In this post, I’m going to give a brief critical overview of loop quantum gravity, the field that I worked in during my time in physics. A fairly strong understanding of physics is assumed.
Loop quantum gravity is an attempt at canonical quantisation of Einstein’s general relativity. Thus the starting point is constructing a Hamiltonian. In a flat spacetime that’s easy, but on a general spacetime manifold it’s not so easy because it requires one to define a time coordinate. The ADM formalism addresses this by assuming that spacetime is foliated. Roughly this means that our spacetime manifold \( M \) is decomposed into a family of spacelike hypersurfaces \( \Sigma_t \) labelled by a timelike coordinate \( t\). Spacelike means that any pair of points on \( \Sigma_t \) are spacelike separated - their spatial and temporal separation is such that light could not travel between them. There are in general many possible foliations of \( M \) that should all be ‘equally as good’ as each other.
Robust standard errors are frequently used in statistics, often in an unthinking way. They are certainly valuable and useful in the context of linear regression; however, they do not serve a similar purpose in maximum likelihood estimation of non-linear models. The basic issue is that the kind of mis-specification that robust standard errors can address in linear regresion does not spoil consistency results for the parameter estimates. On the other hand, it does spoil those results in the context of maximum likelihood estimation of non-linear models. Thus at best you end up with a consistent estimator for the variance of a parameter estimate that is itself inconsistent, which isn’t really of interest except as a diagnostic tool for detecting bad models. I’ll explore this in more detail below.
In my time working in health science, I have been troubled by the number of times I have encountered statisticians and practitioners of statistics who are absolutely sure that either the variables or residuals in a linear regression must be approximately normally distributed, and the model is invalid otherwise.
This idea is completely false. In this post I want to explore why it is nonetheless so widely believed by professionals in the field.
Eric is a podcaster who has most notably made appearances on the Joe Rogan experience (JRE). He received a PhD in mathematical physics from Harvard in 1992, and between 2013 and 2022 he was a managing director of Thiel Capital - Peter Thiel’s investment firm.
Expected utility theory was first influentially expounded by Swiss mathematician Daniel Bernoulli in the 1700s. It seeks to answer the question of how to weigh up alternatives that are uncertain. For example, say I gave you the option of \( £100 \), or a bet consisting of a \( 50-50 \) chance of receiving \( £250 \), how should you choose? While it may seem easy to answer a single question like this, it turns out that building a general framework for how to make such decisions is not so easy, and if you proceed naively you can easily come a cropper.