TBH this post should probably be taken down, or at least explicitly stated as an April Fools joke in the title. I almost didn't come to the comments section, and I didn't read all the way to the bottom date. I definitely would have taken this as fact.

Sounds like you learned a valuable lesson about believing things you read on the internet today :)

Taking it down means others won't be able to learn this lesson.

I agree that it's important to learn these lessons, but if recent history has taught us anything it's that reach and amplification will drown out most voices of reason.

I think Vimes might have had an aphorism about this...

EDIT: aphorism, not proverb

True, but at the same time, it is difficult to overlook the weight of Yale, the fact that this was published there, had I not found it so intriguing that I wanted to see what others were saying about it I would not have fact checked it.

"A lie can travel around the world and back again while the truth is lacing up its boots.”—Mark Twain

This is a glorious example of that.

Sure, it is generally wise to keep your guard up when reading things on the internet (or any source). That's fair enough. But at the same time, I don't think it's unreasonable to expect HN posts to adhere to a higher standard. IMO HN is not the appropriate forum for pseudo-intellectual gotchas.

This a very well known April Fools joke (especially in academia). Maybe the date should be added, but taking it down is a bit much.

My skeptic-radar was pinging at a rate that it sounded like a continuous tone.

While I enthusiastically retweeted it with a little nostrum on how funny people's interests are. Then read the comments, and then deleted the tweet.

It definitely needs the title to be flagged. It's a time waster unless you know it's a hoax and still want to read it.

I was extremely skeptical from the start, simply because it's fairly impossible to stumble on the Mandelbrot set by just messing about, it's a result of iterating a fairly arbitrary function on complex numbers and can't reasonably be generated by hand.

You don't need the full theory of complex numbers. Start with a zero vector, then iterate doubling the angle, squaring the magnitude, and translating by the vector you're evaluating. It's not totally inconceivable that somebody could have come up with it by just messing around geometrically.

But yes, good instincts.

Wow, thanks! Never heard the geometric explanation and it, as usual, is way more intuitive.

Consider this formulation of complex numbers:

Unit is 2x2 identity matrix.

imaginary unit is the matrix

    -1 0
     0 1

It is easy to check that imaginary unit squared is -1. And addition and multiplication is just matrices.

It then quickly becomes apparent that all possible matrices you generate _are_ the rotation and scaling matrices. Instead of drawing a connection between rotation and complex numbers, they all of a sudden are the same thing.

surely it should be:

    0 -1
    1  0

instead?

Wholly correct, sadly I cannot edit anymore :(

The photo definitely looks photoshopped, but it’s just believable enough to warrant reading the comments

Well, that certainly explains why he quotes the lyrics of O Fortuna incorrectly! I was really scratching my head when I got to that part.. and then came here to see if I was crazy. Guess I wasn't!