I will address one single and especially idiotic statement out of a choice of many. That by pghnative is particularly enlightening because it speaks to the core of our discussion:
Quote:
|
Originally Posted by pghnative
"Originally Posted by Maddad
The question the theorem tries to settle is why each of the five regions are unable to touch all the other four. [Knowing that they cannot wasn't ever an issue.]"
From my reading of this thread, that is not what the theorem is trying to settle.Incorrect.
|
Thirty five years ago I picked up the Life Science Library book on Mathematics, copyrighted in 1963 and again in 1969. It presents the Four Color Map Theorem on pages 184 and 185. Since I still have that book in one of my living room bookcases, let me quote you what David Bergamini and the editors of Time said about your post:
"no one has been able to prove what map makers have known for ages—that four colors are enough for any flat map or sphere."
Got that pghnative?
Look, I cannot believe that you guys are really that stupid. You are not; you are probably reasonably intelligent. So what is the problem? Why are you having so much trouble understanding such a simple idea? The answer is that you feel threatened by me. I am asking you to think, and thinking of a new idea is difficult.
One of the members here labeled someone an expert because they had supposedly come up with a proof. Never mind that nobody here can understand that proof. Never mind that we know of nobody who has verified it. Never mind that experts have been known to make mistakes. Never mind that the member making this interesting statement does not really know what qualifications this expert has to earn the title of expert. (Yes, I know you can know go look it up now, but you did not know when you were certain this man was the last word on the subject.) We have called them an expert, and from that concluded that the issue is settled and therefore needs no further investigation. What you are doing is insulating yourself from a need to think. Once you call him an expert, you need think no further.
Pghnative, why in God’s name do you want me to examine worzel’s example? I have not even bothered reading his last post. A month ago he jumped into this thread without a clue; look at his first two posts. He still does not get it; look at his last post. Yes, he is dealing with diagrams that are distantly related to mine because they are colored territories, and some of them do border others. If he though, like you, cannot understand the very most fundamental statement of the Four Color Map Theorem given in red above, then what possible hope does he have of contributing anything useful? Why should I waste my time chasing someone else’s approach to arranging territories when it does not bear on the method I am using to limit possibilities to manageability? I developed this approach specifically to deal with this problem. Saying that my approach is different from what worzel heard about is expected. I solved the problem; worzel and company did not. If it bears a resemblance to something worzel’s heard about, then that does not mean that it must share all characteristics with mine. In fact, it should not, because if it did, everybody here would still not understand why we do not need more than four colors to draw a map.
As I had said I would, I have provided the proof of the Four Color Map Theorem. You may accept it or reject it, as you choose. It is not my job to drag you by the scruff of your collective necks to make you think. Thinking is a privilege and an art, but it is not easy. If you are more secure in finding excuses not to think, then by all means, do so. I am done with this thread and will not return to it to read any further comments.