The Most-Used Mathematical Algorithm Idea in History (2016) | Hacker News Reader

The Most-Used Mathematical Algorithm Idea in History (2016)

writings.stephenwolfram.com

181 pointsdaneelsan36 comments

Amazing... learning of the existence/term of polyominoes is a breakthrough for me.

I’ve recently been working on developing a novel statistical test to quantify sensitivity to the modifiable areal unit problem (MAUP). The limiting factor has been the ability to efficiently generate arbitrarily shaped polygons on a lattice at random. In essence, this is needed to stochastically reallocate a spatial characteristic and measure variance.

Apparently, the exact solution I’m looking for is Donald Knuth’s algorithm X [0]. And I also found this interesting application of the algorithm [1].

I simply cannot express how much my curiosity has just peaked. Moreover, I now have reason to cite both Solomon Golomb and Donald Knuth in a paper.

[0] https://en.m.wikipedia.org/wiki/Knuth%27s_Algorithm_X

[1] https://gfredericks.com/blog/99

Curiosity peaking (I have also seen peeking) is quite an interesting mondegreen for curiosity 'piquing'. The latter means 'stimulating' or 'aggravating', whereas the former implies that when you hear about something for the first time your curiosity is at a maximum - which is a fun interpretation :)

I wouldn't be surprised if peak and pique have similar etymology.

You might find zero suppressed binary decision diagrams (ZDDs) useful. They also allow simple random generation of all kinds of objects (even constrained ones).

Knuth adjusted his algorithm X for ZDD and got some nice speedups.

I had never seen polyominoes used professionally for mathematics.

However, I was reminded of seeing them in the teen novel Chasing Vermeer [0].

[0]https://en.m.wikipedia.org/wiki/Pentomino#Literature

I made a game about polyominoes: https://melonmouse.itch.io/polyominoes

If you try it out, please let me know what you think :)

P.S. work on that led to a sequence on the Online Encyclopedia of Integer Sequences: https://oeis.org/A239658

One QOL consideration: consider allowing the last placed piece to be moved in one click. That is, if you click while "at capacity" the last placed piece gets removed and placed where you click.

If I die famous someday, I really hope Stephen Wolfram doesn't write my obituary...

I hate to admit this, but I'm one of those types too (who you wouldn't want as the authors of your obit).

I've been called every name in the book by my own friends, e.g., Dunning-Kruger, "full of it", etc, etc. I know all these terms. I just don't know how to come across as a humble person, despite it hurting in my personal/social/work life. The only thing that helps is if I interact with others less (there I go again).

Kind of a side note, but Stephen Wolfram really has a way to make things about himself.

For many years, this annoyed me. Now, though, I enjoy it. At least he is someone of note.

How is that your takeaway from the article?

There’s a lot of interesting anecdotes/history here.

He spent quite a lot of time just talking about Golomb and his work.

An obituary where the author casually drops that he was the youngest receiver of this-and-that award? That everything becomes so easy with the Wolfram Language? That he's written a new kind of science book and casts Golomb's work as essentially a precursor for his great accomplishments about cellular automata?

Wolfram is slowly transforming into the Trump of computer science. Soon he'll cast turing machines as just a small precursor of himself having solved computation.

Every single article I've read by Wolfram makes detours to focus on his own accomplishments (e.g. awards or appointments), tied to the main story by extremely tenuous, almost non-existent connections. And there are always multiple references to cellular automata.

I will gladly admit I like his storytelling and the anecdotes are interesting but I have to ignore the detours to make it to the end.

don't be so harsh on the old man. He indeed accomplished a lot. A little bit self-promotion is generally Ok. What did Steve Jobs actually do technically?

> An obituary where the author casually drops that he was the youngest receiver of this-and-that award?

It's more a eulogy than an obituary. It is common in eulogies for the speaker/writer to explain how the subject's life tied in with their own.

His being the youngest winner in the first batch of MacArthur awards is completely relevant because that was why Astrid Golomb came knocking on his door.

> That everything becomes so easy with the Wolfram Language?

He gave one specific example as something that is easy nowadays on computers that Golomb had to do tediously be hand when he needed it in 1954. Nowhere does he say anything about the Wolfram Language making everything easier.

"Surely you're joking mr Feynman" is the same, but there it is celebrated. So I think if it's ok depends on if you have the same level of admiration for the writer as the writer does for himself.

That’s an autobiography. You read it to hear the author talk about themselves.

That's missing my point, though. I'm not saying it's wrong for Feynman talking about himself, but that the way he does it isn't much different from Wolfram.

It's pretty different. If nothing else, it's playful with Feynman—almost done in jest as an aspect of the rogue part he often played, and largely innocuous. Others have already written about the issues with e.g. New Kind of Science at length so I won't go into it, but if you look at the specifics there and ask whether they're things Feynman might also have done, it's easy to see the resemblance is pretty superficial. Feynman's non-autobiographical writing was pretty down to earth imo.

Feynmann doesn't do it in an obituary, is the point.

I wish we had an automatic sticky on all Stephen Wolfram posts to not talk about his self-aggrandising tendencies.

It's not that I don't agree that he does it, it's just that moaning about it happens on nearly 100% of hackernews comment threads about his content, and it's generally much much less interesting than the usually very interesting content.

Awesome article. I’ve a new hero to add to my list of people I’d thank a million times over for their contributions to modern tech. Thank you Sol!

Pretty sure that honor goes to positional number systems and the arithmetic algorithms like carry-based addition.

Is there a reason why it is called a "Mathematical Algorithm Idea" instead of "Mathematical Algorithm"? The pedant wants to know if that's a specific classification of algorithms, and the gatekeeper in me wants to penalize grammar.

When I saw it I just thought it was needlessly redundant. He could have just said 'algorithm' since it's almost always mathematical in some sense and it's always an idea.

> When I saw it I just thought it was needlessly redundant.

Isn't "needlessly" redundant there? :p

I find that a certain level of redundant language in a sentence or paragraph can allow me to sink different hooks for a reader and thus reduce the likelihood of having to repeat myself.

The hook-euphemism is similar in nature but different in application to Feynman's self-labelled "chaotic" approach to teaching

Redundancy is often times a feature. Certainly in natural language as it allows for seemless error correction if there is some word you didn't hear or some letter you can't see. Or in computer communications too, like with CRC or similar codes (mentioned in the article).

When referring to a comment written online though? I agree with your main point

Ask an avionics suite.

Did his grand theory of everything ever come to anything?

> And by comparing delay times from different satellites, the receiver can triangulate its position

Argh! It's not triangulating, it's trilaterating.

Good article, though.

Isn't that dynamic programming instead? Or more generally, the idea of time-memory tradeoff.

I wonder how that would compare to the Fourier transform?

RIP Solomon Golomb

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