Walter Hickey, BI, How to use Math to Crush Your Friends at ‘Risk’ Like You’ve Never Done Before, here.
Here are the five things to take away from this.
- Holding the continent of Europe requires you to hold the fewest number of territories per bonus army. However, almost 60% of European territories lie on a border. The per-territory reward comes with risk.
- That risk can be measured by the ratio of continental bonus armies per border territory. North America has the most favorable ratio.
- Africa is easy to invade but difficult to hold. The amount you need to commit to its defense make it a particularly unsafe Australia.
- When you know battle is inevitable, attack as soon as you have the same number of attacking armies as your opponent has defending armies. You hold the advantage.
- The larger the battle, the larger the attacker advantage.
And of course, never attempt a land war in Asia. That’s just basic.
Steven G. Johnson, Photonic Crystals: Periodic Surprises in Elecromagnetism, 2003-8, here.
Has there been anything new in classical electromagnetism since Maxwell laid down the law in 1864? If so, can one learn it without wading through a vectorial mire of partial differential equations? Come and find out what solid-state physics has brought to 8.02 in the last 15 years: photonic crystals and the surprising new phenomena that arise when light propagates through a periodic medium. This crash course will introduce Bloch’s theorem for electromagnetism, photonic band gaps, the confinement of light in novel waveguides and cavities by synthetic optical “insulators,” startling sub-micron fabrication advances, exotic optical fibers, and will upend what you thought you knew about total internal reflection. We will focus less on gory differential equations than on high-level approaches such as linear algebra, variational theorems, conservation laws, and coupled-mode theory; the course should be accessible to anyone with a grasp of basic electromagnetism and who does not quake in fear at the word “eigenvalue.”
Pink Iguana 