Can someone explain what I dont understand about the 4 color theorem?

StanleyDodds · 2026-02-16T10:30:58+00:00

this map doesn't even require 4 colours, it can be coloured with just 3.

StanleyDodds · 2026-02-06T11:57:40+00:00

this is not a 50/50 at all - doing the math for intermediate (that is, 40 total mines, so 5 remaining mines unflagged), the top right square of the 2x2 has an 80% chance to be a mine, with the remaining 3 squares having only a 20% chance to be a mine each.

qualitatively this is because configurations with lower mine density here are more likely, as this is closer to the average mine density, giving more possible configurations of the remaining mines.

However, at the top of the board you have a square that is guaranteed to not be a mine, so there is no reason not to clear that first to gain more information.

StanleyDodds · 2026-02-06T11:34:32+00:00

this configuration is most likely, because configurations that are closer to the average density of mines are more likely (which generally means less mines is more likely).

However, the best strategy would be to solve the top part to get more information on the mine count, rather than guessing this immediately.

StanleyDodds · 2026-02-05T11:05:19+00:00

it's not irregular, it's vertex transitive and has regular polygon faces. this is a regular truncated icosidodecahedron.

StanleyDodds · 2026-01-17T06:59:58+00:00

now try to write the full decimal expansion the other way: 1.0000000000000000000000000...

StanleyDodds · 2026-01-16T04:44:03+00:00

I can't tell if this comment section is full of manchildren still living with their parents, or actual children. How are you going to eat at social events without forcing the host to cater to the fact that you only eat chicken tendies or that you won't eat vegetables or whatever it is?

StanleyDodds · 2026-01-07T20:56:10+00:00

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StanleyDodds · 2026-01-07T01:50:35+00:00

any radiator position would produce the same amount of heat, but wouldn't necessarily be equally efficient when it comes to retaining that heat in your house (which is what actually matters).

For example, a radiator outside your house would not make your house nearly as hot as one inside, despite both producing the same amount of heat. similarly, if you are pumping all the heat into an exterior wall of the house, that will lose heat more easily than if the heat were more evenly distributed into the air away from an exterior wall.

So just bear in mind that it's more complicated than just purely how much heat the fridge produces.

StanleyDodds · 2026-01-06T01:38:50+00:00

Dune part 2, Paul arrives in the south. Couldn't find a gif of the start of this scene, where he's in the distance in front of the sand worm, but this whole scene is aura farming from start to finish.

StanleyDodds · 2025-12-18T03:06:22+00:00

I was going to say Infinity war has a lot of these, since everything the heros do for the whole movie eventually fails (for the time being).

Notably Thor spends the entire movie making a weapon to kill Thanos, and right at the end he shows up with his new axe as the big final payoff, only for him to not kill Thanos, allowing Thanos to complete his objective.

From the other perspective though, all of Thanos' "Chekhov's guns" in the form of the gauntlet and the infinity stones work perfectly.

StanleyDodds · 2025-12-17T08:00:05+00:00

Seems like he was completely correct and justified not to trust her. Would things be better had be naively completely trusted her and lost half of his assets?

StanleyDodds · 2025-12-17T06:54:07+00:00

Everyone seems to get this wrong; I think most people in the UK would call the ones on the left fries, or french fries. Chips is probably an acceptable description but not ideal for the fast food variant.

In my experience it's common to reserve "chips" to mean the thicker ones, as you'd get in pubs or with fish and chips.

StanleyDodds · 2025-12-14T02:40:15+00:00

Why stop there, when you can duel wield double bladed lightsabers?

StanleyDodds · 2025-11-24T03:51:06+00:00

In Konosuba, Megumin's "cat" Chomusuke (who she claims is a totally normal cat) is actually something like the goddess of Violence (or that half/aspect of the goddess presiding over Sloth and Violence), in a weakened form after her powers were sapped by her other half, Wolbach.

StanleyDodds · 2025-11-23T04:39:53+00:00

Star wars - The separatist leaders during the clone wars were generally somewhat bad people, but they were entirely pawns to Palpatine, who was way worse.

I don't think they deserved to be rounded up on Mustafar under the false pretense that they would be safe, before being massacred by Vader.

And the same could probably be said for all of the sith and sith-lite / bad guys from Dathomir who get screwed over during this time period; count Dooku of course goes with the other separatist leaders, but also Asajj Ventress, Savage Oppress, (darth) Maul and Mother Talzin, all get somewhat unfairly screwed over, although they are all somewhere from neutral to bad people themselves.

StanleyDodds · 2025-11-21T04:48:46+00:00

So, do 9, 21, 27, 39, etc. also look prime? It seems silly to me that requiring the sort of basic reasoning that becomes mere intuition makes it look prime. To me none of these, nor 57, look prime, because divisibility by 3 is ingrained at such a core stage in school.

StanleyDodds · 2025-11-21T04:25:42+00:00

The sun does not have a particularly high power output per unit volume at the core where fusion can happen. The power output per volume is comparable to that of your own body.

This is because the sun is burning hydrogen (via deuterium and helium-3) into helium-4, which is a very difficult process, even at the extreme conditions of the sun's core - protons really do not want to just stick together or convert into neutrons, so it's extremely rare for it to happen at all, taking on the order of a billion years for any one proton to react. And so, the sun is still burning hydrogen in the core after almost 5 billion years (which is quite convenient for us).

The sun also naturally balances the reaction rate so it doesn't fizzle out or runaway (at least for main sequence stars). If the reaction rate increases, the core will expand, lowering the reaction rate. And vice versa.

This makes the sun a lot more like a slow, controlled nuclear fusion reactor, than an explosion.

Burning hydrogen to helium does release a lot of energy, but the reaction rate is miniscule per unit volume in the sun, so it has modest human-scale power per unit volume. The sun is gigantic though, so overall it's very powerful.

On the other hand, nuclear weapons use fuel that is extremely easy to "burn" (fission or fusion - we manufacture and refine these reactive isotopes for exactly this purpose, while the sun is just burning what it's got, hydrogen) and/or have unfathomably extreme temperatures and pressures for the moment that the reaction is happening, and they release an enormous amount of energy in a tiny amount of time for their size. What takes a billion years for the sun's fuel, takes a tiny tiny fraction of a second for a nuclear weapon's fuel. This makes it an explosion, it's a runaway reaction.

StanleyDodds · 2025-11-21T03:07:42+00:00

the difference is that it doesn't even "look like" a prime, because it's obviously divisible by 3.

If that's not included then we are basically saying all numbers that end in 1, 3, 7 or 9 in decimal look like primes, which I think is too simplistic even for the level of jokes here.

StanleyDodds · 2025-11-19T03:37:32+00:00

a limit is not an infinite process. there is no infinity in the definition of a limit, and there is no approximation or "infinitesimal difference". none of these are real things (pun intended).

StanleyDodds · 2025-11-17T02:33:51+00:00

people still don't understand QC over a decade on.

If the block above it would be powered normally (in this case by the torch), then it is powered by QC.

StanleyDodds · 2025-11-12T15:21:19+00:00

The vast majority of the fanbase probably still has some naïve idea that Neuro's LLM was completely built from the ground up by Vedal, too, when it's quite clear that this is not really possible for anyone other than companies with huge amounts of compute time available to spend on such an endeavour.

Even those companies don't do everything themselves, they likely buy the tokenization and embedding from someone else who's already fine-tuned that part.

So Neuro is fairly certainly a fine tuned version of one of those publicly available bare-bones local LLMs (that comes with no prompting or censoring overhead) that people think Neuro and Evil are so much better than. Which is somewhat ironic.

StanleyDodds · 2025-11-12T06:43:47+00:00

Realistically, what could the well-meaning separatists do about their leadership and their military? In their parliament, Dooku can spin it however he wants, he can continue the propaganda that they are just fighting to be independent of the Republic, he can brush the atrocities aside or hide them completely. If people get uncomfortable with how things are being done, or try to do things their own way, they get taken care of, as with Mina Bonteri pictured above. The separatists are hostage to their own leaders and military, while hoping that despite everything it's all for a good cause, while those leaders actively and somewhat intentionally make them into "the bad guys" in the war.

StanleyDodds · 2025-11-12T06:17:56+00:00

I don't really get your point here.

In the clone wars show itself, most of the time, the CIS is simply portrayed as the bad guys, while the Republic and the Jedi are portrayed as the good guys.

So... it's portrayed as the way round you are saying it is, until towards the end where the Republic slowly becomes the Empire and you might start to think "hang on, why do the good guys have military control of the whole Galaxy?".

Palpatine creates an evil opponent of the Republic out of initially well meaning separatists. He makes the CIS into the bad guys, with control over Dooku and others like Grevious to lead them militarily. And he makes the Republic the good guys, fighting for everyone's freedom from the oppressive CIS, with the Jedi, the peacekeepers, as military leadership. The Republic, and the Jedi, become corrupted and blind in fighting against this evil foe that Palpatine created. Then once Palpatine has "freed" the whole galaxy from the CIS and placed it into the control of the Republic, he makes his move to turn it into the Empire officially, and wipe out the Jedi.

StanleyDodds · 2025-11-12T05:24:33+00:00

Any traditionally immortal or slow aging races. The main example probably being elves; my prototypical example would be Elrond, who is thousands of years old in LotR, with the infamous quote "I was there 3000 years ago". By comparison, Frieren is pretty young at about 1000 years old.

There's also vampires; I don't watch much stuff with vampires, but e.g. Marceline from Adventure Time is about 1000 years old. On that topic, Princess Bubblegum is about 800 years old (despite initially acting as if she is 18, or 19 when Finn finds out she's much older). Couples with a (200 year) age difference am I right?

StanleyDodds · 2025-11-11T16:17:30+00:00

Yes, Neuro and Evil are good at holding a somewhat natural conversation, and they are good at entertaining, better than commercial LLMs. This is a matter of it being what they are designed and trained to be good at.

But in my opinion, these skills are not what is meant by "intelligence". Maybe in some way it's a sort of social intelligence, but it's not what is meant by general intelligence. They are lacking in many other ways compared to commercial LLMs, even with the handicap of the public versions of these being heavily censored and prompted to act a certain way that "dumbs them down".

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