Three observations get you there:

`min {a,b,c} = − max {−a, −b, −c}`

`second-from-top {a,b,c,d,e} = max ( {a,b,c,d,e} without max{a,b,c,d,e} )`

`max {a,b,c} ~ log_t (t^a + t^b + t^c ), t→∞`

Putting these three together you can make a continuous formula approximating the median. Just subtract off the ends until you get to the middle.

It’s ugly. But, now you have a way to view the `sort`

operation—which is discontinuous—in a “smooth” way, even if the smudging/blurring is totally fabricated. You can take derivatives, if that’s something you want to do. I see it as being like q-series: wriggling out from the strictures so the fixed becomes fluid.