I have a talk today at Perimeter Institute: here are the slides. I basically showed that even a stochastic multiverse must be generated by precise initial conditions!
Tag: mathematics
I was thinking about how one can use the NBA’s new SportVU system to figure out optimal positions for players on the court. One of the interesting things about the SportVU system is that it tracks player coordinates on the court. Presumably, it also keeps track of whether or not a player located at makes […]
Everyone by now knows about this paper I wrote a few months ago: http://arxiv.org/abs/1604.05266 Using data science / machine learning methodologies, it basically showed that the most important factors in characterizing a team’s playoff eligibility are the opponent field goal percentage and the opponent points per game. This seems to suggest that defensive factors as […]
In a previous post, I showed how given random positions of 5 players on the court that they could “fill” the triangle. The main geometric constraint is that 5 players can form 3 triangles on the court, and that due to spacing requirements, these triangles are “optimal” if they are equilateral triangles. Given that we […]
Most people when talking about cosmology typically talk about the universe in one context, that is, as a particular solution to the Einstein field equations. Part of my research in mathematical cosmology is to try to determine whether the present-day universe which we observe to be very close to spatially flat and homogeneous, and very […]
I tried to derive a general Einstein field equation for an arbitrary FLRW cosmology. That is, one that can handle any of the possible spatial curvatures: hyperbolic, spherical, or flat. Deriving the equation was easy, solving it was not! It ends up being a nonlinear, second-order ODE, with singularities at a=0, which turns out to […]
Here is a really quick derivation of the Cauchy-Riemann equations of complex analysis. Consider a function of a complex variable, , where , such that: , where and are real-valued functions. An analytic function is one that is expressible as a power series in . That is, . Then, . We formally differentiate this equation […]
I’ve been fascinated by the triangle offense for a long time. I think it is a beautiful way to play basketball, and the right way to play basketball, in the half-court, a “system-based” way to play. For those of you that are interested, I highly recommend Tex Winter’s classic book on the topic. There is […]
As usual, here is the post-game breakdown of Game 2 of the NBA Finals between Cleveland and Golden State. Using my live-tracking app to track the relevant factors (as explained in previous posts) here are the live-captured time series: Computing the correlations between each time series above and the Golden State Warriors point difference, we […]
Using my live tracking app combined with the relevant factors based on this previous work, here is my breakdown of what contributed to the Warriors win in Game 1 of the NBA Finals. First, here is the time series graph of several predictor variables: Breaking this down a bit further, we have: Computing the correlations, […]
Relativity Digest 