Algebraic Geometry: A Bridge Between Equations and Shapes

By Mike Sha             A common problem in robotics is finding all the possible positions the hand can end up. This is a question for algebraic geometry, which can be solved by homotopy continuation1. In this article, we’ll be taking the path of least resistance to these topics. Algebra is “the study of mathematical symbols … Continue reading Algebraic Geometry: A Bridge Between Equations and Shapes

We’re All Just Boltzmann Brains, Living in a Boltzmann Universe: A Crash Course in Statistical Mechanics

By Mike Sha Let’s take a quick trip through the groundbreaking theory of statistical mechanics and use it to smash our current understanding of the universe to pieces. Around the late 1800s, Ludwig Boltzmann (Figure 2) started thinking about order, disorder, and atoms, a line of thought that led him to become the father of … Continue reading We’re All Just Boltzmann Brains, Living in a Boltzmann Universe: A Crash Course in Statistical Mechanics