@dpiponi@mathstodon.xyz
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dpiponi

@dpiponi@mathstodon.xyz

Disclaimer:
👽 My opinions are not my own. They're beamed to me by aliens

Current life:
🎮 Epic Games

Previous lives:
🍩 a PhD in Riemann theta functions
💥 many years working in movie visual effects
🎈 some years devising navigation strategies for balloons
🎲 a year drawing random samples from tricky distributions

Likes:
🚴 I like to bike
🏃 I like to run
🎛️ my musical tastes lie towards the electronic end of the spectrum
🚀 I like Andor and The Mandalorian

This profile is from a federated server and may be incomplete. Browse more on the original instance.

dpiponi, to random
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Plant care web sites are all like this:

Here's our handy guide on identifying exactly what's wrong with your plant:

• leaves turning brown? Too much water

• leaves turning brown? Not enough water

• leaves turning brown? Too much sun

• leaves turning brown? Too much shade

• leaves turning brown? Soil too acid

• leaves turning brown? Bacterial infection

• leaves turning brown? This is normal for older leaves

dpiponi, to random
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We have the millennium prizes in mathematics. There should be a similar prizes in computer science. Here's 5 problems I suggest for the list. Maybe they're too hard, I'm not sure.

  • Synchronizing audio and video streams.
  • Detecting an external display has been plugged in. Especially if that display is a projector.
  • Establishing that everything is correctly set up at the start of a video conference call. Especially verifying audio is working, and unmuted.
  • Bluetooth. Especially emulating the straightforward operation we can do with wired devices: unplugging from one and plugging into the other.
  • Printers. Making them work.
dpiponi, to random
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For rainy days we have a treadmill but it's locked into the vendor's subscription service if you want to watch videos.

Except...tap the bottom left 10 times, wait 7 seconds, tap 10 more times, up pops a number, use that as a seed to generate a number with lrand48, reduce modulo 999999 (not 1000000!) and type that number back in, and now you have an Android tablet with web browser and access to YouTube.

dpiponi,
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This information came from YouTube.

https://youtu.be/HyJ8L_ak-Ds?si=T82_5u0q0PNoHqNn

I read the source code for the web page shown there and recognised it as lrand48. I didn't do any reverse engineering myself.

dpiponi, to random
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I don't work in VFX any more but it's still a bit annoying to see articles claiming that I and my many ex-colleagues didn't do work that we did.

The "making of" featurettes can be just as much works of fiction as the movies themselves - especially when they star Tom Cruise and your company is told it can't talk about the work.

https://www.hollywoodreporter.com/movies/movie-features/oppenheimer-mission-impossible-vfx-1235579422/

dpiponi, to random
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I was walking across the park and suddenly an integer came wafting by...

dpiponi, to random
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For me, and presumably countless others, a computer has always been primarily a creativity tool. But I think this idea may be novel or unusual to a large segment of the population.

dpiponi, to random
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One way to view automatic differentiation is to think of it as adjoining an "infinitesimal" element d to the reals, such that d²=0, to the reals, ie. forming ℝ[d]/(d²). If f is a polynomial then f(x+d)=f(x)+df'(x) giving a nice way to compute derivatives on a computer - especially as it can be extended to rational and even transcendental functions f. It doesn't form a field though. For example you can't always divide by d.

TIL There is a field, named after Levi-Civita, that generalises ℝ[d]/(d²) quite a bit. Every element is a kind of power series in an infinitesimal ε. More precisely, each element is a "formal" sum ∑aᵢεⁱ where the sum is over some subset S of the rationals which is left-finite, ie. for any z, S has only finitely many elements less than z. Addition and multiplication work in the way you might guess.

This means we can form things like ε^(1/2) or even the "infinite" 1/ε. It's not just a field, it's an ordered field so we have, for example, that 1 > ε^(1/2) > ε > ε² > 0.

You can even construct a Dirac delta-like function δ(x) = ε/π(x²+ε²).

It's all very similar to non-standard analysis but this particular construction doesn't require anything non-standard.

https://en.wikipedia.org/wiki/Levi-Civita_field

dpiponi, to random
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dpiponi, to random
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When I first came across Voigtländer's paper on speeding up free monads [1] and some of the methods that Hinze mentions [2] I was a bit bemused about why category theory had anything to say about program optimization. But now it seems obvious. Much of optimization is a lot like algebraic manipulation where you're rearranging while hoping to keep the value the same. But in particular, a really common optimization move is to write f(g(x)) as (fg)(x) where (fg) is somehow simpler (or more reusable than) than just applying g then f. Ie. associativity - which is one of the laws of category theory. I think this step also accounts for almost all of the computational reasons for using linear algebra. Eg. graphics pipelines make good use of this kind of associativity.

[1] https://janis-voigtlaender.eu/papers/AsymptoticImprovementOfComputationsOverFreeMonads.pdf
[2] https://www.cs.ox.ac.uk/ralf.hinze/Kan.pdf

dpiponi,
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@davidphys1 I haven't thought about Feigenbaum's constant much since I was an undergraduate so I looked at wikipedia to refresh my memory and I learnt that it also arises from the rate of convergence of the size of the circles in the Mandelbrot set and I'm wondering how I got this far through life without learning this fact.

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

dpiponi, to random
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Imagine, if you will, it's 2023, back in the dark ages when nobody had figured out yet how to make computers usable.

There are two of you in an aircraft, one with an Android phone and one with an Apple phone. What's the best way to get a photo from one phone to another?

Bonus points: do it without paying $14.95 to move the files thousands of miles across the world and back again.

dpiponi, to random
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Some steam escapes from a boiling kettle. In principle you could pick a single molecule and come up with a detailed back story explaining how it started off trapped in a network of hydrogen bonds and by an unlikely sequence of collisions it managed to acquire the energy to bounce its way out the top. But

  1. it'd be a boring story
  2. it would miss the bigger picture of thermodynamics that predicts the escape of steam without knowing any of the individual molecule's details

That's how I feel when I read a news story about a mass shooting and they interview the local head of police and they say "we're still investigating to find out the motive".

You can imagine someone saying "look, it's this collision here that gave it the final push" and then going away satisfied they'd explained how the molecule got out.

dpiponi, to random
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New Chomsky paper on Hopf algebras. Seriously.

https://arxiv.org/abs/2306.10270

dpiponi, to random
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Here's an animation generated by simulating the 2D wave equation kicked off with a Dirac delta pulse. Periodic boundary conditions.

But let's say we want the field value to be as high as possible at a particular point in space at a chosen future moment in time...

video/mp4

dpiponi,
@dpiponi@mathstodon.xyz avatar

But this is much the same problem seismologists solve - finding the material properties based on what signals arrive where from a source. And seismologists were doing this long before convolutional neural nets were invented. So I thought I'd try something closer to what they do. It's also more insightful than just using AD which is something of a black box.

Anyway, here's the result of solving the same problem but getting the focus to happen much later. There's a sort of fractally refractive index now...

video/mp4

dpiponi, to random
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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, to random
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Nobody knows what these Roman dodecahedra were for but another was found in England

https://www.smithsonianmag.com/smart-news/another-of-ancient-romes-mysterious-12-sided-objects-has-been-found-in-england-180983632/

You can buy replicas on Etsy. I should get one just so I can make archaeologists in the year 4000 say "we don't know why this 2000 year old body was buried with a dodecahedron".

dpiponi, to random
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https://www.bbc.com/news/articles/c0kl4glp547o

I blame all the stupid rule based systems for getting your attention. iOS Focus is the most needlessly complex solution to a problem relative to the problem difficulty I've ever seen.

dpiponi, to random
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I don't know if I hallucinated this but maybe someone recognises it:

I'm sure I once (~20 years ago) saw an arbitrary precision real number library for C or C++ that worked by picking some fixed precision and worked until it produced a result at the required precision, or, if it convinced itself it couldn't achieve that precision, did some kind of backtracking so it could redo the computation at a higher fixed precision. Somewhat analogously to how transactional memory works - and I think under the hood there may have been some unusual memory model.

Sound familiar to anyone?

dpiponi, to random
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Annoying that the Kindle retroactively changes book covers. Such nice art for these books, except book 1 now.

dpiponi, to random
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One of my favorite visual effects from pre-CG days was the shield effect in 1984's Dune. Lots of work with an optical printer. Underrated, I think, as I've never heard anyone talk about it.

https://youtu.be/6XFYV2h5gAo?si=eVz-fVrtMJ8wBME0&t=24

dpiponi, to random
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Given a random number generator that generates points uniformly in the unit interval [0,1] can you generate uniformly distributed points in the unit circle using only algebraic functions? In a finite number of steps - so no rejection sampling, loops, recursion. No "almost always" finite either.

Just wondering about sitiations where it seems you can't avoid trig functions.

dpiponi, to random
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I thought of a use for LLMs but I don't see myself having time to code it up for a few weeks. A touch typing tutor. It should be easy to take llama.cpp and adapt it to generate the next token based on which letters and words I need most practice with. So you get to practice with plausible sentences that still train you where you need it.

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