Posts by dpiponi@mathstodon.xyz
(DIR) Post #ArkazMXzNX2QweHh0S by dpiponi@mathstodon.xyz
2025-03-05T16:55:06Z
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@futurebird Reminds me of the Euler spiralhttps://en.wikipedia.org/wiki/Euler_spiral
(DIR) Post #Arl3CibJUajPp9zpD6 by dpiponi@mathstodon.xyz
2025-03-05T17:20:39Z
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@futurebird Also very similar are "partial Gauss sums". It's pure turtle geometry. You keep a count of the number of (constant length) steps you've taken and you turn by its square (or cube etc.) - suitably scaled.https://www.bennetyee.org/ucsd-pages/pub/Yee-IncGaussSum.pdf
(DIR) Post #At2zq7qXc83rt8rPeq by dpiponi@mathstodon.xyz
2025-04-12T21:53:22Z
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@FourOh-LLC @johncarlosbaez These are people worrying about the safety of themselves and their colleagues and you're using this as a platform to push ideology. If you read what they say you'll see that they're trying to find ways to make shared spaces that work.
(DIR) Post #AtA6ngFDuU2Y1QMDIW by dpiponi@mathstodon.xyz
2025-04-16T19:16:05Z
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Before you plug in your new Timex/Sinclair 1000, please take a moment to think about this exciting new adventure. We want to assure you that:1. You will enjoy computing.2. You will find it easy as well as enjoyable.3. You shouldn’t be afraid of the computer. You are smarter than it is. So is your parakeet, for that matter.4. You will make mistakes as you learn. The computer will not laugh at you.5. Your mistakes will not do any harm to the computer. You can’t break it by pushing the “wrong” button.6. You are about to take a giant step into the future. Everyone will soon be using computers in every part of their daily lives, and you will have a head start.-- Steve Vickers, Timex/Sinclair 1000 Instruction Manual (aka the US ZX81 manual)
(DIR) Post #AtA6noeKf0sW5cANXs by dpiponi@mathstodon.xyz
2025-04-16T19:18:28Z
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1. Yes2. Sometimes3. Hmmm...4. It might not laugh but it was being passive-aggressive to me the other day.5. Oh man, you could do so much harm...6. Hey, we're already there!
(DIR) Post #AtJwVPkNS7e9gNBDRg by dpiponi@mathstodon.xyz
2025-04-21T16:03:17Z
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@futurebird @lnlyisol When I worked at Google they made a big deal about the "long tail". They seem to have abandoned that principle now. The assumption is that anything you say must be the most common thing anyone could have intended.
(DIR) Post #AtZyZBvemD9clXIcNs by dpiponi@mathstodon.xyz
2025-04-28T20:30:26Z
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A bunch of languages have a kind of array (which might not be fully reified) whose main purpose is to be expanded out as individual subexpressions in a larger expression.In Python we have *a where a is an array. So we can writea = [1,2,3]print(5, *a)and it's the same as print(5,1,2,3).In C++ we have parameter packs so we can do things liketemplate<typename... Ts> using Type = std::tuple<int, Ts..., float>;And in Mathematica we have Sequence[] that allows things like:x=Sequence[10,20,30];f[1,x,3,4]Out[1]=f[1,10,20,30,3,4]I think Python's *a isn't really an object at all, just a syntactic trick, but a is a proper list of course.Parameter packs only quasi-exist. For example you can't pass one as a template argument without triggering its expansion with ... and a template can't (without some wrapping) accept two parameter pack arguments. But you can operate on them, eg. with folds.Mathematica's Sequence is a fully fledged Mathematica object but trying to examine one is tricky because (like in C++) attempts to pass it to a function expand it first. It's "unstable" in the sense that it expands itself without a * or ... .What are other examples?
(DIR) Post #AtyHPDkFYE8eIgb5BA by dpiponi@mathstodon.xyz
2025-05-11T03:05:55Z
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@futurebird @wakame I think our cat does some of that too. I keep telling my wife he just does it to test stuff out but she takes it personally.
(DIR) Post #AwPFAhG150ny4q0TcO by dpiponi@mathstodon.xyz
2025-07-19T03:29:09Z
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If I ever take up a life of crime I'm gonna buy a load of crime scene evidence markers and leave them around my crime scenes to mess with the detectives.https://arrowheadforensics.com/products/photo-documentation/evidence-marking-cones-and-tents.html
(DIR) Post #AwPFAiJb9BGRMEgqq8 by dpiponi@mathstodon.xyz
2025-07-22T22:40:58Z
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And when I become a Bond villain I think this will be my lair:https://www.zillow.com/homedetails/2900-Buena-Vista-Way-Berkeley-CA-94708/24839827_zpid/
(DIR) Post #AzYPAx9lzpRoOqKg76 by dpiponi@mathstodon.xyz
2025-10-23T20:31:43Z
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Prepare to have your mind blown
(DIR) Post #AzYPB4S6s3H51jxvAO by dpiponi@mathstodon.xyz
2025-10-23T21:39:04Z
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One of these days someone's going to ask me what 1000000/999998 is and I'm just going to casually rattle off the answer to 100 decimal places as if it's no effort at all.
(DIR) Post #AzYPB4mJevRC2PQ3f6 by dpiponi@mathstodon.xyz
2025-10-24T22:42:20Z
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Not a full proof but I hope this makes it clear.Cf. the section on multibyte add in Hacker's Delight.
(DIR) Post #B05aHDmZ3mmUIG4qjg by dpiponi@mathstodon.xyz
2025-11-08T05:17:36Z
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I can't believe I didn't know this fact before today - it seems so fundamental.If you have a real symmetric matrix A, and pick some unit vector x, then it's standard textbook material that x.Ax (the Rayleigh quotient) is bounded by the smallest and largest eigenvalues. So what happens if I pick a random unit vector, how is x.Ax distributed?Let's jump to the case of a Hermitian matrix A and a random unit vector on the complex sphere. How is T=conj(x).A.x distributed? Again it's standard that it's bounded between the smallest and largest eigenvalue.We can start with a 2x2 matrix A. First surprise to me: T is distributed *uniformly* between the two eigenvalues.The first plot below is the histogram of values of T for 1,000,000 vectors x and a randomly chosen Hermitian matrix A. The yellow lines mark the two eigenvalues.Now try 3x3. Remarkably the distribution is piecewise linear with the break points at the eigenvalues.And let's jump to 5x5. We get the third plot, whose curve is given by a cubic B-spline with control points given by the eigenvalues.Bizarrely you can prove you always get B-splines making this one of the few times I've seen B-splines in "nature", so to speak.This is a purely mathematical result but I found it in this paper on wave transport through random media: https://arxiv.org/abs/2511.04602My calculations (pretty much the same as the paper) are here: https://colab.research.google.com/drive/1g7ImBblYAsninp5-sr6uWQTVfTYurerE?usp=sharing
(DIR) Post #B0600hjf2UzX4pVIkS by dpiponi@mathstodon.xyz
2025-11-09T01:23:47Z
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@futurebird Reminds me of the Roman baths under King's College London where I was a grad student. I told lots of people how amazing it was. And then with the advent of the Internet I learnt they weren't Roman at all.https://en.wikipedia.org/wiki/Roman_Baths,_Strand_Lane?wprov=sfti1#Georgian_cold_bath
(DIR) Post #B0qv7Pdn3p1UeDI1Vw by dpiponi@mathstodon.xyz
2025-12-02T22:57:55Z
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@futurebird It's pretty essential for programmable calculators [1] and I wouldn't be surprised if it's there because it shares functionality (and code) with a programmable. I've often wanted it (slightly) to help convert a race time to minutes per mile.[1] Random examples: finding good rational approximations to real numbers and generating random numbers.
(DIR) Post #B1G0B7zLzRIVmUxsxM by dpiponi@mathstodon.xyz
2025-12-15T01:22:25Z
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@futurebird @alexwild @MyrmecolNews I started reading a book on the subject of animals doing mathematics but I had to stop because it annoyed me too much by asking what I felt were the wrong questions to ask of animals that are superbly adapted for their environments.
(DIR) Post #B2Ya9FDfwVgrsiTqee by dpiponi@mathstodon.xyz
2026-01-22T22:22:21Z
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@futurebird Police ants imply criminal ants and I'm disappointed they don't exist.
(DIR) Post #B2cqX5cJfjVkwsEo2C by dpiponi@mathstodon.xyz
2026-01-24T23:35:12Z
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@foone Could be worse, you could be using ChatGPT to do basic arithmetic.
(DIR) Post #B2nEPRnlMcKVEZcrTc by dpiponi@mathstodon.xyz
2026-01-29T23:59:26Z
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@futurebird @smh So impressed I tried to get one on ebay but there isn't a single one, just the manuals.