*New York Times*'s Steven Strogatz uses a Sesame Street sketch to begin unpicking the subtle wonder of numbers:

The best introduction to numbers I've ever seen -- the clearest and funniest explanation of what they are and why we need them -- appears in a "Sesame Street" video called "123 Count With Me." Humphrey, an amiable but dim-witted fellow with pink fur and a green nose, is working the lunch shift at The Furry Arms hotel, when he takes a call from a room full of penguins. Humphrey listens carefully and then calls out their order to the kitchen: "Fish, fish, fish, fish, fish, fish." This prompts Ernie to enlighten him about the virtues of the number six.From Fish to Infinity (Children learn from this that numbers are wonderful shortcuts. Instead of saying the word "fish" exactly as many times as there are penguins, Humphrey could use the more powerful concept of "six."

A further subtlety is that numbers (and all mathematical ideas, for that matter) have lives of their own. We can't control them. Even though they exist in our minds, once we decide what we mean by them we have no say in how they behave. They obey certain laws and have certain properties, personalities, and ways of combining with one another, and there's nothing we can do about it except watch and try to understand. In that sense they are eerily reminiscent of atoms and stars, the things of this world, which are likewise subject to laws beyond our control ... except that those things exist outside our heads.

*via Kottke*)

*Previously:*

- 3D-printed math and science sculptures Boing Boing
- Möbius Bagel: interlocking, endless, doughy rings of math Boing Boing
- March is math holiday month, today is square root day! - Boing Boing
- Game-guilds can be modelled using the math of street gangs Boing Boing
- Wolfram Alpha answers Christmas wishes of world's high school ...
- Starbucks sweepstakes requires Canadians to answer math question ...

The better, longer version.

radiolab has a great show on numbers:

http://www.wnyc.org/shows/radiolab/episodes/2009/10/09

“Six

fish” they say? Wouldn’t that be “sixfishes? Well, I do not know-o…Many philosopher think for reasons similar to those you articulated that numbers don’t exist in our minds and are mind-independent in the way that stars are. See, e.g.

http://plato.stanford.edu/entries/platonism-mathematics/

@Marchhare: He comes across very much a realist: “Viewed in this light, numbers start to seem a bit mysterious. They apparently exist in some sort of Platonic realm, a level above reality”.

A lot of mathematicians are constructivist/idealists, and consider mathematical entities to be ideas (mental constructions) that exist only in our heads. (We communicate things about them in language, which is why we share the same notions.)

Oh yeah, a lot of the mathematics behind computer science is constructivist: Curry-Howard correspondence between proofs and computer programs, constructive set theory/dependent type theory, etc.

No no no. Red Dwarf already proved that saying “fish” six times is superior because it’s much funnier…

Dispensing Machine: Hello. How can I help you?

Cat: Fish!

Dispensing Machine: (spits out a fish) Today’s fish is Trout a la Creme, enjoy your meal.

Cat: Fish!

Dispensing Machine: (spits out a fish) Today’s fish is Trout a la Creme, enjoy your meal.

Cat: Fish!

Dispensing Machine: (spits out a fish) Today’s fish is Trout a la Creme, enjoy your meal.

Cat: Fish!

Dispensing Machine: (spits out a fish) Today’s fish is Trout a la Creme, enjoy your meal.

Cat: Fish!

Dispensing Machine: (spits out a fish) Today’s fish is Trout a la Creme, enjoy your meal.

Cat: Fish!

Dispensing Machine: (spits out a fish) Today’s fish is Trout a la Creme, enjoy your meal.

Cat: I will.

I used to have two cats. I called them for their afternoon treats by using the exact same “Fish!” that Cat did. They even asked for it by name.

No, it wasn’t trout Ã la crÃ¨me, nor was it served in a styrofoam box. But they did get six pieces.

The Cat is my favorite character.

“Time to do somethin’ secret!”

It is six fish, if they are all the same species. If, however, the penguins had a mixed order, say five herring and a cod, then it would be fishes. As the birds didn’t specify, it could be either or. Then again, they might have been ordering from the room service menu, which we haven’t seen. So perhaps they know that the only fish the hotel kitchen stocks is trout, exotic fare for a penguin! That’s one kind of fish, so the plural is simply “fish”.

My wife and I have been renting the original Sesame Street episodes on DVD for our toddler, and I am happily astonished at how awesome that show really is. I grew up with it in the 70’s and 80’s, but had forgotten just how clever, funny, positive and educational that show really is. Highly recommended, you adults will enjoy it as much as your kids.

Unfortunately, the clip ends just before the scene where Ernie justifies his fish counting system using the Peano axioms.

ha funny I literally have a test on the Peano Axioms in 2hrs… coming to boingboing for a little distraction and I see this.