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0 pointsrssoconnor1y ago0 comments

I do think the why that the Four Colour Theorem is true is captured my statement. The reason why it is true is because there exists some finite unavoidable and reducible set of configurations.

I'm fairly sure that people are only getting hung up on the size of this finite set, for no good reason. I suspect that if the size of this finite set were 2, instead of 633, and you could draw these unavoidable configuration on the chalk board, and easily illustrate that both of them are reducible, everyone would be saying "ah yes, the four colour theorem, such an elegant proof!"

Yet, whether the finite set were of size 2 or size 633, the fundamental insight would be identical: there exists some finite unavoidable and reducible set of configurations.

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roenxi1y ago

> I'm fairly sure that people are only getting hung up on the size of this finite set, for no good reason.

I think that is exactly correct, except for the "no good reason" part. There aren't many (any?) practical situations where the 4-colour theory's provability matters. So the major reason for studying it is coming up with a pattern that can be used in future work.

Having a pattern with a small set (single digit numbers) means that it can be stored in the human brain. 633 objects can't be. That limits the proof.

lacker1y ago

To me, the four-color theorem is a very interesting proof of concept, perhaps the most interesting mathematical proof of the past 50 years. Perhaps the "pattern that can be used in future work" is the idea of having computers enumerate a large number of cases, which they then solve in individually straightforward ways.

But, I can understand if pure mathematicians don't feel this way. This might be only really an intriguing and beautiful concept to someone who is interested in scaling up algorithms and AI.

username3322111y ago

> So the major reason for studying it is coming up with a pattern that can be used in future work.

Surely, reducing the infinite way in which polygons can be placed on a plane to a finite set, no matter how large, must involve some pattern useful for future work?

dartos1y ago

But why stop at “some” pattern when you can find the most general pattern.

myst1y ago

The nature does not care whether it fits in our brains.

dartos1y ago

That’s why we use math to describe nature in a way that fits in our brains.

That’s the whole point of math.

gsf_emergency_21y ago

If it were size 2, we could more easily make sure that the answer is definitely mind-blowing.

Have programmers given up on wanting their mind blown by unbelievable simplicity?

seanhunter1y ago

> The reason why it is true is because there exists some finite unavoidable and reducible set of configurations.

OK but respectfully that's just restating the problem in an alternative form. We don't get any insight from it. Why does there exist this limit? What is it about this problem that makes this particular structure happen?

lacker1y ago

Perhaps the key insight is that there is no concise explanation that underlies this particular structure. Many mathematical statements are true for no concise reason. If you want to discover if these things are true or not, perhaps you need a computer-assisted search, and that's the intellectual lesson to be drawn here.

godelski1y ago

I really doubt this. I mean mathematicians spent decades trying to answer if the number 2 exists. People spend a lot of time on what seems fairly mundane and frankly, the results are quite beneficial. What's incredible or mind blowing is really just about your perspective, it is really just about your choice to wonder more. https://www.youtube.com/shorts/lcQAWEqPmeg

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0 pointsrssoconnor1y ago0 comments

I do think the why that the Four Colour Theorem is true is captured my statement. The reason why it is true is because there exists some finite unavoidable and reducible set of configurations.

Yet, whether the finite set were of size 2 or size 633, the fundamental insight would be identical: there exists some finite unavoidable and reducible set of configurations.

0 comments

roenxi1y ago

> I'm fairly sure that people are only getting hung up on the size of this finite set, for no good reason.

Having a pattern with a small set (single digit numbers) means that it can be stored in the human brain. 633 objects can't be. That limits the proof.

lacker1y ago

But, I can understand if pure mathematicians don't feel this way. This might be only really an intriguing and beautiful concept to someone who is interested in scaling up algorithms and AI.

username3322111y ago

> So the major reason for studying it is coming up with a pattern that can be used in future work.

Surely, reducing the infinite way in which polygons can be placed on a plane to a finite set, no matter how large, must involve some pattern useful for future work?

dartos1y ago

But why stop at “some” pattern when you can find the most general pattern.

myst1y ago

The nature does not care whether it fits in our brains.

dartos1y ago

That’s why we use math to describe nature in a way that fits in our brains.

That’s the whole point of math.

gsf_emergency_21y ago

If it were size 2, we could more easily make sure that the answer is definitely mind-blowing.

Have programmers given up on wanting their mind blown by unbelievable simplicity?

seanhunter1y ago

> The reason why it is true is because there exists some finite unavoidable and reducible set of configurations.

lacker1y ago

godelski1y ago

j / k navigate · click thread line to collapse