[There are lights, or something. One figure is talking to itself.]

For my tenth birthday, all I wanted was a puppy. I wanted it more than anything in the world. I begged and begged my parents for months. Instead, my father got me a differential n-form.

'What is it?'

'Why, it's an alternating multilinear map in n vector variables of a vector space V over a field F into F. They make swell pets. You can call him Chester.'

'Does it fetch?'

'No.'

'Does it play dead?'

'Nope.'

'Does it like to chase squirrels?'

'Even better. In a neighborhood U of any point P of a k-dimensional differentiable manifold M, it can be expressed as a real differentiable function f-sub-U on the manifold times the wedge product of n distinct elements of the cotangent bundle to M.'

'Mommy? Make Daddy stop.'

'And you can integrate it over the manifold according to Stokes' Theorem using the exterior derivative!'

'I want a puppy!'

'You ungrateful little shit, I'll teach you to appreciate what you're given...'

And then, as he raised his fist to strike me, the differential n-form leaped! Before I knew it, Chester had swallowed him whole, reducing him to a single real number. I've never been quite sure, but I think it was 6.

'Aw, Chester, you're the best mathematical abstraction a boy could have!'

And we've never looked back.

[Lights out.]

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©2001 Luke Gutzwiller. I really mean it. Violation may result in the unwanted collapse of your state vector. I hated differential geometry.