Here’s a documentary on The Beatles from 1000 years in the future:
I sometimes wonder how much history and science has about as much connection to reality as this reconstruction of The Beatles.
Related post: Paleolithic nonsense
History
Military intelligence from serial numbers
During World War II, America and her allies needed to estimate the number of Panzer V tanks Germany had produced. The solution was simple: Look at the serial numbers of the captured tanks. If you assume the tanks had been sequentially numbered — as in fact they were — you could view the serial numbers of the captured tanks as random samples from the entire range. You could then use statistics to estimate the range and hence the number of tanks produced. More details available here.
A few years later America tried to use the serial number trick to estimate the number of Soviet strategic bombers. This time the trick backfired.
In 1958, American military intelligence believed the USSR would soon have four hundred Bison and three hundred Bear bombers capable of striking the American heartland. Their evidence was the high serial number of a Bison that had flown at a May Day parade in Moscow. In fact, the Soviets knew the Americans were watching, and intentionally inflated that number. — Rocket Men, page 118.
The Panzer estimate was accurate because the Allies had hundreds of data points, enough to support the assumption that the tanks were sequentially numbered and to make a good estimate of the total number.
The Bison bomber was only one data point, but it was consistent with what intelligence services (wrongly) believed. At that time, the US had grossly over-estimated the military capabilities of the USSR. According to Rocket Men, Khrushchev turned down US offers to cooperate in space exploration because he feared that such cooperation would give the US a more accurate assessment of his country’s military.
Related post: Selection bias and bombers
The grand unified theory of 19th century math
The heart of 19th century math was the study of special functions arising from mathematical physics.
It is well known that the central problem of the whole of modern mathematics is the study of the transcendental functions defined by differential equations.
The above quote was the judgment of Felix Klein (of Klein bottle fame) in 1893. The differential equations he had in mind were the second order differential equations of mathematical physics.
Special functions were the core of 19th century math, and hypergeometric series were the grand unifying theory of special functions. (Not every special function is hypergeometric, but quite a few are.) And yet they’re hardly taught any more. I never heard of hypergeometric series in college, even though I studied differential equations and applied math. Later I encountered hypergeometric functions first in combinatorics and only later in differential equations.
It’s odd that what was “the central problem of the whole of modern mathematics” could become almost a lost art a century later. How could this be? I believe part of the explanation is that special functions, and hypergeometric function in particular, fall between two stools: too advanced for undergraduate programs but not a hot enough of a research area for graduate programs.
Related: Consulting in differential equations
Earliest personal account of slavery
According to William R. Cook, there is only one ancient account of slavery written by a slave that still survives: a letter written by Saint Patrick. We have many ancient documents that were written by slaves, but not documents about their experience of being a slave.
Patrick was born in Britain. He was kidnapped at age 16 and became a slave in Ireland. He served as a slave for six years before escaping and returning to Britain. Later he returned to Ireland as a missionary. Although there are many legends surrounding Patrick, historians generally agree that his autobiographical letter, now known as the Confession of St. Patrick, is authentic.
I was surprised to hear that there are no other extant autobiographies of slaves since there were many literate slaves in antiquity. Obviously slaves were not given the liberty to write about whatever they pleased, and slave owners would be unlikely to request candid biographies of their chattel. Still, I imagine some slaves wrote autobiographies, perhaps secretly. But it makes sense that such documents would not likely be preserved.
The lack of first-hand accounts of slavery may contribute to our rosy mental image of classical history. When we think of ancient Greece, we think of Plato and Aristotle, not the anonymous slaves who made up perhaps 40% of the population of classical Athens.
[Update December 2014: The information above comes from a Teaching Company course by William Cook. The original link is dead, and I don’t remember now which of his courses it was from.]
Computing before Fortran
In the beginning was Fortran. Or maybe not.
It’s easy to imagine that no one wrote any large programs before there were compilers, but that’s not true. The SAGE system, for example, involved 500,000 lines of assembly code and is regarded as one of the most successful large computer systems ever developed. Work on SAGE began before the first Fortran compiler was delivered in 1957.
The Whirlwind computer that ran SAGE had a monitor, keyboard, printer, and modem. It also had a light gun, a precursor to the mouse. It’s surprising that all this came before Fortran.
Related posts
Army surplus flamethrowers
It’s hard to imagine the amount of equipment the US Army decommissioned after World War II: parachutes, diesel engines, Jeeps, etc. Apparently even flamethrowers were up for grabs.
An enterprising merchant in Quakertown, Pennsylvania ran a newspaper ad for military flamethrowers, pitching the weapon as a handy household gadget that “destroys weeds, tree stumps, splits rocks, disinfects, irrigates. 100 practical uses. $22 for 4 gal. tank, torch, hose.”
Source: Bright Boys: The Making of Information Technology, page 145.
Deconstructing Thomas Edison
I’m reading Remarkable Engineers to write a review for a website. The prose is pretty bland, though it got spicier in the chapter on Thomas Edison. It seems the author felt he needed to take Edison down a notch.
The career of Thomas Edison was not that of a great man of science, or even that of an inventive genius … His only major scientific discovery was the fact that a vacuum lamp could act as a rectifier, passing only negative electric currents. … He was said to have invented the business of invention.
So Edison was an engineer rather than a scientist. This criticism seems odd in a book devoted to remarkable engineers.
Surely Edison was an inventive genius; he held over a thousand patents, more than anyone has ever held. That is not to say anyone believes he came up with over a thousand unprecedented ideas completely by himself. He built on the work of others. He coordinated the work of his employees. He took ideas that were not being used and commercialized them. Perhaps he was more of an entrepreneurial genius than a scientific genius, but he was a genius nonetheless.
Related posts
Technology history quiz
I was skimming through Big Ideas: 100 Modern Inventions the other day and was surprised at the dates for many of the inventions. I thought it would be fun to pick a few of these and make them into a quiz, so here goes.
Match the following technologies with the year of their invention.
First the inventions:
- The computer mouse
- Radio frequency identification (RFID)
- Pull-top cans
- Bar codes
- Touch tone phones
- Cell phones
- Car airbags
- Automated teller machines (ATM)
- Magnetic resonance imaging (MRI)
- Latex paint
Now the years:
- 1948
- 1952
- 1953
- 1963
- 1968
- 1969
- 1973
- 1977
Two of the years are used twice. Quiz answers here.
All examples taken from Big Ideas: 100 Modern Inventions That Have Transformed Our World
How the central limit theorem began
The Central Limit Theorem says that if you average enough independent copies of a random variable, the result has a nearly normal (Gaussian) distribution. Of course that’s a very rough statement of the theorem. What are the precise requirements of the theorem? That question took two centuries to resolve. You can see the final answer here.
The first version of the Central Limit Theorem appeared in 1733, but necessary and sufficient conditions weren’t known until 1935. I won’t recap the entire history here. I just want to comment briefly on how the Central Limit Theorem began and how different the historical order of events was from the typical order of presentation.
A typical probability course might proceed as follows.
- Define the normal distribution.
- State and prove a special case of the Central Limit Theorem.
- Present the normal approximation to the binomial as a corollary.
This is the opposite of the historical order of events.
Abraham de Moivre discovered he could approximate binomial distribution probabilities using the integral of exp(-x2) and proved an early version of the Central Limit Theorem in 1733. At the time, there was no name given to his integral. Only later did anyone think of exp(-x2) as the density of a probability distribution. De Moivre certainly didn’t use the term “Gaussian” since Gauss was born 44 years after de Moivre’s initial discovery. De Moivre also didn’t call his result the “Central Limit Theorem.” George Pólya gave the theorem that name in 1920 as it was approaching its final form.
For more details, see The Life and Times of the Central Limit Theorem.
Related links:
Cinco de Mayo and the world’s largest cake
Today is Cinco de Mayo, the holiday that celebrates the Mexican army’s defeat of French forces at the Battle of Puebla on May 5, 1862.
Cinco de Mayo is unusual in that it is a Mexican holiday more popular in the United States than in Mexico. According to Wikipedia,
While Cinco de Mayo has limited or no significance nationwide in Mexico, the date is observed in the United States and other locations around the world as a celebration of Mexican heritage and pride.
Cinco de Mayo is a bigger holiday in Texas than Texas Independence Day. (Readers unfamiliar with Texas history may be surprised to learn that Texas was once a sovereign nation. The Republic of Texas existed for nearly a decade between gaining independence from Mexico in 1836 and joining the United States in 1845.)
Texas Independence Day, March 2, usually goes virtually unnoticed. However in 1986, the sesquicentennial, there was a big celebration in Austin. Activities included baking the world’s largest cake. The left-overs were distributed to the dorms at the University of Texas and so I had some of the cake. Quite a bit, actually. You might think that a cake baked for the purpose of setting a world record would be barely edible, but it was actually pretty good lemon cake.