John Venn

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Speaker 1: Welcome to Stuff You Missed in History Class, a production of iHeartRadio. Hello and welcome to the podcast. I'm Holly Frye and I'm Tracy V. Wilson. I bet it's a safe bet that most people listening have heard of a Venn diagram. Seems likely, yeah, But the creator of the concept of the Venn diagram, whose name was John Vin, actually developed a much more complex set of relational diagrams than the simplified ones that we often reference casually or even see used in like, you know, newscasts or whatever, but perhaps even more interesting. Although he is an important figure in the fields of mathematics and logic, he eventually left that work behind to write historical accounts of the places and people that were important in his life. I love this about him. He was also an inventor, not of a lot of stuff, but of something really interesting. So he's just a fun person to talk about. So he is in the spotlight today. John Vin was born on August fourth, eighteen thirty four, to parents the Reverend Henry Vin and Martha Sykes Ven. He was their first child. He was born at Kingston upon hull Port in the East Riding of Yorkshire. In northeastern England. Martha died when John was pretty young, and at the age of twelve he attended Sir Roger Chumley's School in London, which is known more commonly as the Highgate School. This was a really interesting time to attend Highgate, as the headmaster at the time, the Reverend John Bradley Dine, significantly expanded the course offerings there to start, including mathematics and modern languages. Since then would eventually become well known as a mathematician. He seems to have benefited from this newer course of study. John went to secondary school at City of London Academy, Islington. Reverend Henry Ven, John's father, was rector of the Drypool Parish when John was born, and he was also secretary to the Society for Missions in Africa and the East. And he was not the only activist Anglican priest in the family. Henry's father, the Reverend John Vin, a lot of John Ven's were trying to separate him out. Was very influential in the church and had been the leader of a group called the Clapham Sect which lobbied for progressive causes and change within the church, as well as without and the Clapham sect supported the abolition of slavery and advocated for prison reform, among other causes. In John Ven's obituary in the Royal Society's Proceedings publication, it was written, quote, no one could have had a more uncompromisingly clerical ancestry and upbringing than had Ven his five or six immediate ancestors, whose lives he gave in his notable book The Annals of a Clerical Family were vicars or rector's, occupying positions of importance in the Church. When it was time to move on to higher education, Ben attended Gonvillin Keys College at the University of Cambridge, so often simply referred to as Keyes. There he earned a degree in math and ranked sixth among his fellow students in the final exam in eighteen fifty seven, but it was just the beginning of a long relationship with the school. Ben went on to a fellowship at Keys, and when that was completed in eighteen sixty two, he was hired as a lecturer. But Ben wasn't only a mathematician. During that same time period, he became ordained as a priest in the Church of England. Just like his father and grandfather and forebears. Starting in eighteen fifty nine. After becoming a clergyman, he worked for a brief period exclusively in the church at Chesnent, Herstfordshire and Mortlake, Surrey, but then he decided to go back to keyes and mathematics, although he did retain his clergy status. As a lecturer, Ben taught an the discipline known as moral science, meaning he talked about logic and probability. This led to him serving as an examiner for the Moral History Tripos. Tripos Is are academic exams, and Cambridge is often cited as the place this term started. The origin of the word isn't known with certainty, but it might have come from the tripod stool that examiners used sitting on them during the test. Ven's own works would inform these exams later, a guide for students preparing for exams that was written in eighteen ninety one recommended reading several of Ven's books for the logic and methodology section of the test. But even when he was lecturing and serving as examiner himself, he said to have shifted the tripos in developing the exam to reflect developing concepts in probability theory. He eventually stepped aside as examiner because he wanted to focus on studying and writing about the school's history. He also wrote about his own res boots in genealogy, publishing that previously mentioned book Annals of a Clerical Family, which traced the Ven family history to Devin, with a likely earlier origin in Somerset. In his writing, John noted that the name Ben had first been spelled with an F instead of a V, but had changed at some point, and that the change was most likely to align more closely with the common pronunciation that was used in the West Country. A few years into his career teaching at Keys, Ben published a book titled The Logic of Chance that was in eighteen sixty six. Economist John Maynard Keynes is often quoted as praising Ben's book, saying it was quote strikingly original and considerably influenced the development of the theory of statistics. The book sought to shift the way people looked at probability, specifically by incorporating the idea of frequency into mathematical prediction models, meaning how often a thing might happen. He worked against the assay based probability interpretations that presumed causality when looking at effects, which was why he felt that longer runs of observation would offer greater insight. He also made the case that the margin of error on probabilities had to shift in proportion to the data set. Smaller data sets would have larger margins of error, and vice versa. These concepts were applied to scenarios like gambling and birth outcomes. In the book, The Logic of Chance became an important text in probability, and it had three editions printed between its original eighteen sixty six published date and eighteen eighty eight. This was a paradigm shift in its time. We know that, of course having more data means you have better models of probability, but prior to Ven's book, most of probability theory was based on the idea that the right formulas would be accurate predictors regardless of the data set, but that of course led to unpredictable outcomes. Then approach came to be known as frequentism. And in addition to being a big statement about how logic and probability should be applied, Then made another interesting statement with the book right out of the gate, because he said in the preface that he wanted the information in it to be accessible. Writing of probability quote, I am convinced moreover that it can and ought to be rendered both interesting and intelligible to ordinary readers who have any taste for philosophy. The year after The Logic of Chance was released, John Ven got married to Susannah Carnegie Edmondstone. Susannah was born in Marlborough in eighteen forty three, and like John, she was the child of an Anglican priest that was the Reverend Charles welland Edmondstone. After the two of them got married, they settled into married life in Cambridge. They eventually had a child named John Archibald, but that wasn't until sixteen years into the marriage, so Susannah would have been about forty at the time that she gave birth, which is an unusual situation for the time. Susannah is interesting in her own right because she was hardly idle in her time as a wife. Before John Archibald was born. She was in fact a novelist. As her husband was publishing books on probability, she was penning titles like The Gwillians of Bryn Gwillian, which was published in eighteen seventy six, and that told the story of a family of children who are raised by their father and governess after their mother dies. She wrote several more novels, and she also worked with John on some of his historical writing. All of her novels except the last, were initially published anonymously. Her last work of fiction, The Husband of One Wife, came out in eighteen ninety four, and that book tells the story that seems to mirror Susannah's own life. It's about a young woman who gets married and moves to Cambridge to live with her husband. We're about to get to the diagrams, but before we do, we will pause for a sponsor break. In eighteen eighty one, John Ven published another book, this one titled Symbolic Logic, and it was in this work that he introduced the concept of ven diagrams as part of set theory. Ven diagrams, as many listeners already know, often use overlapping circles to represent sets of data. The region that overlaps represents a commonality among those sets of data. This is the most basic way this concept is used in casual conversation, although it's really a visual way to parse information and figure out logic problems, and some ven diagrams can be much more complex, but all of them show the way that sets intersect and join together. For example, you might be given the information that out of a group of people, five are tall and three have green eyes, two are tall and also have green eyes, and five members of the group are neither tall nor have green eyes. Using a Venn diagram with two overlapping circles, you could assign the number two to the overlap section and label each of the circles remaining areas one for the tall people, one for the green eyed people. You've also accounted for two of the tall people in the overlap, so you know there are three more tall people, and the number goes into the circle labeled tall. We've accounted for two green eyed people, and you know that there's three, so a one goes into the circle labeled green eyes. The number five, representing the five people who have neither attribute, sits outside those two circles. To figure out how many people there are in total in the group, you'd add each of the numbers you'd written down together. So the two people who are tall and green eyed, plus the three people who are only tall, plus the one person who only has green eyes, plus the five people who have neither of those attributes, so you know there are eleven people total. There can also be ven diagrams with three circles, and those are used to represent syllogisms. Those are logic arguments in which two premises are a given and then a conclusion is reached using deductive reasoning. A simple example would be to say, all sneakers are shoes. That's premis ie. Premise two is that some sneakers are blue. Therefore, your deductive reasoning leads you to some shoes are blue. The three circles overlap in a way that a central section of the diagram is simultaneously part of all three circles. Those are the some blue shoes. Syllogisms were not new to John Ven. They go all the way back to Aristotle, and though his writings about them do not contain diagrams, some logicians over the years have suspected that he may have used them to work his ideas out. So the Ven diagram is a way to visually represent the existence and non existence of variables within sets. But this isn't really something that he came up with out of nowhere. Gottfried Wilhelm Leibnitz of Leipzig, Germany lived in the seventeenth and early eighteenth centuries, and he studied the use and viability of diagrams to solve logic queries. He thought that Aristotle's concepts on the matter needed some more work, but to be clear, he was drawn to that work because he thought Aristotle's concept was compelling, writing quote, I hold that the invention of the form of syllogisms is a most beautiful of the human spirit. Leibnus's work started to include the use of circles and linear progression to work through syllogistic concepts, which when you look at them, are very clearly a precursor of the ven diagram. Leibniz did eventually favor using lines that created boxes as part of their logical grouping. Yeah, he got away from circles, but circles were favored by another logician, Leonard Euler, who was born in Basel, Switzerland in seventeen oh seven. Although he favored using circles to work out logic puzzles, he was very clear that the shape was not the important thing, noting in writing quote these circles, or rather these spaces, for it is of no importance what figure they are of, are extremely commodious for facilitating our reflections on this subject, and for unfolding all the boasted mysteries of logic which that art finds it so difficult to explain. Whereas by means of these signs, the whole is rendered sensible to the eye. We may employ, then spaces formed at pleasure to represent every general notion. And Euler's diagrams were well known in his time, although he wasn't applying mathematics or specifically algebra to them the way that then eventually would. They were just ways of grouping ideas. There were other mathematicians and logicians who worked in the manipulation of visual diagrams to work out logic, both numerical and theoretical, but John Ben's criticism of those who had come before led him to work out his approach. He wrote, for example, of Uller's work that it wasn't robust enough, stating quote, any system which merely exhibits the mutual relations of two classes to one another is not general enough. We must provide a place and a notation for the various combinations which arise from considering three, four or more classes. In fact, we must be prepared for a complete generalization. Ben also created way more complex diagrams than just two and three circle ones, and some of those are developing ideas put forth by the other two men we just talked about. Ben's book Symbolic Logic was also a defense and expansion of the work of George Boole, who had died twelve years earlier at the age of forty nine, and specifically his approach to algebraic mathematical logic. Boolean algebra represents relationships tween objects or ideas, so it works differently than ordinary algebra. For example, it doesn't require numeric quantities, but it can operate with variables like truth or falsehood. Boolean algebra is important because it's the foundation of things like probability and geometry of sets, but perhaps mostly so because in modern daily life it has impacted the way computer circuits are designed. In eighteen eighty three, Ben decided to resign from his position as an Anglican clergyman. He'd come to the decision that Anglicanism didn't really align with his beliefs anymore, although he did continue to be a part of the Church. According to an account written by his son Quote, it had long ceased to be regarded as an anomaly for a clergyman to preach the then circumscribed evangelical creed and, at the same time, without the slightest insincerity, to devote himself actively to philosophical studies, yet finding himself still less in sympathy with the orthodox clerical outlook, then availed himself of the clerical disabilities Act of a naturally speculative frame of mind. He was wont to say later that, owing to subsequent change and accepted opinion regarding the thirty nine articles, he could consistently have retained his orders. He remained, indeed throughout his life a man of sincere religious conviction. That same year, also eighteen eighty three, John Vin was elected to the Royal Society, and he received his science doctorate from Cambridge. Six years after these events, in eighteen eighty nine, he published The Principles of Empirical or Inductive Logic, and the opening of the Principles makes clear that ven has been troubled by the way concepts of logic have been poorly defined in communication about them, and that not practicing clear establishing rules regarding logic arguments have hurt the field overall. This kind of a long quote, but I want to include it because it gives you grit insight into the way he thinks about things. Quote. Since logic, as conceived and expounded in this work is not an ultimate science in the sense of being concerned directly with really first principles of any kind, we find ourselves obliged, on a general survey of our province, to take for granted that a great deal has already been decided for us in various directions. In other words, we have to demand a variety of postulates, drawn partly from the region of metaphysics, partly from those of psychology, physical science, grammar, and so forth. Some of these postulates will be readily accepted. Others will be admitted by those who have had any philosophic training. Some might take it have hardly yet been duly appreciated or even recognized. This being so, it would seem convenient that the more important of these postulates should be prominently and definitely stated at the outset. For one reason or another, however, such a course seems seldom adopted, and the result has been disadvantageous in more ways than one. This neglect to state the postulates has, for instance, brought down upon the logician charges of inconsistency and shortsightedness, which might as fairly be brought against the representatives of most other sciences, but which sounded damaging when he had to meet them alone. It has also tended, as I shall trust to show in the sequel, to encourage mistaken views as to the functions and province of the science. Whilst the general objections to such an emission on the grounds of method are too obvious to need reinforcement. In a moment, we'll discuss how Ven seemed to sort of turn on a dime in terms of his interests and projects in the late eighteen eighties. First, though, we'll hear from the sponsors that keep the show going. So before the break, we mentioned that in eighteen eighty nine John Ven published The Principles of Empirical or Inductive Life, and even before that in eighteen eighty eight, as he was working on the book, then seemed to have decided that it was going to be his last work in logic and probability theory, because he donated all of his personal Library on those subjects to the Cambridge University Library and after that then ventured into publishing non mathematical works at the end of the nineteenth century, although they were books related to his work in education. He published The Biographical History of Gonville and Keys College thirteen forty nine to eighteen ninety seven in eighteen ninety seven. This was a four volume project and it included portraits of various people related to the school's history, as well as additional illustrations. He also wrote an entry for the Cambridge College series titled Simply Gonvillin Keys College. Ben wrote several books that mentioned Keys, including Early Collegiate Life, which walked through some accounts of what it was like in its early days, laid out as narrative sketches. The published lists of students who had been admitted to the college in the fifteen hundreds and sixteen hundreds. Then worked with his son John Archibald to assemble a list of Cambridge alumni, which was also published as Alumni Cantabrigenses. This included biographies of students and graduates, and it chronicle things like students who had held offices in various organizations. An unnamed colleague was quoted in Ven's obituary as saying, quote, it is difficult for anyone who has not seen the work in its making to realize the immense amount of research involved in this great undertaking. Apparently, Ven's research for this book involved going through the archives and records of not just the school, but also various churches to correctly list all of the available details of each alumnus's life. Like he would go to an alumnus's hometown church and go through all of their records and do that for all of these people on this list. It was like he must have loved research. An obituary for Ben that appeared in the British Medical Journal described his output about Keys this way quote. The works which he wrote about the college are somewhat voluminous and are characterized by thoroughness, but are for the most part full of human interest. As a rule, they are pleasant reading, though in parts they are necessarily statistical statistics. Asie, he clearly had a deep love for the school, where he had been both a student and a teacher, and his dedication was recognized. He was made president of Gonville and Keys College in nineteen oh three. In nineteen oh nine, there is this wonderful and curious moment in Ven's life story, and we're going to talk about it kind of to a disproportionate amount because it is one of those things that is both charming and surprising, but it also shows how broad the interests of his life were. He invented a bowling machine, not in the sense of the sport of bowling that we know it today in the US, but bowling as it relates to cricket. So for our listeners who are more familiar with baseball, bowling is similar to pitching. I'm sorry for any cricket officionados who are like, it's much more complex and nuanced than that. We're just going for wide strokes here. According to the saffron Walden Weekly News from June eleventh, nineteen oh nine, quote, the preliminary of what promises to be a sensation in the cricket world took place on Fenners on Thursday week. Doctor Vin, president of Keyes College, who is a Fellow of the Royal Society and a Doctor of Science, has, in conjunction with his son mister Javen, invented and patented a bowling machine which in all probability will supersede the drudgery of bowling at the practice nets. At the event mentioned in the article, a number of cricketers visiting from Australia were able to observe and test this machine, and they found it to be quite impressive. The write up continues, quote the mission can bowl any kind of ball at any variation of pace or length, and can produce a deadly break either from the leg or off side of the wicket. Batsman wishing to practice any particular kind of stroke or perfect himself in dealing with any kind of ball, may set the machine up at one end of the pitch and practice to his heart's content. And the Australians found it to be formidable. Apparently it got the better of one of their star players. Yes, some descriptions of this suggest that this was kind of a feather in the cap of England in terms of cricket reputation, to have vested the Australians with a machine made by an Englishman. This article describes the machine's design, noting that quote it is not beautiful to look at, but its utility seems to be undeniable, and it notes quote above, an ungainly base equipped with strong springs and cords towers a gaunt iron arm having at its summit a grip of four fingers which rotate in either direction. The article also mentions that people had been trying to invent a bowling machine for cricket practice for quite a while, but no one had been able to create one that could consistently deliver the wide array of pitches that a human could until the VENs did it. And they had, according to the paper, patented this machine in England, the US and Australia. So it seemed like they might be on the verge of a huge business opportunity, but that didn't happen. We're going to loop back to this machine in just a bit. Van wrote a biography of the school's second founder, titled John Keyes, which was published in nineteen ten for Keys's four hundredth birthday. John ven died on April fourth, nineteen twenty three, at the age of eighty nine. He had served as president of Gonville and Keys College right up until his death. To his last day, he had, according to the British Medical Journal obituary we mentioned earlier quote, retained to the full his clearness of mind and much of his activity of body. He was always willing to place his great store of knowledge at the disposal of others. His Royal Society obituary described then in his last years this way and it's quite charming, and the way I would love to be described one day quote A good field botanist, a bit of a mountaineer, a craftsman, and with a gift of dry humor. Then lived his long life to the full. Age treated him kindly, an active spare man. He retained his sprightly walk and his interest in work and play until the end. John's wife, Susannah, died eight years after him. John Archibald Ben continued publishing updates to the Cambridge Alumnilist after his father died for another thirty one years. The younger Van also followed in his father's footsteps in terms of academic leadership roles. He became president of Queen's College in nineteen thirty two, and like his father, worked until his death. In twenty seventeen, Hull Drypool Bridge got a makeover inspired by its famous logician historian. This was a pricey public art project. It cost or reported three hundred twenty five thousand pounds. Artist Sarah Daniels designed the artwork that adorns the bridge, which features interlocking circles in shades of yellow that repeat in a large scale pattern. Two reference, of course ven diagrams, and recently. That bowling machine was in the news in June of twenty twenty four, so just a little more than a month ago if you're listening to this. Around the time it's published, a whole slew of articles ran about a project headed up by Hugh Hunt, professor of Engineering, Dynamics and Vibration at Cambridge. Hunt was driven by the idea of showing what he called John Ven's quirky side, and by the desire to show students that mathematics and fun can absolutely mix. Hunt and his colleagues had only a photograph from when the machine was originally built in the early nineteen hundreds and a patent application to work from the head of Design at the Cambridge Engineering Department, Thomas Glenday led a group of engineers through the process of figuring out exactly how this machine worked and building it at one fifth scale to see if they had the details right. Since patent applications in their diagrams they're all about the concept rather than the technicality. The team had to do a lot of work to just re engineer this bowler, but they did. They tweaked the elements that weren't working on this miniature version before they built a full scale one, and that one works. Yeah. As of last month, I know there was at least one event where it was. I think it was at the Essex County Cricket Club where they were doing a presentation about it. I hope it gets put on display somewhere because it's a really cool idea to build an invention that somebody else made and that you have to figure out how it actually worked. So that is our discussion on John Benn, which I love because he's so much more than the diagrams, and even the diagrams are so much more than the way we usually hear or know about them. So yeah, I always like a little expansion of knowledge. I have a very very cute listener mail from our listener Don. The cute part is the picture. Don writes, good day, Holly and Tracy. I just finished listening to your episode on historical roads and Highways. I was fortunate enough to go to Italy in twenty nineteen with my mother and my sister. We drove the Autostrata, both to Florence and again to Storo, where we have family. I couldn't believe how large the rest stops were, with gas stations on both sides that often had a bridge across the highway to access the auto grill on either side. So convenient when you're driving either direction and need to stop for gas and food. The Church of the Autostrata seems so out of place, but knowing its history, it is in the perfect location. The toll system is not something I'd dealt with before, and we always held onto any change we got when shopping so we'd have enough on hand for the toll boosts that are throughout the Audustrata. I have attached a picture of my daughter's dog, Leo. He is very attached to me and I'm not sure what I will do when my daughter is ready to move out. Thank you for your wonderful work done. This dog is so cute. He's a little terrier. It looks like maybe a Yorkie maybe a little Yorky mix, and it's just one of those pictures where you just know he is curled up right next to her and just wants love and attention, and he's very cute. Those eyes Man dogs get me every time. I know all of this talk of the autostrata makes me want to go back to Italy sooner rather than later, So let's do that. You can write us if you have any email thoughts you'd like to share at History Podcast at iHeartRadio dot com. And if you'd like to subscribe and you haven't gotten around to that yet, you can do that easiest pie on the iHeartRadio app or wherever it is you listen to your favorite shows. Stuff you Missed in History Class is a production of iHeartRadio. For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows,