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linkdropMaking sure you're not a bot! <a href="https://anubis.techaro.lol/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://anubis.techaro.lol/</a> <a href="https://troet.cafe/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a>-of-work <a href="https://troet.cafe/tags/OpenSource" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OpenSource</a> <a href="https://troet.cafe/tags/cloudflare" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cloudflare</a> <a href="https://troet.cafe/tags/protection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#protection</a> <a href="https://troet.cafe/tags/robots" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#robots</a>.txt <a href="https://troet.cafe/tags/scraping" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#scraping</a> <a href="https://troet.cafe/tags/request" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#request</a> <a href="https://troet.cafe/tags/http" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#http</a> <a href="https://troet.cafe/tags/bot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bot</a> <a href="https://troet.cafe/tags/ai" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ai</a>

Hacker NewsA cute proof that makes e natural<a href="https://www.poshenloh.com/e/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.poshenloh.com/e/</a><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/cute" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cute</a> <a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> <a href="https://mastodon.social/tags/e" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#e</a> <a href="https://mastodon.social/tags/natural" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#natural</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/poshenloh" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#poshenloh</a>

Raurquiz<a href="https://c.im/tags/HappyBirthday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HappyBirthday</a> <a href="https://c.im/tags/hugoweaving" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#hugoweaving</a> <a href="https://c.im/tags/actor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#actor</a> <a href="https://c.im/tags/agentsmith" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#agentsmith</a> <a href="https://c.im/tags/thematrix" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#thematrix</a> <a href="https://c.im/tags/reloaded" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#reloaded</a> <a href="https://c.im/tags/revolutions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#revolutions</a> <a href="https://c.im/tags/lordoftherings" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#lordoftherings</a> <a href="https://c.im/tags/thehobbit" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#thehobbit</a> <a href="https://c.im/tags/Vforvendetta" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Vforvendetta</a> <a href="https://c.im/tags/CaptainAmerica" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CaptainAmerica</a> <a href="https://c.im/tags/TheFirstAvenger" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TheFirstAvenger</a> <a href="https://c.im/tags/transformers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#transformers</a> <a href="https://c.im/tags/revengeofthefallen" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#revengeofthefallen</a> <a href="https://c.im/tags/SlowHorses" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SlowHorses</a> <a href="https://c.im/tags/HowtoMakeGravy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HowtoMakeGravy</a> <a href="https://c.im/tags/mortalengines" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mortalengines</a> <a href="https://c.im/tags/HacksawRidge" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HacksawRidge</a> <a href="https://c.im/tags/bodyline" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bodyline</a> <a href="https://c.im/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> <a href="https://c.im/tags/TheAdventuresofPriscillaQueenoftheDesert" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TheAdventuresofPriscillaQueenoftheDesert</a> <a href="https://c.im/tags/babe" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#babe</a> <a href="https://c.im/tags/happyfeet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#happyfeet</a> <a href="https://c.im/tags/expired" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#expired</a>

Knowledge Zone<a href="https://mstdn.social/tags/ITByte" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ITByte</a>: In <a href="https://mstdn.social/tags/Cryptography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Cryptography</a>, a zero-knowledge <a href="https://mstdn.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> or zero-knowledge <a href="https://mstdn.social/tags/Protocol" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Protocol</a> is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information apart from the fact that the statement is indeed true.<a href="https://knowledgezone.co.in/trends/explorer?topic=Zero-Knowledge-Proof" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://knowledgezone.co.in/trends/explorer?topic=Zero-Knowledge-Proof</a>

-0--1-<a href="https://mastodon.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> <a href="https://mastodon.social/tags/JunkieGrifter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JunkieGrifter</a>

Jan :rust: :ferris:Iris Project | A Higher-Order Concurrent Separation Logic Framework, implemented and verified in the Rocq Prover<a href="https://iris-project.org/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://iris-project.org/</a><a href="https://floss.social/tags/FormalVerification" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FormalVerification</a> <a href="https://floss.social/tags/Iris" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Iris</a> <a href="https://floss.social/tags/ConcurrentSeparationLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ConcurrentSeparationLogic</a> <a href="https://floss.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a>

Paul Houle✂️ Dudeney's 120-year-old dissection puzzle solution proves optimal<a href="https://phys.org/news/2025-03-dudeney-year-puzzle-solution-optimal.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://phys.org/news/2025-03-dudeney-year-puzzle-solution-optimal.html</a><a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mastodon.social/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://mastodon.social/tags/puzzles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#puzzles</a> <a href="https://mastodon.social/tags/dissection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dissection</a> <a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a>

Markus RedekerProof by starvation: This is a proof form in which you first prove that a counterexample to the theorem must have property X, then, using X, prove that it must also have property Y, then that it must also have property Z, ... until you have piled up so many requirements on a counterexample that everybody sees that it cannot exist.I have done that a few times. It is a nice way to organize one's thoughts.<a href="https://mathstodon.xyz/tags/Proof" class="mention hashtag" rel="tag">#Proof</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="tag">#Mathematics</a>

Hacker NewsA Proof of the Collatz Conjecture<a href="https://arxiv.org/abs/2502.20642" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://arxiv.org/abs/2502.20642</a><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/CollatzConjecture" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CollatzConjecture</a> <a href="https://mastodon.social/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mastodon.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> <a href="https://mastodon.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mastodon.social/tags/Research" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Research</a>

Univers logiqueThis method estimates π by generating random points within a cube and calculating the ratio of points that fall inside an inscribed sphere . The ratio of points inside the sphere to total points approximates π/6. <a href="https://mastodon.social/tags/MathArtMarch" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathArtMarch</a> <a href="https://mastodon.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> <a href="https://mastodon.social/tags/Irrational" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Irrational</a> <a href="https://mastodon.social/tags/PiDay" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PiDay</a>

Knowledge ZoneIs the <a href="https://mstdn.social/tags/Birthday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Birthday</a> <a href="https://mstdn.social/tags/Paradox" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Paradox</a> real? : MediumHow to Be More <a href="https://mstdn.social/tags/Assertive" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Assertive</a> - Without Being ‘<a href="https://mstdn.social/tags/Rude" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Rude</a>’ or ‘<a href="https://mstdn.social/tags/Aggressive" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Aggressive</a>’ : MiscHow <a href="https://mstdn.social/tags/Anime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Anime</a> <a href="https://mstdn.social/tags/Fans" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fans</a> <a href="https://mstdn.social/tags/Stumbled" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Stumbled</a> upon a <a href="https://mstdn.social/tags/Mathematical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematical</a> <a href="https://mstdn.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> : Sci AmCheck our latest <a href="https://mstdn.social/tags/KnowledgeLinks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KnowledgeLinks</a><a href="https://knowledgezone.co.in/resources/bookmarks" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://knowledgezone.co.in/resources/bookmarks</a>

Hacker NewsAnime fans stumbled upon a mathematical proof — <a href="https://www.scientificamerican.com/article/the-surprisingly-difficult-mathematical-proof-that-anime-fans-helped-solve/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.scientificamerican.com/article/the-surprisingly-difficult-mathematical-proof-that-anime-fans-helped-solve/</a> <a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/Anime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Anime</a> <a href="https://mastodon.social/tags/Fans" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fans</a> <a href="https://mastodon.social/tags/Mathematical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematical</a> <a href="https://mastodon.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> <a href="https://mastodon.social/tags/Anime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Anime</a> <a href="https://mastodon.social/tags/Community" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Community</a> <a href="https://mastodon.social/tags/Scientific" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Scientific</a> <a href="https://mastodon.social/tags/Discovery" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Discovery</a> <a href="https://mastodon.social/tags/Hacker" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Hacker</a> <a href="https://mastodon.social/tags/News" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#News</a>

Rowan Brad QuniThe sets of all math (M), communication (C), and physical matter (P) are subsets of information (I):M ⊆ I (M is a subset of I) C ⊆ I (C is a subset of I) P ⊆ I (P is a subset of I)Alternatively, we can express this as the union of the sets: (M ∪ C ∪ P) ⊆ I (The union of M, C, and P is a subset of I) <a href="https://mstdn.science/tags/InformationalUniverse" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#InformationalUniverse</a> <a href="https://mstdn.science/tags/IUH" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IUH</a> <a href="https://mstdn.science/tags/InformationTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#InformationTheory</a> <a href="https://mstdn.science/tags/Epistemology" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Epistemology</a> <a href="https://mstdn.science/tags/DataScience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DataScience</a> <a href="https://mstdn.science/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mstdn.science/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> <a href="https://mstdn.science/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physics</a> <a href="https://mstdn.science/tags/SetTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SetTheory</a> <a href="https://mstdn.science/tags/Ontology" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Ontology</a> <a href="https://mstdn.science/tags/Reality" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Reality</a> <a href="https://mstdn.science/tags/DigitalAge" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DigitalAge</a> <a href="https://mstdn.science/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a> <a href="https://mstdn.science/tags/QuantumInformation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QuantumInformation</a> <a href="https://mstdn.science/tags/QNFO" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QNFO</a> <a href="https://mstdn.science/tags/StickyNote" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#StickyNote</a>

Akshar Varma<a href="https://mathstodon.xyz/@BernhardWerner" class="u-url mention">@BernhardWerner</a> My favorite alternative <a href="https://mathstodon.xyz/tags/proof" class="mention hashtag" rel="tag">#proof</a> strategy for <a href="https://mathstodon.xyz/tags/induction" class="mention hashtag" rel="tag">#induction</a> proofs are <a href="https://mathstodon.xyz/tags/combinatorial" class="mention hashtag" rel="tag">#combinatorial</a> (counting) proofs.I suppose the standard example might be the proof of the coefficients in the binomial theorem expansion, or for the sum of binomial coefficients being powers of 2. These can be proved by induction, of course, but I'm not sure that's common given how easier it is to do a counting proof. It is also much clearer and avoids tedious algebra.One I like is proving that the sum 1 + 2 + 3 + ⋯ + 𝑛 is 𝑛 + 1 choose 2, the binomial coefficient \(\binom{n+1}{2}\). Bijection proof, counts the same thing in two ways. The thing being counted is the number of ways of choosing two things (distinct, without repetition) from the set {0, 1, ..., 𝑛}. By definition, it is the binomial coefficient we want. The other way to count is to fix the larger number 𝑘, the remaining choices are any of the 𝑘 numbers from 0 to 𝑘 - 1. Thus, across all possible larger numbers, we get the sum from 1 to n.An alternative alternate proof of the same, slightly more geometric is as follows: arrange dots in a triangle, 1 on row 1, 2 on row 2, and so on up to row n, with n dots. Add a phantom row of n+1 dots below. We want to add up all dots in first n rows: ∑ 𝑖. If you think of all of this as a binary tree/DAG, then every dot has two children (imagine Pascal's triangle). If you pick any two dots in the phantom row, their common ancestor is unique. So counting dots is same as picking two dots in phantom row. Which is the binomial coefficient we want.Benjamin and Quinn's book on combinatorial proofs is amazing for interpretations of this form (I learned the first proof from it). See also: <a href="https://en.wikipedia.org/wiki/Combinatorial_proof" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://en.wikipedia.org/wiki/Combinatorial_proof</a>

WordofTheHour<a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> : that degree of evidence which convinces the mind of any truth or fact, and produces belief- French: une preuve- German: abdichten, der Nachweis- Italian: prova- Portuguese: prova- Spanish: prueba------------Fill in missing translations @ <a href="https://wordofthehour.org/r/translations" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://wordofthehour.org/r/translations</a>

C.<a href="https://mindly.social/tags/Mexico" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mexico</a> and <a href="https://mindly.social/tags/Canada" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Canada</a>, and every nation in the <a href="https://mindly.social/tags/EU" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EU</a>, should now insist on proof of vaccination against all generally preventable diseases from Americans prior to entry into their country.If you want Bobby Brainworm in charge of your public health, it's your funeral, but you don't get to spread those germs in our countries to those of our citizens that are too vulnerable to be immunized.<a href="https://mindly.social/tags/RFKjr" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RFKjr</a> <a href="https://mindly.social/tags/BobbyBrainworm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BobbyBrainworm</a> <a href="https://mindly.social/tags/vaccine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vaccine</a> <a href="https://mindly.social/tags/vaccination" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vaccination</a> <a href="https://mindly.social/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> <a href="https://mindly.social/tags/USAnian" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#USAnian</a> <a href="https://mindly.social/tags/USPol" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#USPol</a>

Steva<a href="https://mathstodon.xyz/tags/CollatzConjecture" class="mention hashtag" rel="tag">#CollatzConjecture</a> My work shows: ✅ Asymmetry prevents new cycles ✅ Boundary constraint limits growth ✅ Exponential reduction always leads to {4,2,1} 📄 PDF: 🔗 EN <a href="https://github.com/Clickybunty/Collatz/blob/main/27JanuarCollatzSchrankeEn.pdf" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://github.com/Clickybunty/Collatz/blob/main/27JanuarCollatzSchrankeEn.pdf</a> 🔗 DE <a href="https://github.com/Clickybunty/Collatz/blob/main/27JanuarCollatzSchrankeDe.pdf" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://github.com/Clickybunty/Collatz/blob/main/27JanuarCollatzSchrankeDe.pdf</a> <a href="https://mathstodon.xyz/tags/Collatz" class="mention hashtag" rel="tag">#Collatz</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="tag">#Math</a> <a href="https://mathstodon.xyz/tags/Proof" class="mention hashtag" rel="tag">#Proof</a> <a href="https://mathstodon.xyz/tags/ProofTheory" class="mention hashtag" rel="tag">#ProofTheory</a>

claudeinspired by tavis' deep field <a href="https://post.lurk.org/tags/nebulabrot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nebulabrot</a> <a href="https://post.lurk.org/tags/DeepZoom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DeepZoom</a> images on <a href="https://post.lurk.org/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</a> <a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractals</a> forums, I did a little shader that for each c in the complement of the <a href="https://post.lurk.org/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MandelbrotSet</a> M, colours according to how often z <- z^2 + c hits a given small target disc , weighted by derivative (as a proxy for point density).it looks as though the hit sources are distributed everywhere near the boundary of M, which i think i can prove for target discs outside a sufficiently large esape circle, but i'm not sure how for discs nearer M. intuitively, by the time any cell pair in binary decomposition of exterior escapes, it covers an annulus with radii R, R^2, so any disc outside R will be hit by some region in every cell pair.<a href="https://post.lurk.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://post.lurk.org/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://post.lurk.org/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> <a href="https://post.lurk.org/tags/ComplexDynamics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ComplexDynamics</a>

Jan :rust: :ferris:‘Interpretability’ and ‘alignment’ are fool’s errands: a <a href="https://floss.social/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> that controlling misaligned large language models is the best anyone can hope for (Oct 2024)<a href="https://link.springer.com/epdf/10.1007/s00146-024-02113-9?sharing_token=3rRsMdH1UdNlnQQmqcozX_e4RwlQNchNByi7wbcMAY6BPcdnFvH2qz5wBW_MWVfuP6XiIjUuOaAkAylpJWYcV7ptG9FICiiQIbLIhD2SwblgAxawIQPIF0AJKzQaIv6wgiJRo4GtMJ1R6AewBvbdRekNszwAag_WVijImJA2dlc%3D" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://link.springer.com/epdf/10.1007/s00146-024-02113-9?sharing_token=3rRsMdH1UdNlnQQmqcozX_e4RwlQNchNByi7wbcMAY6BPcdnFvH2qz5wBW_MWVfuP6XiIjUuOaAkAylpJWYcV7ptG9FICiiQIbLIhD2SwblgAxawIQPIF0AJKzQaIv6wgiJRo4GtMJ1R6AewBvbdRekNszwAag_WVijImJA2dlc%3D</a>"This paper [...] show[s] that it is empirically impossible to reliably interpret which functions a large language model (<a href="https://floss.social/tags/LLM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LLM</a>) <a href="https://floss.social/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a> has learned, and thus, that reliably aligning LLM behavior with human values is provably impossible."This affects much more than just alignment!<a href="https://floss.social/tags/LLMs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LLMs</a> <a href="https://floss.social/tags/Paper" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Paper</a> <a href="https://floss.social/tags/ArtificialIntelligence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ArtificialIntelligence</a>

Knowledge Zone<a href="https://mstdn.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Proof</a> of <a href="https://mstdn.social/tags/Perfection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Perfection</a> : Medium<a href="https://mstdn.social/tags/Scientists" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Scientists</a> figured out the <a href="https://mstdn.social/tags/Optimal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Optimal</a> cup of <a href="https://mstdn.social/tags/Coffee" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Coffee</a> : Pop Sci<a href="https://mstdn.social/tags/Physicists" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physicists</a> describe <a href="https://mstdn.social/tags/Exotic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Exotic</a> ‘<a href="https://mstdn.social/tags/Paraparticles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Paraparticles</a>’ that defy <a href="https://mstdn.social/tags/Categorization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Categorization</a> : NatureCheck our latest <a href="https://mstdn.social/tags/KnowledgeLinks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KnowledgeLinks</a><a href="https://knowledgezone.co.in/resources/bookmarks" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://knowledgezone.co.in/resources/bookmarks</a>

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