stop referencing yourself!

hey mathletes, get this: when the above formula is graphed using a set of predetermined ranges for x and y—it produces itself! it’s called tupper’s self-referential formula and was invented by lee iacocca when he was developing the rack and pinion steering on the dodge caravan (a wildly successful minivan in its day). many years later, a minivan fitting this description ran over my neighbor’s pet snake, betelgeuse. accounts vary as to whether the minivan was swerving to get out of betelgeuse’s way or to hit him (presumably as a social service). no matter the intent, we have the rack and pinion steering to hold accountable for the result (a smear of snake guts along west church street).

see also these robo-jokers.

chaz babbage’s windows error report

ever since i posted the marvelous letter from charles babbage, father of your laptop, to alfred tennyson, i could not shake babbage’s neuroses from my thoughts. the one that struck me the most was that he actually tallied and categorised the causes of 464 broken windows of a nearby factory in a ten month period. what mad mind would do this? whatever the state of his mind, his data was ripe for the pickin’ and plottin’—thus this chart (you can distend it with a well-placed mouseclick).

for the inquisitive: this is the first treemap that i have had occasion to make and i didn’t quite know how to start—my slapdash solution involved these two programs.

the gall-peters projection -or- the earth as your imperialist overlords never meant you to see it »

Arno Peters promoted his map as a superior alternative to the Mercator projection, which was suited to navigation but also used commonly in world maps. The Mercator projection increasingly inflates the sizes of regions according to their distance from the equator. This inflation results, for example, in a representation of Greenland that is larger than Africa, whereas in reality Africa is 14 times as large. Since much of the technologically underdeveloped world lies near the equator, these countries appear smaller on a Mercator, and therefore, according to Peters, seem less significant.

On Peters’s projection, by contrast, areas of equal size on the globe are also equally sized on the map. By using his “new” projection, poorer, less powerful nations could be restored to their rightful proportions. This reasoning has been picked up by many educational and religious bodies, leading to adoption of the Gall-Peters projection among some socially concerned groups.

related: the colour green as your imperialist overlords never meant you to see it.

news bulletin (for immediate release): my former boy-bandmates, rafi kam and dallas penn, who style themselves the internets celebrities, have just released a new video on the topic of street vending called the vend diagram for which they approached me to concoct some venn diagrams (wordplay!). the above chart is perhaps my favourite as it deals with creole and mixed languages and ends rather absurdly where it all began—with a ginormous slice* of pie.

rafi and dallas’ investigation into how the economy is effing up the most micro of businesses—the street vendors, can be found here. i made the charts for it, but i will not now confirm (nor double confirm) that i made a cameo in it.

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*properly speaking, the shape of this slice is a reuleaux triangle (maths!)

beta-testing a new puzzle

many are the puzzles that i attempt to solve, far fewer are the ones that i actually do solve—but a still smaller category are the puzzles that i write myself. i developed the following puzzle last night while suffering from insomnia and staring at a digital clock.

the setup: each numeral on a clock is composed of digital sections (eg. 8 has seven sections; 9 has six). using the 12-hour clock…

easy: determine the difference (in minutes) between the time with the fewest total sections and the time with most total sections.

hard: determine the time with the single greatest net change in sections from the minute before it (e.g. the net change between 3:34 and 3:33 is 1 section).

comments are now enabled (for 1 day only) in anticipation of the avalanche of answers, feedback, and derivatives that you might have.

UPDATE: the correct answers to both the easy and hard questions appear in the comments, so if you want to submit your solution without reading anyone else’s you can always email me via email.

a severe constraint

yesterday, i received a very curious volume from a friend who knows how much i relish (1) well designed books, and (2) texts written under an elected constraint. the book is severance by robert olen butler (2006). the book’s jacket says:

After decapitation, the human head is believed to remain in a state of consciousness for one and one-half minutes.

In a heightened state of emotion people speak at the rate of 160 words per minute.

Inspired by the intersection of these two seemingly unrelated concepts, Pulitzer Prize-winning author Robert Olen Butler has written sixty-two stories, each exactly 240 words in length, capturing the flow of thoughts and feelings that rush through a mind after the head has been severed. The characters are both real and imagined - Medusa (beheaded by Perseus, 2000 B.C.), Anne Boleyn (beheaded at the behest of Henry VIII, 1536), a chicken (beheaded for Sunday dinner in Alabama, 1958), and the author himself (decapitated on the job, 2008). These final thoughts are not a morbid or macabre reflection on death; they are a very distilled way of looking back on life and capturing its essence.

here, the author reads some of his stories on all things considered.

if you’re havin’ algorithm problems, i feel bad for you son

think your latest algorithm problem has got the best of you? consider the formulae and tables needed to determine the exact sunday on which to observe easter. this calculation is so convoluted that the very act of forecasting the date was given its own name—computus—and was considered by many to be the most significant calculation of the middle ages.

for you to engage in computus requires that you perform a series of complex calculations that factor in the (idealized (ie. integerized)) cycles of three heavenly bodies—the earth, moon and sun—through duodecimal and sexagesimal numbering systems and various other (religious and time) constraints initiated by the likes of hindus, jews, christians, sumerians, babylonians, greeks, and romans over the course of several millennia. even the great carl friedrich gauss° had a hard time nailing down the formula in the 1800’s when computers were only able to run windows 3.1.

for much more, including what the above image is all about, there is wikipedia.

your weekend todo list: solve the dorabella cipher »

The Dorabella Cipher is a letter written and enciphered by Edward Elgar [the guy who scored your graduation ceremony] to Miss Dora Penny [a young girl who was also the inspiration for one of his enigma variations]. She was never able to decipher it and its meaning remains unknown to this day.

A count of the 87 characters reveals a symbol frequency very close to that that would be expected if the cipher were a simple substitution cipher, based on a plain text in English, but attempts to decipher it along these lines have so far proved fruitless, leading to speculation the cipher may be more complex.

of course, it could also be an unelaborate hoax. but this should not stop you from making it your weekend project and finally showing the world the potentially pervy message that lies hidden under all those squigglies.

symphony No. 0 in d minor »

The composer Anton Bruckner regarded his early Symphony in D minor to be unworthy of including in the canon of his works, and he wrote ‘gilt nicht’ on the score and a circle with a crossbar, intending it to mean “invalid”. But posthumously, this work came to be known as Symphony No. 0 in D minor.