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Last Notes

2025-09-21 23:36:32 UTC

"Yes, I agree with everything you said – it's antithetical to learning, it's led by terrible companies, etc. — but I think we should encourage students to use it because it can't be avoided and they'll be left behind and we'll look ridiculous if we don't jump on this train."
How's your Monday going

2025-05-19 17:01:51 UTC

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I often wonder if things might get clearer/easier when using index notations from differential geometry, rather than the vector-looking-but-not-a-vector nabla. For example, that (v ⋅∇) operator is a bit tricky to manipulate (not sure how it's to be done in non-cartesian systems of coordinates)

2025-05-19 14:22:00 UTC

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funny, I just had tabs open in my browser regarding conservation of helicity in electromagnetic fields – things like Lipkin's 'zilch', dual-symmetric media, Kerker condition, etc.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.104.163901
https://www.mdpi.com/2073-8994/11/9/1113

2024-12-27 02:40:48 UTC

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Incidentally, do you think this might provide an intuitive interpretation/example of the less-intuitive terms appearing in the Maxwell stress tensor? A colleague of mine once alluded to this magnetic field lines-as-rubber-bands intuition, but didn't elaborate further.
I (think I) understand the ∇(E²) intuitively (e.g optical tweezers where a trapped dipole wants to minimise its energy), and the Poynting one (light sail), but the (E•∇)E (or ∇x∇x whence it appeared) eludes me.
https://cdn.masto.host/vissocial/media_attachments/files/113/722/465/568/385/103/original/b8f20f250fd0c83a.png

2024-11-16 21:48:32 UTC

Me, opening google maps:
"I wonder if there's interesting teaware produced around where I'll be staying—Suzhou"
"Oh"

2024-11-16 03:02:08 UTC

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I will be very disappointed if I don't read further down in the comments, that there is in fact an entire subfield of mathematics defining concepts such as these, and extending them far beyond the point of comprehensibleness—and of course a dedicated set of macros on CTAN

2024-10-27 20:52:25 UTC

I'm looking for black ink that is i) very black, ii) water soluble, iii) dye, not pigment based
Any recommendations?
#FountainPens
#FountainPen
#FountainPenInk