Your answer is intuitively correct, but unfortunately has a couple of flaws
Supercomputers once required large power plants to operate
They didn’t, not that much anyways, a Cray-1 used 115kW to produce 160 MFLOPS of calculations. And while 150kW is a LOT, it’s not in the “needs its own power plant to operate” category, since even a small coal power plant (the least efficient electricity generation method) would produce a couple of orders of magnitude more than that.
and now we carry around computing devices in out pockets that are more powerful than those supercomputers.
Indeed, our phones are in the Teraflops range for just a couple of watts.
There’s plenty of room to further shrink the computers,
Unfortunately there isn’t, we’ve reached the end of Moore’s law, processors can’t get any smaller because they require to block electrons from passing on given conditions, and if we built transistors smaller than the current ones electrons would be able to quantum leap across them making them useless.
There might be a revolution in computing by using light instead of electricity (which would completely and utterly revolutionize computers as we know them), but until that happens computers are as small as they’re going to get, or more specifically they’re as space efficient as they’re going to get, i.e. to have more processing power you will need more space.
First of all this is not a paradox, unless you’re not explaining something, there are two yous past and future, if past self turns off the machine before seeing the numbers nothing happened, if he turns it off afterwards the information has already been transferred so nothing happens either.
I have a feeling you might have recently watched Primer and are thinking of a similar working tome machine, where the machine needs to be powered on from past until future. But if this situation happened in Primer it wouldn’t be a problem either because you’re not in the box after you leave it. It’s a bit weird, but if you imagine time as horizontal lines, the box allows you to travel diagonally, so you only exist inside the box in that timeline at the moment of exiting, before that you were in a different timeline, so if you exit the box, wait a while and turn it off you’re only preventing yourself from using the box again. In fact that’s one of the big reveals of the movie, except it’s said in passing by mentioning that the boxes are multi-use.