This figure contains 15 lines and 15 points, with three points on each line and three lines through each point, yet no three points are connected by three lines to form a triangle.
It’s named after mathematicians Luigi Cremona and Herbert William Richmond, who studied it in the late 19th century.
As Washington State University anthropologist Grover Krantz was dying of pancreatic cancer, he told his colleague David Hunt of the Smithsonian:
“I’ve been a teacher all my life and I think I might as well be a teacher after I’m dead, so why don’t I just give you my body.”
When Hunt agreed, Krantz added, “But there’s one catch: You have to keep my dogs with me.”
Accordingly, in 2003, Krantz’s skeleton was laid to rest in a green cabinet at the National Museum of Natural History alongside the bones of his Irish wolfhounds Clyde, Icky, and Yahoo.
Krantz’s bones have been used to teach forensics and advanced osteology to students at George Washington University.
And in 2009 his skeleton was articulated and, along with Clyde’s, displayed in the exhibition “Written in Bone: Forensic Files of the 17th Century Chesapeake.”
From a letter of Charles Darwin to Charles Lyell, April 1860:
I must say one more word about our quasi-theological controversy about natural selection, and let me have your opinion when we meet in London. Do you consider that the successive variations in the size of the crop of the Pouter Pigeon, which man has accumulated to please his caprice, have been due to ‘the creative and sustaining powers of Brahma?’ In the sense that an omnipotent and omniscient Deity must order and know everything, this must be admitted; yet, in honest truth, I can hardly admit it. It seems preposterous that a maker of a universe should care about the crop of a pigeon solely to please man’s silly fancies. But if you agree with me in thinking such an interposition of the Deity uncalled for, I can see no reason whatever for believing in such interpositions in the case of natural beings, in which strange and admirable peculiarities have been naturally selected for the creature’s own benefit. Imagine a Pouter in a state of nature wading into the water and then, being buoyed up by its inflated crop, sailing about in search of food. What admiration this would have excited — adaptation to the laws of hydrostatic pressure, &c &c For the life of me I cannot see any difficulty in natural selection producing the most exquisite structure, if such structure can be arrived at by gradation, and I know from experience how hard it is to name any structure towards which at least some gradations are not known.
Ever yours,
C. Darwin.
In 1852, British artist Benjamin Waterhouse Hawkins engaged to make 33 life-size concrete models of extinct dinosaurs, to be arranged in a park in southern London around the relocated Crystal Palace. Throughout the work he conferred with a team of leading British scientists, and on New Year’s Eve 1853 they celebrated their accomplishment with a dinner party held inside one of the sculptures:
Twenty-one of the guests were accommodated with seats ranged on each side of the table, within the sides of the iguanodon. Professor Owen, one of the most eminent geologists of the day, occupied a seat at the head of the table, and within the skull of the monster. Mr. Francis Fuller, the Managing Director, and Professor Forbes, were seated on commodious benches placed in the rear of the beast. An awning of pink and white drapery was raised above the novel banqueting-hall, and small banners bearing the names of Conybeare, Buckland, Forbes, Owen, Mantell, and other well-known geologists, gave character and interest to the scene. When the more substantial viands were disposed of, Professor Owen proposed that the company should drink in silence ‘The memory of Mantell, the discoverer of the iguanodon,’ the monster in whose bowels they had just dined.
They concluded with a “roaring chorus” in praise of the “antediluvian dragon”:
A thousand ages underground
His skeleton had lain;
But now his body’s big and round,
And he’s himself again!
His bones, like Adam’s, wrapped in clay,
His ribs of iron stout,
Where is the brute alive to-day
That dares with him turn out?
Beneath his hide he’s got inside
The souls of living men,
Who dare our Saurian now deride
With life in him again?
(Chorus) The jolly old beast
Is not deceased,
There’s life in him again. (A roar.)
In fairy land are fountains gay,
With dragons for their guard:
To keep the people from the sight,
The brutes hold watch and ward!
But far more gay our founts shall play,
Our dragons, far more true,
Will bid the nations enter in
And see what skill can do!
For monsters wise our saurians are,
And wisely shall they reign,
To spread sound knowledge near and far
They’ve come to life again!
Though savage war her teeth may gnash,
And human blood may flow,
And foul ambition, fierce and rash,
Would plunge the world in woe,
Each column of this palace fair
That heavenward soars on high,
A flag of hope shall on it bear,
Proclaiming strife must die!
And art and science far shall spread
Around this fair domain,
The People’s Palace rears its head
With life in it again.
(From Routledge’s Guide to the Crystal Palace and Park at Sydenham, 1854.)
The familiar posture of victory — raising the arms, tilting the head back, and expanding the chest — appears to be hard-wired into the human brain, probably because it was a universal sign of dominance in our ape ancestors.
In 2008, psychologists Jessica Tracy and David Matsumoto compared the expressions and body language of sighted, blind, and congenitally blind judo competitors representing more than 30 countries in the 2004 Olympic and Paralympic Games. They found that the blind athletes used the same gestures as their sighted peers, even though they’d never seen anyone else use them.
“Since congenitally blind individuals could not have learned pride and shame behaviours from watching others, these displays of victory or defeat are likely to be an innate biological propensity,” Tracy told the Telegraph.
The same victory gesture is seen in children as young as 3. Tracy said she was studying similar behaviors in chimps and that “anecdotal evidence mentioned in the paper suggests that, yes, the human pride and shame displays are very similar to non-human displays of dominance and submission, seen in a wide range of animals.”
(Jessica L. Tracy and David Matsumoto, “The Spontaneous Expression of Pride and Shame: Evidence for Biologically Innate Nonverbal Displays,” Proceedings of the National Academy of Sciences 105:33 [August 19, 2008], 11655-11660.)
In the 1970s psychologist David Rosenhan sent healthy volunteers to 12 psychiatric hospitals, where they claimed to be hearing voices. Once they were admitted, they behaved normally, but the hospitals diagnosed all of them as seriously mentally ill. In this week’s episode of the Futility Closet podcast we’ll describe the Rosenhan experiment, which challenged the validity of psychiatric diagnosis and set off a furor in the field.
We’ll also spot hawks at Wimbledon and puzzle over a finicky payment processor.
In a series of experiments in 2009, Stanford psychologist Daniel Casasanto investigated whether right- and left-handed people differ in how they associate abstract concepts such as good and bad with horizontal space.
He found that right-handed people associate the space to their right with good things like intelligence, attractiveness, honesty, and happiness more readily than the space to their left. With left-handed people, the opposite applies.
“This means for example that the same portrait photo, when placed on a table to the right of a right-hander, will be seen in a more positive light than when it happens to be placed on the other side,” writes Rik Smits in The Puzzle of Left-Handedness. “It’s as if the preference for one hand over the other radiates out into the vicinity of that hand. It may even mean that when an employer looks at a list of brief descriptions of job applications that has been laid out in two columns, those in the column of the same same side as his or her preferred hand will be judged more favourably. If this turns out to be true, then perhaps elections, selection procedures and recruitment are even less rational processes than we already feared. It seems there isn’t an awful lot we can do about that.”
(Daniel Casasanto, “Embodiment of Abstract Concepts: Good and Bad in Right- and Left-Handers,” Journal of Experimental Psychology: General 138:3 [August 2009], 351–367.)
Woodworking engineer Matthias Wandel built a 6-bit wooden adding machine driven by marbles.
More info (and more gizmos) at his website.
This French alexandrine encodes π to 126 decimal places:
Que j’aime à faire apprendre un nombre utile aux sages!
Immortel Archimède, artiste ingénieur,
Qui de ton jugement peut priser la valeur?
Pour moi, ton problème eut de pareils avantages.
Jadis, mystérieux, un problème bloquait
Tout l’admirable procédé, l’œuvre grandiose
Que Pythagore découvrit aux anciens Grecs.
Ô quadrature! vieux tourment du philosophe!
Insoluble rondeur, trop longtemps vous avez
Défié Pythagore et ses imitateurs.
Comment intégrer l’espace plan circulaire?
Former un triangle auquel il équivaudra?
Nouvelle invention: Archimède inscrira
Dedans un hexagone; appréciera son aire,
Fonction du rayon. Pas trop ne s’y tiendra:
Dédoublera chaque élément antérieur;
Toujours de l’orbe calculée approchera;
Définira limite; enfin, l’arc, le limiteur
De cet inquiétant cercle, ennemi trop rebelle!
Professeur, enseignez son problème avec zèle!
Translation:
How I like to teach this number useful to the wise.
Immortal Archimedes, artist, engineer,
In your opinion who could estimate its value?
For me, your problem had equal advantages.
Long ago, mysterious, a problem blocked
All the honorable process, the great work
That Pythagoras revealed to the Ancient Greeks.
Oh quadrature! Old philosopher’s torment
Unsolvable roundness, for too long you have
Defied Pythagoras and his imitators.
How to integrate the plain circular space?
Form a triangle to which it is equivalent?
New invention: Archimedes will inscribe
Inside a hexagon; will appreciate its area
Function of a ray. Not too much to hold onto there:
Will split each previous element;
Always the calculated orb will approach
Will define the limit; finally, the arc, the limiter
Of this disturbing circle, an enemy too rebellious
Teacher, teach its problem with zeal.
I don’t know who came up with it — Alfred Posamentier traces it as far back as the Nouvelle Correspondence Mathematique of Brussels, 1879.
Mathematician John Rainwater has published 10 research papers in functional analysis, notably in the geometric theory of Banach spaces and in convex functions. The University of Washington has named a regular seminar after him, and Rainwater’s Theorem is an important result in summability theory.
This is most impressive because he doesn’t exist. In 1952 UW grad student Nick Massey received a blank registration card by mistake, and he invented a fictional student, naming him John Rainwater because it was raining at the time. “Rainwater” was adopted by the other students and began to submit solutions to problems posed in the American Mathematical Monthly, and he’s gone on to a 60-year (so far) career of considerable distinction — his top paper has 19 citations.
Asked why he’d published that paper under Rainwater’s name, John Isbell quoted Friedrich Schiller: “Man is only fully human when he plays.”
