How I Think About Math,
Lecture 1: Relations

The Internet protocol suite is wonderful, but it was designed before the advent of modern cryptography and without the benefit of hindsight. On the modern Internet, cryptography is typically squeezed into a single, incredibly complex layer, Transport Layer Security (TLS; formerly known as Secure Sockets Layer, or SSL). Over the last few months, 3...

…in the integers mod 2 (a.k.a. the finite field of order 2). Multiplication mod 2 is AND: A B (AB) A B AND 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 Adding one mod 2 is NOT: A (A+1) A NOT 0 1 1 1 0 0 So, multiplication plus one is NAND: A B (AB+1) A B NAND 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 Since NAND is universal, and any finite composition of polynomials...

Thanks to fellow Hacker Schooler Leah Steinberg for inspiring this post! Having intermittently struggled with apache2 configuration files for the majority of my adult life, I find nginx an absolute joy to set up. I’m completely sincere about that. But, for those who are just getting into Web development, nginx is just about as much of a struggle...

The Virtual Network Computing (VNC) system for accessing the GUI environments of remote computers uses a protocol called Remote Frame Buffer (RFB) to exchange data about graphics output as well as keyboard and mouse input. RFB turns out to be a very sane protocol (specification PDF here) compared with X11, and infinitely more sane than Cocoa...

Now that nearly every computer has some form of multi-processing (that is, multiple CPUs sharing a single address space), some high-level languages are starting to get attention for their concurrency features. Many languages refer to such features as “concurrency primitives.” But since these are high-level languages, we know that these...