is there a finite-time singularity in fluids?
(euclidean 3-d euler/navier-stokes, smooth IC)
this is the data we collected at @CRMatematica today...
we voted on a scale from 0 to 10 where
0-nope! ==== 5-??? ==== 10-yeah!
here's the vote : euler in blue, navier-stokes in red...
but wait...there's more...
after voting -- in private! -- we then did a public vote-by-show-of-hands with yes/no/???
(all eyes were on terry tao, sitting in the back...)
then we did a second private vote...
can you guess how terry voted?
more data! the same exact question was asked at a meeting in 2007 at the 250th anniversary of the euler equations at a meeting of experts in Aussois, CH
(thanks to Kai Schneider for the data!)
here's what the data was in 2007
if you want to see the change in sentiment over time 2007 => 2024 1st vote => 2024 2nd vote, here's the euler equations...
and the same historical trends for navier stokes
so what have we learned?
* opinions have drifted more towards singularity
* opinions can change in real-time due to influence by neighbors -- very relevant to information flows...
* MS excel doesn't like indexing from 0 to 10
special thanks to kai cieliebak, @evamirandag , and kai schneider for suggesting and helping to get out the vote! (and for allowing me to conduct this little opinion dynamics experiment...)
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1/ yesterday’s thread on the genesis of figures in “Elementary Applied Topology” ended on a cliffhanger: what do all the chapter heading illustrations mean? it’s a puzzle.
get ready for a myth/math mishmash.
2/ the title page & the back cover carry an iconic stylized pomegranate, with some motion induced on what looks like half-a-dozen seeds? hmmm… that reminds me of something…
3/ of course, this is a persephone myth – she who was seduced by hades and descended to the underworld. what does that have to do with topology?
1/ in 2009, i began writing a book on topology, meant to be a short introduction to the core concepts, in the context of lots of interesting applications. every idea would be paired with one or more uses, as much outside of mathematics as possible: “applied topology”.
2/ i wanted the book to have a lot of pictures – at least one per page on average – and i wanted the pictures to be the exercises. each picture is a puzzle, and if you understand the picture, then you have solved the exercise & understand something.
1/ this week in multivariable calculus @Penn ...
constrained optimization
2/ this builds on previous investigations into level sets of scalar fields -- a topic for which my students often struggle to grasp the notation & motivation...
a bit of animation can help!
3/ one converts constrained optimization into an unconstrained problem by adding a new variable -- the lagrange multiplier
1/ this past week in multivariable calculus @Penn
the chain rule & its consequences...
2/ my students all remember how to use the chain rule "by hand", even if writing out / explaining the principle takes more thought. we start off discussing composition and what it means for functions and rates of change...
3/ this is the 1st big payoff for all the linear algebra we've done in class thus far: composition of derivatives as linear transformations corresponds to matrix multiplication
mathematical art is increasingly important in research & AI is about to revolutionize what can be done... 🧵
i have been doing art & animation for my research & teaching for years & have been convinced that this is the future of imaginative thinking & teaching... but it's hard & has a high learning curve...