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07 January 2014

Slightly tarted up V.2 t-shirt & (someone else's) explanation of solution to 4CC = 4CP


Click t-shirt to enlarge,
view vid in Fullscreen

A neighbor seems to sincerely enjoy my whack t-shirts, so for Christmas i cranked him out the 4CC / postage meter t-shirt after i made the red brighter on the metered postage from the math department of the University of Illinois / Champaign-Urbana. Haken and Appel stole about 2 years of time off the federal supercomputer on campus to analyze a huge number of distinct geopolitical map cases.

FOUR COLORS
....SUFFICE

The math department featured the postage ad when they published their proof in 1976. (The faint PB is for Pitney-Bowes, the Ruler of Earth with hand-cranked and electromechanical business postage meters.)

With some help from their Big Silicon Friend (an IBM), they put UI C-A on the math map and on the Big List of Platonic Objects.

One tiny aspect of this perfectly legitimate proof wafts up the nostrils of many mathematicians like the 5-day-old sidewalk harring in my hotel minibar fridge.

Only a digital computer can assemble this proof.

And having claimed to have proven it, only another digital computer can verify the work of the first computer.

4CC is the first Proof humans have encountered or cobbled together which is too vast to reside in a single human brain. Thus the stale harring aroma to the nostrils of many carbon-based sentients.

In the video, a very nice nerdo Italiano (YouTube courtesy PatfromCH) gives a vidboard demonstration proving a famous aspect of the 4CC = 4CP.

Since this idiot-easy child-grokable question

For any conceivable geopolitical map, what is the most distinct colors needed so no contiguous regions (regions sharing a border of non-zero length) are colored alike?

 
... was first asked (by Francis Guthrie) in 1852, it took Earth's brainiest mathematicians 124 years to prove (or help the supercomputer prove) the answer.

Minkowski told his graduate students that the reason no one had proved 4CC was that only third-rate mathematicians had studied the problem. Some months later he announced: "Heaven is angry at my arrogance. My proof is defective."

Worse than idiot-simple ... print shops had been printing such geopolitical maps for centuries, and THEY always knew they'd never, ever have to print a map that needed 5 colors. In centuries of printing screwy, arbitrary-shaped maps -- Guthrie used the counties of England, other examples are the countries of Eurasia or the "lower 48" USA states -- they'd never found a map that couldn't be printed in 4 colors. (Most only require 3 colors.)

But of course it's not a commercial printer's job to prove fundamental platonic object conjectures in topology. They just print maps.

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Maybe more later. I'm hungry. And the Polar Vortex has trapped us and the cats in the cabin. If we go outside for longer than 15 minutes we will get frostbite and have to have body parts amputated.


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