The Eternal Doorman

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See the full series of lectures here .  Course notes and other materials at https://www.cs.cmu.edu/~kmcrane/Projects/DGPDEC/ .   This is really excellent and it makes a great complement to Frederic Schuller's Geometrical Anatomy of Theoretical Physics course . There is also a good Bright Side of Mathematics course on Manifolds .  Subscribe to Keenan Crane . 

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From ICFP 2015. See the paper Automatic refunctionalization to a language with copattern matching: with applications to the expression problem by Tillmann Rendel, Julia Trieflinger and Klaus Ostermann and John Reynolds' Definitional Interpreters for Higher-Order Programming Languages .  17:02 Person asking about how you represent infinite streams with finite data. I think the answer is that you use a cyclic data structure. That is the clever trick in Reynolds' defunctionalization transform. See  David MacQueen on his Ideas for Successor ML  and  Open, extensible object models (2006) by Ian Piumarta and Alessandro Warth.  Subscribe to ICFP Video . 

See Petrification in Contemporary Set Theory: The Multiverse and the Later Wittgenstein by José Antonio Pérez-Escobar, Colin Jakob Rittberg and Deniz Sarikaya and Philosophical Investigations into AI Alignment: A Wittgensteinian Framework by José Antonio Pérez-Escobar and Deniz Sarikaya. My comment : 39:54 Our intuition may be more closely tied to language than it seems. There is evidence from linguistics that the kinds of intuition we have about time and space have an intimate connection with the language we speak and even how we write. Lera Boroditsky has done lots of talks about this. The coherence of the foundation, whatever that "actually" is, must ultimately be in our ability as human beings to understand each other's descriptions of their personal direct experience, so in this process of establishing symbols and meanings we will produce various systems, some of which will have more or less rigour than others, depending upon the culture. With...

If you want to emulate a machine you can write a VHDL description of the hardware and then compile that into a C program which runs on another machine. This is how Angelo Papenhoff does it. Compare this with the top-down semantics and formal proof approach of CakeML: David MacQueen on his Ideas for Successor ML . I wonder if there is a way to combine these approaches in a kind of analytic/synthetic dialectic?  See also  How Could One Unify CMU and MIT and  Nada Amin - Metacircular Interpretation ad infinitum . Levy's book Hackers was an inspiration for these projects.   See https://pidp.net . Subscribe to Computerphile .  Here's some of the story behind these emulators: 1:14:17 New lunar lander game written three months earlier.  Subscribe to David Greelish . Mike Stewart made a gate-level emulator of the Apollo Guidance Computer and a few weeks ago he did an industrial archaeology project to find out what happened to one of the core rope memory mod...

... and physics, ... given in April 2015. Subscribe to UMD Department of Mathematics . This was given in September 2006: Subscribe to  Center for Advanced Study University of Illinois at Urbana-Champaign . The curious thing is that at the beginning of that talk he describes analogy in the same way Euclid described it (following Eudoxus) as "A is to B as C is to D" and if you write that as a ratio you get A:B = C:D. More generally you have A:B::C:D = A:C::B:D which holds for irrationals and  ἀναλογία  as well as irrationals (See Proposition 16 of Book V of Euclid's Elements ). This is analogous to Hofstadter's "Interchange" relation ( 22:35 ) he describes in the first talk above ( 14:25 ). Yesterday I was wondering about duality (see  Dual Spaces, Lie Groups and Conservation Laws ) and whether there could be any reason behind why it seems so ubiquitous in formal reasoning. I think analogy must be something fundamental in our ability to learn and interpret lan...

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This is really impressive:     Subscribe to  blargoner .   I wonder what YouTube will suggest in the auto-reply to my comment : @VisualMath  1:20 on compactness and averaging, ... and on smooth geometric structure in euclidean spaces. I have this intuition about variational calculus that I am also hoping to be able to explain once I have a nice representation of differentiable manifold, or maybe it'll work the other way around and I'll be able to get a nice representation if I follow this intuition? Maybe there's a way to find it by converging from both directions under some duality assumptions? The intuition is that in some sense the physical reason why the principle of least action works (and why Lagrange called it least action, not just stationary action) is that if we are observing some system and trying to deduce laws of motion for it, then we want to only select those paths through the configuration space which are the ones the system follows spontaneou...

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I have only just heard about this idea which goes back to the early eighties. See  Reflection and semantics in LISP  (1984) by Brian Cantwell Smith, Reification: Reflection without metaphysics  (1984) by Daniel Friedman and Mitchell Wand, Intensions and extensions in a reflective tower  (1988) by Olivier Danvy and Karoline Malmkjaer, The reflective language Black  (1996-2025) and Compiling a reflective language using MetaOCaml (2014) by Kenichi Asai. Also this summary Reflective Towers of Interpreters (2021) by Nada Amin. Scheme code at https://github.com/namin/reflective-towers. For more on Extended CPS see Abstracting control  (1990) by Olivier Danvy and Andrzej Filinski.  See also  Open, extensible object models  (2006) by Ian Piumarta and Alessandro Warth, and https://piumarta.com/software/cola/ : Programming languages often hide their implementation at a level of abstraction that is inaccessible to programmers. Decisions and trad...

He demonstrates a really slick programmable constraint solver that works from diagrams. See  On Getting Machines to do Stuff  and How Could One Unify CMU and MIT . This was held in St. Louis, Missouri.  See also  https://www.inkandswitch.com/  (and https://www.inkandswitch.com/crosscut and https://www.inkandswitch.com/untangle ).  Subscribe to Strange Loop .  8:10 On the programming model. See constraint solvers and type inference ideas in  On Getting Machines to do Stuff and  A New Kind of Science  and John Baez and Mike Stay's 2009 paper  Physics, Topology, Logic and Computation: A Rosetta Stone  and  David Jaz Maiers - Compositionality via 2-algebra . Subscribe to ACM SIGPLAN .  You can do things like this in that world too. See Thinking About How AI Can Make Better Programmers, ...   Subscribe to Dynamicland . Clemens Nylandsted Klokmose on Software as Computational Media and "Personal Digital Sovereignt...

I found this talk by accident, on William Byrd's web page . It was given at Stanford in March 2013 whilst I was living in Rurrenabaque trying in vain to sell my logic books to get some money to buy food. See the book  Surfaces and Essences Analogy as the Fuel and Fire of Thinking . Subscribe to ccrmalite  (?!). There used to be a distinction between symbolic logic and formal logic. If you ask Google AI what this distinction is it says it is no longer, since formal logic before 1900 was found to be wanting in rigour and thanks to the efforts of Frege, Russell et al it has been superseded by symbolic logic. Well, if Google AI says that then it must be true. What if Frege, Russell et al  had actually not properly understood what formal logic was? Then there would be a distinction between Formal Logic and modern symbolic logic which is unknowable to anyone who only recognises modern symbolic logic. In fact you don't have to look very far to see that this is clearly the case...

See this 2020 paper Gentzen-Mints-Zucker duality by Daniel Murfet and William Troiani: The Curry-Howard correspondence is often described as relating proofs (in intutionistic natural deduction) to programs (terms in simply-typed lambda calculus). However this narrative is hardly a perfect fit, due to the computational content of cut-elimination and the logical origins of lambda calculus. We revisit Howard's work and interpret it as an isomorphism between a category of proofs in intuitionistic sequent calculus and a category of terms in simply-typed lambda calculus. In our telling of the story the fundamental duality is not between proofs and programs but between local (sequent calculus) and global (lambda calculus or natural deduction) points of view on a common logico-computational mathematical structure.  See also  Program Synthesis and  On Getting Machines to do Stuff  and then  Jean-Yves Girard - Lectures at IHP thematic trimester : Semantics of proofs and...

See  https://freenet.org . See  Polylog on Oblivious Transfer and Zero Knowledge Protocols  and  HTML in Blog Posts . See also  Taylor and Amy Experiment With an Open Source, Decentralised, Encrypted Way to Message Complete Strangers . For the background, see  Ian Clarke on Freenet  and  Ian Clarke Answering Questions About Freenet . Subscribe to FUTO .     Subscribe to FUTO .  

See  https://github.com/dmacqueen/NewFrontEnd  and  https://standardml.zulipchat.com . 9:33 On disallowing static declarations within expressions: from MLFW2025.txt : 1.3. [Core] No static (type/module) declarations within expressions   Moto: "Keep the core and module levels separate", or "no static declarations within   dynamic expressions".   What does it, or should it, mean to have a (statically generative) datatype declaration   in the body of a recursive function.   [Karl Crary (and Bob Harper?) won't like this, since definition of modules within   expressions is a feature of his dialect of (S)ML. It also appears to be supported in   Moscow ML. The CMU (Harper, Crary, etc.) view of the static semanatics of (S)ML seems to   base on some fundamental "type theoretic" notion of a _module_ that seems to be   different from my own intuitive understanding of the module system of (S)ML. Their ideas   are described in papers s...

I just found out that POPL 2024 had some talks about program synthesis. This reminded me of the Criterion Problem. See  Ways to Do Telecommunications : Subscribe to ACM SIGPLAN .

This is great! See Hackaday Europe 2026: Half Quad, Half Blimp: Test. Fly. Survive . Subscribe to Hackaday .

See  Jean-Yves Girard - Lectures at IHP thematic trimester : Semantics of proofs and certified mathematics  for more charcuterie. It's where the sausages are all hanging up around the ceiling, ... Subscribe to Julie Nolke .  

My comment : That was a really clear explanation, thank you. Can you talk sometime about how it is that these protocols are not used for basic data protection? I mean why is age verification such a big deal? Can't a zero knowledge protocol be used to verify someone's age without divulging their full identity? I know there is probably a different motive behind the age verification thing, but why does nobody talk about alternative solutions that don't involve personal identity data? I think it has much wider application though. For example, say I want to order and pay for something and have it delivered to me without divulging my identity or the delivery address or my bank details. One would think that it would be possible for my bank to give me some proof that I have commited to pay a certain amount to some entity, a sort of single use cheque, which I could then commit to using to pay the supplier, who then commits to send the goods via a chain of carriers who each similary ...

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Just testing stuff: SVG You can click on the blue circle: MathML There is not much you can do with this. See Mathematical Markup Language 1.01 Specification   7.1.5 Mixing and Linking MathML and HTML . It's the big problem  of how you compose languages.   a x 2 + b x + c = 0 You can click on the discriminant: x = − b ± b 2 − 4 ⁢ a ⁢ c 2 ⁢ a 2D Canvas Sound  Beep! WebGPU Next level Parser expression grammar compiler:  https://peggyjs.org/online.html Devine Lu Linvega's unxtal assembler/debugger:  https://wiki.xxi...

We have all these machines, but they aren't doing the right stuff because of the hidden agenda : they were never meant to do stuff we needed them to do, they were meant to be ways for other people to use to get us to do stuff. See  FUTO FUBS and the Everything App . I was prompted to write this by Girard's question "What is a question?" and his remarks about a DVD player at 17:42 in  Jean-Yves Girard - Lectures at IHP thematic trimester : Semantics of proofs and certified mathematics .  The example question he gives is how do you know that it is a DVD player? And the answer is that you put in a DVD and it asks you a question!  It struck me the other day that the way most people think of programming is quite different to how I think of it. I think of it as composition of ideas in a bottom-up sense: I have some ideas and they're like Legos, so I have a box of all sorts of ideas and each time I learn a new one it goes in the box. Then when I am feeling creative I im...

Lectures given in April 2014. You can really tell he was at a French University in 1968 ! Qu'est-ce qu'une réponse ? (l'analytique)  47:53 On Gentzen's distinction between implication and cut and Lewis Carroll's What the Tortoise said to Achilles . Around the time he was presenting these lectures in Paris I was homeless in Caranavi, Bolivia writing to people in Cambridge about exactly this subject. He doesn't seem to have thought of the possibility that Lewis Carroll, who was a geometer, might have been talking about something more than symbolic logic. The form of the five common notions in the Elements is that of formal rules of inference, and that is how they are used implicitly in proofs: (A) Things that are equal to the same are equal to each other. (B) The two sides of this Triangle are things that are equal to the same. (Z) The two sides of this Triangle are equal to each other.   Consider whether the character of (A) is that of a statement about a geome...

On Aristotelian physics, I was wondering about the last line of this Proposition: To set out the sides of the five figures and compare them with one another . Here Euclid proves that if a dodecahedron and an icosahedron are inscribed in the same sphere, then side of the icosahedron is greater than the side of the dodecahedron. One might think (because I did) that the icosahedron , having twenty faces, would have a greater volume than the dodecahedron inscribed in the same sphere, because the dodecahedron has only twelve faces and so should be a poorer approximation to a sphere as a result, but this intuition is false. One similarly might expect the sides of the icosahedron to be shorter than those of the dodecahedron for similar reasons, but neither is that true. However, the dodecahedron and icosahedron are dual each to the other, meaning that they each have the same number of edges, and if you swap faces with vertices you get the dual polyhedron. In both figures, opposite edges are ...