Supertasks are more philosophical than physical, but they do make for a fun few minutes of contemplation. They make us ask what happens when an infinite number of things happen in a finite amount of time. In this case, they show that things can spontaneously start moving.

Supertasks have been devised by philosophers asking questions like, if you turn a lamp on and off an infinite amount of times in a minute, at the end of that minute, will it be on or off? Recently, supertasks crossed over to the realm of physics (if only theoretical physics). They indicate that, with Newtonian mechanics, a group of particles can spontaneously start moving.

The idea is called The Beautiful Supertask, or the Laraudogoitia's Supertask, after Jon Perez Laraudogoitia, who came up with it. Imagine a meter-by-meter square with an infinite number of particles. A particle, traveling at a meter per second, knocks into the square. Because the particle's speed is a meter per second, and the square is a meter wide, within a second, all the motion that was introduced into the square is gone. But there is no particle ejected. The infinite amount of collisions means there is no final particle. The motion just stops.

These are Newtonian collisions, so we're not messing around with quantum mechanics. One principle of Newtonian physics is they can be run backwards; so say, after a certain amount of time, we run this backwards. We see nothing, nothing, no movement, no energy going into the square — and then suddenly there is movement. Despite no force being introduced into the square, the original particle comes jetting back out of it at a meter per second. There is motion from nothing.

Even in theory, there are questions about this supertask. How do the collisions come about, and what are their properties? Still, it's a cool little thought experiment that shows how, with understandable principles, motion spontaneously seems to generate itself.

*Top Image: **Taprogge**.*

[Via Two Ways of Looking at a Newtonian Supertask]

## DISCUSSION

And at least since Cantor's time these questions about infinity have been addressed in a logically rigorous way. And Godel told us that at least we have the means of recognizing and expecting contradictions and paradoxes to arise in mathematics.

What state is a lamp in after being switched infinitely? Maybe that's something math will leave as undefined, just like the division of zero by zero. Maybe it'll just be accepted as an undefinable given like the concept of a singularity or point. Maybe it will be handled with fuzzy logic where the light is left as half on and half off, half true and half false.

There might a be a lot of ways to handle this with mathematical logic but we can be certain that most of it will be very counterintuitive, just like Cantor's Set Theory was in the first place.