### Building a Personal Supercomputer

It's time for a workstation upgrade; here's what I've assembled.

The massive case has plenty of space for additional drives to store the extreme amount of data that nearly every sport is now collecting together with the associated video footage. The case, power supply and motherboard allow up to 3 additional video cards to use as GPU units as your analytical needs demand (and budget can handle).
1. Cooler Master Cosmos II - Ultra Full Tower Computer Case

An absolutely massive case - plenty of room for an E-ATX motherboard, large power supply, multiple video cards and hard drives.

2. PC Power & Cooling 1200W Silencer MK III Series Modular Power Supply

An exceptionally large power supply, but platinum rated and plenty of room to spare allows it to operate nearly silenty, plus it'll handle any additional video cards you'll add later for GPU computing.

3. ASUS Rampage IV Black Edition LGA 2011 Extended ATX Intel Motherboard

Space for 4 video cards, 8 memory sticks (up to 64GB), superb quality and extreme tweakability.

4. Intel i7-4930K LGA 2011 64 Technology Extended Memory CPU

Ivy Bridge, 6 cores, exceptional ability to overclock. My day-to-day overclock is 4.5 GHz.

5. Corsair Hydro Series H90 140 mm High Performance Liquid CPU Cooler

Fits well in the Cosmos II case. Whisper quiet and keeps the CPU at comfortable temperatures even when overclocked to 4.5 GHz.

6. (2) Corsair Dominator Platinum 32GB (4x8GB) DDR3 2133 MHz

Total of 64GB. Top-quality, you'll need your RAM in matched sets of 4 to enable quad-channel.

7. EVGA GeForce GTX TITAN SuperClocked 6GB GDDR5 384bit

Top-of-the-line NVIDIA Kepler card for GPU computing. 2688 CUDA cores that reach 4800 TFLOPS single-precision and 1600 TFLOPS double-precision.

8. (2) Seagate NAS HDD 2TB SATA 6GB NCQ 64 MB Cache Bare Drive

Solid hard drive; you'll need 2 or more drives for a RAID 10 array.

9. Samsung Electronics 840 Pro Series 2.5-Inch 256 GB SATA 6GB/s Solid State Drive

Small, fast SSD for quick booting and anything bottlenecked by drive read/write times.

10. Silverstone Tek 3.5-inch to 2 x 2.5-Inch Bay Converter

Needed to adapt the SSD to the Cosmos II case.

11. Ubuntu Linux

Ubuntu Linux - what else?

1. approx 6020 usd
if you take windows 7 professional instead of ubuntu

### A Bayes' Solution to Monty Hall

For any problem involving conditional probabilities one of your greatest allies is Bayes' Theorem. Bayes' Theorem says that for two events A and B, the probability of A given B is related to the probability of B given A in a specific way.

Standard notation:

probability of A given B is written $$\Pr(A \mid B)$$
probability of B is written $$\Pr(B)$$

Bayes' Theorem:

Using the notation above, Bayes' Theorem can be written: $\Pr(A \mid B) = \frac{\Pr(B \mid A)\times \Pr(A)}{\Pr(B)}$Let's apply Bayes' Theorem to the Monty Hall problem. If you recall, we're told that behind three doors there are two goats and one car, all randomly placed. We initially choose a door, and then Monty, who knows what's behind the doors, always shows us a goat behind one of the remaining doors. He can always do this as there are two goats; if we chose the car initially, Monty picks one of the two doors with a goat behind it at random.

Assume we pick Door 1 and then Monty sho…

### What's the Value of a Win?

In a previous entry I demonstrated one simple way to estimate an exponent for the Pythagorean win expectation. Another nice consequence of a Pythagorean win expectation formula is that it also makes it simple to estimate the run value of a win in baseball, the point value of a win in basketball, the goal value of a win in hockey etc.

Let our Pythagorean win expectation formula be $w=\frac{P^e}{P^e+1},$ where $$w$$ is the win fraction expectation, $$P$$ is runs/allowed (or similar) and $$e$$ is the Pythagorean exponent. How do we get an estimate for the run value of a win? The expected number of games won in a season with $$g$$ games is $W = g\cdot w = g\cdot \frac{P^e}{P^e+1},$ so for one estimate we only need to compute the value of the partial derivative $$\frac{\partial W}{\partial P}$$ at $$P=1$$. Note that $W = g\left( 1-\frac{1}{P^e+1}\right),$ and so $\frac{\partial W}{\partial P} = g\frac{eP^{e-1}}{(P^e+1)^2}$ and it follows $\frac{\partial W}{\partial P}(P=1) = … ### Solving a Math Puzzle using Physics The following math problem, which appeared on a Scottish maths paper, has been making the internet rounds. The first two parts require students to interpret the meaning of the components of the formula $$T(x) = 5 \sqrt{36+x^2} + 4(20-x)$$, and the final "challenge" component involves finding the minimum of $$T(x)$$ over $$0 \leq x \leq 20$$. Usually this would require a differentiation, but if you know Snell's law you can write down the solution almost immediately. People normally think of Snell's law in the context of light and optics, but it's really a statement about least time across media permitting different velocities. One way to phrase Snell's law is that least travel time is achieved when \[ \frac{\sin{\theta_1}}{\sin{\theta_2}} = \frac{v_1}{v_2},$ where $$\theta_1, \theta_2$$ are the angles to the normal and $$v_1, v_2$$ are the travel velocities in the two media.

In our puzzle the crocodile has an implied travel velocity of 1/5 in the water …