Comics I Don’t Understand

How Indeed?

Cidu Bill on Feb 14th 2010

Filed in Abstruse Goose, Bill Bickel, CIDU, Valentine's Day, comic strips, comics, humor | 14 responses so far

14 Responses to “How Indeed?”

Kit Feb 14th 2010 at 08:32 am 1

This is a spoof of Cantor’s diagonal proof. The rational numbers are countable, the real numbers are not. “Let me count the ways . . .”
Wayne Feb 14th 2010 at 09:04 am 2

“Let me count the ways….” and here’s how to count the rationals.

But surely love is a bit irrational, isn’t it?
Winter Wallaby Feb 14th 2010 at 09:10 am 3

Yep. At the original ( http://abstrusegoose.com/117 ), the title is “Countably infinite,” and alt-text is “I can count the ways”
Powers Feb 14th 2010 at 09:30 am 4

But all of the numbers in this diagram are rational — they have to be, to be expressed as fractions.

And why are 2/2, 3/3, 4/4, and 5/5 not hearts but 1/1 is? And why 2/4 but not 1/2 and why 4/2 and not 2/1?
Derek Feb 14th 2010 at 09:43 am 5

Powers:

All of the numbers here are rational. If each axis was extended infinitely, it would contain ALL the rational numbers.
The numbers that are not in hearts have already appeared, and can’t be counted twice.
Kit Feb 14th 2010 at 09:44 am 6

@Powers they are reducible to numbers already counted.
Wayne Feb 14th 2010 at 12:50 pm 7

I take it that Powers’ question is how this could show that the real numbers aren’t countable. Answer: it doesn’t.

This diagram has nothing to do with Cantor’s diagonal proof, which shows that the set of all real numbers (rational and irrational) can’t be put into one-one correspondence with the natural numbers; it’s the diagram for the proof (also due to Cantor) that the set of all rationals *can* be put into one-one correspondence with the natural numbers. Follow the arrows, and count the hearts as you go!
Chakolate Feb 14th 2010 at 01:48 pm 8

I love you guys. Where else on the web would a comic lead to a discussion of Cantor’s diagonal proof?
James Schend Feb 14th 2010 at 02:30 pm 9

Proof aside, I still don’t get the joke.
mitch-4 Feb 14th 2010 at 02:36 pm 10

I get the difference between the entries in hearts and those without. But I don’t get the difference between those with up arrows and those with down.
Arthur Feb 14th 2010 at 03:19 pm 11

Mitch: As Wayne said, “Follow the arrows, and count the hearts .”
That shows that there’s a way to go through the whole table without
ever having to “go to infinity” along a row or column.
furrykef Feb 14th 2010 at 03:59 pm 12

I love you guys. Where else on the web would a comic lead to a discussion of Cantor’s diagonal proof?

The xkcd forums, perhaps?
Mark in Boston Feb 14th 2010 at 04:37 pm 13

I knew someone who gave a very clever handmade (well, copy-machine-made) card (booklet actually) to his girlfriend.
Cover: “How do I love thee? Let me count the ways.”
Page 1: Copy machine picture, his hand on the glass, index finger up, meaning “one”.
Page 2: Two reduced pictures, one with two fingers, one with three.
Page 3: Four reduced pictures and so on, with each page having twice as many pictures (each half the size) as before until you can’t even tell how many hands there are.
Jim in Phx Feb 16th 2010 at 07:14 pm 14

Mark - I don’t see how that worked starting on page 3, 3rd picture. Four reduced pictures, one with 4 fingers, one with 5 fingers, one with 6 fingers (borrow the killer on Monk for this one?), one with 7 fingers (?????).