Futility Closet - 140-Ramanujan

Starting point is 00:00:00 Welcome to the Futility Closet podcast, forgotten stories from the pages of history. Visit us online to sample more than 9,000 quirky curiosities from an invertible autograph to a goddess in a hotel. This is episode 140. I'm Greg Ross. And I'm Sharon Ross. 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 today's show, we'll

Starting point is 00:00:38 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 McCuller's heart and puzzle over a well-proportioned amputee. Just a reminder that Futility Closet is supported primarily by our amazing listeners. We want to thank everyone who helps us be able to keep making the show. And this week, we're sending out an extra special Futility Closet thank you to A.J. Rupakalu, our newest super patron.

Starting point is 00:01:13 If you would like to join A.J. and all the other wonderful supporters of our show to help us keep bringing you your weekly dose of the quirky and the curious, please check out our Patreon campaign or see the Support Us section of the website. Srinivasa Ramanujan was born in 1887 in southern India. His father was a clerk in a cloth merchant's shop and his mother was a housewife. The family were of the middle class, but they were very poor, living essentially together in a single room. Despite this misfortune, he did extraordinarily well in school, invariably coming first in class examinations. At age 12, he borrowed S.L. Loney's book Plain Trigonometry from an older student and worked through every problem in the book.

Starting point is 00:01:52 And at 16, he borrowed a second book from a local library, G.S. Carr's A Synopsis of Elementary Results in Pure and Applied Mathematics. That book contained 6,000 theorems, but it had no proofs. Ramanujan had to prove to himself that the facts it presented were true, which is remarkable. I mention these two books by name because they form almost the whole basis of his mathematical education. Most of what he came to know he taught himself. In school, he easily outstripped his classmates. One said he would clear in half the time examination papers in algebra and geometry, and a few seconds thought always used to suggest to him the solution to any question, however difficult. He used often to entertain his friends with theorems and formulas, even in those early days,

Starting point is 00:02:27 which doubtless appeared to his hearers as mathematical tricks. When he finished high school, he tried twice to obtain a college education, but he was so obsessed with mathematics at this point that he failed his other subjects. Finally, he left college and pursued mathematics on his own, living in extreme poverty. When he got married, he found he needed a job, and he had great difficulty finding one because of his unfortunate college career. He applied for a clerkship at the revenue department, and as it happened, the man he applied to was V.R. Iyar, who was founder of the Indian Mathematical Society. When Ramanujan showed him his mathematics notebook, Iyar said, I was struck by the extraordinary mathematical results contained

Starting point is 00:03:02 in it. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department. So he sent him to R. Ramachandra Rao, a wealthy mathematician and revenue collector in the town of Nelore. Rao describes their meeting like this. A short, uncouth figure, stout, unshaven, not overclean, with one conspicuous feature, shining eyes, walked in with a frayed notebook under his arm. He was miserably poor. He opened his book and began to explain some of his discoveries. I saw quite at once that there was something out of the way, but my knowledge did not permit me to judge whether he talked sense or

Starting point is 00:03:32 nonsense. I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches. Rao gave him a stipend so he could work on math, but Ramanujan felt uneasy about accepting money without working for it, so in 1912 they gave him a job as a clerk in the Madras Port Trust office. His wife later said that he would work on math from the time he got home until 6 a.m. the following morning, then sleep for two or three hours and go to work. He was just completely obsessed with math. His friendship with these mathematicians gave him entree to their circles, and he began to publish his results in the Journal of the Indian Mathematical Society. But the editor noted,

Starting point is 00:04:11 Mr. Ramanujan's methods were so terse and novel, and his presentation so lacking in clearness and precision, that the ordinary mathematical reader, unaccustomed to such intellectual gymnastics, could hardly follow him. This is because he was self-taught. But though his methods were not rigorous, the formulas behaved correctly and were the wonder of mathematicians. His friends encouraged him to write to English mathematicians about his discoveries. Publishing there would bring him the attention he deserved, and in England he'd have access to the latest mathematical literature, which was hard to get in India at the time. Ramanujan began to send his work to professors at English universities. One of them seemed to misunderstand and only recommended a book, and two of them just returned his work without any comment. At last he wrote to G.H. Hardy at Cambridge because he'd seen his 1910 book Orders of Infinity. His letter read, I have had no university education,

Starting point is 00:04:49 but I have undergone the ordinary school course. After leaving school, I have been employing the spare time at my disposal to work at mathematics. I have not trodden through the conventional regular course, which is followed in a university course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general, and the results I get are turned by the local mathematicians as startling. He enclosed nine pages of his work with about 60 theorems and formulas without any proofs. Hardy later wrote, I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true because if they were not true, no one would have had the imagination to invent them. Still, Hardy at first thought they might

Starting point is 00:05:28 be a fraud. He recognized some of the formulas, but others, he said, seemed scarcely possible to believe. So that evening in the chess room at Trinity College, he showed them to his colleague J.E. Littlewood. He said he couldn't decide whether Ramanujan was a crank or a genius. The two studied the pages for two and a half hours, and they emerged from the room certain that he was a genius. Hardy called him a mathematician of the highest quality, a man of altogether exceptional originality and power. He wrote back to Ramanujan saying that he must see proofs of his assertions, and urging him to come to England. Ramanujan resisted this at first, as going to a foreign land conflicted with his Brahmin upbringing, but eventually his parents

Starting point is 00:06:03 withdrew their opposition, and he departed by ship, leaving his wife to stay with his parents. He moved into a house in Cambridge, then transferred to rooms in Trinity College and began immediately to work with Hardy and Littlewood. Littlewood commented, I can believe that he's at least a Jacobi, and Hardy said he can compare him only with Euler or Jacobi, who are Leonard Euler and Carl Jacobi, two of the mathematicians of the first rank in all of mathematical history. Ramanujan was self-taught, which left curious gaps in his knowledge, which they had to negotiate. Hardy said, what was to be done in the way of teaching in modern mathematics? The limitations of his knowledge were as startling as its profundity. Littlewood was asked to help teach him the traditional methods of European mathematics,

Starting point is 00:06:38 but he said this was extremely difficult because whenever he introduced a subject, Ramanujan would respond with an avalanche of original ideas that made it almost impossible for him to continue. As they were working on this, war broke out that summer, World War I, taking away most of the students and much of the university faculty. Hardy stayed because he was an ardent pacifist, and the two of them continued to work together, but it left them at a disadvantage. Hardy wrote,

Starting point is 00:06:59 In one respect, Mr. Ramanujan has been most unfortunate. The war has naturally had disastrous results on the progress of mathematical research. It has distracted three-quarters of the interest that would otherwise have been taken in his work, and has made it almost impossible to bring his results to the notice of the continental mathematicians most certain to appreciate it. It has, moreover, deprived him of the teaching of Mr. Littlewood, one of the great benefits which his visit to England was intended to secure. All this will pass, and in spite of it, it is already safe to say that Mr. Ramanujan has justified abundantly all the hopes that were based upon his work in India, and has shown that he possesses powers as remarkable in their way as those of any living

Starting point is 00:07:33 mathematician. His work is only the more valuable because his abilities and methods are of so unusual a kind, and so unlike those of a European mathematician trained in the orthodox school. Altogether, Ramanujan worked for three years at Trinity, making gigantic progress. Littlewood wrote, there is hardly a field of formulae except that of classical number theory that he is not enriched and in which he has not revealed unsuspected possibilities. The beauty and singularity of his results is entirely uncanny. Unfortunately, Ramanujan's wife and mother were not there to take care of him, and he tended to neglect his health. Reportedly, he cared more for math than for eating or sleeping, and would work for 24 or 36 hours at a stretch. Worse, he was a vegetarian, and it was hard to get vegetarian food in England in World

Starting point is 00:08:12 War I, so his diet suffered. In May 1917, he came down with a mysterious illness that was eventually diagnosed as tuberculosis and a severe vitamin deficiency. He couldn't return immediately to India because of the war, so for two years during his stay in England, he was confined to at least five different nursing homes and sanitaria. This is the occasion for probably the single most popular anecdote that's told about him. Hardy visited him at one point. He was in a sanitarium in Putney. Hardy showed up and said offhandedly, I rode here today in taxicab number 1729. This seems to be a dull number, and I hope it is not an unfavorable omen. Ramanujan immediately replied, no, it is a very interesting And he just saw that immediately. Well, when the anecdote is told, people often present it as if he just worked that out on the spot. He didn't.

Starting point is 00:09:05 He had recorded it in his notebooks in India, but he had it ready to his mind in that way. It was that facile. And in fact, numbers that can be expressed in this way are now known as taxicab numbers in honor of that just passing happenstance. Hardy said after Ramana Jhan's illness, he started to recover a bit. Hardy wrote, I think we may now hope that he's turned the corner and is on the road to a real recovery. His temperature has ceased to be irregular and he has gained nearly a stone in weight. There has never been any sign of any diminution in his extraordinary mathematical talents. He has produced less naturally during his illness, but the quality has been the same. He convalesced in England until 1919 when the seas were considered safe for travel and he was well enough to return to India. His wife later said that his first words to her on getting off the boat were, If I had taken you with me, I would not have become ill. said that his first words to her on getting off the boat were, if I had taken you with me, I would not have become ill. He continued to work in India as much as his health would permit, but

Starting point is 00:10:10 unfortunately, it started to decline again. And as he lay in bed, he wrote again to Hardy with some unproven theorems, just as in his first letter, just sent some unproven theorems to him. And 15 years elapsed before the final theory in that package was understood. He died in 1920 at age 32, and a 1994 analysis suggests that he actually had hepatic amebiosis rather than tuberculosis, which was curable at the time. That's kind of speculative, but kind of makes it sadder. So he died at 32, which makes for a short life. Hardy made the point, though, that even he himself might have preferred

Starting point is 00:10:42 to have a short period of fully realized potential in England, which is what he had, rather than a long life of frustrated ambition in India. Also, Hardy points out, he says a mathematician is comparatively old at 30. Most mathematicians of the first class do their most important work in their 20s. So even though he's

Starting point is 00:11:00 producing brilliant things right up to the end, it probably wouldn't have continued at that level into, say, his 50s. So Hardy says his death may be less of a catastrophe than it seems, at least to the discipline of mathematics. Introducing a lecture in 1937, Hardy said, the difficulty which is the greatest for me has nothing to do with the obvious paradoxes of Romano John's career. The real difficulty for me is Romano John was, in a way, my discovery. I did not invent him. Like other great men, he invented himself. But I was the first really competent person who had the chance to see some of his work, and I can still remember with

Starting point is 00:11:28 satisfaction that I could recognize at once what a treasure I had found. And I suppose that I still know more of Ramanujan than anyone else, and am still the first authority on this particular subject. There are other people in England, Professor Watson in particular, and Professor Mordell, who know parts of his work very much better than I do, but neither Watson nor Mordell knew Ramanujan himself as I did. I saw him and talked with him almost every day for several years, and above all, I actually collaborated with him. I owe more to him than to anyone else in the world, with one exception, and my association with him is the one romantic incident in my life. The difficulty for me, then, is not that I do not know enough about him, but that I

Starting point is 00:12:00 know and feel too much, and that I simply cannot be impartial. Hardy called Ramanujan the most romantic figure in the recent history of mathematics, a man whose career seems full of paradoxes and contradictions, who defies almost all the canons by which we are accustomed to judge one another, and about whom all of us will probably agree in one judgment only that he was in some sense a very great mathematician. Rating pure mathematical talent on a scale from 0 to 100, Hardy gave himself a score of 25, Littlewood 30, David Hilbert 80, and Ramanujan 100. That is the greatest possible genius. At Ramanujan's death, he left behind three notebooks, which he'd written before coming to England. They contained as many as 4,000 results stated without proofs, and these have become treasured objects among mathematicians.

Starting point is 00:12:39 The absence of derivations has inspired many papers in which they try to prove what he found. He also left behind the papers he'd written in England, many with Hardy, and the results he'd discovered in his last years. He mailed these to Hardy, and in 1976 they were discovered in the Library of Trinity. They're known as the Lost Notebook. The University of Illinois mathematician Bruce Berndt says this was roughly equivalent to discovering a 10th symphony of Beethoven. Romano-John's published papers made a volume of 400 pages, but much of this simply reproduced work that had already been accomplished elsewhere, again because he was self-taught. Hardy estimated that two-thirds of the work Ramanujan had done in India before coming to

Starting point is 00:13:13 England was a rediscovery of work that had already been done. He wrote, It was inevitable that a very large part of Ramanujan's work should prove on examination to have been anticipated. He had been carrying an impossible handicap, a poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe. He'd had no real teaching at all. There was no one in India from whom he had anything to learn. Since his college education lasted only one year, he didn't have a clear idea of what constituted a rigorous proof. Sometimes his arguments when they can be reconstructed are not rigorous, but Berndt says nonetheless he very seldom committed serious errors. He had an uncanny ability to determine when his methods produced correct results and when they did not. Asked about Ramanujan's methods,

Starting point is 00:13:49 Hardy said they were arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account. George Andrews of Penn State said it is nice to say that if Ramanujan had had more education, he would have done more, but we can't run a controlled experiment on geniuses that occur uniquely in history. It is at least plausible to say that more education would have ruined Ramanujan had had more education, he would have done more, but we can't run a controlled experiment on geniuses that occur uniquely in history. It is at least plausible to say that more education would have ruined Ramanujan. That means that another such genius might appear anywhere. In 1987, the physicist Freeman Dyson said, of course, we're always hoping. That's one reason why I always read letters that come in from obscure places and are written in an illegible scrawl. I always hope that it might be from another Ramanujan.

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Starting point is 00:15:14 eyewear. And because Kryzol's labs use extensive tests to ensure your lenses meet the highest standards, you can be completely confident in their quality. Look better, feel better, and most importantly, be prepared for whatever comes your way with clear vision. Go to Krizal.com to learn more. That's C-R-I-Z-A-L.com and start living life in the clear. In episode 137, we discussed how the writer William Sharp had a second career as the novelist Fiona McLeod. Colin McGuire wrote in from Edinburgh to say, I know a little bit of information that is quite interesting regarding the Fiona McLeod story.

Starting point is 00:15:57 The American novelist Carson McCullers wrote her most famous and successful novel, The Heart is a Lonely Hunter, and it is interesting to note that the title itself came from a poem written by William Sharp. The line from the poem is, My heart is a lonely hunter that hunts from a lonely hill. I believe Sharp wrote the poem under the pseudonym Fiona McLeod. McCullers herself may have been bisexual, and her novels all contain an element of ambiguity regarding some of the character's sexuality and often behave in a way not conforming to gender. This may have been one reason McCullers chose the title. That's really interesting. I had no idea. Yeah, no, I didn't either.

Starting point is 00:16:33 And I looked into it, and it does appear that it is widely acknowledged that McCullers was bisexual, and the poem The Lonely Hunter that contains the line that Colin mentioned was written by Sharp as Fiona McLeod. Because I think it's safe to say most people don't know who Fiona McLeod is. I mean, she's sort of been forgotten. Yeah, right. And I hadn't heard, I mean, I've definitely heard of the McCullers novel. I hadn't heard of the poem and didn't know the connection to the title myself. Also on the topic of William Sharp, Leah Kendall wrote, I've been a fan for a long time. I have read the website since almost the very beginning. I wanted to point out some things about your last On the topic of William Sharpe, Leah Kendall wrote, in the manner that you describe. I've seen this both in others and myself. For example, when I was younger,

Starting point is 00:17:26 I didn't really know that transitioning was an actual option, so I first imagined that the explanation for how I felt was that I was a woman in a previous life, and then later that there was a feminine presence, much like Fiona, that I sometimes embodied. This type of thinking has faded upon transitioning. However, this also seems common in how others perceive you. E.g., I have been told explicitly by others that their perception of me is as if I am literally a different person from my previous self.

Starting point is 00:17:54 As if your twin or your cousin left and you came and took his place. And Leah notes that obviously she can't say for sure whether Sharp was transgender or not. But it does seem to me to be one very plausible explanation. And as you noted in the story, he unfortunately didn't express himself clearly enough on the subject, so we can't be quite sure what was actually going on for him. But Leah's experience does seem to be at least fairly similar to the things that Sharp did say. Yeah, that's very interesting. That's pretty close to how he described it. I sort of gather he was somewhat baffled

Starting point is 00:18:27 himself about what was happening. Right. But that description does sound very much like what appears in his own writings about this. Leah ended her email with, love the podcast and the futilicat. P.S. Sharon, I know Greg isn't nearly as good at lateral puzzles as you are,

Starting point is 00:18:44 but that's no reason to give him hints. Let him squirm. And I will note that in the interest of the episodes not becoming indefinitely long, I also get hints during the puzzles. Yeah, we both do that. Yeah, we do. Some of those puzzles would take either of us quite a long time without any hints. We would just be going forever.

Starting point is 00:19:03 So, Charlie Goodliffe from Swansea, United Kingdom wrote in about the coal torpedoes and rat bombs that we talked about in episodes 99 and 101. Hi, Greg, Sharon and Sasha, longtime follower of the website and the podcast and appreciate all the hard work that goes into both looking forward to a new year of what you guys do best. Following on from the many stories about hand grenades disguised as coal, when we went to stay with my dad over Christmas, he asked me if I'd read in the paper about the hand grenade in the coal. I said no, but was ready to beat him to the punch with my futility closet acquired knowledge on the subject. However, he looked at me blankly when I launched into the stories of Civil War

Starting point is 00:19:45 coal bombs and World War II exploding rats, then handed me the attached newspaper cutting from the Daily Telegraph, which must be some sort of ying to your story's yang in that, well, read on and you'll find out. Looking forward to new episodes and more Sasha updates on Patreon. Charlie Goodliffe and Robin, aged one, listens in the car with daddy. Youngest futility closet listener, I wonder? And Charlie sent a scan of a clipping that turned out to be from the Telegraph, October 16, 2016. Sir, aged 10, in the summer of 1956, I discovered a practice hand grenade in what had been a Second World War Canadian army camp to the rear of our house in Horley, Surrey. I secreted the find in a shed, which during the winter was used to store coal.

Starting point is 00:20:33 By November, all knowledge of the grenade had faded until, that is, the time my father added a hand shovel of coal to the sitting room fire. fire. After about 10 minutes, he leapt to the fire, grabbed something from it, burst through the French windows without releasing the door catch, and hurled with all his might the hand grenade into the field at the rear of the house. My mother thought he had gone mad until she was apprised in no uncertain terms that he had spotted a Mills bomb, now he hoped safely dispatched. The house was soon visited by every emergency service, including the heroic UXB squad, who, having evacuated the occupants of the adjacent houses and ourselves, subjected the bomb to what is now called a controlled detonation. The Cole board conducted a full inquiry. We received a ton of anthracite free of charge by way of compensation. 30 years later, I confessed.

Starting point is 00:21:23 Mother knew it was me all along, and I escaped with a wry smile from both parents. Robert Strick, Oakham, Rutland. So his father just recognized a hand grenade in the fire. And grabbed it out! Without any warning. Oh my god. And it's funny, his parents didn't say anything, but I guess they got a ton of coal for free, so. Yeah, so there's that. didn't say anything, but I guess they got a ton of coal for free. So yeah, so there's that. And we have a bit of a mystery that has developed about the lateral thinking puzzle in episode 138.

Starting point is 00:21:57 Spoiler alert, this will spoil the puzzle if you haven't heard it yet. The answer to that puzzle about a ballerina who received a silent reception to her dancing involved a young Audrey Hepburn dancing in a fundraiser for the Dutch Resistance during World War II. At the time that I wrote up the puzzle answer, all the resources that I checked agreed that this had occurred. However, after we posted the episode, Greg Askins wrote to let us know that the Wikipedia page for Hepburn now had a link to an organization claiming that this did not appear to be the case. The Wikipedia page now says, A Google Translated article linked to on the page seems to say that the Airborne Museum was unable to find any evidence to back up the many stories that claim that Hepburn had worked for the resistance. And as best as I can understand the somewhat awkward English translation of the page, they seem to be saying that a Hepburn biographer may have actually started the story.

Starting point is 00:23:05 started the story. I found this refutation of the Hepburn story to be a bit perplexing because I had seen several sources that seemed to back up the story, including a transcript on the CNN website of an interview between Larry King and Hepburn's son. According to that transcript, during the interview, King plays a video clip of Hepburn herself saying, didn't know how long the war was going to last, so I went to a ballet school and learned to dance. And then about 1944, about a year before the end of the war, I was quite capable of performing. That was sort of some way in which I could make some contribution, and I did give performances to collect money for the underground,

Starting point is 00:23:37 which always needed money. So that seems rather unambiguous to me, that she seems to be saying she participated in helping the Dutch resistance. Yeah, maybe they consider that to be different from working for them. Well, they didn't say working for them. They were saying that there didn't seem to be any evidence that she had participated in the resistance.

Starting point is 00:24:00 Yeah, but maybe raising funds is different. Yeah, but so, you know, that's what we know right now. And we'll post these links in the show notes. So if any of our Dutch listeners want to try to pursue this further, they can look into it. At least they would be able to better read the report from the Airborne Museum than I was, and maybe they'll make more sense out of it than we did. and Sam Boyd wrote in to add to the list of in-rem cases that Greg gave in episode 137 these are cases in which a court asserts power over objects rather than over a person for example to decide their legal ownership or status and Sam wanted to add to the list United States versus one crystal covered bad tour glove and other Michael Jackson memorabilia, United States of America versus one Michael Jackson-signed thriller jacket and other Michael Jackson memorabilia, and a personal favorite of his,

Starting point is 00:24:53 which involved an illegal dog-fighting operation, United States versus approximately 64 dogs. Sam says, you can just imagine the federal marshals trying to get the dogs to stand still to be counted and the numbers coming out differently each try and them eventually giving up and saying, oh, fine, approximately 64. So thanks so much to everyone who writes into us. If you have anything you'd like to comment on, please send it to podcast at futilitycloset.com. you'd like to comment on, please send it to podcast at futilitycloset.com. And if you find that people don't always pronounce your name quite the way you'd like them to, then thank

Starting point is 00:25:29 you in advance if you give me some pointers. It's Greg's turn to try to solve a lateral thinking puzzle. I'm going to present him with a strange sounding situation. He has to try to figure out what is actually going on, asking only yes or no questions. And this puzzle comes from Tyler Russo. My friend has 10 fingers, 10 toes, two arms, two legs, two ears, and a nose. He is an amputee,

Starting point is 00:25:58 despite not missing any of those. And I'm not quite sure if the rhyme was intentional or a happy accident, but it was kind of those. And I'm not quite sure if the rhyme was intentional or a happy accident, but it was kind of cute. Amputee, meaning he's missing some part of his body.

Starting point is 00:26:11 Yes. Is he, is he, apart from that, normal in every other way? Yes. Are there other people involved in some?

Starting point is 00:26:18 Okay. Thank goodness. They amputated off his, I don't know, his identical twin. I mean, his Siamese twin. Yeah, i was thinking of that yeah um okay amputee is he human yes does it matter that he's his friend no so it's just a normal human is missing some body part other than fingers toes arms legs ears or nose i wouldn't agree to what you just said okay depending on let's go through it it's a normal human being yes who's

Starting point is 00:26:56 missing some body part yes by at least by missing explain what you mean by missing. Well, I think of an amputee as having, as differing from a sort of ordinary human being in the lack of a body part. I wouldn't agree with that. Think of a different definition of amputee. Amputee. Another definition of amputeee you defined it a very particular way you could define it a little differently had this person okay i think you said this person's missing a body part or you agreed that this person was um i agreed but then i then i backtracked a little bit because it depends on what you define as missing. Amputee.

Starting point is 00:27:48 That's why I started to ask you to define what you mean. Okay. Amputee means amputated, that something has been amputated from this person's body. I will agree with that. All right. Thank you. We're getting somewhere. A part of that person's body has been amputated yes meaning removed yes yes a part a part of this person's body has been removed correct what was i saying

Starting point is 00:28:11 before don't answer that okay so so where i was with that was the part of the person's body that's been removed is not a finger a toe an arm a, or a nose. I would not agree with that statement. Okay, the person's missing a body part. That had previously been there? Yes, yes. Okay, is it a toe? You said the person has 10 toes. Yes.

Starting point is 00:28:39 Oh, had they previously had 11 toes? It's fingers, yes, but that's it. And Tyler says, polydactyly is a deformity in which the hand has one or more extra fingers in any of three places. And his daughter was born with two almost fully functioning thumbs on her right hand. And it didn't bother them, but the outer thumb was starting to cause problems for her when she was trying to develop her fine motor skills. So they decided it would be best to have the thumb removed. And as a result, she is now by definition an amputee. With 10 fingers.

Starting point is 00:29:10 Yeah. And Tyler says, on a funny side note, whenever we hear someone say, as long as they have 10 fingers and 10 toes, I'll be happy, I am always quick to respond with, eh, 11 is not so bad. So thanks to Tyler and indirectly his daughter for that puzzle. And if you have a puzzle you'd like to have us try, please send it to us at podcast at futilitycloset.com. That's our show for this week.

Starting point is 00:29:34 If you're looking for more quirky curiosities, check out the Futility Closet books on Amazon or visit the website at futilitycloset.com where you can sample more than 9,000 Extonius Omniana. At the website, you can see the show notes for the podcast Thank you. iTunes or other podcast directories. If you have any questions or comments about the show, you can reach us by email at podcast at futilitycloset.com. Our music was written and performed by the inimitable Doug Ross. Thanks for listening, and we'll talk to you next week.

Futility Closet - 140-Ramanujan

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