And paper: https://people.csail.mit.edu/rrw/time-vs-space.pdf
Actually I don't have any intuition for why that's wrong, except that if we catenate the rows into one long row then the picture can be considered as a number 307200 digits long in base 256, and then I see that it could represent 256^307200 possible different values. Which is a lot: https://www.wolframalpha.com/input?i=256%5E307200
https://images.lsnglobal.com/ZFSJiK61WTql9okXV1N5XyGtCEc=/fi...
if there were only 78 million possible pictures, how could that portrait be so recongizably one specific person? wouldnt that mean that your entire picture space wouldnt even be able to fit a single portrait of everyone in Germany?
I did a lot of raster graphics programming, in my career, and graphics work makes heavy use of lookup tables.
Yesterday, I posted a rather simple tool I wrote[0]: a server that “frontloads” a set of polygons into a database, and then uses them, at query time. It’s fairly fast (but I’m sure it could be a lot faster). I wrote it in a few hours, and got pretty good performance, right out of the starting gate.
Pretty basic stuff. I doubt the pattern is unique, but it’s one that I’ve used for ages. It’s where I try to do as much “upfront” work as possible, and store “half-baked” results into memory.
Like I said, I always “just worked that way,” and never really thought about it. There’s been a lot of “rule of thumb” stuff in my work. Didn’t have an MIT professor to teach it, but it’s sort of gratifying to see that it wasn’t just “old wives” stuff.
There’s probably a ton of stuff that we do, every day, that we don’t think about. Some of it almost certainly originated from really smart folks like him, finding the best way (like the “winding number” algorithm, in that server[1]), and some of it also probably comes from “grug-brained programmers,” simply doing what makes sense.
[0] >>44046227
[1] https://github.com/LittleGreenViper/LGV_TZ_Lookup/blob/e247f...
I imagine if you have a good idea of the data incoming you could probably do a similar encoding scheme where you use 7 bits to point to a ~512 bit blob and the 8th bit means the next 512 couldn't be compressed.
All this accomplishes is discrediting science. Trading personal gains for eroding the very thing that they make their money off of. This is a major part of why Americans (and people) have such high distrust for science. News outlets, and in particular science focused news outlets, constantly spew inaccurate information. It really should be no wonder that so many people are confused about so many scientific topics, as unless they actually take the years it takes to become an expert in a field, they are going to have a difficult time distinguishing fact from fiction. And why shouldn't the average person expect to trust a source like Quanta? They're "full of experts", right? smh
[0] This is the earliest archive I see with the note. Press back one day and it should not be there. Article was published on Nov 30 2022, along with a youtube video https://web.archive.org/web/20230329191417/https://www.quant...
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] >>44067043
Edit: Aaronson even mentions the n^100 problem in the section about P!
My article was quite explicit in multiple places that the universal/comprehensive character of the result was that counterintuitive part:
- In the first paragraph: "memory was more powerful than computer scientists believed: A small amount would be as helpful as a lot of time in all conceivable computations."
- Further down in the introduction, in the passage you quoted: "Until now, the only known algorithms for accomplishing certain tasks required an amount of space roughly proportional to their runtime, and researchers had long assumed there’s no way to do better. Williams’ proof established a mathematical procedure for transforming any algorithm — no matter what it does — into a form that uses much less space.
- In the third section, I explicitly state that researchers do believe space is more powerful than time in the specific sense that you're criticizing my article for misrepresenting: "But complexity theorists suspect that PSPACE is a much larger class, containing many problems that aren’t in P. In other words, they believe that space is a far more powerful computational resource than time. This belief stems from the fact that algorithms can use the same small chunk of memory over and over, while time isn’t as forgiving — once it passes, you can’t get it back."
- In the fourth section, I explain why researchers didn't think the HPV75 result could be improved further, despite their intuition that space is more powerful than time in the above sense: "While many problems can be solved with much less space than time, some intuitively seemed like they’d need nearly as much space as time."
TCS (and complexity theory specifically) are complicated subjects. I spend a lot of time interviewing researchers and thinking about how to distill the results of my reporting into a form that is accessible to readers with widely varying levels of familiarity with the subject matter. You are of course well within your rights to critique my stylistic choices, the narrative aspects of the story, and the order in which I presented information, but I will push back against the claim that my article is spreading misinformation about complexity theory. You're referring to a misconception that arises, by your own admission, when you don't read carefully. If it's the headline you object to, you could lodge a similar complaint against the complexity theorist Lance Fortnow: https://blog.computationalcomplexity.org/2025/02/you-need-mu....
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