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Wiesław Kubiś - Generic Mathematical Structures

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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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Elle Cordoba - A Grammatical Murder Mystery

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Assumptions of Physics - From Classical Mechanics to Field Theory

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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...
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Taylor and Amy Experiment With an Open Source, Decentralised, Encrypted Way to Message Complete Strangers

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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 .
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Stefan Milius - Demystifying Codensity Monads through Duality

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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...
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Sheafification of G - Finding the Billionth Prime Number

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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 . 
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Gonzalo Chavez Alvarez on the Bolivian Economy

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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 . 
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Vladimir Voevodsky - What if Current Foundations of Mathematics are Inconsistent

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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...
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Amilcar Zenteno on Some of What's Happened in Bolivia Since the General Election Last Year

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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 . 
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OpenAI Announces Construction of New Datacenter on Top Of Sick Child

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