Four Color Theorem
ecently, the famous "four color theorem" was solved by an extensive computer proof.
The fact that this theorem required an extensive proof in the first place gives evidence of how far research mathematics has descended since Gauss and Euler.
It is now a pathetic embarrassment being followed closely by theoretical physics and preceeded by philosophy and 'modern' art.
The fundamental knowledge now lacking in mathematics are answers to questions such as:
What constitutes a "proof"?
What is induction and deduction?
And . . . most importantly . . . What does the term "self-evident" mean in mathematics?
For those unfamiliar with the Four Color Theorem it is simply:
What is the maximum number of different colors on a map (two dimensional, standard) that can be 'forced out' by the requirement that no two same color areas can touch at more than a point?
Here is a 5-color map, but, obviously, I could make the black area blue and the yelow area green instead and reduce the number of colors required to 3 .
After a little inspection (very little), one can see that if four mutually touching color areas are drawn, the only way to 'force out' the fifth would be to put in another color such that it touches the other four yet does not break any of the former connections.
It then rapidly becomes clear to anyone (except mathematicians and perhaps lotto ticket buyers) that this is just plain impossible.
[Whenever you attempt this, simply recolor the map with just four colors as in the example where the yellow was cut thereby allowing it to be recolored.]
Now this is the 'rub'.
Suppose you cut that gray piece into any number of smaller pieces.
Perhaps you could fool geometry into having to take another color.
Doesn't seem too promising but can you "prove" it ???????
You see what I mean? Intuitively, you suspect that this cannot be done. But why? Why can't you put a name to your 'intuit' and call that a proof? Why is this not a proof? What is meant by the term "proof"?
Induction and Deduction
All proof is deductive. We derive an acceptable (acceptable to the consensus of informed opinion) understanding of a thing based on its non-contradiction of the body of accepted, mutually consistent, induced principles.
An induced principle is one which has been identified by independent observers through the mechanism of common observation. Thereafter, the induced principle is used as a tool in the process of "proof" but is, itself, unproven by definition.
1 + 1 = 2 is an induced principle. It cannot be proven (Bertrand Russell to the contrary notwithstanding). It is simply identified by multiple independent observers who then mutually agree on a statement of "identification", i.e. it would do no good to identify something then have it described in multiple fashions (this would make the principle useless as a tool of proof for other propositions).
If all the parts of a mechanism obey the laws of physics then the mechanism as a whole obeys the same laws of physics.
This statement and variants of it are what is not understood by present day mathematicians. Apparently they now require a proof of this "old saw". For clearly, if you cannot force the fifth color out in the simple situation, you cannot do so in any multiple area example regardless of quantity or configuration.
I.E. If every set of five touching areas obeys the four color theorem (and they must by the former observations) , then, the entire configuration must obey the four color theorem.
The idea of the modern mathematician is to "trick" logic into "chasing its tail" (a fantasy as old as civilization). One must then say to these mathematicians "Take your place with the seekers after gold" as did DaVinci in reference to perpetual motion inventers.
In general, an induced principle of logic is exceedingly simple. It must be simple if men are to accept it as true by its mere identification. That OLD SAW is, in fact, an induced principle. It is not to be proven but is, rather, to be used as a "means" of proof.
What we are dealing with is the file/folder problem.
An individual colored area is a "file".
A set of colored areas is a "folder".
We then throw around the folders as if they were files. So that what was true of files is also true of folders or folders of folders and so on to any size or configuration.
Any set of colored areas which obeys the four color theorem is a LOGIC DOMAIN.
Any logic domain can be treated as just another single color.
Five logic domains are just as easily comprehended as any five area map.
This case was closed before it was opened.
The entire matter is an embarrassment.
Some Philosophical Insight
Every subject whatsoever has an obvious hierarchical structure. For instance, in mathematics addition and subtraction are the main concepts then comes multiplication, algebra, trig, calculus . . . just like you learn 'em in school. One presupposes the other. Addition is logically anterior to calculus.
Yes, there are problems with the hierarchical concept but it's still the MAIN THING in existence.
Hierarchy is universally denied by all current mainstream endeavors.
Nothing is better than the other . . . only "different". No top and bottom . . . just "sideways".
Man is not the end product of evolution . . . he's just random.
A Zulu grass hut culture is equal to Italy in the high Renaisance.
Michaelangelo is no better than Picasso.
Brahms is no better than a "rap artist".
No one person is better than another no matter what his accomplishments or lack of them. We're all "just different".
The purpose of this self-inflicted blindness is to legitimize and sanction failure as the modern way of life. It infects every human endeavor including mathematics.
I continue to find it disgusting.
Ebtx Home Page