The Physics Of Moving Ski Moguls

As an avid skier I have always considered moguls to be large, immovable, obstacles. Solid piles of difficulty that haphazardly push my skis around with no regard for my intentions.

Three researchers in Colorado, David B. Bahr, W. Tad Pfeffer, and Raymond C. Browning, have discovered that moguls actually move! And not only that – they move up hill!

The math goes something like this:

A specific representation for the erosion–deposition wave W at position x created by a skier n may be given by the sinusoidal form Wn(x) = a sin(2πx/2rn + ϕn), with positive W corresponding to deposition.

The layman explanation goes something like this: as a skier turns on a mogul, snow is scraped from the bottom of one mogul to the top of the next one, having the overall effect of “moving” the moguls. And, although skiers invariably push snow down the mountain, the ski moguls move uphill.

Mogul Diagram

Below is a time-lapse photo of video showing the uphill migration of ski moguls on the Riflesight Notch ski run at Winter Park Ski Resort. The movie spans five months, starting in early December and ending in late April of the 2006/2007 ski season. Each frame of the movie represents one day.

Fuckin’ Math

If my highschool math text books were more like this I probably would have grasped onto abstract algebra a lot easier – Fuckin’ Concrete Contemporary Abstract Algebra Introduction By First Course Radical Solution Dummies: Dummit, Foote, Hungerford, Shifrin, Gallian, Fraleigh, Beachy, Herstein, Saracino, Artin, Deskins (Paperback), by Nicolas Bourbaki Junior, ISBN 1441451579, 100 pages, published 2009. Here is an excerpt:

For fucking example, the symbols could be fucked as symmetries of a fuck, as the fuck of a switch, as an instruction to a machine fuck, or as a way to fuck a statistical experiment. The fucks could be manipulated using some of the unusual fucks for fuckers. For fucking example, the fucked polynomial 3x²+2x-1 could be fucked to and multiplied by other fucking polynomials without ever having to interpret the fuckbol x as a fucker.

UPDATE: Unfortunately Nicolas Bourbaki Junior’s book has been erased from the Amazon database. It can now be found here or here.