Post B0XGcOvAi4OLB3xe0e by pozorvlak@mathstodon.xyz
 (DIR) More posts by pozorvlak@mathstodon.xyz
 (DIR) Post #B0XGcNIqj48w9v1Wdc by pozorvlak@mathstodon.xyz
       2025-11-23T09:49:21Z
       
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       The slides for my talk on dual numbers are at https://docs.google.com/presentation/d/1Y_ZjVf5iuiWHI690SI0QhCdqBm94_Kf-RiQVNtUaZF8/edit?usp=drivesdk Not sure how much sense they'll make without my narration, but I'm not sure how much sense they made *with* it 😅 I'll try to get the video up on YouTube soon! #BigMathsJam #mathsjam
       
 (DIR) Post #B0XGcOvAi4OLB3xe0e by pozorvlak@mathstodon.xyz
       2025-11-23T09:52:59Z
       
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       The extremely alert viewer may detect some slight similarity between my presentation of dual numbers and the one @dpiponi used in this post, where I first learned about them: http://blog.sigfpe.com/2005/07/automatic-differentiation.html?m=1#BigMathsJam #mathsjam
       
 (DIR) Post #B0XIsxAjKiXjwkG74C by drgeraint@glasgow.social
       2025-11-23T11:50:03Z
       
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       @pozorvlak That's really neat! I hadn't come across dual numbers before.I was baffled to start with. d^2=0 implies d=0, so why bother including it? But when I saw the connection to neglecting higher powers of delta (small change) in differentiation, it made sense. And the connection with complex numbers, and therefore evident efficiency of computation, makes this look really useful.Certainly a better way of tackling some simulation problems where I used symbolic algebra in the past.
       
 (DIR) Post #B0YHdIxceNzU5q3uVM by pozorvlak@mathstodon.xyz
       2025-11-23T12:31:49Z
       
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       @drgeraint yes, that's exactly it! Taking this idea to its logical extreme gives you "differentiable programming": https://en.wikipedia.org/wiki/Differentiable_programming
       
 (DIR) Post #B0YHdKCC3hExvJt3r6 by drgeraint@glasgow.social
       2025-11-23T23:08:42Z
       
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       @pozorvlak I'm relieved to see that this became a thing roughly 15 years after I was doing things the old way.Now I need to think about how to introduce this to the next generation of engineers. They'll need it, but won't know why until they do.