We talked about Navier Stokes equations and how they are a mathematical abstraction of the world around us. We talked about how such differential equations cannot necessarily be solved in practice, and therefore we need to form numerical solutions. We mentioned that the Met office solves these equations on 1km^2 sized grids across UK for weather prediction. We discussed a little what uncertainty meant in this context, and how modelling could have a deterministic part and a stochastic part.
Triggered by talking about what had come up in the first week of lectures, we discussed the relationship between Computer Science and Maths. In absolute terms we talked about how many of the challenges of Computer Science are how to implement maths on a Computer (e.g. the Turing test, the way a processor works). But for Mathematics, particularly pure mathematics, there is a lot of interest in separating the maths from the implementation. Mathematics can stand alone, outside implementation, emerging purely through abstract thought. We looked at the wikipedia page for Principia Mathematica and talked a little about set theory with a focus on Godel’s incompleteness theorem and the barber paradox.
In the end we talked about the Spell Correction challenge for internet companies make spell corrections? We speculated it was on the basis of past data and probability may be used to rank the suggestions. We thought that it might be a good idea to look at n-gram models to understand this better. We are hoping for Daniel Bernhardt to visit us (from Facebook’s London office) to give a talk on this material.