Discrete Math

cosmology / Discrete Math / Geometry / etc.

Quantum Geometry: Causal Dynamical Triangulations

jonah 49
An example causal triangulation

A “quantum gravity expert” is presumably someone well acquainted with the details of our immense ignorance of the subject. I suppose I count. ~John Baez I long ago promised that I would discuss some of my own research. Here’s the first post that makes good on that promise. Today I’ll discuss a theory of quantum gravity. Why Quantum Gravity? Without a doubt, the two greatest advances in physics in the last 120 years were the advent of general relativity and quantum mechanics. These two amazing theories have totally changed the way we see the world. Quantum mechanics describes the

Discrete Math / Mathematics / Science And Math

Probability: Part 1

Michael T. Schmidt 5

Hi everyone! This week, I was traveling to Park City, Utah, to participate in the 3-week Park City Mathematics Institute. It’s currently a blast! I have more time now, but in the meantime, I asked my good friend Mike Schmidt to write a guest article for me. He wrote on probability which, if you’ve been reading for a while you know, is deeply connected to modern physics. Anyway, here’s the article. Thanks, Mike! The laws of Probability So true in general So fallacious in particular. ~Edward Gibson   Probability is just so fantastic, I could eat it all up.

Computer Related / Discrete Math / Mathematics / etc.

R.I.P. Kenneth Appel

jonah

Imagine that you’re a stingy cartographer and that you want to make a colored map of the united states. Because you’re stingy, you want to avoid spending money on ink. You have to color the map so that no two adjacent states are the same color—otherwise you wouldn’t be able to tell them apart! If you want to buy the fewest colored pens possible, how many colors must you use to make your map? Very early on, mathematicians guessed that the answer was four colors. However, no one could prove it. An example map is in the tittle figure,