I was talking about the one between Detroit and Windsor, where one can drive in a southward direction from the US into Canada

Wow, guys & gals, I didn't mean to start a conspiracy (ahem) about trisecting an angle. There seems to be some gaps in the general idea. Specifically, I don't actually know what the original theorem says (trisecting angles) and why there is a "fake" proof

Could someone please state for me exactly what the theorem is, and thy there is a "fake" proof for it? (As far as I know, you can't trisect an angle with a stright edge and compass) Is there an exception maybe for a specific case?

L8R

Pete

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PJE

There's so much I don't know about astrophysics. I wish I had read that book by that wheelchair guy.

The construction I linked to is an actual trisection, but the classical construction uses a rule with no marks, and a compass that collapses as soon as you lift it up from drawing a circle--so that construction is illegal according to those criteria. And so is worzel's idea of transferring a chord length and marking it off from another point--but there are alternate ways of achieving the same thing.

Ah, the Ambassador Bridge. Longest suspension bridge in the world...in 1929. 1850 foot span and 7490 feet long. And a lovely bridge.

The Big Mac has an 8614 foot span and is five miles long.

I proved it 34 years ago in high school with pencil and paper before anyone had computers. I've since given talks on why the current attempts to solve the problem are not trying to solve the problem, but rather trying to rename it. I've also taken the obligatory cheap shots at computers used in a supposed proof. An image of the proof is the only tatoo that I've ever considered getter, but I chickened out.

Yep. That how I started too.

David Madison
Maddad@Hotmail.com?Subject=FourColorMapTheorem

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http://members.elirion.net/~maddad
There are ten kinds of people. Those that understand binary, and those that do not.

Wow! I don't suppose you've got your proof on the web somewhere, have you?

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There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.

No sir, not on the web. I've been thinking of trying to find someone to officially recognize a solution. I remember talking to a guy in the science department (head?) at Ohio State University several years ago. He said, "Yeah, sure, send in your proof so that I can disprove it" or something like that. He also was worried that I'd submit reams of computer data, and he didn't want to have to read through it all. He considered himself a lightning rod for people working on the puzzle.

It's not really hard at all. I should have spoken with him again, but I was a bit frosted by his demeanor, and just never got around to it. Think I'll write it up tonight and put it on my website. My temporary website ( http://www.geocities.com/davidmadison01 ); my regular one ( http://www.maddad.org ) is down.

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http://members.elirion.net/~maddad
There are ten kinds of people. Those that understand binary, and those that do not.

Has anyone checked it over for you? (not that I'm offering, not much of theorem cruncher me)

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There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.

Post it! if we can't find the error within a day, I'll eat my hat.

I just asked Phil in an email if he would support my authorship if I posted the solution here. If he agrees, I'll step you through it.

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There are ten kinds of people. Those that understand binary, and those that do not.

Maddad said: Are you referring to the four colour theorem in total, or just a part of it. It would be a remarkable achievement to do something like that in high school, although I am a bit skeptical that you have a valid proof....

As far as I know, the computer proof of this takes into consideration all 2000 (or so) possible cases that arise from the theorem. I'm curious to see how you could reduce that into something simple

Looking forward to it! I'm assuming that I'll be able to follow your proof as you had only highschool training at the time

I'll also look forward to sharing it with my grade 12 Data Management class, where I actually discuss the theorem with the class (briefly)

L8R

Pete

__________________
PJE

There's so much I don't know about astrophysics. I wish I had read that book by that wheelchair guy.

I notice in your resume that you say yours is the only proof so far. Why do you discount the one by Appel and Haken (cite--and I notice they say they have another proof)?

Oh that's up now. I came across it in google the other day but it was down.

Wish I had a resume like that, you know, pretty normal really, up until the last line of other interests, "Oh yeah, and I'm the only person to have proved fermat's last theorem in the space of a margin."

Hope Phil agrees to supporting your authorship, Madad.

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There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.

Valid question. As mentioned in that page, that proof is not satisfactory.

There are a number of reasons that a computer cannot support any proof of the theorem. The problem starts because the logic is faulty. If I told you that my good friend Fred who lives in the apartment down the street is really smart, has worked on the thorem a long time, and has been unable to solve it, would you accept that as proof that a map needs no more than four colors? I don't think so. You would say that you have no way of knowing what methods Fred tried, why he even thinks it can't be done, and since you have no way of knowing the method he used, you cannot ensure that he didn't skip some important step, smart as he is or not (or so I claim). There is no way to get the same answer that Fred did, so the reproducibility requirement of science is left unsatisfied. Even if he's tried and failed, we have no way to tell that he he finished looking, so we have no way to tell if he would solve it by putting in another five minutes of study.

A computer proof suffers from exactly the same problem, plus some others. Who wrote the program that performed the solution? Did he write it accurately, or did he fall victim to GIGO? Remember that nobody has checked the answer because it is too big, so in effect we have no reproducibility. Was the method used by the programmer capable of testing the problem? All you know is that some progammer somewhere thinks so. Has there ever been an error in programming anywhere in the history of computing? How do you know one of them didn't show up here? Was his computer search exhaustive enough? The programmer claims so, but how do you actually know since his work cannot be checked? And what about hardware failures? Some of you may remember the difficulty with the original pentium that inaccurately performed some obscure mathematical calculations. Intel had to recall those processors and replace them with ones that had been fixed. Could such a problem ever happen agin? You say no? How do you know that, for certain, when you must know that for certain to say that the problem has been proved? Suppose that this is not the first time that microprocessors have been manufactured and sold that incorrectly performed math operations? If the original Pentium was the second offence, not the first, would you worry a bit more that such a problme MIGHT arise again? While you probable are familiar with the inadequacy of the original Pendium, few people remember that the 386 chip had a similar problem that went undetected until the release of Autocad 10. Intel went to work, fixing the problem, and released a replacement processor, which makes the Pentium problem the second time around. But it's not even the second time, because Intel botched the repair. Their fix was still broken, so they had to release yet a third version of the 386 to get it to quit making math errors.

This track record with computer hardware is stark explanation of why a computer cannot be used to prove the Four Color Map Theorem. The problem though is even bigger. Had the computer drawn the desired map in which five territories each touched another, it still would not have prooved the problem. Can anyone guess why?

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There are ten kinds of people. Those that understand binary, and those that do not.

He strongly advised against it. Suggested that I submit it to an official publication somewhere for peer review. I don't know who might take it though.

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http://members.elirion.net/~maddad
There are ten kinds of people. Those that understand binary, and those that do not.

Ya, too bad we don't, you know, write down what we tell our computers to do. If only there was some kind of "code" we could write, that was algorithmic, and other people could check...

If only other mathematicians would develop and learn this "code" they could check it so easily...

And if only the program was only made to show us its work instead of just printing "proved" or "not proved".

Hardly obscure... they knew about it when they began making them. They just assumed (rightly) that the error would be small enough that it wouldn't effect most people.

And if only they could some how use this hypothetical "code" to check if the program gave the same "proved" or "not proved" answer on systems with different components...

Ok, the last part of that long post asked the question, "If someone drew a satisfactory map with five colors, why would it not prove the theorem?"

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http://members.elirion.net/~maddad
There are ten kinds of people. Those that understand binary, and those that do not.

Because the theorem states that it can be done with 4. It had been known for a century or more IIRC that 5 is sufficient. Just because it can be done with 5 doesnt prove that it can be done with 4.

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Yo Adrian. The Phillies won the Series.

Actually, what you asked was:
If the computer, or anyone else for that matter, drew a map where five territories each touched one another then wouldn't that disprove the four color theorem.

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There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.