Re: Why Archimedes Plutonium will never proof the 4CT


bill wrote:
Proginoskes wrote:
[...]
Here are the two basic facts that AP is ignoring:

(1) If you can color every triangulated map with 4 colors, that does
not mean you can color any map with 4 colors.

What is a 'triangulated' map?

Every region is a triangle, and you are coloring regions. (Note that if
you are coloring the VERTICES, you CAN assume that every region is a
triangle.)

BTW, the error in ignoring (2) is called "arguing from ignorance",
which is basically, "I can't imagine any other possibility, so my
possibility must be true". The same error is present, in the same form,
in the following "proof":

What is frustrating is;
"I can't imagine any other possibility, therefore, I can't evaluate
the other possibilities!"

Well, then you don't have a proof then, and you need to do some more
thinking.

BTW, a list of countries and a list of which countries are adjacent to
which is all that is needed in order to color a map. The following
scenario should make it clear, even to AP:

"The leaders of the various countries got together and decided they
would like to have high-speed roads ("highways") connecting the capital
cities of their countries. To reduce the cost and eliminate routing
conflicts, it was decided that two capitals would have a highway
between them only if those two countries were adjacent (but not at a
point), and that the route between the two capitals should pass through
their common boundary."

I imagine that the citizens of Denver and Phoenix might be disappointed
with this plan? [...]

Colorado and Arizona aren't adjacent, because they only have a single
point in common. To be adjacent, the regions have to have a line
segment in common.

--- Christopher Heckman

.

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