[simpaticoder]

Be generous - it saves a lot of time. Once you say "polynomial" readers will think, "like, ANY polynomial, even like n^100?!" and you'll have to explain, yes, but that's STILL better than exponential, etc. They avoided all of that

[godelski]

Quanta targets people who are above average. So I don't think it is too much for them to give a sentence or two stating that. Or even a little graphic could do wonders. I don't think it would take much time or effort to make a graphic like the one on wikipedia[0] and just throw in some equations within the ring. You can easily simplify too, by removing NL and merging EXP. Hell, look at the graphics here[1]. That's much more work.

I don't think Quanta should be afraid of showing math to people. That's really their whole purpose. Even if I think they've made some egregious mistakes that make them untrustable...[2]

[0] https://en.wikipedia.org/wiki/PSPACE#/media/File:Complexity_...

[1] https://www.quantamagazine.org/june-huh-high-school-dropout-...

[2] https://news.ycombinator.com/item?id=44067043

[simpaticoder]

I suppose my point is that the readers who will wonder about this are a) very likely to know about complexity classes already, or b)capable of learning about it themselves. Perhaps a simple link to something like https://complexityzoo.net/Petting_Zoo would have been a nice middle-ground.

Edit: Aaronson even mentions the n^100 problem in the section about P!

[godelski]

I disagree and even think that this is besides the point. It is hard to wonder about what you don't know to wonder about. It is the job of the communicator to prime that and provide any critical information that the reader is not expected to know about. Without some basic explanation here then these terms might as well be black boxes to readers.

The point is that a single line[0] and a minimal graphic could substantially improve the reader's comprehension while simultaneously providing them the necessary nomenclature to find relevant material to further increase their understanding.

Look at this line:

  | One of the most important classes goes by the humble name “P.” 

It tells us almost nothing, except of its importance. Only to be followed by

  | Roughly speaking, it encompasses all problems that can be solved in a reasonable amount of time. An analogous complexity class for space is dubbed “PSPACE.”

This tells us nothing... My first thought would by "why not PTIME and PSPACE" if I didn't already know what was going on.

The whole work is about bridging these two concepts! How can we understand that if we don't know what we're building a bridge between? It's like reporting on a bridge being built connecting England and France but just calling it a bridge. Is it important? Sounds like it by the way they talk, but how can you even know the impact of such a thing when not given such critical context? You get tremendous amounts of additional context with the addition of so few words.