Turns out that chips supporting the "monstrosity of an instruction" I showed at #BigMathsJam are being used by SpaceX for inter-satellite networking (with LASERS, no less). Dual numbers IN SPAAAAAAAACE!!!¹

https://newsroom.st.com/media-center/press-item.html/p4733.html

¹ I have no idea whether they're actually using the dual number instructions.

#mathsjam

Everyone¹ knows the Haberdasher's Puzzle, in which a square can be dissected and reassembled into an equilateral triangle. But only a very small number of extremely cool people know that the same dissection can also be used to make a noble buffalo and a wise llama.

¹ For suitably small values of "everyone".

#mathsjam #BigMathsJam

Now I've given my talk, I have some more questions about dual numbers to investigate - some from here, and some from people who talked to me at #BigMathsJam.

- Apart from the duals and complex numbers, what other interesting degree-2 extensions of the reals exist? (HT George, didn't catch his surname)
- The dual numbers are the "first formal neighbourhood" of the reals - but what does that mean? (HT @RobJLow )
- The dual quaternions can be used to model mechanical linkages - see https://pure.hw.ac.uk/ws/portalfiles/portal/15726128/JMR161273_PURE.pdf How does that work? (HT @robinhouston )
- More generally, is there a connection between dual numbers and Lagrangian mechanics? How about Hamiltonian mechanics?
- I sketched a proof that the soul of f(x + ε) is f'(x) for any function f: R-> R that can be evaluated in finitely many arithmetic operations. Can we extend that to analytic functions? What about functions which are differentiable but not analytic? (HT @RobJLow )
- Let f be an analytic function, and g a polynomial approximation to f in a neighborhood of x. How well does the soul of g(x + ε) approximate f' in that neighbourhood? I guess that's the same as asking how well g' approximates f'...

#mathsjam

RE: https://mathstodon.xyz/@pozorvlak/115605084962357616

Jeff Egger informs me that the thing I thought was unique actually has a model for every uncountable cardinal (and countably many countable models). So I was not merely infinitely wrong, there is no infinite cardinal large enough to express how wrong I was. #BigMathsJam #MathsJam

@BigMathsJam #bigMathsJam #mathsjam
Some people were asking me for the solution to the Expo Dough competition, but I had to rush off.

Here's one way:
https://drive.google.com/file/d/1e0jmZhP1T8QRwe2njATCXQWw_XsvMFkH/view?usp=sharing

and here's a Geogebra to visualise it
https://www.geogebra.org/classic/ggfyxhan

Big #MathsJam -ers who took the train home today and are also movie fans might have recognised the railway station building from 1987's Superman IV.

Various other buildings in CMK were used as locations for bits of Metropolis in the movie.

https://www.bbc.co.uk/news/uk-england-beds-bucks-herts-36881560.amp