The Mandelbrot Monk (1999) | Hacker News Reader

The Mandelbrot Monk (1999)

users.math.yale.edu

157 pointsrfreytag56 comments

This is a fun little piece, but worth noting:

It is absolutely a work of fiction (“hoax”, as Wikipedia puts it [1]). I was fooled the first time I read it…but the date at the bottom gives it away.

[1] https://en.wikipedia.org/wiki/Udo_of_Aachen

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.

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.

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

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.

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.

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

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.

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!

This kind of thing, whilst fun, is kinda dangerous. I'm not so sure what to make of it. I sniffed it out quickly because I have extensive experience with maths. Many people don't, because unlike me most people have social lives.

My dad still believes that the Sun makes the "Om" sound after seeing a post by some kind of Hindu nationalist on Twitter. I have told him many times, in the kindest way I can, that it's a load of rubbish. He still doesn't really believe me, mostly because the idea of the Sun making that sound is a pleasant idea that agrees with his world view.

Send this article to a hundred people and a lowball of seventy will take it as fact. Of that seventy, there will be a fraction who will believe it - or rather, internalise the notion of it - even despite being told that it is false.

In all fairness it's also very likely that I'm a just a nasty killjoy.

> Send this article to a hundred people and a lowball of seventy will take it as fact. Of that seventy, there will be a fraction who will believe it - or rather, internalise the notion of it - even despite being told that it is false.

So what's your solution? Living in a world with no jokes, no satire, no hyperbole, no poetry, no simile? A world where Jonathan Swift's "A Modest Proposal" would've never been published because some people might take it a bit too seriously? I posit that this is the real danger.

I think some people might actually be taking A Modest Proposal a bit too seriously. ;)

"Send this article to a hundred people and a lowball of seventy will take it as fact. Of that seventy, there will be a fraction who will believe it - or rather, internalise the notion of it - even despite being told that it is false."

And there will be at least some people, who got a valuable lesson, that not everything which looks like a proper citation, is real.

But btw. most people will not read the whole thing alltogether and of those who do, because they know the Mandelbrot set - they will likely figure it out, too.

Is believing the sun makes an "On" sound, or people believing this hoax is true, harmful (or, how harmful, and How/why)?

I'm not sure how many of those 70 will have ever heard of this mandlebrot equation.

Jan Hendrik Schön would agree with you.

Hindsight is 20/20, of course.

This is a good fun - but there is a 13th century painting that does make you wonder a bit:

https://home.ubalt.edu/NTYGFIT/ai_03_illuminating_love/ai_03...

I thought this is a hoax as well but https://en.wikipedia.org/wiki/Bible_moralis%C3%A9e

Good one, thanks!

I am sorry to have posted this. I was duped by the source seeming credible (https://users.math.yale.edu/public_html/People/frame/Fractal...).

I was so pleased to have found a "gem" at the bottom of a 'serious' page on my intended topic of 'Julia' and 'Mandelbrot' sets that it got past my filter.

I am going to be thinking on this for a while as I look UP from the ground at what used to be my high horse.

> I am sorry to have posted this. I was duped by the source seeming credible

The source is credible; it's a mathematical April Fools joke. Kind of how the HTTP 418 "I'm a teapot" status code is a nerdy computer science April Fools joke.

No harm, no foul.

Ack, had me fooled. I wanted it to be true!

But I don't agree with the comments suggesting that we need to be more skeptical - and that not as many people should have been fooled if they were.

If an article/expert goes to great lengths to fool you, bringing in-depth falsehoods and an impressive platform, at some point you aren't the one to blame.

With the Basilisk collection (https://suricrasia.online/unfiction/basilisk/), this is the second time this month that I get fooled by a hoax! My disappointment is big every time

my disappointment is immeasurable and my day is ruined. can anyone point me to an actual monk who was 700 years ahead of their time please?

Thomas Bayes?

...but you might have wait another 400 years to be sure

Roger Bacon, although probably 300 rather than 700.

Bede is another contender.

Though unnamed and I won't provide links, the monks that doodled pictures of things like nuns picking penises off a tree in the margins of books might qualify. It's called marginalia if you're interested.

Not seven centuries ahead, but who comes to my mind is:

https://en.wikipedia.org/wiki/Athanasius_Kircher (1602–1680)

> One of the first people to observe microbes through a microscope, Kircher was ahead of his time in proposing that the plague was caused by an infectious microorganism and in suggesting effective measures to prevent the spread of the disease.

> wearing facemasks to prevent the inhalation of germs

so about three hundred years ahead of the WHO, then...

Albertus Magnus, perhaps.

https://en.wikipedia.org/wiki/Albertus_Magnus

This is really a great lesson at always taking things in skeptically. I saw yale.edu and the great detail in multiple sections and the block of citations at the bottom that I let my guard down.

>> (I say 'lucky' because Buffon's Method converges extremely badly, and it's well possible that Udo achieved this good result by choosing his stopping point judiciously - perhaps influenced by the 3.1418 quoted by his contemporary, Leonard of Pisa, otherwise known as Fibonacci).

Udo was truly well ahead of his time [1]. Martingale theory wasn't discovered until the 20th century, but Udo finds a way to subtly apply martingales in a way that many of us would struggle to understand even today.

[1] https://en.wikipedia.org/wiki/Optional_stopping_theorem

The article is an April fools joke. I let my guard down and it got me as well until I looked at some of the other comments.

My comment is a joke as well. If you frame Buffon's needle game as a Martingale, playing until you get an answer that agrees with Fibonacci's previous work does not meet the preconditions for the optional stopping theorem. Intuitively, it's equivalent to starting with $1 and making fair bets with infinite credit until you have $2. Sure, it's possible, but it's not a "fair" betting game.

I just thought the quote from the article was unbelievably good -- "choosing his stopping point judiciously" is such a well-done understatement.

Ooh, man I’m really not on the top of my game today. Thank you for the explanation!

I was about to share this with my peers and end the day with a happy discovery but you had to ruin it, didn't ya?

Say what you will about this hoax but these made-up lyrics to O Fortuna are pure math/philosophy ecstasy. From the article:

Schipke continues: "What was interesting at this point was that we looked back at the words of O Fortuna, and suddenly they fell into place. Verse two - Luck / like the moon / changeable in state / We are cast down / like straws upon a ploughed field / Our fates measuring / the eternal circle - is very clearly an allusion to the Buffon's Needle method." [*8]

I was completely taken in; and astonished. It's a tale well-told.

> The book The Broken Dice by Ivar Ekeland gives an extended account of how the method was invented by a Franciscan friar known only as Brother Edvin sometime between 1240 and 1250.[3] Supposedly, the manuscript is now lost, but Jorge Luis Borges sent Ekeland a copy that he made at the Vatican Library.

https://en.m.wikipedia.org/wiki/Middle-square_method

Heart of Jesus with the cross. Seems to my eyes to be similar in shape.

https://www.wallpaperflare.com/collage-cover-art-cross-heart...

It is the same shape! Namely, the Cardioid[1]. It's simply a happy coincidence that the human heart and Mandelbrot set have the same basic geometric shape, and probably not a Dan Brown-ian conspiracy :)

[1] https://en.wikipedia.org/wiki/Cardioid

Short previous thread: https://news.ycombinator.com/item?id=14614196

This is great stuff. Udo of Aachen being the first discoverer of the Mandelbrot set brings to mind other famous clergymen:

Alfred Young, discoverer of Young's Tableux and Young diagrams, which are widely used in mathematical physics and representation theory, was a parish priest in Birdbrook, Essex

https://mathshistory.st-andrews.ac.uk/Biographies/Young_Alfr...

Johann Werner (1468-1822), an ordained priest in Nuremberg, discovered a way to determine your position from sightings of the moon, discovered trigonometric identities and worked on conic sections, and was a pioneer of modern meteorology.

https://mathshistory.st-andrews.ac.uk/Biographies/Werner/

Marin Mersenne (1588-1648), of Mersenne Prime fame, was a French monk, a member of the The Order of the Minims "having been set up by St Francis of Paula in 1436, was thriving at this time. They believed they were the least (minimi) of all the religions on earth, and devoted themselves to prayer, study, and scholarship. They wore a habit made of coarse black wool with broad sleeves and girded by a thin black cord (as seen in the portraits of Mersenne). "

https://mathshistory.st-andrews.ac.uk/Biographies/Mersenne/

Magnus Joseph Weininger (1919-2017) was a mathematician, ordained priest, and Benedictine monk who discovered constriuctions for the remaining set of uniform polyhedra, and authored over 25 books on mathematical topics related to convex geometry.

Edwin Abbot (1938-1926) was an ordained priest, schoolmaster, and author who wrote many books including the pop-math books such as "Flatland" as well as "Shakespearean Grammar", "How to write clearly", and exegetical texts on the works of Paul and John in the New Testament, and Koine Greek grammars.

John Polkinghome (1930-2021) as an anglican priest, mathematical physicist, and theologian who worked on high energy physics. A student of Murray Gell-Mann at Caltech, he authored many research papers on Scattering matrices, renormalization, pertubation theory, spinors, and other topics in quantum mechanics, with fellowships at SLAC, Cern, Berkeley and Princeton. He was elected to the Royal Society and received a knighthood.

https://mathshistory.st-andrews.ac.uk/Biographies/Polkinghor...

Francesco Maria Grimaldi (1618-1663) was a Jesuit priest who worked in mathematics, astronomy, mechanics, and optics. His most famous discovery was the diffraction of light, by creating a prototype of Young's double slit experiment.

https://mathshistory.st-andrews.ac.uk/Biographies/Grimaldi/

Are all of these hoaxes as Udo of Aachen was? Or are you mixing real discoveries with the hoax? I’ve always despised April Fools jokes of this sort because they tend to outlive the joke.

Many are real.

April 1st 1999 in the footer had me thinking.

Another thing that gives it away is that Udo's fellow monk is Thelonius.

This is priceless, thank you!

Reply on news.ycombinator.com