Podcasts about euclid's elements

Dr. Carol Day: Lining Up Numbers, The Place of Books 7 - 9 in Euclid's Elements by Thomas Aquinas College Lectures & Talks

From an undergraduate perspective, coming from the rigid proofs and concrete constructions of middle- or high-school courses, the broad discipline of geometry can be at once intimately familiar and menacingly exotic. For most of its history, and perhaps for many of the same reasons, geometers struggled to come to terms with the unsolved problems, unstated assumptions, and untapped generalizability contained in the "bible of mathematics", Euclid's Elements. In their recent text, Geometry: The Line and the Circle (MAA Press, 2018), Maureen T. Carroll and Elyn Rykken have produced a unified survey of Euclidean and many significant non-Euclidean geometries, one that draws from the patterns of historical development to immerse students into progressively new territory. Their book is organized around the Elements but soon (and often) detours into spherical, finite, and other geometries that bring the limitations of the classic text—and the contributions of subsequent geometers—to the fore. Throughout, they examine the shifting roles and behaviors of two fundamental geometric concepts, the line and the circle—a narrative hook that might deserve more play in mathematics texts! In addition to their historical vignettes, Carroll and Rykken include rich selections of exercises and incorporate a variety of tactile and online tools, and their treatment is held together in an accessible and absorbing writing style. The book is tailored to an upper-level undergraduate course but could also support a history of mathematics or introduction to proofs course. Suggested companion works: Edwin A. Abbott, Flatland: A Romance of Many Dimensions (+ sequels & film adaptations) Norton Juster, The Dot and the Line (+ film adaptation) Cory Brunson (he/him) is a Postdoctoral Fellow at the Center for Quantitative Medicine at UConn Health. Learn more about your ad choices. Visit megaphone.fm/adchoices

Here are some links to find out even more: Our guest for this episode: Dr Clare Moriarty! * her personal webpage at KCL is here (https://www.kcl.ac.uk/people/dr-clare-moriarty), and you can find her on twitter @quiteclare (https://twitter.com/quiteclare). * Here's Clare's excellent piece for History Ireland which discusses A Masterclass in Trolling from an 18th Century Bishop: 'Berkeley vs. Walton' (https://www.jstor.org/stable/26853081?seq=1) For some introductory things to learn more about Berkeley's views: * here (https://plato.stanford.edu/entries/berkeley/) is the Stanford Encyclopedia to Philosophy's entry about Berkeley by Lisa Downing * here (https://www.maths.tcd.ie/~dwilkins/Berkeley/) is David Wilkin's (TCD) page which has links to online texts and other resources, especially about the Analyst controversy We talk a bit about what it's like to on a temporary employment contract in univerisities (I think I say that I've held 2 or 3 'permanent' appointments, but I meant to say 'temporary'!), and there's widespread growing concern about the way that universities have decided to keep people on 'precarious' contracts. * The British Philosophical Assocation issued a report 'Improving Careers: Philosophers in non-permanent employment (https://bpa.ac.uk/wp-content/uploads/2018/10/phillips-improving-careers.pdf)' in 2010 * and an updated piece in 2018 'Improving Careers in Philosophy: Some Information and Recommendations for Heads of Departments (https://bpa.ac.uk/wp-content/uploads/2018/10/improving-careers-in-philosophy.pdf)' * as well as a 'Guide for Philosophers in Non-permanent employment in the UK (https://bpa.ac.uk/wp-content/uploads/2018/10/Guide-for-Philosophers-in-Non-Permanent-Employment.pdf)' (2017) We also talk a bit about some of the challenges that go with working on a topic of research that straddles several different disciplines (history, philosophy, mathematics). Jo Wolff mentions the latter in his column for the Guardian here (https://www.theguardian.com/education/2014/sep/23/universities-make-scholarship-more-confusing-exciting), including a shout-out to Berkeley's ideas about tar water! At one point in our talk we touch briefly on some examples of reviews of philosophical books (by other philosophers) which are pointedly blunt (to the point of being amusing). Here are some links: * Nina Strohminger's review (https://static1.squarespace.com/static/520cf78be4b0a5dd07f51048/t/53a029dce4b0ba2ac791103b/1403005404701/Strohminger.EmotionReview.2014.pdf) of a book about disgust. * Kerry Mckenzie's review (https://watermark.silverchair.com/fzt073.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAl8wggJbBgkqhkiG9w0BBwagggJMMIICSAIBADCCAkEGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMf7eGyup-uT8S7-S-AgEQgIICErKh7Y9iH-Xq4Wli5bbua-SqU0IF7EN55_gVsq4gUwFKC0R3m5Tw9hVdVfiVoCUoq17kc_MPnLWJLsBZbdk_4CbJTIJCbr60Y82MlyM52uALI6xVtbYZ5iWhuGlXTGGtXc2VT0gd7sSnDvOmkhccMclyjFDAJQYN8LilCR9BbxOJU5tZGRRXe8UQ8_29H_6NZ7JysktBymyeqJGUc5xpgq-6u5zDTejppQz523lqRH986p8aSJuo25ul1Qvbhx_f4P7LaIy5jN4aW1vTBxB6-Rc1Ngure4KqW-VIs5u0uiilX_Xob0Dew-5aIk45PDOj23t_hEnBQf618ySfqO-1-eAvD-bDpJ2m1KXei-nlnBXKwBVNvpARMP1ISHM6GXdq209PbucZWVtci7wQEtOhGqXQsUujMKubdz0PT65auLiCKAj8xJWaXf5nkzJ1YqV3PSytY5WpiHQqg-EnmBMTH4u5MNdXu_uVftsg8EXEFd7FfLgSs3Rv7ESuzebxkJqwNhm0G9SAX_dorLHl3woHdUVNjIWtImfiYQKEnz0Pz6jTXMeIDlsh7vyFJ-hDx85vbiL0_L2All1Hbv9wP2jPGW0hubHCCvisqpObyTzTGygrltI0cpyqvCwa7M7RH2ruUl1IYBhs1DjgyIF18QCuICn5CkV5kxi3yiHeWAmv2-RjxLHTizI6As0j2wd1aIYMOvOt) of a book about metaphysics. * The now historical UCL tit-for-tat 'hachet job' reviews, summarised (https://www.ucl.ac.uk/~uctytho/McGinnHonderichRossJCS.html) by J Andrew Ross. In this episode I try (in the first couple of minutes) to summarise what I understand Berkeley's 'idealism' to involve, and then I try to explan why it might mean that a Berkeleian idealist has some resistance to some bits of mathematics. I don't think I did a great job of summarising it, but here's what I said, if it helps to read it: Berkeley’s famous for maintaining a position that we call ‘idealism’, which says that the only things that exist are minds and mental events – that’s all there is, minds and mental events. So, for example, physical things like coconuts or trampolines or jellyfish exist only in so far as they’re being perceived by a mind. It’s as though there aren’t really any coconuts or trampolines independently of us, instead they’re just sort of composed out of bundles of our ideas. But while this is the normal story that we tell about what Berkeley thinks about everyday objects in the external world, I really didn’t know much about Berkeley’s philosophy of mathematics before talking with Clare. I suppose one way to think about it is this: that if like Berekely you think that for something to exist it has to be perceived by a mind, then there’ll be some things that mathematicians talk about which Berkelian idealists are going to balk at. For example, mathematical work in calculus deals with infinitesimals, and one of the things that we know about infinitesimals is that they’re really hard for us humans to think about, or to imagine or conceive of. And if Berkelely’s right, and that for something to exist it has to be perceived by a mind, then since we can’t perceive infitinitesimals (even in our imaginations), I guess he’s going to want to say that they don’t exist. And the upshot would mean that Berkeley would have to say that the whole of calculus is concerned with something that doesn’t really exist. And as it happens, that’s precisely what he did say: in his book The Analyst Berkeley refers to Isaac Newton’s infinitesimal calculus as dealing with the ‘ghosts of departed quantities’. The challenge that Berkeley created for himself by being an idealist is that he then needed to be able to give mathematics, and the newly invented calculus (which was proving to be really successful!), a more secure foundation in the kinds of qualities that our minds can perceive. And as Clare mentions in the episode, one person who tried to carry out this Berkelian project is Oliver Byrne (https://en.wikipedia.org/wiki/Oliver_Byrne_(mathematician)) (1810–1880), and Irish mathematician who wrote a work called The Trinal Calculus which says on its title page: "The object of the Trinal Calculus, like that of Geometry, is the investigation of the propositions of the assignable extensions, and there is no need to consider quantities, either infinitely great or indefinitely small". Byrne also made a 'coloured Euclid', a version of the first six books of Euclid's Elements "in which Coloured Diagrams and Symbols are used instead of letters for the greater ease of learners". While it sounds like the colours are there to assist people to understand the mathematics, it's clear that Byrne's ultimate goal is to show that a huge amount of mathematics can be successfully carried out without appealing to any entities (like infinitesimals) that cannot be perceived by a mind. Shortly after we recorded this episode, Clare was working in TCD's archive of historic books, and sent me some snapshots of their copy of Byrne's Trinal Calculus (in the back of which he had included his annotated copy of Berkeley's Analyst – a gift to posterity). Here they are: https://i.imgur.com/DFPb00w.jpg https://i.imgur.com/dAgJM7h.jpg and here the text says "the differential and integral calculus, under different forms and titles, have been based on visionary notions and false logic; these defects, which Bishop Berkeley and other writers clearly exposed, are fully remedied by The Trinal Calculus" https://i.imgur.com/PTOi9Ca.jpg and here's an example of one of Byrne's delighful illustrations: https://i.imgur.com/K4Y6bPg.jpg

Euclid's Elements is considered one of the most foundational bodies of work in the field of mathematics. Written around 300 BCE (over 2,000 YEARS AGO!), it was a textbook that provided students the opportunity to learn most of the theories and propositions written at that time. However, even though it was groundbreaking, there was already a history of math that preceded this book, as you will find out. If you are interested in learning more about the history of math and science, please feel free to visit me at my website, www.mathsciencehistory.com! Until next week, carpe diem! Gabrielle Birchak 

#12 Dealing with cultural differences in the workplace The stark cultural differences between China and the West are frequently identified as key barriers in productive professional exchanges. However, the mechanisms by which people can actually improve their cultural understanding — or “cultural literacy” — are less clear. How can professionals in China and the West bridge gaps in understanding to ensure that business can sail smoothly?   Featuring: Vincent Vierron – director Vincent’s LinkedIn  | Vincent’s company website    Beatrix Frisch – general manager, Mackevision Mackevision’s website Joey Wang – script writer Joey’s Instagram  And, as usual, your host, Aladin Farré. Aladin’s LinkedIn | Aladin’s Twitter   Three main takeaways from this week’s episode:       1) In Chinese workplaces, flexibility is key.   Partially as a result of China’s incredibly competitive labor market, workplaces in China tend to be much more flexible than their counterparts in the West. Media professionals should be ready at any moment for a change in a script or the editing of a commercial, with little notice or supporting budget. At the same time, Chinese workers will almost always respond to their emails on a Saturday evening or late at night (a habit that is far from widespread in Europe, for example). All of this results in sky-high rates of employee turnover as burnout and ambition take their toll.   2) Top-down approaches are standard in China. In the office, the boss is king. He (or she!) will always get the last word, no matter how much work went into a project beforehand. However, if an employee is flexible and patient, they can hopefully avoid the worst surprises. 3) Chinese work culture is constantly evolving. Whether the workplace is a state-owned enterprise or a private, international firm, internal procedures will inevitably vary wildly. What remains constant is that China has come a long way since the beginning of the reform and opening up period, so “middlemen” who take commissions only to put people in contact tend to be less important.  Recommended watching and listening:  The Flower of War (2011): Wikipedia   Sinica Podcast: “Dashan and David Moser on the Chinese language”: Link   Answers to the episode quiz: Matteo Ricci (1552–1610) was an Italian Jesuit priest who became the first European to enter the Forbidden City of Beijing in 1601, when the Wanli Emperor 万历帝 sought his services in court astronomy and calendrical science. He converted several prominent Chinese officials to Catholicism and translated Euclid's Elements into Chinese as well as the Confucian classics into Latin. Da Shan 大山, or Mark Henry Rowswell, is a Canadian comedian and television personality who is one of the most famous Western personalities in China. He has appeared several times on CCTV’s Spring Festival Gala since 1988. The Flower of War (2011) is the second-biggest flop at the Chinese box office after The Great Wall (2016). Zhang Yimou directed both films. 

Online Great Books founder Scott Hambrick and seminar leader Emmet Penney tackle the first scientific work on the podcast, Euclid's Elements. The Elements are a collection of treatises, postulates, and propositions that ultimately drive toward important mathematical concepts such as the Pythagorean theorem and the theory of numbers, i.e. integers, divisibility, prime numbers.   Everyone who has attended American public school has heard of these concepts, and their mention likely dredges up memories of endless, boring, rote work about triangles and algebra. Indeed school teaches the formulas, but it does not teach Euclid, who compiled numerous propositions form earlier mathematicians and weaved them into a thoughtful, cogently argued work about the nature of geometry and mathematics. Studying Euclid prompts the question: are these concepts discovered or invented? Does mathematics represent a fundamental truth of the universe, or does it merely describe the truth?   And that's why we study Euclid and other formative scientists and mathematicians at Online Great Books; they prompt us to consider the nature of truth and how the things we are taught in school came to be. It's quite a philosophical exercise. Yet philosophy and science exist in diametric opposition, at least in today's age. Emmet points out a difference between the practice of science (and the technological fruit it bears) and scientism, the faith in science as a diviner of absolute truth. Reading Euclid, he argues, shows us the deep interconnection between science and philosophy, and leads us to a deeper understanding of the truth.   You can find Emmet on Twitter as Emmet Martin Penney. You can read some of his written work at: Popula Paste Magazine

A tutor talk by Dr. Carol Day

Euclid's Elements takes a disciplined, formal approach to proving assertions based only on simple axiomatic statements. While most of these axioms are elegant, one of them is more complex and wordy. It seems as if it should be provable from the others. Several mathematicians have tried, but eventually they found a surprising result. Beware when proving your own assertions that you don't make the mistake of assuming something that seems obvious. Category theory isn't as complex as you might be lead to believe. A category is nothing more than a contract that sets rules on how a type is to behave. Functors, despite having a weird name, are just types that can map functions into a different space. The List type is an example of a functor, because it can transform a function on its elements into a function on lists. And Applicatives are just wrapper types. They are especially useful for building pipelines. CQRS, Command Query Responsibility Segregation, is a pattern that applies the Single Responsibility Principle to components such that they either change the system (commands), or observe it (queries). Segregation alone gives us the ability to prove some very useful things about a system: safety, determinism, and consistency for example. But it does not prescribe asynchrony or eventual consistency. Those are architectural decisions left to you.

Melvyn Bragg and guests discuss Euclid's Elements, a mathematical text book attributed to Euclid and in use from its appearance in Alexandria, Egypt around 300 BC until modern times, dealing with geometry and number theory. It has been described as the most influential text book ever written. Einstein had a copy as a child, which he treasured, later saying "If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker." With Marcus du Sautoy Professor of Mathematics and Simonyi Professor for the Public Understanding of Science at the University of Oxford Serafina Cuomo Reader in Roman History at Birkbeck University of London And June Barrow-Green Professor of the History of Mathematics at the Open University Producer: Simon Tillotson.

Melvyn Bragg and guests discuss Euclid's Elements, a mathematical text book attributed to Euclid and in use from its appearance in Alexandria, Egypt around 300 BC until modern times, dealing with geometry and number theory. It has been described as the most influential text book ever written. Einstein had a copy as a child, which he treasured, later saying "If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker." With Marcus du Sautoy Professor of Mathematics and Simonyi Professor for the Public Understanding of Science at the University of Oxford Serafina Cuomo Reader in Roman History at Birkbeck University of London And June Barrow-Green Professor of the History of Mathematics at the Open University Producer: Simon Tillotson.

Professor Dana Scott, Carnegie Mellon University, presents his Distinguished Lecture entitled "Geometry Without Points". Ever since the compilers of Euclid's Elements gave the "definitions" that "a point is that which has no part" and "a line is breadth-less length", philosophers and mathematicians have worried that the basic concepts of geometry are too abstract and too idealized. In the 20th century writers such as Husserl, Lesniewski, Whitehead, Tarski, Blumenthal, and von Neumann have proposed "pointless" approaches. A problem more recent authors have emphasized it that there are difficulties in having a rich theory of a part-whole relationship without atoms and providing both size and geometric dimension as part of the theory. In this lecture, a solution will be proposed using the Boolean algebra of measurable sets modulo null sets along with relations derived from the group of rigid motions in Euclidean n-space. (Joint work with Tamar Lando, Columbia University.) This lecture was recorded on Monday 23 June at the University of Edinburgh's Appleton Tower.