There is a lot about Euclid’s Elements that is easily misunderstood. Some proofs seem to have logical gaps. Some constructions seem pointless, others seem needlessly convoluted.
Each of these provides a window into how the ancient Greeks thought about math and the philosophical role that geometry played.
In the fifth and final of a series of guest videos I've been posting, @BenSyversen delves into a question anybody who has had to do ruler and compass constructions in a geometry class may have wondered: What's the point?
youtu.be/M-MgQC6z3VU
Very comprehensive takedown of Galileo by @viktorblasjo
I don't think anyone has tried to frame a rebuttal, which I would find interesting because I don't share the anti-philosophy biases of the author
arxiv.org/abs/2102.06595
Yesterday we got a new @viktorblasjo podcast all about Torricelli's trumpet, infinite geometric objects, and myths of math history. Entertaining, informative, hilarious, & way more detail than you probably want on parsing passages from the 17th century. intellectualmathematics.com/…
Today I learned (ht @viktorblasjo) how Huygens summed the reciprocals of the triangular numbers. He regrouped the series and showed that it equals the geometric series 1+1/2+1/4+... = 2, like so!
Endless Stories, opens on 28 Sep at Cambridge University Library. It showcases the extraordinary manuscripts collected by 17th-century visionary, Thomas Van Erpe. The exhibition includes works in Arabic, Hebrew, Persian, and Malay.
Book your free ticket: lib.cam.ac.uk/endlessstories
Interesting comments on the geometrical algebra hypothesis in this review indeed. Among other things, "well-founded arguments have been advanced by V. Blåsjö" 🤗
... algebra and arithmetic", says Athanase Papadopoulos's review zbmath.org/1539.01003.
The review gives also a detailed update on the state and recent discussions on the field of geometric algebra, closely related to the second book of Euclid's elements. 2/2
The innovative and, at times, wonderfully surreal engravings from Johann Zahn’s Oculus Artificialis (1685), an early and comprehensive account of the function and usage of a number of optical instruments, including the camera obscura and magic lantern: buff.ly/2mBHRMb
So moths end up inside your house at night because their brains evolved to navigate a world in which geometry is projective, where rotations=translations; yet human lighting breaks that expectation, and places them inside the much uglier world of non-projective spaces. (11/11)
Spot the equilateral triangle! The king strikes such an unnatural pose in order to invoke Proposition 1 of Euclid’s Elements, thereby conveying that his authority is as immutable as the demonstrations of geometry.
A rare chance to own a 1st ed. of Hobbes’s Leviathan, complete with probably the most famous frontispiece ever.
It’ll set you back £35k but given “the life of man, solitary, poore, nasty, brutish, and short", if you have it, what are you saving it for?
buff.ly/4bXHz7l
In the 20th century, philosophy of mathematics was hogged by logic and set theory nerds. So much so that the actually interesting part of philosophy of mathematics had to be rebooted under a new name: "philosophy of mathematical practice". link.springer.com/referencew…
Diagrams 2024
14th International Conference on the Theory and Application of Diagrams.
DIAGRAMS’24 will be held 27 September – 1 October 2024 in Münster, Germany
diagrams-2024.diagrams-confe…