Mathematica et cetera

Category: Miscellaneous

The Shoe-Banging Incident and Historiography

A montage, obviously.

In 1960, the Cold War was in a crescendo. The communists had won the civil war in China, reasserted themselves in Korea and weren’t showing any signs that they would withdraw from Eastern Europe. Another war was underway in Indochina and the United States was starting to get involved. Year after year the opposing sides would develop bigger nuclear weapons and deadlier missiles to deliver them. On this day 61 years ago, before hundreds of reporters and delegates from every UN member state, Khrushchev had his finest hour. Irate at Sumulong, the Philippine delegate who had accused the Soviet Union of “swallowing up”  the rights of the nations of Eastern Europe, he walked up to the podium and berated him while banging his shoe on the table. Or did he?

The United Nations official transcript for the assembly contains Sumulong’s speech, but not Khrushchev’s, and no mention of any shoe. An article in the UN’s site claims he was not at the rostrum when the incident is claimed to have occurred. It claims that it was the Romanian representative who called the point of order, not Khrushchev. Another issue of contention is the origin of the shoe. One version has it that Khrushchev hit his hand on the table so hard he broke his watch, and after that he took off his shoe to bang with instead. The Wikipedia article says his granddaughter claimed he was wearing tight shoes and took them off, so when he stood up shoeless and banged his hand on the table and his watch fell off he saw the shoe and picked it up. But the source it cites for that is incomplete in the archive and the original is down. Note that in the first version the watch stopped and in the second it fell off. Another version claims he somehow arranged a third shoe just to bang it. The New York Times article also has one version by John Loengard who says he never banged it.

Come and take it

It’s an irresistible story isn’t it? Xerxes, king of kings, demands Leonidas give up his weapons; Leonidas replies “Come and take them!”. So irresistible that twenty-three centuries later separatist Texans remembered it when asked to return a cannon.Another example, when the Ottoman Sultan demanded:

Sultan Mehmed IV to the Zaporozhian Cossacks: As the Sultan; son of Muhammad; brother of the sun and moon; grandson and viceroy of God; ruler of the kingdoms of Macedonia, Babylon, Jerusalem, Upper and Lower Egypt; emperor of emperors; sovereign of sovereigns; extraordinary knight, never defeated; steadfast guardian of the tomb of Jesus Christ; trustee chosen by God Himself; the hope and comfort of Muslims; confounder and great defender of Christians – I command you, the Zaporogian Cossacks, to submit to me voluntarily and without any resistance, and to desist from troubling me with your attacks.

— Turkish Sultan Mehmed IV

The Cossacks replied:

Zaporozhian Cossacks to the Turkish Sultan!

O sultan, Turkish devil and damned devil’s kith and kin, secretary to Lucifer himself. What the devil kind of knight are thou, that canst not slay a hedgehog with your naked arse? The devil shits, and your army eats. Thou shalt not, thou son of a whore, make subjects of Christian sons. We have no fear of your army; by land and by sea we will battle with thee. Fuck thy mother.

Thou Babylonian scullion, Macedonian wheelwright, brewer of Jerusalem, goat-fucker of Alexandria, swineherd of Greater and Lesser Egypt, pig of Armenia, Podolian thief, catamite of Tartary, hangman of Kamyanets, and fool of all the world and underworld, an idiot before God, grandson of the Serpent, and the crick in our dick. Pig’s snout, mare’s arse, slaughterhouse cur, unchristened brow. Screw thine own mother!

So the Zaporozhians declare, you lowlife. You won’t even be herding pigs for the Christians. Now we’ll conclude, for we don’t know the date and don’t own a calendar; the moon’s in the sky, the year with the Lord. The day’s the same over here as it is over there; for this kiss our arse!

— Koshovyi otaman Ivan Sirko, with the whole Zaporozhian Host

This one is also a cultural phenomenon in Ukraine and to a lesser extent Russia. The painting was bought by Tsar Alexander III by the highest price paid for a Russian painting at the time. For example here are Ukrainian people’s deputies (members of parliament) reenacting it, but as a reply to Putin:


The takeaway

This might seem like a trivial point to historians, but we shouldn’t take these stories too seriously. They’re very popular with the general public, probably because we use them to imagine the events unfolding like a movie. People make lists of this type of thing. And they’re usually stated as fact too. Contrast with, for example, the seven kings of Rome which people usually make sure to say the story is legend and not to be taken literally. We can’t determine with certainty what happened in living memory during a period when cameras existed. It was on the New York Times the following day, and yet there’s still debate about it. It seems hopeless to try to determine what Caesar said when crossing the Rubicon, or what Louis XIV claimed his metaphysical relation to the state was. I think the best policy is to always emphasize that these things are apocryphal when talking about them.

Book Recommendations

  • Seeing Like A State by James C. Scott.

I just had to reproduce the cover below. It’s a picture of a road that is simultaneously supposed to be straight and run across a line of constant latitude. It’s very representative of the theme of the book: states trying to achieve certain narrow goals and getting unexpected results.

  • Nabokov’s Favorite Word Is Mauve by Benn Blatt.

Blatt quantifies several famous authors’s quirks. George RR Martin likes to describe things as “black as pitch”; women authors use the words pillows, lace, curls, dress, china, skirt, and curtains more often than men; the word most indicative of a British as opposed to an American writer is wanked.

  • Homage to Catalonia by George Orwell.

Orwell’s memoir of his time fighting in the Spanish Civil War. Funnier than you would expect.


This is a list of links to things I find interesting.


A blog series on the classical theorem of multivariable calculus.

A blog post with a proof of the Abel-Ruffini theorem. Complete with javascript group actions.

A blog post by Terence Tao.

A blog post by Scott Aaronson.

Using computers to generate numerical conjectures. My favorite is

    \[-\frac 4\pi =-1+\frac 1{-3+\frac 1{-3+\frac 4{-5+\frac 9{-7+\frac {16}{\dots}}}}}\]

This is very difficult to explain. Anyway, it’s a great explanation of what mathematics is, what axioms are, etc.

Twofold performance increase on the greatest common divisor operation by using the binary variation of Euclid’s algorithm.

The probability of ending up with a single coin when you start with n and toss them and discard the tails.

The highlight of this post is the identity

    \[\sigma_7(n) = \sigma_3(n) + 120\sum_{m=1}^{n-1}\sigma_3(m)\sigma_3(n-m).\]


A blog series defending a tentative theory that the obesity epidemic is caused by environmental contaminants.

A collection of courses which attempts to teach physics concepts with the minimum amount of overhead.

A derivation of the Boltzmann distribution (of the density of the atmosphere versus height) in a not handwavey way.

  • Saving the earth from the Sun’s red giant phase

A game about an universe where you can run at light speed. It’s great for building intuition about relativistic phenomena.


A graph of the S&P 500 Shiller PE since 1872.

The source of that data, Shiller himself.

Aswath Damodaran investigated the motives for China’s recent crackdown on its tech companies.


  • Earth and Stars – Thomas Pesquet

Picture taken aboard the International Space Station.

Earth and stars


A podcast series on the history of Rome, from its founding to the fall of the Western Empire. In astounding detail.

Orwell ponders about the consequences of the then new atomic bomb technology. This also explains something I always found unclear in 1984: why is it that the world is divided into superstates? Wouldn’t an autocracy of many conventional sized states be as plausible? In his words “we have before us the prospect of two or three monstrous super-states, each possessed of a weapon by which millions of people can be wiped out in a few seconds, dividing the world between them”.

A project that makes exhaustive lists of war related things, notably a list of all the wars between 1816 and 2007.

Successful bioterrorism attack.


Measurements of the latency of several computers and phones.


A university decided to do the obvious and minmax their ranking.

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