Misconstructions and Misconceptions

Dated Aug 2, 2021; last modified on Sat, 06 Nov 2021

A collection of instances in which I believed something that wasn’t true. A reminder to read not to believe, but to weigh and consider .

The Four Color Theorem does not claim that 4 colors suffice to color a planar map. Instead, 4 colors are sufficient to color any planar graph so that no two vertices connected by an edge are colored with the same color. For any \(n\), there is a map that requires at least \(n\) colors.

Ericsson, whose work is widely cited by 10,000-hours rule proponents like Gladwel’s Outliers, did not claim nor does he endorse the rule. See more discussion at 10,000 hours +/- 10,000 hours .

References

  1. Four Colors Do Not Suffice. Hudson, Hud; Marcus. The American Mathematical Monthly, Vol. 110, No. 5, May 2003, pages 417 - 423. https://www.jstor.org/stable/pdf/3647828.pdf . https://blog.computationalcomplexity.org/2021/08/do-four-colors-suffice.html .