Maps have a rule that incredibly frustrates me, so I'm gonna purposely avoid it. 𓅱
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0:00 - WORST Rule
0:30 - Innovator
1:07 - Starting Map
2:38 - Adjustments
3:26 - New Map
4:39 - Finding "Proof"
5:19 - YOUR Maps
5:59 - 3D MINECRAFT MAPS
6:34 - DETERMINATION
7:39 - Ŝ̬ᴜβŜ̬ᴋʀiβ𓅱
This guy trying to break the second most famous theorem in the entirety of mathematics, and I love it.
Just create math 2. It can't be that hard. He made a new alphabet, and the romans used letters. Just make all the numbers out of egypt bird and monke
Me, checking if this is an April fool's video... …it isn't.
me: "man this guy's dumb"
"second most famous math theorem" 2+2 left the chat
@@quneptune “second”
I have an idea: Simply don’t. Make the colors touch, be the true rebel that you are
exclaves work
I seen a map like that (globe, more precisely). Pakistan and China and Russia and Estonia and Lithuania and Ukraine were all colored yellow. It was the most cursed coloring ever.
@@Penguin4096-si9fz Please, I beg of you, just use commas for lists. It hurts.
Fix colors plz
Colours
love the fact that he looked up a formal proof, saw that it was a formal proof and elected to ignore it, 10/10 video, good luck in your lifes mission, Im sure it will break and/or fix maths
imo, all formal proofs should have informal proofs as summaries so that more people can understand it
@@9nikolai that's what the "An Elegant Proof?" article is, informal just means it explains in English and not using formal logic.
I did it!
Well I proved it wrong using ms paint I made five circles and made it so every circle was touching every other circle and it worked
Theres formal proof that disproves the four color theorem
The 4 colors theorem will never stop bothering me to death
Same, the only reason I know why is that it's a constraint
You can disprove it easily, just make sure the ocean HAS to be blue. It doesn't matter if the ocean is on opposite corners, it has to be blue.
@@xXJ4FARGAMERXx that actually still doesn't work
@@xXJ4FARGAMERXx All of the oceans will be the same area, no borders between oceans.
so it will never be disporvin
The 4 color theorem only applies to maps on a plane or sphere. If you draw the map on a torus (doughnut shape), you need seven colors.
That is why in the fantasy book I'm writing, among other reasons, the main planet is a torus. Hubworld, or The Hub, or something like that I'm still working on the name. Created by a wizard that was fed up with the xenophobia between the peoples of the 5 realms, they wanted to make a realm for every species to live together and as a centralized hub to connect all the realms together, and got annoyed by a detractor that called their initial designs stupid and mentioned the four color theorem in his criticisms. This started a trend with powerful magic users creating their own realms, and the number of realms quickly increased from 5 to dozens of large open realms and many hundreds of smaller personal realms.
I don't understand how. Could you explain that more?
@@kianthornton2856 I can't, but Wikipedia mentions this in their article on the four-color theorem.
@@kianthornton2856 A torus can be thought of as a normal plane, but the left and right edges and top and bottom edges connect. That gives more room for regions to connect, which increases the number of colors you can force a map to have
As a math teacher, watching this man attempt the impossible so confidently is sending me.
idk much about this but cant you just make a circle with a square inside of it thats split into 4 quadrants, then you'll need 5 colors
@@vintage-radio If I understand your idea right, then you can color the square with only 2 colors, and use a 3rd color for the circle, you don't even need 4 let alone 5 RED | BLUE ------------------- BLUE | RED
@@vnXun oh right
*Exclaves have entered the chat*
Actually, you can use the exclaves more times, so a “five colour theorem” can’t exist.
If you give a country an exclave between two or three countries, you will need a 5th color. The 4 color theorum only stands to countries with consistent bobrders (no exclaves or enclaves)
Wouldn’t the exclave be the same color as the original country since it wouldn’t be touching it
@@al_rusty420 Yes, which is why you need a 5th color
@@al_rusty420 yep
What are exclaves and enclaves?
@@mozipuggamer Imagine an island that's owned by a country, but it's completely surrounded by another country.
The only thing the 4 color theorem fails in is exclaves(originally i said enclavs, but it was an autocorrect), then you need to use another color.
you can use 2 colors no matter how many there are
the 4 color theory still always works in enclaves as long as all regions are continuous
3d map is on a plane x plane y plane and z plane
@@eduardoxenofonte4004 exclaves make a country not continuous...
@@theshadowking3198 and?
If this man actually broke this theorem during a Twitch stream would be funny as hell
Well I did in about ten minutes
@@blockmanhatecommentguy6280The mathematics community would be very interested in seeing your work.
@@blockmanhatecommentguy6280 show the map
@@blockmanhatecommentguy6280 I doubt that, considering you would be world-famous if you did.
if you allow discontiguous regions (real maps do this for things like the US+Alaska) then the minimum number of colors is unbounded.
But then you're not following the theorem anymore...
The way he so casually just tried to disprove a mathematical theorem on stream is amazing to watch. Appreciate your creativity!
Hmm, I wondered if anything about non-Euclidean geometry could get past this, but apparently in graph theory it just doesnt matter.
Because you can stretch it back.
i mean may not be related but on a donut you need 7
My favourite part is when he talks about maps
Same
Timestamp?
You don't have to follow the rule. The fact is that you *can* colour every map in at most 4 colours *IF* the regions aren't disjoint. It's called "Four colour theorem". You can, however, use more than 4 colours if you wish. Or you may *have to* use than 4 colours if there are disjoint regions (which they can be irl). There's no """four colour rule""". Edit: I watched some more of the video, and uh... yeah. I already told you how to make it need at least 5 colours.
You could color a map in with as many colors as you want, but the point is that you don’t need to use more than four to make every country that touches a different color. He’s trying to find a map that can’t be colored in like that with just four colors
@@L_Aster Yeah, but my point is that he calls it a "rule", which is misleading.
@@floppy8568 it’s a mathematical rule
@@L_Aster there's a difference between a rule and a theorem. "A scientific principle and a rule are, as far as I can tell, the same thing as a law. A mathematical theorem is a statement that has been proven on the basis of previously established statements, such as other theorems-and generally accepted statements, such as axioms." -google when you look up "What is the difference between a theorem and a rule?"
I’m living for him trying to disprove random things
I personally find the 4 colour theorem super easy to prove geometrically in 3 steps. 3 colours around a 4th is the most you can do before coloured regions start becoming independent. You can't join two unconnected regions to make them dependent without splitting two other regions to make them independent. Independence means they can be the same colour. Simples🎉
That's the general rationale, but it doesn't prove it. Two regions being disconnected doesn't mean they can't influence each other, and showing that they don't influence each other enough is what took the proof so long.
@@GammaFn. yeah, I realised after thinking some more that I was thinking about concentric circles spilt into sections, and things can be more complicated than that.
So, there are a number of interesting ways that you can do this, although they are all accounted for by the theorem and specifically excluded. 1) The most obvious example is to just make a 5-slice pie. If we consider the corners to be touching, then we need five colors, although the theorem explicitly does not count corner connections. 2) If your map is allowed to be a fractal, then this is possible. I couldn't find an actual example, but the Newton-Raphson fractal seems like a good place to start. Though technically, if you zoom in on this fractal, the shapes _only_ ever touch at corners, so by the standard rules of the map theorem, you could just color the whole thing one color, since corners don't count. 3) The four color map theorem also doesn't work if you draw the map on a donut. On a normal one-hole donut, the number of colors increases to 7, and then adding more holes slowly increases the number of colors required from there. 4) For an example that might actually matter for real-life maps, the four color map theorem does not work if countries are allowed to have separated sections that are part of the same country, but not touching the rest of the country, and that we require the whole country to be one color. So, this is like how Alaska is part of the US, dispite not actually touching the rest of the US. If you have some countries like this, then you could need more than four colors for your map.
Oat: tries to disprove the four colour theorem Me: *laughs in geographical mathematics*
Exclaves and enclaves: *I AM 4 PARALLEL UNIVERSES AHEAD OF YOU*
What we need is a map with 5 shapes that all touch every other shape on the map
That's the neat thing. You can't.
@@tokatstorm9270 are you sure about that?
@@kirbos2529 Well, not a flat one at least. Donuts, I believe, could solve this problem, as they can for most problems.
@@tokatstorm9270 I made it on a flat one. q u a d r I c e. i just cant figure out how to send the link.
@@kirbos2529 That's a shame. It'd be pretty sick. What's a quadrice?
tried it myself, so I tried connecting 5 dots where all dots touch the other dots and no lines intersect, but that doesn't seem possible since there will seemingly always be something stuck inside that can't reach the outside
4:28 literally how we just proved the 4 colour problem 😂
I like how he says "I am not going to read all that" when he finds formal real proof. He is just ignorant and determined.
When Oat pulls out Minecraft, you know it’s series.
At 7:00, look at the hexagon. If you extend the area of the right purple sligjtly so it touches the other purple, does that not require one purple to become a 5th color? You would also need to push back the purple a bit to make the blue touch the red and same at the top for the blue to touch the red, but otherwise, what stops it? Edit: i juat realized, to make the blue touch the yellow, you either need to disconnect the purples or cut off a purple from the red, F to my idea.
On the first one you could swap the middle circle color
You need to make a rose-like shape. You start with a circle and layer it like a rose but makes sure that the next layer is connecting to enough of the previous layers
it is impossible to make 5 shapes all in contact with each other
@@jaspervandijk1328 it would need some weird borders
@@Geckoreo no, it is just impossible
I think that guy was telling you to make a hexagonal map rather than just a section. But if he wasn’t, then I’ll suggest that…
this whole theorem goes into fire when you show them exclaves (landmasses separated from the main landmass)
Make a video revamping checkers please, I rewatched your chess 2 video a while back and think checkers deserves to also be revamped
But technically, a circle with pizza slices like you drew would immediately prove it wrong, because these lines are borders which can be thought of as extremely thin. Therefore, the corners are all touching and there are as many colors needed as there are slices.
It has to have a shared boundary in order to be considered adjacent- in other words, touching corners don't count. So with a pizza like shape, you could just color it with two alternate colors- three if it has an odd number of slices.
@@TraitorousHomeworlder that is sad. And sounds like a stupid rule qwq (nothing against you!!! against the rule)
Hm, other idea. What do we do with countries that have multiple spaces. Do they have to be colored the same color? Cause with that rule, we could easily trick, right? (For example USA and Alaska have to be the same color or something like that)
@@kaiiimee The theorem specifies that it must be a plane divided into contiguous regions, so it's not quite the type of map you would expect. The word you're looking for is an exclave, which would require an unlimited number of colors for any possible map.
Bro I was trying for so long to prove this hypothesis about this game that if you skip the cutscene for an animation it will show the most amazing thing first but kept getting proven wrong so don’t try doing this for eternity, it’s not worth your life getting wasted on something
4 corners and a ring going over it all
Oats Rule 🔥 >>>> Original Rule 🤢 Oats will solve the mystery we’ve all been waiting to be solved! Disproving a theorem 😎
imagine if he disproves it, then he'll get the nobel prize
I love how we all know it’s impossible, but at the same time we’ve all tried it before
Me: laughs in exclaves
Funny thing is that there probably is a 4 color map theorum for 3-d spaces too! It's defiantly not 4 colors
Infinite colors
There already is kind of a solution. With a world map, the 4 color theorem doesn't work because of exclaves.
only because they need to be the same color as the country they belong to
@@jankkhvej434 exactly
technically they don’t have to be the same color, so no it stays true. But if you wanna be pretentious with it according to the wiki you need at most 7 colors.
@@ThePenguinMan most maps that respect themselves will put the same country in the same color. It will be quite confusing if Vancouver will be a different color from the rest of Canada, or Hokkaido will be a different color from Honshu
@@pigi1004 so ig the rule is more an abstract geometrical theorem and the map thing is kind of an analogy
I honestly believe that the only way to "Prove" the 5 color theorem, is to have a map with borders that are so thin and "undefined", that you cannot possibly have 2 colors be diagonal without it almost seeming like they may be the same area.
A computer checked every single one.
Oats: there's no proof Oats: *shown proof* Oats: I'm not reading that
Fun fact: the proof for the 4 colour theorem was the first proof that was partially developed with the use of a computer
Make a map to the subscribe button
Yeah
A square with curved stick attached! Needs 5 colors
Ahem. The theorem is stated to apply to only 2d maps. A donut requires 7 colors instead of 4. A cube needs 6.
This video will be the catalyst for future generations of dedicated researchers on this matter. And we WILL disprove the 4 color rule. I WAS HERE, I BELIEVED; AND SO SHOULD YOU.
I just did, check my channel
well just use a fuckton of exclaves like the state of Michigan (cant think of any other exclaves)
my guy oats jenkins five-color theorem was the ORIGINAL theorem for years until some random guys starting in the 1880s and proven by computers in the 1960s proved the four-color theorem so no, you are not the maker of this theorem, sorry
Five different countries sharing a corner
Oats ignoring every single demand for goblin zone lore we asked for.
Cough cough exclaves ma man
03:11 If you do this design, then put an X in the middle of the square, and change the colours of the X so that is coloured with all four colours, then keep the remainder of the circle to colour a different colour
a qualified mathematician who spent years studying math wrote a dozen page long proof that is unanimously agreed on by the community and your dumbass is here saying this crap
colors are allowed to touch diagonally so you wouldn't have to use 4 different colors on the x in the middle
@@Lillla57 or in other words, they are allowed to share a corner
As much as I want this rule to be disproved, once you do four shapes touching each other, one of them gets blocked off by the others.
I was in the live-stream and he mentioned me!!! It got cut-out from this video, unfortunately. But it’s okay! also I don’t know how we’ll disprove the 4-color map theorem, but it’ll be disproven eventually.
I found a way 🎉
my guy. they literally used a computer to check every map
Well, that's a computer who did it so thats cheating. Humans need to prove it themselves to show us how they cool are
@@viggosevenhant5595so you want a human to go through and do exactly what the computer already did, checking each of the over 1,000 cases?
I have an idea that might work make a make square with circle draw lines connecting all of them
Schrödingers map, make 4 shapes meet each other but draw it so bad you dont know if its a 4way touching or 1 diagonal touches, then you need 5 colours to make sure youre not wrong
The 4 colors instantly disproved by only using 3 who said you need 5
Actally it's pretty simple: Create 5 Shapes where each one touches every other one so the fifth needs to be a seperate color BOOM
It's impossible to do that
great idea, if you can show me a shape that does this ill give you a million dollars
woah, now show me how to do that
5 triangles connecting at the middle.
The intuitive statement of *the four color theorem* - "given any separation of a *plane* into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" *A plane* is a *two-dimensional* doubly ruled surface spanned by two linearly independent vectors.
Michigan is a state with 2 parts. theoretically, you could take 2 separate parts, make them the same, and make them touch the opposite side.
explanation on why you can't have a map that requires 5 colors to fully color is because in order to force a 5th color, you would need 5 regions that is connected to all of the other 4. No matter how hard you try, this is impossible
I figured out a solution: Exclaves apart of a country that isn't connected to the rest of the country
1. Make a rect 2.4 quadrants, misaligned so only one pair of opposites 3. Circle in middle 4.Join opposites outside shape
I'm a nerd that read the proof and they said "Any research on the inexistent minimal graph G should be not only very difficult and inefficient, but also too hard to understand."
A map that requires more than 5 colors is trivial to make when you make use of exclaves. Places like Kaliningrad, Russia but much more intentional and careful
Actually, you only need 2 colors. All you need to do is throw out the boarders drawn up by rich people and grid the earth in a checkerboard.
> "There's no proof" > Looks at proof > I'm not reading all that, therefore there's no proof
Actually the definition of touching is the real problem because if diagonals can touch then 4 map color theorem would be disproved
Here’s an idea, create a new country that only exists in the airspace with no actual land, thus forcing maps to be represented in 3 dimensions
What is your discord btw? I might have done it? I'm not sure but I can't figure out how to prove me wrong lol
its very simple to bypass really. picture a circle with 4 lines that connect up to a circle inside the circle now you have 5 things you need to colour in you can colour the 4 sections but the centre colour is the big problem because no matter which 4 you choose it will collide with a colour already there. it doesnt even need to be a circle just so long as its a shape with 4 outer palettes and 1 inner palette.
Nah. In your example, you don't need to use 4 different colors for the 4 outer areas. 2 Colors in an alternating pattern are enough; followed by a third color for the middle.
Hey Oats! You should make a weather 2. People are always complaining about it, so it seems like something that u should fix! Your welcome!
My day gets brighter when you up load
oats: says he will use 5 colours to make a map also oats: *USES 4 OF THE 5 FUFKIJG COLOURS*
Ty for including me in vid also, THIS WILL BE A MISSON TO PROVE THIS WRONG
What about drawing circles within circles and dividing them up into equal sections and with every ring you add one more section
maps dont have to make sense what if a country (A) has some territory inside another country (B) that isn't even touching the (A) country? they'll have to be the same color right? i don't want a headache so I wont try anything
two things, the discord link doesn't work and where do i sent you the solution?
i came up with a map that i’m pretty sure needs five colors. i tried the discord link but it was expired so i friend requested you
I have an idea if you make the four corners one with the circle in the middle, instead of just having the lines touch the ends make the bottom left corner stretch out across the perimeter until it reaches the top right corner, so the bottom left corner and the top right corner will have to be different colors so the middle circle will have to be a new color.
The top left corner and bottom right corner can be thw same color too. Your idea: 🟥🟥🟥🟥 🟥🟦🟦🟩🟩 🟥🟦⬜️⬜️🟩 🟥🟥⬜️⬜️🟨 🟥🟥🟥🟨🟨 Solution: 🟥🟥🟥🟥 🟥🟦🟦🟩🟩 🟥🟦🟨🟨🟩 🟥🟥🟨🟨🟦 🟥🟥🟥🟦🟦
I just (probably) found a solution: darw a square, and another square inside of it, then split the small square to 4 peices by matching the edges
corners can be the same color
Is it not possible to put a lot of v connection to touch 2 boxes. So that the V shape connections touch both boxes And So that there is literally 4 V touching 1 part of the box and the other box is touching. So that makes 5 connections. So the image looks like a handbag with 4 holders
I got it:first, draw a pentagon,then draw a circle,then attach five lines to the circle, then draw a square with eight lines (center then corner)but make one section (of the circle)which is touching the four sections of the square out of the eight
oh no he's trying to disprove a proven mathematical theorem *eats popcorn*
Easy; make an enclave of each country inside every other country. This forces the map to have 5 colors as one or more countries could be forced to have one of the 4 colors whilst also having an enclave in the other country on the map that is also forced to be that color.
bro is your parents when you win an argument
"Unless someone like you cares a whole awful lot, it's never going to get better. its not" -Dr Suess
If five countries meet at the same point then you need five colours
the same color can share a corner
Pentagram. Five identical sections all bordering each other at a center point. BOOM. 5 colors needed.
I think I did it, you know when there are small dots of country in other countries. You can use that same thing in this map. Make a outer circle very big and a dot in the middle. This is one country, so one color. Then split the rest as a pizza in three. Last but not least create a outer circle around the dot. You should have 5 countries and need 5 colors to complete it
i have a idea: draw a circel in a circel and make some lines from the circel to circel
Love the random faint Nintendo music in the background.
i cant join the discord it says that the invite is invalid or has expired. how i fix
Extra in Exile made in his video Exclaves: The good the bad and the ugly made an example where there have ti be five colours
"people can't prove that it's right. the only way to prove that it's right is to make every single conceivable map ever. you can't do that, nobody can do that" funfact: people did infact do that, using computers. thats one of the reasons why this proof is so popular, and was questioned when it first came out. nowadays however we have accepting computer based brute forcing as a valid method of proof.
I found the most great example of one make a rectangle with a circle at the canter cut a line to that circle and make something around the the rectangle devide the rectangle into 2 diffrent portions make sure they are going in the middle then do that same thing to the circle colour it in you will see that the big blob around everything touches all coulers so there is no way to colour everything with 4 colours
Make four countries that all border each other, and then make a country that touches all those four countries
This is just like the circle-in-middle version, you only need 2 colors for the quadrant and the third one can be the outside square.
You can have a 2D map that requires more than 4, but only if a country is non-consecutive(it split like it has an island or something).
Bro thanks for using pokemon gen 7 music i love it :)