The Eternal Doorman

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At around 34:00 you get a glimpse of why measure theory is such a mess!  See Charles Fefferman's 1971 paper  The multiplier problem for the ball . Jonathan Hickman's 2025 paper:  The Kakeya Conjecture: where does it come from and why is it important?   Subscribe to John Baez .

With a guest host in North Carolina,... See  Spiritually Depraved, Misery Inducing Landscapes of North America Episode III .  Compare this with Brad Lancaster's barrio in Tucson: See Urban Planning Problems and Americans Doing Real Science . Subscribe to Crime Pays but Botany Doesn't . 

See  An Open Letter to Chancellor Friedrich Merz . So-called leaders behaving like children.  Richard Wolff a few days ago:  Subscribe to Glenn Diesen . 

My comment : I think the web as it was designed doesn't work anymore, and this is just another issue in a long list of issues. So we need something better, but Google are not going to help with that. So I don't know how it is going to come about. But Google didn't start this thing, they just got a foot in the door because the original design didn't have a way for people to search. You had to ether know the URL for the information you needed or you had to know a directory that would link you to it, but there was no top level to that system, and it was all multilingual and distributed across continents. Google have now joined it all up and they're monetizing it and sitting at the top and trying to make it so nobody can knock them off their perch.  Subscribe to  General Musings .  My comment : The last sentence,... Ouch! Call Justin Trudea! Call Barack Obama, call the RCMP, call a lumberjack,... Hell I don't know what you're supposed to do when stuff like thi...

See  Stefan Milius - Demystifying Codensity Monads through Duality  and  Terence Tao Formalising Riemann-Stieltjes Integrals in Lean Mathlib .  Subscribe to  IHES France .  Subscribe to  Weizsäcker-Zentrum Universität Tübingen .  53:29 He describes a type theory as a living object, programmed in some language [and running on computers.]  Subscribe to  Institute for Advanced Study This talk by Steve Awodey was given in December 2010 Subscribe to Institute for Advanced Study .  See the list of the 4th Huawei IHES workshop talks here . This is the one by Olivia Caramello on Grothendieck Toposes in Mathematics:  8:22 See  Morita equivalence in nlab . Also more on finitary models at  35:50  and 45:08 . See also  Wiesław Kubiś - Generic Mathematical Structures .  See the  Toposes in Como 2018 talks here . See also these posts of mine:  Alain Connes on Toposes and Integers  and  Terence T...

22:00  Some of the interesting problems that come up in healthcare data management.  43:04 How to set up a private IPFS fragment, and how to get web API access through firewalls.  See  https://vereign.com/ Subscribe to  IPFS . 

Becky G - Mi Gran Amor Subscribe to  Santana . 

Some great advice at 20:42 about how to program computers.  See  Janet Axelrud on the Soul .  Subscribe to  Cybernetic Explorer . 

See  Nika Dubrovsky and Alistair Parvin on the David Graeber Institute and the Museum of Care, The Survival Kit Collection and the Open Systems Project . Mondragon is a worker owned cooperative with its own University. See  https://www.mondragon.edu . Subscribe to  Hazel Thayer . He just moved himself by paying the post office. The postal service in Canada seems pretty impressive if you can send a 28 Kg package across the country without taking out a mortgage to pay for it!  Subscribe to  Robert Elder Software . 

  Wouldn't it be nice if one day in the future you could specify the string/surface diagram representation as a morphism in CAT and have your computer generate the code to display the diagrams in your slides? That would be even cooler than HTML-in-canvas, wouldn't it?  See  Laurie Wired on Richard Gabriel's 35-year-old essay "Worse Is Better" Subscribe to Topos Institute . 

See her Patreon post .

It sounds like Richard Gabriel is the inventor of the term Software Architecture . See his 1996 book  Patterns of Software . See  https://dreamsongs.com/ . In answer to her question at the end: I think the best thing is to make stuff better and better. So for example, I think it would be nice if Lean's Mathlib one day proved the Generalised Stokes Theorem on differential manifolds and derived the proofs of the Fundamental Theorem of Calculus from that. At the same time, it would be nice if people could work on teaching the basic ideas of simplicial forms and cohomology to high school students so they could understand the Generalised Stokes Theorem in simplicial complexes before they were taught how to do epsilon-delta proofs of calculus on the real line. In computer science, the equivalent process is one where, instead of designing new languages like C++ and Lean and producing a never-ending stream of concrete implementations that are all different, people specified the lang...

From the video description : Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on the full space? This formulation of the consistency problem for conditional probabilities is significant in Bayesian epistemology and probabilistic reasoning, as it describes the conditions under which a collection of agents can reach agreement by sharing information. We derive a necessary and sufficient condition under which joint compatibility is equivalent to pairwise compatibility. This condition is stated in terms of the cohomology of a simplicial complex constructed from the given probability measures, exposing a novel application of algebraic topology to Bayesian reasoning. See  Topological Obstructions to Shared Priors  by Owen D. Biesel, Colin McSwiggen, Ted Theodosopoulo and Michael G. Titelbaum.  ...

6:03 In Mathlib they try to formalise theories at the highest level of abstraction they can to avoid having to prove the same theorems many times for specific instantiations.  So for example, they use a general multi-dimensional integration theory of box-additive measures in  Mathlib.Analysis.BoxIntegral.Basic : In this file we define the integral of a function over a box in ℝⁿ. The same definition works for Riemann, Henstock-Kurzweil, and McShane integrals. As usual, we represent ℝⁿ as the type of functions ι → ℝ for some finite type ι. A rectangular box (l, u] in ℝⁿ is defined to be the set {x : ι → ℝ | ∀ i, l i < x i ∧ x i ≤ u i}, see BoxIntegral.Box . Let vol be a box-additive function on boxes in ℝⁿ with codomain E →L[ℝ] F. Given a function f : ℝⁿ → E, a box I and a tagged partition π of this box, the integral sum of f over π with respect to the volume vol is the sum of vol J (f (π.tag J)) over all boxes of π. Here π.tag J is the point (tag) in ℝⁿ associated with the ...

See  https://dannypineros.com/  This is going to be something amazing!  Subscribe to  Dust  and  Daniel Piñeros . 

See  Wiesław Kubiś - Generic Mathematical Structures .  55:12 Wouldn't it be great if you could cook up a comonad that gives a tower of categories that sum to differential calculus on a real vector space? See below .  Subscribe to  Topos Institute .  What is a comonad on a category? It's just a monad on the opposite category:  ... "Set theory is linear coalgebra on vector spaces":  Subscribe to  Sheafification of G .  But they have to make everything much more complicated: We discuss differentiable smoothness structures on 𝑹⁴ from three different categorical perspectives. The first one relies on considering open atlases on 𝑹⁴ with certain (not all) of its local charts residing in a smooth topos. Thus exotic smooth functions on 𝑹⁴ are finelly approached without any use of Casson handles and handle decompositions. The second approach takes into account entire space of all smoothness structures on 𝑹⁴ . Forcing extensions naturally order the...

See the video description : A mathematical object can be called “generic” if it appears, up to isomorphism, with probability one as the result of a natural stochastic process. Instead of [using] probability, one may [give] its topological counterpart, using the Baire category theorem . Yet another option is using a natural infinite game for two players, declaring an object U ”generic” if one of the players has a suitable winning strategy leading to the isomorphic copy of U.... ... The story of generic mathematical structures goes back to Cantor, who was the first to identify the set of rational numbers as the generic countable linearly ordered set. About half a century later, Fraïssé developed an abstract theory of universal homogeneous structures (nowadays called ”Fraïssé limits”) which until recent years was viewed as a part of model theory. As it happens, Fraïssé limits are particular cases of generic mathematical objects which can be found in several branches of mathematics, starti...

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13:13 How do you define volume in an infinite dimensional phase space on a finite whiteboard ?  1:05:39 I enjoyed listening to this discussion. Thanks to everyone who took part.  I was thinking about causal sets as modeling those second countable collections of empirically verifiable statements. That may not be how Sorkin sees it though! See  Geometry from order: causal sets .  Subscribe to  Assumptions of Physics .  See also this discussion with Urs Schreiber on Gauge fields and configuration spaces at 44:33 . The earlier discussion he referred to on differential geometry and compact spaces is at 17:05 . He's saying that you do not want to restrict physics to describing only compact spaces. But you do want to restrict observations to compact spaces. At 26:03 you can get a coherent notion of field configuration spaces in a topos. 35:10 Lawvere started out in physics, but then he asked "What is a vector space, really?" and within a decade wrote a paper...

It does configuration by WebUSB to download the firmware onto the modules, but I'm sure that's all encrypted too. See  Ian Clarke Answering Questions About Freenet  and  Wi-Wi 900 MHz Radio-synced Oscillators  so that you can use a distributed computation to authenticate messages. See  Ian Clarke on Freenet .  Subscribe to  Taylor and Amy Show .  Tomaz has made a 10Gb/s router and fiber optic cable is pretty cheap: from 10 cents per meter. So you are all set to help each other with offsite backups now: see How to Create a Successful Open Source Project FUTO - Immich Demonstration and Technical Talk FUTO FUBS Subscribe to  Tomaž Zaman .

Duality is not just good, it's the good!   Codensity monads  though,... See William Lawvere's remarks on the semi-lattice construction of Set in  About Logic Interview with Urs Schreiber .  52:21 In case you're like me and don't remember what an ultrafilter  on a set is: Filters are dual to ideals .  Subscribe to  Topos Institute .  Daniela Petrisan - Operations on languages and Codensity monads Talk given at  Simons Institute in November 2016: Given some operation on languages, a natural question to ask is what is the corresponding operation at the level of recognisers. For example, the concatenation of two languages recognized by monoids M and N, respectively, is recognized by the Schutzenberger product of M and N....  See  The Schützenberger product for syntactic spaces  by Mai Gehrke, Daniela Petrisan and Luca Reggio.  See also  https://www.irif.fr/~petrisan/  and  The Vietoris monad and weak distrib...

Using LLVM IR:  https://github.com/SheafificationOfG/QueenJewels . He did another one about groupoid models but it has lots of annoying video clips which make it a bit hard to follow, but it's still interesting.  Here's the one on equality, which you might want to watch first:  But you might want to watch this one first: See  About Logic Interview with Urs Schreiber  and  Vladimir Voevodsky - What if Current Foundations of Mathematics are Inconsistent .  Subscribe to  Sheafification of G . 

This gives a far better idea of the background to the problems that lead to the current situation. See  Amilcar Zenteno on Some of What's Happened in Bolivia Since the General Election Last Year .  Subscribe to  Gonzalo Chavez Alvarez . 

Talk given at the Institute of Advanced Studies at Princeton in 2010. It's good that some people were allowed to talk about this. See  About Logic Interview with Urs Schreiber  and in particular Lawvere's  Cohesive Toposes and Cantor's 'iaufcer Einsen' .  The answer is to use a plurality of formal systems and a plurality of formal translations between those systems. Then the provable sentences are not vulnerable to such accidental coincidences of interpretation which are constructed by diagonalisations such the Gödel sentences. This is just a greatest fixpoint. Unfortunately it depends upon mathematicians and logicians actually speaking to one another.  See  An Excellent Talk about Computability and Hilbert's Entscheidungsproblem .  Subscribe to  Institute of Advanced Studies .  Talk at the he IMU in September 2016, a year before he died.  "... it came out, as a result of practical work on formalization we just discovered that the law o...

It's a balanced summary of information and a lot better than most of the so-called reporting I've seen so far. Subscribe to  10Centavos . 

I don't understand why they need to do this. Get it in-print:  https://membership.theonion.com/ . Subscribe to The Onion . 

I think this is the first time they've actually publicly announced anything about this project. See these posts: Eron Woolf on Why Open Source is Failing Matt Mikhailov and Vincent McKibbon on The Problem with Open Hardware Jason Kridner talking About BeagleBoard.org and Software Development .  See these places:  https://danielc.dev/rk/ https://github.com/petabyt/rk https://github.com/futo-org/ret See also  https://pine64.org/devices/pinebook_pro/ . Subscribe to  FUTO .  See  https://github.com/nir9/low-level-learning-resources/tree/master/setups/debian . Subscribe to  Nir Lichtman .  If you're looking for a cool init process, try  https://ctx.graphics/terminal/ . See  Artful Bytes - When to Use a RTOS  and  How to Create a Successful Open Source Project . 

On Che Guevara's birthday. See  Sayaka's Digital Attic - Interview With Lee Felsenstein .  Subscribe to  Vintage Computer Federation . 

See  Assumptions of Physics - Symplectic Group and Uncertainty .  Subscribe to  About Logic .  Lawvere on the Dialectic of the Continuous and Discrete. Talk given at Nancy, France 26-29 July 2011. See Lawvere's 1966  The Category of Categories as a Foundation for Mathematics .  See Lawvere's  Cohesive Toposes and Cantor's 'iaufcer Einsen'  ( cf.  my "vague inkling" about cardinality in Frederic Schuller on Metric and Topological Spaces ) and  cohesive topos in nlab .  16:57 On structures and cohesion, with Lie groups as an example. See Anthony Bordg and Nicolò Cavalleri  Elements of Differential Geometry in Lean .  1:03:12 On applications to dynamical theory. See  Toposes of laws of motion in nlab  and this transcript of a 1997 lecture given in Montreal. 1:08:54  He goes back to Frege and the idea, from correspondence with Peano, that certain minimal atomic subsets have properties completely independent o...

It can't go on like this folks. It doesn't matter if you're American, Chinese, Russian, whatever, you cannot have responsible Government if it depends upon the same money that thieves pass around amongst themselves.   See  https://www.patreon.com/michaelhudson  and  https://www.patreon.com/cw/LenaPetrova . Subscribe to Lena Petrova . 

This was on Saturday: see  Coordinate invariant measures/entropy . It's such a shame that the well-established experts can't talk about these things , because they're much more interesting than the stuff you read in textbooks. See  Frederic Schuller on Metric and Topological Spaces .  Subscribe to  Assumptions of Physics Research . See also  Entropy is not continuous in standard probability spaces .  Subscribe to Gabriele Carcassi . 

They can do position measurements with millimetre accuracy. So you will soon have surveillance cameras that can recreate 3D representations. You will also have very good sound systems for public spaces. Subscribe to Leve l2 Jeff .

See  Curious Marc - Apollo Comms . 1:25:00 Question about ISS frequencies: see  Curious Marc Fixing a US$33,000 HP 3GHz Signal Generator he Bought for US$150   Subscribe to Vintage Computer Federation .

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Happy birthday Laura!!!   Subscribe to  Laura Pausini  y Camila Cabello .

  3:08 He's right, but once you know all that you should also be able to work out that most of it is needed only because the other bits are there, and there is no way that all that cruft should be running "in production". See  Artful Bytes - When to Use a RTOS . Subscribe to Plan 9 Foundation .

Subscribe to  FUTO .  If you're American you can build a 200TB NAS for your photos and backups out of trash you probably have lying around the house: Maybe FUTO will sponsor a project that allows you to contract out to be offsite backup for your friends.  Subscribe to  Level1Techs .  Or you can start downloading the whole web for your personal use,... Subscribe to  TechHut . 

My comment: That was really good, thanks. Are there any systems that can take a high-level specification of a set of tasks and compile them into machine code that implements just the necessary functionality without the overhead of code which provides the OS primitives for use by any rogue code that may have been introduced to the system somehow? I am thinking of code that just sets up interrupt handlers, DMA channels, etc. so the system can really only do the one thing it was designed to do and nothing else.  Subscribe to  Artful Bytes . 

  See McCarthy's 1960  Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I . Subscribe to Yoshiki Ohshima (大島芳樹) .  Subscribe to  Javier Livas Cantu U7 .

It would be very hard to believe the moon landings were faked once you see how much effort it took to build and run the communications systems. But you have to put in quite a bit of effort even to get a vague idea of how much effort went into restoring a working instantiation of it. See the full set of videos here:  Apollo S-band Communications System .  It's a shame people don't want to put that sort of effort into creating terrestrial communications systems for ordinary people to use. See  Curious Marc at VCF Montreal  for more on the restoration. Subscribe to  Curious Marc . 

I just opened a random PDF file I got from  https://pdfobject.com/pdf/sample.pdf  in Firefox and it opened in a separate browser tab with the above URL. Then I right-clicked on the body of the displayed text and chose "Inspect" and it popped up with an HTML document. It looks like Firefox parses the PDF and builds a DOM object on the fly for each page which contains all the contents of the PDF objects in the file. If someone had told me they were planning to do this I would have said "forget it!" How do they handle embedded fonts? Do they convert them all to outlines and display them as SVG? I just would never expect two high-level formats like HTML and PDF to be inter-convertible. I would have thought they would have to translate to a common lower-level format, and then maybe there would be a class of documents you could quotient out which would be faithfully translatable at the higher level, but is that what they're doing, or does this work for anything?

He's also writing a Sci-Fi script by the sounds of it! See the video description for more information: Video supplement to some exploration into hiding information in apparently-natural patterns.  The frequency content of the ring on the left encodes ASCII characters. The shape associated with each character morphs into the next, creating the wiggly animation. You can recover the characters by performing an FFT on the x/y coordinates that describe the ring. The sound that you hear carries exactly the same information as the ring that you see, as evidenced by the scope trace in the lower left. Will add a link to an explanatory webpage once I've finished it.  Subscribe to  V. Hunter Adams .

See  The phonology of sperm whale coda vowels  and  https://www.projectceti.org/ . More links in the video description . I wonder what we would need to know before we could start communicating meaningfully with whales? Subscribe to Anton Petrov.

Listening to Freya Holmér last night I started to get glimmers of an idea I had long ago about how to represent vector spaces in computational processes using this recursive abstract type :  abstype 'a point = POINT   of {getx :  'a vector,       diff :  'a point -> 'a point,       move :  'a point -> 'a point,       scale : 'a -> 'a point,       proj :  'a point -> 'a} with    fun new i (op +) (op -) (op * ) dot =    let fun self x =  POINT       {getx = x,        move = fn (POINT pr) =>           (self (x + (#getx pr))),        diff = fn (POINT pr) =>          self (x - (#getx pr)),        scale = fn i =>          (self (x * i)),        proj = fn (POINT pr) =>     ...