iiinova — where your digital self keeps evolving

That's quite a bit of lovingly filling in the details of my prompt.

But the spider web itself is implemented using an ad hoc solver of Hooke's law - the solver iteratively moves each free node in the direction of its net force. That is why adding a radius visibly shifts the hub and deforms the frame rather than simply drawing a new straight segment.

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There are some cinematics in there - the code that generates the impression of a thread moving in the wind is just a really nicely chose parametric curve...

0.25 * np.sin(2 * PI * (1.5 * s - 0.6 * t)) * s

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Orb-web spider builds web / Build a realistic spider web

And for all us children that like to build correct spiderwebs in their living room, I thought I try Claude with manim to animate and narrate this. Amazing, honestly m.youtube.com/watch?v=qF87...

m.youtube.com

YouTube video by Moritz Schauer

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Moritz Schauer @mschauer.bsky.social · 24/09/2026

Sick child last week - but the scientifically correct spider net kept us entertained.

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#MathSky Trying to demystify Caratheodory's measure extension theorem: mschauer.github.io/share/friend...

mschauer.github.io

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Moritz Schauer @mschauer.bsky.social · 22/09/2026

Obviously, offices shrink when you use them.

This is fun! 𝓕(m) ∨ 𝓕(n) = 𝓕(lcm(m,n)), 𝓕(m) ∩ 𝓕(n) = 𝓕(gcd(m,n)).

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The σ-algebra viewpoint also gives a nice form of the Chinese remainder theorem: for pairwise coprime n₁, …, nₖ it holds σ(x mod n₁, …, x mod nₖ) = σ(x mod n₁⋯nₖ). Knowing the residues separately is exactly the same information as knowing the residue modulo the product.

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But each 𝓕ₚ is finite, and finitely many finite σ-algebras generate a finite σ-algebra. Hence 𝓕 cannot be generated by only finitely many 𝓕ₚ. Therefore P is infinite: There are infinitely many primes. ☐

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Since every integer except −1 and 1 has a prime divisor, ℤ ∖ {−1,1} = ⋃ₚ pℤ, so {−1,1} ∈ 𝓕. Each 𝓕ₚ contains the translations of its elements, hence so does 𝓕. So {−1+k,1+k} ∈ 𝓕 for every k ∈ ℤ. These sets are all distinct, so 𝓕 is infinite...

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For example, 𝓕₂ = σ(2ℤ, 1 + 2ℤ) has four sets: ∅, ℤ, the even integers, and the odd integers. Now let P be the set of primes and combine all this information into 𝓕 = ⋁ₚ 𝓕ₚ (p ∈ P).

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Moritz Schauer @mschauer.bsky.social · 14/08/2026

Furstenberg gave a fascinating proof that extracts the infinitude of the primes from seemingly innocuous manipulations of clopen sets. Here is a retake: The σ-algebra 𝓕ₚ = σ(n ↦ n mod p) encodes exactly the information contained in knowing n mod p. That is natural, σ-algebras model information.

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How many times does the Moon go around the Earth in a year? About 13 times relative to the stars. But Earth itself goes once around the Sun. So the roughly 12 lunar months in a year are really a 13 − 1 phenomenon — the same geometry as a circle rolling inside a larger circle.

Moritz Schauer @mschauer.bsky.social · 13/07/2026

Modern search: “You came looking for X, but wouldn’t you rather spend some time on the more addictive Y?”

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Moritz Schauer @mschauer.bsky.social · 10/07/2026

We could try to build a very expensive high energy quantum computer ring under Paris

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Moritz Schauer @mschauer.bsky.social · 03/07/2026

Dank Kompositionalität lernt man das Einmaleins aber nicht mehr das Einmaleinmaleins

For that price, we get all of mathematics with randomness added. A bit like adjoining complex numbers to the reals for the price of losing the natural order. It’s funny to think how such things commute: think of complex random variables versus complex probabilities.

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The redeeming feature is that this price is paid only once.

Right, you don't need error bars on error bars.
Probabilistic uncertainty about uncertainty collapses. This is the “monadic join” in probability.
Instead of a coin with random bias p ∼ π, you can flip a coin with the deterministic bias μ.
Just take μ = E[p].

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Probability theory causes a certain mathematical inflation: random variables are functions, events are sets, and probabilities are countably additive set functions of total mass one defined on σ-algebras.

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[PLDI 2026] Flatirons 3 - PLDI Research Papers (Jun 19th)

Gaurav Arya’s presentation at PLDI'26 on "Gradient Estimation as Probabilistic Inference" bringing sound, compositional and automatic gradient estimation for expectations in probabilistic programs. Great job, Gaurav!! www.youtube.com/watch?v=0aWz...

youtube.com

YouTube video by ACM SIGPLAN

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Moritz Schauer @mschauer.bsky.social · 09/06/2026

No feeling like arguing for 40 minutes with a confident idiot, only to realize they were right for all the wrong reasons. [1.2em]

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Moritz Schauer @mschauer.bsky.social · 06/06/2026

Zorn's lemma: Transfinite induction as a service

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Moritz Schauer @mschauer.bsky.social · 25/05/2026

Probably there is no secret “scientific method” and emerges automatically from discussions running in circles

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Moritz Schauer @mschauer.bsky.social · 03/05/2026

AI is not allowed to make goblin-metaphors anymore but it will appreciate my hidden goblin poetry

ArXiv Paperboy (Stat.ME+Econ.EM) @paperposterbot.bsky.social · 30/04/2026

Reposted by Moritz Schauer

arXiv📈🤖 The Difference Between "Replicable" and "Not replicable" is not Itself Scientifically Replicable By Devezer, Buzbas

Replication studies estimate the replicability rate of scientific results by aggregating binary verdicts of experiments. Exact replications are rarely attainable, so most replication sequences are non-exact. Experiments differ in ways that matter and do not share a single data-generating process. We formalize two statistical interpretations of non-exactness. In a shared latent rate (benchmark) model, experiments are exchangeable and depend on a common random replicability rate. In a conditionally independent rates (operational) model, each experiment has its own replicability rate drawn from a population distribution. Under the benchmark model, even small variability among replicability rates induces an irreducible variance floor on the estimated mean replicability rate that no amount of replication can eliminate. Under the operational model, the degree of non-exactness is not identifiable from standard replication data, because one binary verdict per experiment carries no information about between-experiment heterogeneity. Researchers cannot tell which precision regime they are in or whether high- and low-replicability sequences can be distinguished in principle. The usual data structure cannot support reliable demarcation between "replicable" and "not replicable" results and systematically understates uncertainty, making high- and low-replicability sequences appear discriminable when they are not. We show how common sources of heterogeneity amplify these problems and demonstrate practical consequences in a reanalysis of Many Labs 4. Aggregating replicability rates across heterogeneous literatures produces averages that conflate incommensurable regimes and lack a stable interpretation. Replicability rate is not a reliable demarcation criterion. The replication crisis, if there is one, cannot be established by the methods used to declare it.

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Moritz Schauer @mschauer.bsky.social · 24/04/2026

(Thinking about causal discovery more than estimating effects in a given causal model, there I don't know really)

Moritz Schauer @mschauer.bsky.social · 24/04/2026

To me one very striking issue is the apparent lack of success stories...

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Reposted by Moritz Schauer

ArXiv Paperboy (Stat.ME+Econ.EM) @paperposterbot.bsky.social · 24/04/2026

arXiv📈🤖 Betting on Bets: Anytime-Valid Tests for Stochastic Dominance By Arnold, Choe, Scarsini et al

How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic ordering), a classical and popular notion for comparing entire distribution functions. The problem is distinct from the popular problem of testing for dominance in means, which would not capture distributional differences beyond the first moment. We first derive powerful, nonparametric e-processes that quantify evidence against the null hypothesis that one prospect is dominated by another. For first-order SD, these e-processes are constructed as a mixture of asymptotically growth-rate optimal e-variables and yield a test of power one. The approach further generalizes to sequential testing for SD beyond the first order, including any higher-order SD. Empirically, we demonstrate that the resulting sequential tests are competitive with existing non-sequential SD tests in terms of power, while achieving validity under continuous monitoring that existing methods do not. Finally, we sketch the complementary and challenging problem of testing the non-SD null hypothesis, which asks whether a prospect has a definite upside, and describe the conditions under which we can derive a nontrivial anytime-valid test.

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Moritz Schauer @mschauer.bsky.social · 23/04/2026

Causal inference tells you that some features of DAGs are identifiable from the observations (the v structures!). So if you are lucky that alternative candidate DAGs differ in v-structures, the data tells them apart (e.g. by computing the model fit/evidence for corresponding Gaussian linear SEMs)

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Reposted by Moritz Schauer

Will Lowe @conjugateprior.org · 11/11/2025

Yes, that's the contrast of interest The relevant observations are imo 1. MH is a causal inference problem first and a probability problem second, and 2. the association usually called collider bias is information you can make use of for decision rather than just being, as it normally is, a problem

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Moritz Schauer @mschauer.bsky.social · 24/03/2026

I have not getting filter coffee in a coffee place and not getting gyros in a Greek restaurant until acing the local speech patterns… Don’t people have priors?? PS: ”Chyros? really, Dutch friends, chyros?”

Moritz Schauer @mschauer.bsky.social · 11/03/2026

Dust behaves as if someone put a minus sign in front of the Laplacian: dust ends up in the corners instead of spread out.

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Moritz Schauer @mschauer.bsky.social · 28/02/2026

The key to a successful career is dying wealthy

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Moritz Schauer @mschauer.bsky.social · 28/02/2026

Witnessing the birth of the marginal differential product theory about hiring your enemies

Moritz Schauer @mschauer.bsky.social · 24/02/2026

I like that people genuine think in intervals. Maybe there is hope to explain the confidence interval

Darren Dahly @statsepi.bsky.social · 23/02/2026

Reposted by Moritz Schauer

This is basically my villain origin story. "How old are you?" (unique responses)

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Moritz Schauer @mschauer.bsky.social · 15/02/2026

For me for a song to click there must be specific harmonic patterns present, you have them in m.youtube.com/watch?v=EKe9... for example but also in the notorious C&A song m.youtube.com/watch?v=UFDn...

m.youtube.com

Nina Hagen - Du hast den farbfilm Vergessen (Subtitulado)

YouTube video by PakoChile