dpiponi

dpiponi, 11 months ago to random

Poulnabrone Dolmen, a 5-6000 year old tomb just sitting there on the most incredible limestone landscape in The Burren, Ireland. The tomb was originally covered in earth - what's left is just the bare structure.

image/jpeg

dpiponi, 11 months ago to random

The view from the front of our bus on the West Coast of Ireland. Quiz question: which 3D renderer am I thinking of?

dpiponi, 11 months ago to random

Timecrimes is a fun movie. The obvious comparison is with Primer but it's enjoyable without you having to have a brain the size of a planet.

dpiponi, 11 months ago to random

New Chomsky paper on Hopf algebras. Seriously.

https://arxiv.org/abs/2306.10270

dpiponi, 11 months ago to random

I watched the Tom Cruise/Emily Blunt movie Live Die Repeat aka The Edge of Tomorrow for the second time. I think the gold standard of sci-fi action flicks is often thought to be Aliens but this movie may be even better.

I'm reminded of a lecture by Leonard Bernstein when he talks about how the underlying logic of a musical composition dictates that what should follow is a repetition, but that would be uninteresting, at which point the creative tool of the composer becomes deletion. The movie is a masterclass in how to repeat without repeating. The same events happen hundreds of times over and yet at no point does the movie start flagging. Much of the story is told through the implication of what was deleted. I feel like this film should have received an Academy Award for editing.

https://youtu.be/r_fxB6yrDVo

dpiponi, 11 months ago to random

No matter how much you scale and rotate a regular icosahedron you can't arrange that all vertices have rational coordinates. There are appearances of √5 in the relations between the vertices so if you manage to make some rational, some others will be irrational.

OTOH if you don't mind giving up regularity you can perturb each vertex to make it rational. Each vertex is free to move in the sense that you can keep it connected to its 5 neighbours without messing up the combinatorics of the edges and faces so it's still an icosahedron.

Similarly a regular dodecahedron can't have all coordinates rational. This time it's trickier to perturb because each vertex is contrained to lie in 3 separate planes that each contain 4 other vertices. But there's a trick - perturb the equations of the faces so they have all rational coefficients. The vertices will lie at intersections of these planes and so have rational coordinates.

Amazingly any 3-polytope can be perturbed into one with all rational coordinates.

But just in case you thought this was trivial - there's a 12 vertex 8-dimensional polytope that can't be realized with all rational coordinates.

Anyway, I learnt about this from Ziegler's notes on "Non-rational configurations, polytopes, and surfaces"

https://arxiv.org/abs/0710.4453

A dodecahedron wireframe

b0rk, 11 months ago (edited 11 months ago) to random

used magic wormhole for the first time to transfer files between 2 computers in my house and it's great

computer 1:
$ wormhole send myfile.pdf
Wormhole code is: 7-crossover-clockwork

computer 2:

$ wormhole receive 7-crossover-clockwork
Receiving file (7924 bytes) into: myfile.pdf

https://github.com/magic-wormhole/magic-wormhole

dpiponi, 1 year ago to random

Sometimes I feel like software engineers are a bit culty and puritanical. So many times I go to stackoverflow and someone has asked "how do I do X with Y" and the replies are standard dictums like "you should never (in bold!) do X with Y" or "why are you doing X yourself? use this or that library", usually expressed pretty rudely. In the workplace it's often a good idea not to keep reinventing the wheel, but outside of that learning by experimentation shouldn't be discouraged.

dpiponi, 1 year ago to random

So when linear regression was first invented was there hype about it? "Experts say they can use regression to predict things in fields ranging from biology to engineering!" "If you use regression with biased data it'll give biased results!" "Scientists say that one day linear regression will be used in almost every published paper even though it has known limitations and can give misleading results!"

dpiponi, 1 year ago to random

Fun question:

"what are...non-trivial examples of mathematics where the parity of an integral parameter makes a crucial difference?"

https://mathoverflow.net/questions/447780/oddities-of-evenness

I expect many of these are related. I find the difference between odd-dimensional and even-dimensional rotation groups interesting and that has wide-ranging ramifications.

dpiponi, 1 year ago to random

A new article about old work:

https://beforesandafters.com/2023/05/15/the-matrix-reloaded-is-20-what-it-did-for-digital-humans-was-huge/

Quick summary of my contribution as I don't think I've ever written much about it outside of one paper.

At the time we wanted to capture the motion of human faces in detail but despite the claims made about many people, nobody seemed able to reliably reconstruct 3D geometry like this using video taken from multiple viewpoints. Around 2001, finding the correspondence between images just wasn't good enough.

So my contribution was to go to the tangent space. Reconstructing facial geometry from images was hard, but if you already have an accurate facial reconstruction at some moment in time (obtained by other means) reconstructing the 3D motion from frame to frame - the deltas - turned out to be easy. And then you just integrate up the deltas to get the face geometry at any moment.

It's a terrible method. Errors pile up exponentially over time as you integrate. And yet it was less terrible than all of the other methods at the time. With guidance from human artists it worked well enough for the job.

At the end of the day this worked because it was easier to find correspondences between points in images taken from the same viewpoint, but at slightly different times, than to find correspondences between points at the same time, taken from different viewpoints.