“Mathematics, rightly viewed, possesses not only truth, but supreme beauty”*…
Maryam Mirzakhani did not enjoy mathematics to begin with. She dreamed of being an author or politician, but as a top student at her all-girls school in Tehran she was still disappointed when her first-year maths exam went poorly. Her teacher believed her – wrongly – to have no particular affinity with the subject.
Soon that would all change. “My first memory of mathematics is probably the time [my brother] told me about the problem of adding numbers from 1 to 100,” she recalled later. This was the story of Carl Gauss, the 18th-century genius whose schoolteacher set him this problem as a timewasting exercise – only for his precocious pupil to calculate the answer in a matter of seconds.
The obvious solution is simple but slow: 1+2+3+4. Gauss’s solution is quicker to execute, and far more cunning. It goes like this: divide the numbers into two groups: from 1 to 50, and from 51 to 100. Then, add them together in pairs, starting with the lowest (1) and the highest (100), and working inwards (2+99, 3+98, and so on). There are 50 pairs; the sum of each pair is 101; the answer is 5050. “That was the first time I enjoyed a beautiful solution,” Mirzakhani told the Clay Mathematics Institute in 2008.
Since then, her appreciation for beautiful solutions has taken her a long way from Farzanegan middle school. At 17 she won her first gold medal at the International Mathematics Olympiad. At 27 she earned a doctorate from Harvard University. The Blumenthal Award and Satter Prize followed, and in 2014 she became the first woman to be awarded the Fields Medal, the highest honour a mathematician can obtain.
Before this particular brand of wonder became perceptible to Mirzakhani, she experienced feelings many of us can relate to: to the indifferent, her subject can seem “cold”, even “pointless”. Yet those who persist will be rewarded with glimpses of conceptual glory, as if gifted upon them by a capricious god: “The beauty of mathematics,” she warned, “only shows itself to more patient followers.”
This concept of “beauty” found in maths has been referred to over centuries by many others; though, like beauty itself, it is notoriously difficult to define…
For an experienced mathematician, the greatest equations are beautiful as well as useful. Can the rest of us see what they see? “What makes maths beautiful?”
[From The New Humanist, via the ever-illuminating 3 Quarks Daily]
Maryam Mirzakhani died last Friday, a victim of breast cancer; she was 40. As Peter Sarnak (a mathematician at Princeton University and the Institute for Advanced Study) said, her passing is “a big loss and shock to the mathematical community worldwide.” See also here.
* Bertrand Russell, A History of Western Philosophy
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As we accede to awe, we might spare a thought for Andrey (Andrei) Andreyevich Markov; he died on this date in 1922. A Russian mathematician, he helped to develop the theory of stochastic processes, especially those now called Markov chains: sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors. (For example, the probability of winning at the game of Monopoly can be determined using Markov chains.) His work on the study of the probability of mutually-dependent events has been developed and widely applied to the biological and social sciences.
“What’s it mean; are you determined / To make modern all mankind?”*…
Over the past century, there have been numerous expeditions to find a mythical lost city in the Mosquitia rainforest. La Ciudad Blanca keeps being discovered, over and over again; practically any time anyone finds the remains of any settlement, they call it that. I know of half a dozen large sites that have each been deemed ‘the White City’; there must be others. In all cases, the ‘discoverers’ are outsiders, and their find is presented as a heroic accomplishment. They want us to believe that they are intrepid explorers – achieving what others couldn’t because of their guts, money, technology, business acumen and grit.
Nothing in their description is accurate. The cities aren’t lost; the people living in these areas know all about them. And the original legends do not even reference cities; rather, they refer to locations that, for whatever reason, represent a golden age for indigenous communities. Even the landscape is not particularly dangerous; children grow up there, after all…
Archaeologist Christopher Begley asks: “Ancient ruins keep being ‘discovered’: were they ever lost?”
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As we dig, we might send acquisitive birthday greetings to Baron Nils Erland Herbert Nordenskiöld; he was born on this date in 1877. A Swedish archeologist and anthropologist, he was a foremost scholar of South American Indian culture in his time. From 1913, he built an extensive collection of “discovered and recovered” South American native artifacts at the Gotebörg Ethnographic Museum, which he headed. His work was influential in the study of archaeology and anthropology throughout Scandinavia.
“To me, pictures are like blintzes – ya gotta get ‘em while they’re hot”*…
Sure. I’d like to live regular. Go home to a good looking wife, a hot dinner, and a husky kid. But I guess I got film in my blood. I love this racket. It’s exciting. It’s dangerous. It’s funny. It’s tough. It’s heartbreaking.
-Weegee
Weegee wanted his pictures to show some humanity. He walked back about a hundred feet. Set up his camera. Used flash powder and Kazam! There was the whole scene. The corpse. The blood. The cops. The balcony seat of people looking out to see what had just happened. Drama. Humanity. Crime.
Weegee came out of Złoczów now part of the Ukraine. He was born Arthur Fellig in June 1899. He emigrated with his family. They landed New York 1909. Lived in the Lower East Side. His father was a hatmaker and part-time rabbi. Weegee took whatever work came. He became a janitor. Got the nickname “Squeegee Boy.” He hung around with the bums on the Bowery. Started taking photographs. First passport pictures, then commercial work. At the age of thirty-five, he upped his game, quit commercial work, became a freelance news photographer.
He went out nights, hung around the police station waiting for the stories to come in over the teletype. Off he went taking pictures of murders, fires, fender benders, wacko kids on their way to juvie hall. He spent two years with no accreditation following the police all around town. In 1938, the cops gave him his own police radio. Weegee could tune in and pick up on what was happening. Most times he got to the crime scene before the cops. The cops thought he must be psychic. This gave rise to the apocryphal story his nickname was the phonetic spelling of “Ouija.” Weegee added a darkroom to the trunk of his car. He took his picture, developed it at the scene, put his print on the back, and sold it to the papers. During his ten years at police headquarters, Weegee said he must have photographed 5,000 murders—“at least one murder every night.”…
More of the story– and more examples of the extraordinary work– at “Through a Lens, Darkly: Weegee’s Photographs of Death and Disaster.”
For more of Weegee in his own words: “Altering life by holding it still”*…
* Weegee
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As we snap it up, we might send pacific birthday greetings to Mildred Lisette Norman; she was born on this date in 1908. Better known by the descriptor she gave herself, “Peace Pilgrim,” she was a non-denominational spiritual teacher, mystic, pacifist, vegetarian activist, and peace activist. In 1952, she became the first woman to walk the entire length of the Appalachian Trail in one season; she then walked across the United States to speak with anyone she encountered about peace– and journey that lasted for 7 cross-country round-trips over 28 years.
“Any kid will run any errand for you, if you ask at bedtime”*…
Truly, bedtimes are one of the great injustices of American childhood. Turns out, they’re also a pretty good example of how sleep — a biological need that we can’t live without — is intertwined with the much more subjective vagaries of culture. It’s culture, after all, that convinced my parents that I needed to be in bed by 7:30 p.m. in July. And my still slightly simmering resentment of that fact, while anecdotally pretty normal among my late Gen X/early millennial American peers, might not be universal…
Hit the hay on your own time at: “Don’t Tell The Kids, But Bedtime Is A Social Construct.”
* Red Skelton
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As we move into the arms of Morpheus, we might celebrate one of the greatest contributions to a good night’s sleep: on this date in 1902, Willis Carrier completed drawings for what became recognized as the world’s first modern air conditioning system. He kept improving his design… and in the process created the air conditioning industry.
“With recording, everything changed”*…
To the question “When were recordings invented?,” we might be tempted to answer “1877” — the year when Thomas A. Edison was first able to record and playback sound with a phonograph. But what if we think of recordings not as mere carriers of sound, but as commodities that can be bought and sold, as artifacts capable of capturing and embodying values and emotions; of defining a generation, a country or a social class? The story then becomes one that unfolds over three decades and is full of many layers and ramifications. Without Edison’s technological innovations, recordings would have certainly never existed — but hammering out the concept of recording were also a myriad of other inventors, musicians, producers and entrepreneurs from all over the world. Most of them were enthusiastic about being part of a global revolution, but they worked in close connection with their milieu too, shaping recording technologies and their uses to relate to the needs, dreams, and desires of the audiences they knew…
The full(er) story: “Inventing the Recording.”
* “With recording, everything changed. The prospect of music being detachable from time and place meant that one could start to think of music as a part of one’s furniture. It’s an idea that many composers have felt reluctant about because it seemed to them to diminish the importance of music.” – Brian Eno
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As we drop the needle, we might recall that it was on this date in 1900 that “His Master’s Voice,” the logo of the Victor Talking Machine Company (later RCA Victor), was registered with the US Patent Office. The logo famously featured the dog “Nipper” looking into the horn of a gramophone.
“Behold the child, by Nature’s kindly law pleased with a rattle, tickled with a straw”*…
The plastic straw is a simple invention with relatively modest value: For a few moments, the device helps make beverages easier to drink. And then, due to reasons of sanitation and ease of use, the straws are thrown away, never to be seen again.
Except, of course, the straw you use in your iced coffee doesn’t biodegrade, and stays around basically forever, often as ocean junk. That, understandably, is leading to chatter around banning plastic straws—notably in Berkeley, California, often the first place to ban anything potentially damaging to the environment.
And while the rest of the world won’t be banning straws anytime soon, maybe they should start thinking about it, because the problem with straws is one of scale. According to National Geographic, Americans use 500 million straws every single day—more than one per person daily…
Whence this waste? “A Brief History of the Modern-Day Straw, the World’s Most Wasteful Commodity.”
[Your correspondent highly recommends Tedium, the original source of this piece.]
* Alexander Pope
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As we suck it up, we might recall that it was on this date in 1869 that Hippolyte Mège-Mouriès patented margarine, the creation with which he won the contest held by Emperor Napoleon III to find a substitute for the butter used by the French Navy.
A rough contemporary of Jules Verne, Mège-Mouriès was surely one of the reasons for Verne’s scientific and technical optimism: Mège-Mouriès began his career at age 16 as a chemist’s assistant. By the 1840’s he had improved the syphilis drug, Copahin, after which he patented a variety of creations including tanning, effervescent tablets, paper paste, and sugar extraction. By the 1850s he had turned to food research and developed a health chocolate (featuring a proprietary calcium phosphate protein) and developed a method that yielded 14% more white bread from a given quantity of wheat. After 1862, he concentrated his research on fats– the primary product of which was his invention of margarine (though he also scored yet another another patent, for canned meat).
“What was the best thing before sliced bread?”*…
Rohwedder’s bread slicer in use by the Papendick Bakery Company in St. Louis
Some products are so ubiquitous that it can feel as if they were never invented at all.
Take sliced bread. Around 130 years ago, the idea of buying a pre-sliced loaf would have been met with confusion, writes Jesse Rhodes for Smithsonian Magazine. “In 1890, about 90 percent of bread was baked at home, but by 1930, factories usurped the home baker,” Rhodes writes. But the two breads weren’t the same thing–”factory breads were also incredibly soft,” she writes, making them difficult to slice properly at home with a bread knife.
Since breadmaking had moved to factories, why not bread slicing as well? On this day in 1928, in Chillicothe, Missouri, the Chillicothe Baking Company became, in the words of its plaque, “The Home of Sliced Bread.” It was the place where the bread-slicing machine was first installed, wrote J. J. Thompson for Tulsa World in 1989. Thompson was speaking with the son of the bread-slicing machine’s inventor, Richard O. Rohwedder. His father, Otto F. Rohwedder, was a jeweler who started work on the bread-slicing project years before…
It took a surprising amount of technological know-how to make the bread that birthed the expression: “Take a Look at the Patents Behind Sliced Bread.”
* George Carlin
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As we reach for the PB and J, we might recall that it was on this date in 1868 that Alvin J. Fellows patented his Improvement in Tape Measures– the first spring-click (retractable) tape measure.
