Comment by IIAOPSW | Hacker News Reader

Comment by IIAOPSW | Hacker News Reader

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Mildly off topic, but I sometimes re-imagine the myth of the Minotaur as a parable about how the only bars which can't be bent by brute force are the ones made of computational hardness.

Why did they build a maze for the Minotaur with a possible escape route rather than just an ordinary prison? Why leave the possibility of escape open?

Well see, the Minotaur was arbitrarily strong. No material could build a wall strong enough that he couldn't bash through nor a door that he couldn't break down. But, he wouldn't try and break down anything if there was obviously a path right there he could use to go around it normally. By putting him in a maze, he will always keep trying the next path thinking it might be the exit, never attempting to break any wall. The puzzle is harder than any material they could have used to build a prison, as it cannot be bent by the Minotaurs brute force.

Computation (eg cryptography) can be "unbreakable" in a way that bank vaults and deposit boxes can't.

>Why did they build a maze for the Minotaur with a possible escape route rather than just an ordinary prison? Why leave the possibility of escape open?

Because it was not a maze, the Minotaur lived in the center of a labyrinth. A labyrinth is a continuous path that leads to the center. The objective was to send people into it so they would end up in the Minotaur's lair and be devoured. The reason the monster stayed was that he had everything he needed there, especially food.

That's a really interesting distinction between the words, but sources from Wikipedia indicate that the minotaur was trapped in a maze:

> Although early Cretan coins occasionally exhibit branching (multicursal) patterns, the single-path (unicursal) seven-course "Classical" design without branching or dead ends became associated with the Labyrinth on coins as early as 430 BC, and similar non-branching patterns became widely used as visual representations of the Labyrinth – even though both logic and literary descriptions make it clear that the Minotaur was trapped in a complex branching maze.

Surely, if it wasn't a maze, then there would have been no need for Ariadne to have given Theseus a ball of thread to find the way back out.

The ancient textual and pictorial tradition are in contradiction to each other here, which probably cannot be resolved. Ariadne's thread suggests a branching labyrinth, but in ancient pictures we actually only find unicursal labyrinths.

For the textual tradition: https://www.theoi.com/Ther/Minotauros.html

Some images of Roman labyrinths: https://www.labyrinthos.net/photopage02.html

Maybe they just found it hard to draw a branching labyrinth? It’s easy for us with Wikipedia and all, but if you’d potentially never seen a branching labyrinth then a non-branching labyrinth is a lot easier to draw.

It’s especially hard for modern people to conceive of a world before the printing press where information wasn’t easy accessible.

The challenge may have also been artistic. I don’t know if those artists would have been up for a branching labyrinth. I have seen how medievals drew cats and they do not look right.

TIL labyrinth and maze aren't the same thing! I always thought they were synonyms.

I grew up in Croatia, and there the word for both maze and labyrinth is "labirint"

They overlap in meaning to the extent that I would use either interpretation for either word. For instance in England there are chalk figures called miz-mazes (https://en.wikipedia.org/wiki/Mizmaze) which are non-branching.

A forest isn't a maze, but if it's my first time going into an unknown forest, you bet your ass I would take a compass with me.

If I lived in it for 20+ years, I probably wouldn't.

Ok, but surely if there are no branches, but only a single path, there would be no way to get lost? The only way would be if you forgot which direction you were facing?

You could have side-paths that quickly go nowhere, but without any hints as to which ones do or don't. That way, backtracking towards the main path is pretty trivial and leads to a constant forward progression.

A labyrinth by definition has no side-paths, not even ones that quickly go nowhere.

I like mazes and I saw that distinction be made before, but I am not sure how universally accepted it is? Other than English how many languages even have two different words? I spent some time now on Google Translate and the only language I find (not that I tried ALL) is Finnish. Modern Greek for instance uses the same word (assuming Google is correct), so did people on Crete, whatever their language was, even have two different words?

This is an edge case which google translate is going to be bad at. You can at a minimum add dutch to your dataset: doolhof vs labyrint.

But Google Translate is correct about Dutch. It was just not one of the languages I tried before. I do not think it is a particularly difficult case for translation.

The reason I checked was in my native Swedish there is only one word (labyrint).

Was it really always two different things even in English? I looked the words up in Gutenberg's public domain Webster's Unabridged Dictionary (1890?) a labyrinth there was "an ornamental maze" ... "Labyrinth, originally; the name of an edifice or excavation, carries the idea of design, and construction in a permanent form, while maze is used of anything confused or confusing, whether fixed or shifting. We speak of the labyrinth of the ear, or of the mind, and of a labyrinth of difficulties; but of the mazes of the dance, the mazes of political intrigue, or of the mind being in a maze." And from the definition of maze: "A confusing and baffling network, as of paths or passages; an intricacy; a labyrinth". Did the meaning drift a bit since then or was it only in mathematics that the words began to be used in the way that they are often used now for branching vs non-branching mazes?

https://www.gutenberg.org/ebooks/29765

Literally the first definition of a labyrinth is that it is a synonym for maze.

Your definition is wrong.

In common use the terms are interchangeable. Differentiating between them is essentially jargon, but it's not wrong. Inflamable famously means something is both flammable and not flammable depending on who you ask. Words not only have multiple definitions, they sometimes have multiple incompatible definitions.

that immedately makes it a maze, not a labyrinth.

Are you suggesting that the labyrinth in Minos was more open like a forest?

Interesting how the choice of design of ancient coins will, many years later, lead to comments like this.

I don't think you're right. I won't pretend to be an expert on any of this, but as a speaker of modern Greek I can confidently say that λαβύρινθος (labyrinth) is the only word in Greek to describe both your definition of a labyrinth and a maze.

For example, this Wikipedia article[1] on labyrinth in Greek, which has the picture [2] of a maze and calls it a labyrinth.

[1] https://el.m.wikipedia.org/wiki/%CE%9B%CE%B1%CE%B2%CF%8D%CF%...

[2] https://commons.m.wikimedia.org/wiki/File:NAMA_Tablette_1287...

It’s kind of hard to describe why we feel this is so irrefutable, but one of my favorite thought exercises is doing exactly that.

My algorithms prof once took us on a fun journey describing the median-of-medians variation of the SELECT algorithm, and had us play around with different partition sizes to see its effect on asymptotic running time. Turns out if you choose any other value than 5, you get superlinear running time.

This is probably the most random display of fatuousness I’ve encountered from mathematics. There should be absolutely no reason the number 5 - not 3, not 4 - has anything to do with recursively selecting a median, and yet here we are.

It makes me wonder. Maybe there are computational rules similar to gravity or conservation of energy, but similar to physical machines, there seem to be computational ones that can be built defy them.

You're asking one of the questions that was an early skepticism of quantum computing. Namely, until very recently there was a line of thought that while you could draw machines on paper which break certain computational limits by leveraging quantum mechanics (or other physics), just like with perpetual motion machines before them, all of these designs would be doomed to fail because they would violate a fundamental principle to how the universe works. In other, the line of thought was exactly like you said, that computational rules were similar to gravity or energy conservation and thus couldn't really be broken.

Presently this line of thought is dead because quantum computers have demonstrated doing something that can't be done classically. So we know there's no theoretical reason not to have a quantum computer. But the thought that the laws of the universe might be underpinned by computation is still very much alive. Its just all qubits at the bottom rather than classical bits.

There's a cliche in the field. "Information is physical". Roughly it means, information only exists encoded on some form of physical medium, and all physical systems are reducible to the information encoded as the state. Physical things are information, information is a physical thing. Information is physical.

It ain't cryptography, though, it's just a a shortest path algorithm on a graph, which has wide and obvious applications for trade networks. Most computational problems we consider now were outside the scope of the easily expressible terms at hand.

This is a great observation! I just hesitate to romanticize the applicability of modern concepts to classical situations.

I just hesitate to romanticize the applicability of modern concepts to classical situations.

Check this out:

https://en.wikipedia.org/wiki/Ariadne%27s_thread_(logic)

This is really cool! I just don't think this implies a sense of general computation as opposed to puzzle-solving. I think there's a crucial difference here. There's just a lot of computational understanding that only comes up when you introduce combinatorics generally out of reach of casual classical conversation.

I know it's a myth, but what would stop the Minotaur from just going full Juggernaut and smashing through all the walls should the Minotaur realize the paths are too difficult to traverse?

>what would stop the Minotaur from just going full Juggernaut and smashing through all the walls

Imposter Syndrome

Only the mythical head-canon of the Minotaur’s psychology. Whereas I tended to believe that the Minotaur had everything it wanted to a reasonable degree of comfort as long as it continued to be fed.

Also the Minotaur just might not be strong enough, depending on what the labyrinth is made of, given that its purpose in the myth is to keep the Minotaur trapped. He's half man, half bull, which makes him a lot stronger than a human but AFAIK bulls can't just bust through stone walls.

He never has that realization, for he is arbitrarily strong not particularly bright.

But in such case the labyrinth wouldn't need an actual exit, only the Minotaur would have to think there is one.

Perhaps the Minotaur has a good sense of smell and the exit is needed to supply fresh air in order to encourage him to keep searching for an exit.

I think with a good sense of smell he would find the exit too easily, but you're on to something here: perhaps the Minotaur would suspect there's no entrance had there been no occasional human entering the labyrinth from time to time!

I think with a good sense of smell he would find the exit too easily

I thought about this as well, after my first remark. I think this issue could be solved by building a secondary labyrinth of ventilation ducts to channel the fresh air into the dead ends, in a way that entices the Minotaur in very confusing ways. The ducts could even have baffles that open and close, just like real ventilation systems in houses with zone-control airflow.

The ventilation ducts could also work to confuse and terrify any humans who were sent into the labyrinth. They’d carry sounds allowing the human to hear the heavy breathing and bellowing of the Minotaur in ways that make it sound like he’s always just around the corner!

If there is no exit there is no entry to send in prisoners.

;)

Why doesn't Sisyphos simply stop pushing the stone?

Hades has total control over the (physical) rules of the underworld[1]. Hades can make the stone roll back for arbitrary reasons. But keeping hope alive in Sisyphus is the harder problem. Hades can essentially force Sisyphus to keep trying by making it arbitrarily painful to stop trying, but then hope is no longer his motivation. Hades could reset Sisyphus' memory such that hope remains, but then this loses the profundity of an eternal punishment.

The more interesting case is that Sisyphus can contemplate the nature of the system, and reason toward an out that involved undermining Hades power over the Underworld. If he could pause and do experiments, discover the limits of the enchantment, and work around them, that would be ideal. However such an option would also be an excellent way for Hades to extend and deepen the severity of the punishment. A god's arbitrary power is arbitrarily powerful, after all.

1 - https://en.wikipedia.org/wiki/Sisyphus

Because he was condemned to do it.

Perhaps what all those Greek epics taught me, is that once someone condemns you to a destiny, then that’s it. No other destiny can open up.

What, and do nothing for eternity instead?

Because he was promised that once he gets it to the top, he'll be free. So, he keeps pushing, hoping that this time he'll succeed.

Follow the rule principal.

You'll never achieve what you believe to be impossible

Scorpion and frog

This might be an allegory for a mind looking for an exit from the maze of increasingly complex thoughts, and eventually falling into the hands of madness.

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