column will run on alternate Fridays. Given that it has to do with numbers, I'm absolutely delighted that it kicked off yesterday, Friday the 13th.
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8 comments:
You should find plenty of grist for the mill in "1 2 3 Infinity" by George Gamow.
Exactly who is the expected reader class of this article? I believe non-mathematics related people should find it interesting. For others it should be somewhat trivial, at least this post.
Exactly who is the expected reader class of this article?
People like you.
Harshad: It is clear you found "this article" interesting enough to read and comment on. Unless you waste your time writing trivial comments on trivial posts - which seems at variance with the high opinion you clearly, and perhaps rightfully, hold of yourself as well as of Dilip. I therefore deduce, by the law of large numbers, that you are a non-mathematics related person. Did I do the arithmetic correctly or am I profoundly innumerate?
@Anonymous:
Nice attempt, but you did not consider other possibilities. I am a regular reader of Dilip's blog and thus go through every post with almost equal attention.
Your comment reminds me of this -
I give you a black pen, I give you another black pen, I give you 'n' number of black pens. Now I give you (n+1)th black pen. So by principal of mathematical induction all pens in the world are black. Spot the fallacy. :)
Well, it happened because infinity is a fundamentally different number from every other in Gangaipudupettai, or in fact on this planet.
I am no mathematician, but is infinity a number or a concept? I am aware that in some circumstances, one can treat infinity as a number ("extended real line" for example) but I still would not think of infinity as a number.
And I think the first Anonymous commentator is right in in that your hotel anecdote is based on Gamow's similar anecdote in his "One Two Three... Infinity." However, apparently, the story was known among mathematicians even before...according to this website:
Yes, you can find the Hilbert Hotel story in Gamow's entertaining "One Two Three...Infinity", first published in 1947. Gamow's footnoted attribution reads "From the unpublished, and never even written, but widely circulating volume: "The Complete Collection of Hilbert Stories", by R. Courant".
I think you should have acknowledged Gamow but that is just my opinion.
Finally, a pedantic note: The hotel can accomodate my friends and me if I turn up with a countable infinity of my friends. But if uncountable infinity of my friends (say, one for each real number on [0,1]) turned up at the hotel (which I assume only has a countable infinity of beds), then the clever girl couldn't accomodate them, could she?
Anon #1 and Suresh, here's a confession: I actually own an old copy of Gamow (found it being sold without the cover) but have never read it. So I honestly did not know the infinity hotel story is in there. I suppose someone must have told it to me, I guess one of my maths teachers while teaching us about infinity.
Since I wrote this column (which I actually did in early March), I have read a version of it in another book called, I think, just "Infinity". So while I would be glad to acknowledge Gamow or this other book, at the time of writing the column I didn't know about either.
To me, infinity is better thought of as a concept; and yet in this column I thought making that distinction would add another layer of complexity I didn't want to get into. And of course you're right about countable/uncountable infinities: I hope to address that in some future column.
Harshad: Since you are a regular reader of Dilip's column your comment must be a "Black Swan" (Taleb) and not a "Black Sheep". As for the pen - isn't that the deductive fallacy and not an inductive one?
Dilip: I am sorry, the "I didn't know" defense is not valid. This is only applicable to politicians like Reagan. Plausible deniability. However since you have confessed, please report back once you have finished the book from (cover+1) to cover. I assume it still has the back cover.
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