Of all the formal constructions of the set of the real numbers, Eudoxus reals are to me the most elegant, even if completely impractical. The idea, due to Schnauel, is that any line in the plane, be its slope rational or irrational, can be described using only points with integer coordinates: taking the floor (or ceil or round or worse, doesn’t matter) of the y-values associated with integer x-values does characterize uniquely, asymptotically, any line....
Physics Languages The Latent Structure of Dictionaries: how many words do you need? Experiments Compact subpicometer Michelson interferometers: LIGO and such go a lot deeper, but are kilometers wide. GINGER MICROSCOPE mission: Another test of the equivalence principle. GENESIS: Co-location of Geodetic Techniques in Space: Big project to improve time and space reference frames. May be interesting like GINGER, dunno. Gravity assists as a test Alt Bell test in pilot waves...
Geometry and simmetry Div, grad, curl are dead – by William L. Burke: an unfinished cryptic Nietszchean masterpiece on unveiling the nature of vectors and differential forms. Divine Proportions – by N. J. Wildberger: trigonometry with only rational numbers (the only true numbers). Topological Methods in Hydrodynamics – by Vladimir I. Arnold and Boris A. Khesin: Uncle Arnold generalizes named-after-Euler equations on Lie Groups. “Most Likely To Be Random Generated, Judging From The Title” Award Winner....
Files InfiniDrive: converts any sort of data into flower images. Fix Onedrive Zip TMSU Utilities entr: do stuff whenever a file changes Dispatch Proxy: use multiple internet connections at once. Marginalia Search Social media youtube-dl Unlisted Videos Nitter: Twitter replacement that doesn’t require login. Music Beets: tag and organize music collections automatically Openbook: an open source real book written in LilyPond. Musescore Downloader Librescore: open source MuseScore. PiKaraoke Maths Theorem Graphs: relazioni tra teoremi...
Blogs Maths: Blog on maths blogs (hope this doesn’t count as cheating…) Terence Tao: guy with IQ higher that Einstein that doesn’t understand Physics. John Baez: absolute category-theoretical physicist madman. Not Even Wrong: Peter Woit, aka “String Theory Bad" Man Francesco Polizzi: cool blog on maths in Italian. Adam Marsh: author of mathph notes with marvelous illustrations. Eigil Fjeldgren Rischel Ingali Dakis: a schizo obsessed with Bach and Mathematics. Intellectual Mathamtics Annoying Precision Embûches tissues Ars Mathematica Nico Belmonte: Hopf fibration Notation and though What Is…?...
When I attend talks I try to write down three insights that stroke me the most. I heard the idea somewhere and think it’s a good habit. Terence Tao, Riemann Prize Lecture: Analyzing a variation of the problem can help you rule out strategies that rest on their common features The main reason for problems with Navier-Stokes in 3 dimensions is a d/2 critical exponent When you come up with counterexamples you must design them with the ingenuity of an engineer “Come fotografare l’indescrivibile”, 5th International Light Day Daniele Faccio:...
Dirac’s derivation of his famous equation seems to involve finding some king of “splitting algebra”. Are there other equations that need such treatment?
It is often said that epicycles, a fundamental mathematical tool of the Ptolemaic planetary model, which I was always taught were as primitive, obsolete and embarassing as the conception of our solar system, are nothing more and nothing less than Fourier series expansions. I realize, with much consternation, that this is true, but the question arises: Has anybody done the calculations and got that Fourier series for Kepler orbits do agree with the epicycle description?...
I heard a rumor from a friend of mine who talked to one of our professors. He said the professor told him about how his highschool background on basic electronics circuits let him easily “imagine” the integral representation of Bessel Functions. How?
The Dirac measure looks like the Lebesgue measure composed with the Dirac delta distribution. Does this generalize to other measures (on spaces that admit a Lebesgue measure)?