lies that a mathematician friend might tell you, because i do.

so today i told several lies .. i think,
but these are very common lies for mathematicians.

twice today, i was asked about the things that i study: once by my sister and once by a friend from high school, and both of them are neither mathematicians nor know much mathematics.

oh well; nobody's perfect. q:
then again, they dared ask and that is something!

---

perhaps "lie" is the wrong word, and "simplification" is more correct. as a general rule, i never explain actual mathematics to non-mathematicians. the best i can hope for is to suggest an idea, or give a rough explanation of one key idea which is key in the work i do.

have i written about this before?
i must be getting redundant.

so to err on the side of caution, let me not rant excessively. spot the 'lies' if you find any, but

1. to my sister i described rectifiable sets as surfaces which look like terribly crumpled aluminium foil, because i couldn't think of a way to describe to a general audience the currents of federer and fleming, much less the notion of a current on a metric space.
   
   happily, she remembered what a tangent 2-plane was .. intuitively, at least.
   
   i then suggested the minimal surface (plateau) problem as an application, and to motivate the study of general metric spaces, i speculated that there are plenty of strange geometries which are interesting, even in real-world terms, like the parameter space for a bicycle or connectivity graphs from a computer network.
   
   
2. to my friend i tried to explain why limits aren't as intuitive as the terminology suggests. he fancies the example of achilles and the tortoise, and i suggested the pathology of porosity:
   
   what if the racetrack was full of holes, at all scales? so say that you want to sample various times to determine how achilles will finish; how do you avoid choosing bad sample times over the race?
   
   i then suggested to him that as a sequence, an orthonormal basis on an infinite-dimensional hilbert space [1] has no limit, even though no point is that much farther from another. as a concrete example of why infinitely many dimensions is reasonable, i suggested possible states of an electron ..
   
   .. even though i don't know any quantum mechanics. i wonder if that remains true.
   

[1] more true to words, "suppose you had two coordinate axes, and now three. now imagine four, which could be, so why not five .. and so on: imagine that there is no end, and there are an infinite number of independent directions .."