For those of you who found this too easy, here is a problem I don't know the answer to that is inspired by the last one: Let N be a positive integer. Suppose we are given 3N points in 3-space such that no 4 of them are coplanar. Say the points are divided into 3 mutually exclusive groups of N points each: the reds, the greens, and the blues. True or false: There exists a partition of the 3N points into sets of size 3 that each contains one red, one green, and one blue point, such that there are no intersections among the resulting N triangles. (The triangle of a triple is the convex hull of its 3 points.) —Dan

On Jan 6, 2016, at 10:18 AM, Dan Asimov <asimov@msri.org> wrote:

I just read this puzzle and thought math-fun might enjoy it:

Let N be a positive integer.

Suppose that we are given 2N points in the plane such that no 3 of them are collinear.

Assume N points are chartreuse and the other N are heliotrope.

Prove there exists a one-to-one correspondence between the chartreuse points and the heliotrope points such that if each point is connected to its buddy by a line segment, then the N line segments are disjoint.

Andy, I like your suggestion about exclamation points; I hope you'll post it as a comment after I take the essay public. (Has anyone undertaken quantitative rhetorical analysis of internet debates? I suspect that there's some data-mining that interested linguists could do.) Your remark about people who admit that they'd lose more often than they'd win but still insist that the odds are 50-50 remind me of the results of a poll I administered to students in one of my classes last fall. After reading my essay on .999..., most of them averred that the sequence .9,.99,.999,... converges to the limit 1, but denied that .999... is equal to 1, even though mathematicians take the former assertion to be the definitional meaning of the latter. I'm going to have to write a follow-up essay sometime to address that. Jim On Wednesday, January 6, 2016, Andy Latto <andy.latto@pobox.com> wrote:

I don't know if it's useful for your blog post, but here's an observation I made based on meta-analysis of MH debates (which erupted periodically on several USENET groups I used to read; sci.math, rec.puzzles, rec.gambling, sci.logic, etc...)

I was able to read the arguments on both sides, and evaluate them on their merits to figure out which was correct. However I asked myself the question,

"Suppose I was not able to understand the arguments well enough to convince me that one side was correct and one was incorrect; was there a way I could figure out which side was right without understanding the mathematics myself?"

It turns out there were two very reliable ways:

1. The people on one side of the debate used ALL CAPITAL LETTERS and EXCLAMATION POINTS way more often than the other!!!!

2. The offers to bet on the results of an experiment designed to determine which side was right were always made by proponent of the same side (the non-capital letters side).

This is more along the lines of "how to figure out whether you are wrong" than "how to be wrong", so maybe it's not relevant to your article, but I thought you might find it interesting.

I've talked about this often in the past, but only just now realized that my observation on part 2 is a bit of a cheat. Many times the offer to gamble was met with comments of the form

"Yes, I agree that if I gambled on it, gaining $6 when switching lost, and losing $4 when switching won, I would lose all my money; but that has nothing to do with probability; the probabilities that it's behind each door ARE STILL BOTH 1/2!"

I understood enough math to understand that this is contradictory, and reflects a lack of understanding of the meaning of probability. If I didn't have this amount of subject matter understanding, I couldn't really use technique 2 for deciding who was right. The capital letters heuristic still works fine, though.

Andy

On Wed, Jan 6, 2016 at 1:01 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:

...

I've posted a draft of my essay "How to Be Wrong" and would appreciate comments:

https://mathenchant.wordpress.com?p=482&shareadraft=568d547f0934f

If you send comments via WordPress, keep in mind that they're anonymous by default, which may suit you or may not.

I plan to publish, as always, on the 17th.

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If I'm planning to run a program that I think will take a "long" time, I try to get it running as quickly as possible, and only then *think about it*. Since it's going to run a long time, I'll have plenty of time to think once the program is running, but I want to be able to overlap my thinking with the running of the "dumb" program. However, many times I can think of a better/more efficient way, and have the opportunity to quit the running program to test out the better idea. The definition of "long" is flexible -- the longer the program takes, the more time I have to think about it and optimize it. ("Necessity is the mother of invention".) Perhaps I'm forever scarred from my keypunch-and-submit-card-deck days. At 06:59 AM 1/7/2016, Veit Elser wrote:

Jim's article reminds me of another strategy for being on the right side of wrong.

Cornell physicist Peter Lepage, who develops Markov chain Monte Carlo methods for computing properties of hadrons from "lattice gauge theory", had heard about the MH controversy and decided he would simulate it with a computer program. After he'd written the program and stared at it a while the winning strategy was obvious. He never actually ran the program.