Geometry quickie: volume of a tetrahedron

I saw this formula on Wikipedia for the volume of tetrahedron and was intrigued.

Any two opposite edges of a tetrahedron lie on two skew lines, and the distance between the edges is defined as the distance between the two skew lines. Let $d$ be the distance between the skew lines formed by opposite edges... 

then it gave a volume formula. I want to derive it. This post gives my thought process, where I keep using the trick of reducing a general problem to a good example. This is a general strategy for solving problems, often written as "wlog".
(I write it as "wolog" and pronounce as "volog", as if it's a German adverb. So that I can write "We assume wolog that...", "... and thus wolog we have...")

How would a true geometer approach this problem? She would first do a dimension analysis. The volume has dimension $meter^3$, and the lengths have dimension $meter$, so it ought to look like
$$Volume = k \cdot AB \cdot CD \cdot h$$
where $h$ is the distance between the two skew lines of $AB$ and $CD$, and $k$ is some dimensionless number yet to be determined.

Self-awareness in to-do lists

I was trying out Google Tasks, a to-do list app, and it just asked me to download an app of it on my phone, and on the bottom it says "add to task". I clicked it and it added "download the tasks mobile app" to the to-do list.

I found this amazingly life-like in its self-serving purpose. It's self-referential and trying to survive. It's asking me to keep its existence using its own to-do list powers.

Pointless Notes: human failed the Turing Test, updates on XiaoIce, and other chatbots

Human failed Turing Test

This part of the post is based on Turing Test, Etc (1992), by Peter Seibel.

The Loebner Prize is a prize for programs that could pass a kind of Turing Test. It started in 1991:

The first Loebner Prize competition was held on November 8, 1991, at the Boston Computer Museum. In its first few years, the contest required each program and human confederate to choose a topic, as a means of limiting the conversation. One of the confederates in 1991 was the Shakespeare expert Cynthia Clay, who was, famously, deemed a computer by three different judges after a conversation about the playwright. The consensus seemed to be: “No one knows that much about Shakespeare.”

Cynthia Joyce Clay is still online, with a blog and stuff. Search "Cynthia Clay Turing" for yourself. She apparently likes to boast the distinction of being considered not human:

I was judged to be a computer program on Shakespeare at the First Loebner Prize Competition of The Turing Test—a truly science fictional experience. I'm an author who likes to write sf, fantasy, updated versions of old myths.

Pointless Notes: Murder and Complex Analysis

Theodore John Kaczynski, BA (Mathematics, Harvard University, 1962), PhD (University of Michigan, 1967), is famous for being a series bomber, but to mathematicians, he's also known as a complex analyst. Not a (mathematically) famous one, but a competent one at least, and some also said he was brilliant. In 1969, he resigned as an assistant professor at Berkeley.

There was a news article about his math, and it contained the usual kind of flailing about how research level math is too hard for layponies. No need to be so dramatic about it... 

I was amused by this:

Writing in the first person plural is common in mathematics, said Kenneth Ribet of UC Berkeley. So in hindsight, the Unabomber's manifesto may provide an obscure hint at its alleged author's former profession. 

The mathematician's habit of writing in the Royal We has been exposed!