I’m currently in the midst of an international move, from the UK back to the US. This means that my days unfold in confused montages of jet-lag, scone-longing, and trying to get in on the wrong side of the car. Haven’t had much time for the blog, but I did have these cartoons lying around.
ME: What do you think of these drawings?
MY WIFE: Hey, a cat with a mustache. What’s not to like?
ME: That’s not a mustache. It’s whiskers.
MY WIFE: Okay. I’m not going to tell you what to call your cat’s mustache.
Cats have a symmetry group of order two, because there are two ways to transform a cat while preserving its basic structure: reflect it in a vertical mirror, or leave it alone.
Most cats prefer the latter.
A cat’s activity can be modeled by a delta function. That’s a function whose value is zero everywhere, except at a single point, and yet whose integral is 1. Similarly, the cat is motionless except when it is destroying furniture in the space of a single Planck time.
Note: a delta function is not really a function, just a distribution with good branding.
Are cats more like pure mathematicians, or applied?
Well, like pure researchers, they are aloof from reality. But like applied ones, they benefit off the hard work of others. Best of both worlds, really.
I’m not sure the words “logic” and “cat” belong in the same sentence, except perhaps for sentences about the incongruity of unifying those two words in a single sentence.
And if that sounds too self-referential for you, well, what is logic if not the art of careful self-reference?
There is no theoretical limit on the number of people that a cat can scratch in the span of a minute. Millions, billions… anything is possible. It’s just (thank goodness) very unlikely.
Aw, how cute! The double torus is playing with its toy.
14 thoughts on “A Mathematician Looks at a Cat”
This may be a stupid question, but why would the topology of a cat be a double torus? Wouldn’t it just be a torus?
There is the obvious end-to-end hole …
But then I think the nostril to nostril path counts as another.
And unless we get microscopic, that might be it?
But the nostril end to end path (and the Eustacian tube) are connected to the end to end hole. (I’m embarrassed to say I’ve had this argument with a mathematician before.) Moreoever, they all develop from the same endodermic tissue, so from a developmental biology perspective it’s all one tube.
If the nostrils are connected to the end-to-end hole, that makes it a triple torus. Add in the Eustachian tubes (aren’t they blocked by the eardrums though?), and you’d have a quintuple torus. And that’s not counting such things as sweat pores or the gaps between individual cells…
I’m not sure gaps between cells would count as a path through the body, unless you’re willing to think about spaces between molecules etc. Then the concept of topology becomes ridiculous anyway. But hey, I’m a biologist, not a mathematician haha!
Can I just say that I love this entire conversation?
I think I was picturing the ear-to-ear passage as the second hole, which I guess reveals my low unconscious estimation of cat brains.
You superior thinkers have persuaded me that a single torus is more appropriate, unless your cat has a pierced ear. (A cat with an earring would look pretty cool, actually.)
I’m pretty sure all mammals, birds, and reptiles, are tori.
Was going to comment, but your wife’s quote was too wonderful. I re-blogged instead and went off on an absurd tangent.
I love your blog. Thanks for writing it! 🙂
Yeah, she sees through my posturing.
And thanks for reading!
Great post! Very clever. I love cats!
After reading this, it is probable you own a cat! HA!
Hey, I ( physicist / nanotechnologist ) loved your article. It takes balls to write about math in a blog, man. And I think double totrus is an almost accurate hypothesis. All the best !