Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. ~Hermann Minkowski Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore. ~Albert Einstein In my previous discussions of how we know the speed of light is constant and how this results in special relativity, I used Albert Einstein’s thought experiments to derive the time-dilating, length-contracting results. There’s another way to describe special relativity, though, invented by the Polish mathematician Hermann Minkowski. It
math
Mathematics / Science And Math
Panning For Primes With the Sieve of Eratosthenes
They consider me to have sharp and penetrating vision because I see them through the mesh of a sieve. ~Kahlil Gibran I know that last time I promised to talk more about quantum mechanics. Unfortunately, finals hit me with all the force of a great typhoon; I don’t feel like I have the time to write an article on quantum I’d be happy with. So here’s some filler on prime numbers. Our regular programming returns next week. A prime number is a counting number that is greater than one and only divisible by one and itself. For example, 2
Physics / Quantum Mechanics / Science And Math
The Charming Doubleness: Particle-Wave Duality
But the beauty here lay in the duality, in the charming doubleness… ~ Thomas Mann (Felix Krull) I apologize to those of you who have requested a topic. The current requests are all pretty in-depth and I want some time to think about how to explain them properly. So, in a bid to buy time, I’m going to do a multi-part series on quantum mechanics. In this part, I’ll describe some of the experimental results motivating the fundamental principle of quantum mechanics: particle wave duality. As amazing as it may seem, quantum mechanics tells us that every particle is
Education
Some Thoughts on Education: Part 2
Bonus content! This is a follow-up entry to my previous post, A Few Ideas on Education. Enough people have given me thought provoking content, that I wanted to share what they’ve said and what I think about it. Using Computers to Teach Math (I’ve already posted this in a comment on the original post, so if you’ve read that, you can skip this section.) Someone on my facebook feed asked me for my thoughts on the ideas promoted by this video: http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html For the most part, I think this school of thought is spot on. Conrad Wolfram is simply
Analysis / Mathematics / Science And Math
Taming Infinity: infinite sums, infinite primes and the sizes of infinity
The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. ~Howard Phillips Lovecraft To infinity, and beyond! ~Buzz Lightyear Infinity: The Early Years When I was about ten, I had the following conversation with my friend: Me: I want Pokemon Yellow the most of anyone! My Friend: No, I do! I want it twice as much as you! Me: I want it