Viktor Blåsjö

@gregeganSF Ever since @viktorblasjo came up with his series on Galileo (intellectualmathematics.com/blog/the-case-…) I had the tools to mock those that namedrop him as the paragon of science

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

Viktor Blåsjö's review of the book "Form & Number: A History of Mathematical Beauty" by Alan J. Cain, is now live at tug.org/books/reviews/…

@3blue1brown The 11th-century text by Biruni mentioned in this clip: archive.org/details/ilmeta…

I just put up a new video, which was a collaboration with Terence Tao about the cosmic distance ladder. You can find the full video on YouTube, and here's a bit of extra footage that didn't make it into the final.

@mmeijeri @yvanspijk @YoeriGeutskens "The term 'focus' for these points [foci of conic sections] was introduced by Kepler ... I know of no ancient or medieval term." Toomer, Diocles on Burning Mirrors, p. 15. Even though the Greeks certainly knew about the concept, both theoretically and practically.

@yvanspijk @YoeriGeutskens Wacht, dit is een vraag voor @viktorblasjo!

@dodecahedra Certainly. The "rigor" I don't like is for example proving the FTC using the Intermediate Value Theorem and such things. A purely intuitive proof of the FTC is much more useful in a calculus context, whereas the "rigorous" proof in that context only obscures the key idea.

@viktorblasjo And to say this finite truncated trumpet has volume L is to say the sum of the finite number of thin discs can be made arbitrarily close to L by taking the discs thin enough. This kind of discussion is good, IMO. So score one for the rigor that makes this discussion possible!

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/blog/torricell…

@dodecahedra Yes, I agree that Hobbes's argument basically doesn't work for this kind of reason. He is perhaps trying to say that infinitesimal methods generally assume non-Archimedean quantities, not referring to the specific slices used in any particular proof such as that of Torricelli.

In short, I don't think the Blåsjö interpretation of Hobbes's quote makes sense either since the Archimedean property only applies if the infinitesimal elements (thin discs) being added indefinitely are the same. But they are not the same, so hard to see Hobbes making that error.

hyperbolas

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!

Euclid in Syriac, from the new exhibition at @theUL. x.com/theUL/status/1…

@VisualAlgebra When integrating a separable diff eq, incorporate the initial condition as bounds of integration.

Lots of good guesses here, but I haven’t seen the right answer so far. Here’s a hint: it involves differential equations!

I’m teaching a topics grad class in Algebraic Systems Biology. There are 8 math students and 6 from other depts (Phys, Chem, BioE, and Med Biophys). This week I covered a mathematical topic. All non-math students had seen it, but 1/8 math students had. Can you guess the topic?

@MBarany Yes, the confrontational approach is crude and imperfect (certainly including my contributions) but still better and more fruitful than the milquetoast bland fest some seem to prefer.

Interesting comments on the geometrical algebra hypothesis in this review indeed. Among other things, "well-founded arguments have been advanced by V. Blåsjö" 🤗

@mmeijeri Indeed. Numerical calculations of areas and volumes by multiplying numbers were certainly commonplace in practical economic contexts. Formal mathematics often hides its intuitive or applied origins, then as now. Høyrup is good on this.

@viktorblasjo I sometimes wonder if any non-mathematical historians believe the ancient Greeks were unaware of the similarities between numbers and other types of quantities like lengths and areas. Surely any educated Greek must have had some vague notion of area equals length times width?

@snezanalawrence Alchemy Hall of Fame

Newton, guess where and on what account? A little surprise today when I saw him in such company.

@Helenreflects Way beneath the ambition of Leibniz. Galileo couldn't quit his shitty university professorship fast enough when his fame took off. Newton too grew way too elite for a provincial Cambridge job and quit. And these were much better universities!

How to Triangulate Your Dragon

Physical manifestation of the question: What’s the rate of change of the area of a square with respect to its diagonal? johanneslangkamp.com/growing-archiv…