Podcast Episode 140: Ramanujan


In 1913, English mathematician G.H. Hardy received a package from an unknown accounting clerk in India, with nine pages of mathematical results that he found “scarcely possible to believe.” In this week’s episode of the Futility Closet podcast, we’ll follow the unlikely friendship that sprang up between Hardy and Srinivasa Ramanujan, whom Hardy called “the most romantic figure in the recent history of mathematics.”

We’ll also probe Carson McCullers’ heart and puzzle over a well-proportioned amputee.


W.H. Hill’s signature was unchanged when inverted.

Room 308 of West Java’s Samudra Beach Hotel is reserved for the Indonesian goddess Nyai Loro Kidul.

Sources for our feature on Srinivasa Ramanujan:

Robert Kanigel, The Man Who Knew Infinity, 1991.

K. Srinivasa Rao, Srinivasa Ramanujan: A Mathematical Genius, 1998.

S.R. Ranganathan, Ramanujan: The Man and the Mathematician, 1967.

Bruce C. Berndt and Robert A. Rankin, Ramanujan: Letters and Commentary, 1991.

G.H. Hardy, “The Indian Mathematician Ramanujan,” American Mathematical Monthly 44:3 (March 1937), 137-155.

Gina Kolata, “Remembering a ‘Magical Genius,'” Science 236:4808 (June 19, 1987), 1519-1521.

E.H. Neville, “Srinivasa Ramanujan,” Nature 149:3776 (March 1942), 293.

Bruce C. Berndt, “Srinivasa Ramanujan,” American Scholar 58:2 (Spring 1989), 234-244.

B.M. Srikantia, “Srinivasa Ramanujan,” American Mathematical Monthly 35:5 (May 1928), 241-245.

S.G. Gindikin, “Ramanujan the Phenomenon,” Quantum 8:4 (March/April 1998), 4-9.

“Srinivasa Ramanujan” in Timothy Gowers, June Barrow-Green, and Imre Leader, eds., Princeton Companion to Mathematics, 2010.

“Srinivasa Aiyangar Ramanujan,” MacTutor History of Mathematics (accessed Jan. 22, 2017).

In the photo above, Ramanujan is at center and Hardy is at far right.

Listener mail:

“Myth Debunked: Audrey Hepburn Did Not Work for the Resistance” [in Dutch], Dutch Broadcast Foundation, Nov. 17, 2016.

“Audrey Hepburn’s Son Remembers Her Life,” Larry King Live, CNN, Dec. 24, 2003.

This week’s lateral thinking puzzle was contributed by listener Tyler Rousseau.

You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation on the Support Us page of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

A Visitation

mead snow angel

The residents of Brattleboro, Vt., awoke to a surprise on New Year’s Day 1856: An angel of snow stood at the corner of Linden and North Main streets, holding a pen and notebook as if ready to record the events of the new year.

The artist turned out to be 21-year-old Larkin Goldsmith Mead Jr., the son of a local lawyer. He had worked through the night to fashion the eight-foot figure by lantern light, shaping it by hand from snow brought to him by two friends. He sculpted some parts separately in order to mold them more easily, attaching them later with wet snow, and he poured water over the finished creation to give it a smooth finish. The Vermont Phoenix marveled:

The inhabitants of the village discovered ‘The Snow Angel,’ in the prismatic glow of the morning sun’s reflection. The early risers and pedestrians about town were amazed, when they drew near, to see what appeared at a distance like a school-boy’s work turned to a statue of such exquisite contour and grace of form. … The passing school-boy was awed for once, as he viewed the result of adept handling of the elements with which he was so roughly familiar, and the thought of snowballing so beautiful an object could never have dwelt in his mind. It is related that the village simpleton was frightened and ran away, and one eccentric citizen, who rarely deigned to bow to his fellow men, or women either, lifted his hat in respect after he had gazed a moment upon Mead’s work.

The angel was featured in newspapers in Boston and New York, and it brought Mead commissions for more lasting works, including a statue of Ethan Allen and a wooden figure symbolizing agriculture for the Montpelier statehouse. His later projects include Lincoln’s tomb in Springfield, Illinois.

In 1886 he reproduced the angel in marble — it stands in the public library in Brattleboro. Across the street, commemorating the site of the original angel, stands a drinking fountain designed by his brother, architect William Mead — who immortalized the family name in his own way.


A desire path is a route made evident by foot traffic, often easier or more direct than a provided avenue:

Image: Wikimedia Commons

A holloway is a sunken lane formed by traffic or erosion — some in Europe date to the Iron Age:

Image: Wikimedia Commons

A snowy neckdown is a disused area of a roadway made evident by snowfall:

Image: Wikimedia Commons

In the absence of snow, some Australian engineers have dusted intersections with cake flour to reveal traffic patterns. Others study the oil stains left by traffic. Dan Burden, director of the Walkable and Livable Communities Institute, says, “I call something like that highway forensics.”


Image: Wikimedia Commons

Classical statues tend to lose their noses, and in the 19th century museums would commonly replace them with “restoration” noses, to preserve the appearance of the original sculpture.

In the 20th century some museums changed philosophies and “de-restored” their collections, thinking it better to present each piece in its authentic state.

This created a superfluity of noses, and some museums collect these into displays of their own. Charmingly, there’s even a word for this: A collection of noses is a Nasothek.

Above is the collection in the Ny Carlsberg Glyptotek museum in Copenhagen.

(Thanks, Carsten.)


You know the singularity has arrived when the robots start playing marimbas. Shimon, engineer Guy Hoffman’s robot musician, doesn’t play programmed music — it improvises in ensembles with human players, communicating with a “socially expressive head” and favoring musical ideas that are unlikely to be chosen by humans, so as to lead the performance in genuinely novel directions.

“The project, therefore, aims to combine human creativity, emotion, and aesthetic judgment with algorithmic computational capability of computers, allowing human and artificial players to cooperate and build off each other’s ideas,” notes the Georgia Tech Center for Music Technology, Shimon’s patron. “Unlike computer- and speaker-based interactive music systems, an embodied anthropomorphic robot can create familiar, acoustically rich, and visual interactions with humans.”

More at Georgia Tech.



A harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression (so an example is 1/1, 1/2, 1/3, 1/4 …). When tutoring mathematics at Oxford, Charles Dodgson had a favorite example to illustrate this:

According to him, it is (or was) the rule at Christ Church that, if an undergraduate is absent for a night during term-time without leave, he is for the first offence sent down for a term; if he commits the offence a second time, he is sent down for two terms; if a third time, Christ Church knows him no more. This last calamity Dodgson designated as ‘infinite.’ Here, then, the three degrees of punishment may be reckoned as 1, 2, infinity. These three figures represent three terms in an ascending series of Harmonic Progression, being the counterparts of 1, 1/2, 0, which are three terms in a descending Arithmetical Progression.

— Lionel A. Tollemache, “Reminiscences of ‘Lewis Carroll,'” Literature, Feb. 5, 1898

Grass Photographs

Heather Ackroyd and Dan Harvey make photographs using grass. When grass is grown from seed on a vertical surface, it can record complex images much as photographic film does: Each germinating blade produces chlorophyll in proportion to the light that reaches it. Stronger light produces greener grass, and blades deprived of light grow but produce no chlorophyll, leaving them yellow. “In a sense we have adapted the photographic art of producing pictures on a sensitive film to the light sensitivity of emergent blades of young grass; the equivalent tonal range of black-and-white photographic paper is created within the grass in shades of yellow and green.”

“A grass photograph has the power to elicit strong emotional responses in the viewer, and it is undeniable that the beauty of the freshly grown grass canvas suggests all that is fertile and life-enhancing. Our desire to alleviate the process of decay has encouraged us to journey into the world of science and genetics, and has opened our work to a greater number of people throughout the world.”

More here.

(Heather Ackroyd and Dan Harvey, “Chlorophyll Apparitions,” in Eduardo Kac, ed., Signs of Life, 2007.)