I watched Dangerous Knowledge, a 90-minute BBC video documentary from 2007 which explores the imaginations of four great thinkers. (It’s in two parts. Watch Part Two) These guys opened doors to areas of mathematics that enable today’s technology. And then . . . then, these intellectual giants’ lives spun out of control, toward madness and suicide.
Georg Cantor
Ludwig Boltzmann
Kurt Goedel
Alan Turing
The four:
Georg Cantor (1845 – 1918), mathematician. Inventor of set theory, he created the Continuum Hypothesis, which explored the possible sizes of infinite sets. He suffered from manic depression and spent long periods in sanitoria.
Ludwig Boltzmann (1844 – 1906), physicist. Made sense of disorder. Probability theory pioneer.
Kurt Gödel (1906 – 1978), shook mathematics, philosophy, and logic, with his incompleteness theorem. Close friend of Albert Einstein while at Princeton Institute for Advanced Studies.
Alan Turing (1912 – 1954), “the father of modern computing”
In this interview with physicist Janna Levin (51 minutes), she explains the importance of the insights of mathematicians Kurt Gödel and Alan Turing.
(Originally published October, 2014) The new British film The Imitation Game illustrates the remarkable life of mathematician and computer science pioneer Alan Turing. It will open in theaters on November 21.
This 30-minute video interview with the film’s director Morten Tyldum, actors Benedict Cumberbatch and Keira Knightley, and screenwriter Graham Moore, is worth watching. I can’t wait to see the movie. I’m happy that the screenplay is based on Andrew Hodges’ definitive biography Alan Turing: The Enigma. (Hodges is a mathematician, so if you’d like, he can walk you through Turing’s reasoning based on number theory that led to the routine decryption of messages that were encrypted by the German Navy’s Enigma machines.) Hodges’ biography is a wonderful book that I use as a reference.
Screenwriter Moore describes Mr. Turing as “the outsider’s outsider”. Director Tyldum calls The Imitation Game “a story about outsiders, those who are different.” “The mission of the movie is to celebrate uniqueness — individuality.”
Update, 28 Dec 2014 Mathematician Simon Singh saw the movie and quipped in a Science Friday interview that it’s “filled with factual errors, full of flaws, and in that respect it’s a terrible, terrible film” but in other ways it’s a “brilliant, great film”. According to Singh, the movie errs in dozens of details. Notable errors:
At Bletchley Park during WW2, Turing is shown building a general purpose computer dubbed “Christopher”, which supposedly was used to decipher scrambled German messages that had been encrypted with the Enigma machine. This is wrong. Turing did create the algorithms for, design, and participate in the construction of multiple dedicated electromechanical single-purpose calculators that were used to decipher Enigma-encrypted messages. These machines were called bombes.
In 1952, through detective work, the Manchester police discovered that Turing was a homosexual. In fact, Alan’s flat was burgled by, he suspected, a homosexual paramour. Outraged, he reported it to police, and mentioned that, yes, he had had a few trysts with the suspect. The police charged him with “lewd and indecent acts” (the same crime that had put Oscar Wilde behind bars a few decades earlier).
I view these errors as serious flaws, but I suppose that Hollywood feels a need to juice up the facts.
November 2015: I’m not going to watch this movie. Reviews by knowledgeable people who’ve seen it decry its many inaccuracies. Just one of many negative reviews on IMDB:
Another Weinstein production that is obvious and sad. Pushing the main Hollywood agenda of homosexuality. Sad and practically comical A very demeaning exploitation of the real heroes and suffering in WWII and woe is the lone gay guy losing the battle to the evil empire of the moral world. Save your money. The acting was made trite by the twisted story and the depth was a deep as a sippy cup. Really disappointing but of course will get tons of attention due to the publicity budget from this group. This once again confirms that you can no longer see a big name production without expecting the story to be trivialized and contain the jaded view of the liberal left who is in a ship going down.
Numberphile uploaded a brief video clip of John Conway, mathematician and inventor of the Game of Life. The interesting thing about the Game of Life is that the only player input that’s needed is initial setup. Then, a computer applies a predefined set of rules to your initial configuration and you watch as your creation either prospers or dies with each iteration. Surprisingly complex patterns can emerge from simple origins. It’s been called “a fun way to consume otherwise unused CPU cycles”.
There’s a good free Game of Life in the Android Play Store.
Dr. Conway is the Von Neumann professor of mathematics at Princeton University.
Last December, mathematician Simon Singh spoke to Google employees about the role of math in The Simpsons.
The math references in The Simpsons episodes are only a few seconds long but contain timeless questions. Mr. Singh tells about them as well as math references in Matt Groening’s Futurama in this entertaining YouTube video, which was recorded at a recent Google gathering.
I’ve found a new fave site with dozens of short, funny, yet educational video clips. It’s about mathematics and is called numberphile.com. It’s produced in the U.K..
The videos are less than ten minutes long. Most of the presenters are college professors. Wait! Wait! Don’t hold that against them! These guys are informal and Brady Haran masterfully edits and produces them with simple graphics so that they’re fun and easy to follow.
Ada Lovelace, 19th century British mathematician (1836)
Painter: Margaret Carpenter (1793-1872)
October 7 honors the first computer programmer.
Ada Lovelace was a gifted mathematician who was born in 1815, the daughter of poet Lord Byron. She composed plans that calculated Bernoulli number sequences for Charles Babbage’s Analytical Engine. Today we’d call these plans a “program”. She also proposed that the steam-driven Analytical Engine could not only perform arithmetic, but could compose music and create graphics. This was around 1845! The Analytical Engine was never completed and Ada died of cancer at age 36. She never saw the Analytical Engine execute her program.
A modern computer language, Ada, is named in her honor. I’ve been fascinated with this language because it contains features similar to Pascal that result in reliable programs. It’s designed for use in real-time applications and is used today to create fly-by-wire and similar critical systems. In 1987 the US Department of Defense mandated that Ada would be the only acceptable language for new defense systems.
In 2009, some Brits set aside a day to commemorate Ada Lovelace as well as all women in technology and science. That day was originally in March. It was moved to October 7 this year. A website, findingada.com, has been created for Ada Lovelace Day.
“Babbage intended to use punched cards to feed instructions and data into the Analytical Engine.
The smaller cards are ‘Operational Cards’ which specify the mathematical operations to be performed – multiplication, division, addition or subtraction. The larger cards are ‘Variable Cards’ which dictate where the numbers to be operated on are found in the machine and where the results should be placed.”
Punched cards for programming the Analytical Engine, 1834-71 · Science Museum, London
Ada Lovelace reported in her notes on the Analytical Engine: “Mr. Babbage believes he can, by his engine, form the product of two numbers, each containing twenty figures, in three minutes”. By comparison the Harvard Mark I [large electromechanical calculator c 1944] could perform the same task in just six seconds. A modern PC can do the same thing in well under a millionth of a second. (from Wikipedia) Learn more about Charles Babbage’s Analytical Engine from:
This is a video biography (produced by PBS’ NOVA in 1997) of the man who changed our understanding of time and space. This 1 hr 46 minute dramatization introduces a very human Albert Einstein. Andrew Sachs (who in the brilliant British sitcom Fawlty Towers played Manuel, the hapless waiter!) seems to have the look and mannerisms of Einstein. The portrayal of Einstein as a dashing young man, and his spotty schooling paint a very human picture.
What did Einstein think of Isaac Newton? Read Einstein on Newton, By Albert Einstein.
I loved this production: it both explored the human side of Dr. Einstein and explained in easy-to-follow steps, the meaning of his special theory of relativity, his general theory of relativity, and his unfinished unified field theory. His initial thought method was simple: he imagined situations that led to a paradox, and then tried to solve the paradox. He seemed to want a simple married life, yet two marriages fell apart, presumably at least in part because of his obsession with learning the universe’s secrets. The qualities that helped him solve puzzles may have been the undoing of his personal life: he described himself “as stubborn as a mule”.
How stubborn? Lying on his deathbed, within hours of his passing, he asked for his reading glasses, a fountain pen, and his notes, so that he could continue working on his unified field theory.
December, 2015: I’m no longer able to view this terrific biography on pbs.org, so I’ve stored it on a server from which you may download or stream it.
For some reason, I found myself wondering why we have 60 seconds in a minute, 60 minutes in an hour, or 360 degrees in a circle. It turns out that these divisions are a 4000 year old legacy from Babylon (a Mestopotamian city-state located about 50 miles south of Baghdad, Iraq). The Babylonians used a base 60 number system. We, of course, use a base 10 (or “decimal”) number system.
Babylonian numerals
I’ve found a number of conjectures that attempt to explain why the Babylonians used a base 60 number system. None makes complete sense to me.
Apparently they also thought that there were 360 days in a year.
If you program computers at anything beyond the most elementary levels, you will be familiar with the binary (base 2) and hexadecimal (base 16) number systems, so a number system with a base other than 10 won’t seem entirely strange. After working in other number systems, I’ve become aware that “numbers” (such as depicted in the first illustration) are mere symbols that represent a quantity. Each of the four symbols below depicts exactly the same quantity: 12.
12 (in decimal, or base 10, notation)
0C (in hexadecimal, or base 16, notation)
00001100 (in binary, or base 2, notation)
(in Babylonian, or base 60, notation)
I’m happy that in the intervening 4000 years, we’ve switched to the decimal number system. Why have we kept the 360 divisions to a circle idea? Maybe I’m missing something, but couldn’t we just decide to divide the circle into, say, 100 divisions? Or 1000 divisions? Does anyone care to join me? I’ll meet you by the third pyramid.
In this interview with physicist Janna Levin (51 minutes), she explains the importance of the insights of mathematicians Kurt Gödel and Alan Turing.
(Originally published October, 2014) The new British film 
The math references in The Simpsons episodes are only a few seconds long but contain timeless questions. Mr. Singh tells about them as well as math references in Matt Groening’s Futurama in this entertaining 
(in Babylonian, or base 60, notation)
Russ' space 