New proof dramatically compresses space needed for computation

This seems very theoretical, just a lower bound on space required, without talking about what is being computed. Does it have any import on real algorithms?

Lower bound tells you how much it's worth to improve the SOTA. It gives you a hint that you can do better.

So it's more like polar star. Maybe not directly practical, but it will lead tons of people in the right direction.

> Does it have any import on real algorithms?

As-in algorithms you'll care about if you're a programmer and not overly interested in theory? Not really, no.

Thanks. I think the title is quite misleading then? I would have expected better from Scientific American.

It does have an impact. It wont give you stackoverflow like code to copy-paste though.

Analogy is thermodynamics says how efficient a heat engine _could_ be. If your engine is way below that you know there how much of an improvement there _could_ be, that it's not an impossible problem. That will get people to build better stuff.

Upper bound on the space required. Anything, that is computable.

> Does it have any import on real algorithms?

It depends on the constants, but if the constants are good, you can have VMs for example that make memory usage smaller.

It's a reduction from multitape Turing machine to tree evaluations. If your "real algorithm" is straightforwardly modeled by a multitape TM, then it might be possible to use this proof to reduce the space. Otherwise, I don't think so.