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.
Other members of the Haberdasher's Menagerie: a friendly capybara, an angry swan, and a crafty fox.
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".
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'...
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
@BigMathsJam #bigmathsjam #mathsjam a short video you may enjoy if you like taskmaster type shortcuts to problems. x
https://youtu.be/S_pPdZQw44A
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.
www.bbc.co.uk/news/uk-engl...
Superman IV film recreated in ...
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
Also of potential interest to Big #MathsJam folk & other maths fans: don't forget to submit recent maths stuff ready for December's Carnival of Mathematics: aperiodical.com/carnival-of-...
Carnival of Mathematics
Also of potential interest to Big #MathsJam folk & other maths fans: don't forget to submit recent maths stuff ready for December's Carnival of Mathematics: https://aperiodical.com/carnival-of-mathematics/
I wanted to make a poster about this for the new Big #MathsJam feature, but I don't have a printer, so:
I wanted to make a poster about this for the new Big #MathsJam feature, but I don't have a printer, so:
If you're interested in some intersection of history and maths (e.g. history of maths, or the maths of history) and the potential for each to enrich education of the other, then I have the free fledgling network for you: https://historyand.mathsy.space/
Another excellent Big #MathsJam. Somehow I'm less tired than usual. Maybe it's the travel that does it‽
Another excellent Big #MathsJam. Somehow I'm less tired than usual. Maybe it's the travel that does it‽
My train was ten minutes late leaving Milton Keynes; tight for my fifteen-minute connection at Crewe, but not impossible. Then it sat at the platform for an additional ten minutes at Rugby, and it's just got later and later since then. The driver is saying that we'll still arrive before my connection leaves, but realtimetrains.com says different, and I know which one I believe. The next train to Edinburgh isn't for an hour and it gets in at midnight. I hate travel.
@ColinTheMathmo Thank you for another fun weekend. Upset that I had to leave early, but care duties called.
Fished my keys out of my back pocket at stupid o'clock this morning as I was going to check out and they were magically untangled. I think #MathsJam was just messing with me.
Lovely weekend at #mathsJam . Thanks to all those who organised and those who gave talks. Hope to see you all next year! Safe journey home everyone.
To start the final set of talks at #mathsjam, Vanessa Madu sharred her explorations of sequences of consecutive odd semiprimes. You can read her blog post about it here: https://www.vanessamadu.com/posts/consecutive-odd-semi-primes/
@BigMathsJam is officially over! Many thanks to everyone who organised, contributed to it, maintained the Gather town remote space etc. #mathsjam #remoters 👏👏👏
