## Roundup of the poll aggregators

While looking for something for work (!), I came across an interesting set of PowerPoint slides How to predict election results from Jan-Michael Frahm at UN . This nicely summarizes the methodology of the 2012 iteration of Nate Silver’s election forecast at FiveThirtyEight. The 2016 iteration is explained here but is largely similar.

If you like these sorts of models, there’s also Sam Wang (Princeton Election Consortium), Josh Katz (New York Times / Upshot), and Huffington Post, Daily Kos PredictWise is David Rothschild’s site which aggregates results from the prediction markets. Slate has been running a feature on Trump vs. Clinton: Who’s Winning Today’s Forecasts of Who Will Win the Election?, which is a bit tongue-in-cheek . They average the other forecasts. As they tell us, “averaging is a sophisticated econometric technique that combines addition and division”.

The slides come from a course COMP 066: Random Thoughts at UNC, a first-year seminar in the CS department which is as far as I can tell intended for non-majors, which is described at the epartment’s web page as follows: “explores the notions of “randomness” and its antithesis, “structure.” What does “random” mean? How do computers generate “random” numbers and just how random are they? Is the addition of random noise to a signal always bad? (The answer is no!)” I would have liked to teach a class like this back when I taught (or for that matter, to take such a class back when I took classes).

## Hamilton Day

Today is Hamilton Day. (William Rowan, not Alexander.) 173 years ago today, William Rowan Hamilton figured out how to multiply quaternions. The story goes that he was trying to figure out how to multiply triples of numbers, but eventually realized he was going to have to multiply quadruples. He figured it out while walking along Broom Bridge in Dublin, where he carved the equation $i^2 = j^2 = k^2 = ijk = -1$. There’s a plaque (you should always read the plaque), and a few years back John Baez posted some pictures. Maynooth University does an annual Hamilton Walk retracing his steps on this day, which you missed, but there’s an audio guide.

## Applied circle packing

Circle packing is made harder by the following constraints:

• The circles are not all the same size, because summer squash are not even close to being cylindrical.
• Your grill is too small, because you didn’t read the size when you registered for wedding gifts.
• The plane on which you are trying to pack circles is hot.

## Voting

Bill Clinton: “if you don’t vote, it’s half a vote for the other guys” – just heard on CNN at a campaign event.

This is a property of elections that hadn’t occurred to me. The quantity Clinton cares about is C – T, where C is the number of votes for Clinton and T the number of votes for Trump.If this is positive, Clinton wins; if it’s negative, Trump wins.  If you vote for Clinton, that goes up by 1; if for nobody, it doesn’t change; if for Trump, down by 1.  So not voting is makes this margin one less than Clinton would like; voting for Trump makes this margin two less.  Hence, half a vote for the other guys.

(My vote can be inferred from my choice of sign convention in this post.)

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Skipped last week because of illness… but we’re back.

How to become a Bayesian in eight easy steps, which is basically an advertisement for the paper of the same name

Stop calling the Babylonians scientists, says Philip Ball regarding the recent discoveries in Babylonian astronomical history.

How Visas Shape the Geopolitical Architecture of the Planet, an analysis of communities among countries based on which countries allow visa-free travel to citizens of which others. Actual paper.

Keith Devlin uses high-dimensional geometry to prove that you are exceptional.

Mike “Pomax” Kamermans has a primer on Bezier curves with both mathematics and demonstrations you can play with.

Junaid Mubeen doesn’t understand his PhD dissertation any more and wonders what this means for mathematics education.

The folks at Vox ask what is the Midwest?, like FiveThirtyEight did two years ago.

Jeremy Kun explains why there is no Hitchhiker’s Guide to Mathematics for programmers.

Milo Beckman uses simulation based on actuarial tables to show why Scalia’s death will be felt through 2060.

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## How many shuffles suffice in Nevada?

Ties in Nevada caucuses will be decided by drawing cards from a deck that has been shuffled seven times.  The higher card wins.  (Suit matters – spades are high, then hearts, clubs, and finally diamonds.). I can’t find a source that says if the players draw at random from the deck or if they take from the top (and if they take from the top, who takes first?)

This is a sighting of seven shuffles suffice in the wild. In this case it’s probably overkill, because the whole deck doesn’t need to be well-mixed.