Posts

Frederic Schuller on Topological Manifolds and Manifold Bundles

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22:54 Bundles. 36:52 Sections.  52:44 Bundle Isomorphisms.  1:09:25 Pullback of a Bundle.  1:18:04 Viewing Manifolds from Charts and C⁰-compatibility.  Differentiable structures 9:23 See  Cauchy–Riemann equations .  1:05:52 Amusing observation about the number of possible smooth manifolds you can construct on a four-dimensional compact topological manifold such as Einstein's space-time.  Tensor spaces over a ring:  45:33 Proof of the Hamel Basis Theorem for a division module.  1:33:52 Because the smooth functions on a manifold are not a division ring, one cannot think of tensor fields in terms of their component functions. Locally, this is always possible, but not globally.  See Frederic Schuller on Metric and Topological Spaces and Tensor Fields and Simplicial Complexes .  Subscribe to  Frederic Schuller . 

Modern Politics is Mass Psychosis

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The loonatics are running the asylum, at last! Subscribe to  Glenn Diesen .  Clara Mattei interview with Roberto Mendoza See  Jeffrey Sachs on Judge Napolitano's Talk Show . Subscribe to  FREE . 

Juan Browne on Aircraft Evacuation Dangers

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Subscribe to  VASAviation Many people don't follow the procedures: My comment : Wow, what a thing to to happen. I seem to remember hearing on VASAviation the flight crew telling the tower they were going to evacuate. These incidents always remind me of being flown from San Diego to some place in Louisiana with a few hundred fellow asylum-seekers, all of us in shackles, both hands and feet. No way any of us were going to bring stuff with us in an emergency evacuation. Subscribe to  Blancolirio . 

Jeffrey Sachs on Judge Napolitano's Talk Show

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My comment: See  Clara Mattei on Institutions and Economics .  Subscribe to  Judging Freedom .  My comment : If you only look at capital flows then you will never be able to find any solution to the problems. You have to look at material and energy flows and at the web of dependencies they create and then at how that web would look in a properly functioning (i.e. sustainable) economy. A very important part of this analysis is information, knowledge and the necessary human skills to realise any industry. Economists try to understand all this by abstracting all the details away and then end up talking absolute nonsense about value as if it is measured in US dollars.  We need to build stable systems with convergent dynamics. See  Jenann Ismael - Laplace meets Godel: How Self reference Foils Prediction .  See  Frederic Schuller on Metric and Topological Spaces  and  Tensor Fields and Simplicial Complexes .  Subscribe to  Radhika D...

DemistifySci Podcast - Paradox Lost

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It's their new book  on presale now . Part II coming up:  My comment :  You've pointed out that there was a moment in human history when energy became separated from matter. That's what electricity was all about. I had never realised this before. It was not a moment of course, because if you look at the history of thermodynamics and theories about light and radiation then some things like Crookes radiometer are just as tricky as the photoelectric effect.  I still don't know what you mean by the material comprehension of Nature though. The problem I have is that it is more than the material, it is the particular way in which that material is arranged, and the arrangement of the material is something we do when we set up an experiment in a laboratory, and it is only once we get very skilled at arranging material that we find we can, for example, generate sufficient electrical potential to be able to measure it quantitatively with volt meters and compare the measurement...

Tensor Fields and Simplicial Complexes

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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) =>     ...

George Galloway and Crispin Flintoff on the Starmer Rentboy Arsoning Case

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He deleted the video. Too bad. See Disgusting British Establishment and Kim Iversen and Ben Swann on Pizzagate .  Here's his Victory Day monologue: Subscribe to  George Galloway . 

Audrey Henson on the Genesis AI Scam

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She says it's not to support the AI bubble, it's an evil plan to develop targetted bioweapons and stuff. See  Angela Collier on the US Department of Energy AI Scam . Y'all be on your best behavior now, ... see  Audrey Henson on Oracle and Healthcare Data . Subscribe to The Drey Dossier .  

Happy Mother's Day - Even if you aren't from Baja California!

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Frederic Schuller on Metric and Topological Spaces

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1:16:57 On metrics that don't measure and hair-dressers! See  Intransitive dice . See  Tensor Fields and Simplicial Complexes  and  observable in nlab : In physics and in the theory of dynamical systems (deterministic, stochastic, quantum, autonomous, non-autonomous, open, closed, discrete, continuous, with finite or infinite number of degrees of freedom…), an observable is a quantity in some theoretical framework whose value can be measured and observed in principle. Any good theoretical framework of physical phenomena should come with carefully established notion of an observable.  ... See also measurement in nlab : In principle, any interaction between two physical systems is a measurement, whereby each system measures the state of the other. In practice, we break the symmetry by treating one system as the real physical system S of study and the other system as merely a measuring apparatus A with the sole purpose of measuring S. If the properties of A are mo...