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C9 Lectures: Dr. Brian Beckman - Covariance and Contravariance in Physics 1 of 1

44 minutes, 31 seconds


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By now, you know Brian Beckman given how many times he's been featured on Channel 9 and, well, just how amazing he is. Brian is an astrophysicist and software architect currently working on a technology we can't talk about...yet... Smiley Stay tuned for that. Dr. Beckman is the perfect choice for a new lecture in the C9 Lectures series. This is a single lecture, but there will be more interesting conversations to come on this deep and beautiful topic (in some sense, this is all about symmetry).

In the Rx interview with Brian and Erik Meijer, a short discussion on covariance and contravariance took place as a tangential topic (which often happens in real conversations - and we love that!). The concepts of co/contravariance can confuse and confound. Also, they are not just related to programming.

Here, Dr. Beckman teaches us about covariance and contravariance in physics. Are these universal properties? Do they apply to the mathematics of physics (from quantum mechanics to black holes) in the same basic way they do for general purpose programming with objects and lists, for example?
Tune in. This is a deep dive lecture and quite mathematical. Don't be scared. As usual, Brian explains complex things in a readily understandable fashion for mere mortals. If you have no experience with math and physics, this may be a bit challenging, but certainly not entirely over your head.


NOTE: You should download the supporting document and slides (you should download the MathType fonts here). This will help you learn faster!


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  • ChevalN2Cheval Why not null?

    I'm getting the error "Media Failure. Try reloading the page or visiting the main site for assistance." when watching throught the browser.

  • CharlesCharles Welcome Change

    This could be due to transient networking issues on your network. It works fine for me on my home DSL via Earthlink... The files are on the servers Smiley


    What version of Silverlight are you using? Which browser?


    What happens when you click Media Downloads and choose WMV?


  • Awesome! I never thought we'd actually get to hear Brian riff on this topic, it's great that MS and C9 give their uber brains the time and platform for these kinds of videos. This has been a vintage year for Channel 9 and it's merry band.

  • AuxonRichard.Hein Read it: ​http://bitc​oin.​org/bitcoin.​pdf

    The video stops playing whenever I try to go full screen in the browser.  Windows 7, IE8.

  • CharlesCharles Welcome Change

    This may be a bug with our player. We will look into this. For now, download the high res version and enjoy full screen in Windows Media Player.


  • CharlesCharles Welcome Change

    This topic is entirely original, by the way. Brian wrote the attached document that provides much greater detail, mathematically, for the beautiful story Brian is telling. Do read it.


    In some sense, the physical world is composed of monadic symmetric fractal structures. Well, that's what Brian's thinking and writing evoked in my simple mind Smiley


    And thank you for the kind words. I have to agree with you: this is the best year in C9's history and the new team is the best ever. I've been a member of all iterations of the C9 Team and this group simply represents the most creative and capable to date. Further, the content quality (and quantity) that is created by folks not on the C9 Team is just stellar. I'm loving this.


    You will see and hear Brian again on Friday as he talks to me about Complexity in the latest edition of C9 Conversations. C9 Conversations is a new series that will focus on big problems and the big brains trying to solve them - all in a conversational, well-produced, unscripted, real way. Consider it C9 Classic++




  • Sparkywil2300 Super #

    His interview with Erik on Rx was wicked. Looking forward to this one!

  • I'm working on the concept that a monad is a "coordinate system," and that going from one monad to another is analogous to a coordinate transformation. If this concept is right, then covariance and contravariance will just "fall out" the way they do in physics. A good friend of mine has shown me how to do the "chain rule" in the lambda calculus, so I think we can close this all up. It will be a LOT of calculations, but calculations are fun and a really great way to do proofs Smiley  We'll see if this works out.

  • CharlesCharles Welcome Change

    I sense more lectures, dear Brian Smiley




  • I do have the same problem.

    The video isn't Silverlight.


    When I click "open link in new tab" I get windows media player.
    I can use that full screen.

  • Oh my god... all this actually made sense to me.

  • Slight correction -- the galaxy cluster on the first slide is a CL cluster, not a CT (Cerro Telolo) cluster. Here's the data dump



  • That makes the whole thing worthwhile for me.

  • The docx file opens and displays fine, but a few characters in the pptx file show up as boxes. Could you upload a PDF version of the slides? Smiley

  • I can't download this AVI. The downloading stops after a few minutes (Using IE). Same if I use the Silverlight player. I live in Australia and have no problems downloading AVI's from other sites (.NET Rocks, IT Conversations etc.)

  • CharlesCharles Welcome Change

    This could be due to our CDN. We will find out.


  • ChevalN2Cheval Why not null?

    Transient networking issues? Probably as my Australian ISP is currently upgrading their network and hijacking the DNS service.


    Browser? Silverlight is 3 and it happens in both IE8 and Firefox 3.5.5.


    > What happens when you click Media Downloads and choose WMV?

    I only get 33MB of the file and the download quits.


    Oh well, I was really looking forward to this.

  • CharlesCharles Welcome Change

    The boxes are supposed to be math symbols but aren't since the required font is not on your machine. You can get the font by installing a math program... Brian knows the exact one.


  • MathType from dessci dot com I believe will let you install the proper fonts for free. Turns out the boxes are just equals signs with little deltas on top, meaning "defined as," meaning it's not only an equation but a definition of the symbol on the left-hand-side.

  • Ah yes, searching for "MathType font installer" on the web and then install the found installer solves the problem. Smiley

  • Brian,


    Hope this post isn't too late. I'm reading through the attached paper and having trouble in the "Transformations, Jacobians" section (and in the example that follows). your definitions of "bold x" and "bold y" look infinitely recursive to me:


      x = X . y

      y = Y . x


    In the example, I find the same thing when defining x1 (squiggle) and x2 (eta). They are defined in terms of y1 (rho) and y2 (theta). y1 and y2 are then defined in terms of x1 and x2!


    I am sure I am thinking too operationally here but any enlightment would be appreciated!



  • Hi, Justin -- think of these as formulas-to-evaluate or equations-to-solve rather than as definitions-qua-rewrite rules. If you happen to have the values of the coordinates of some point in rectangular coordinates, then use the rectangular-to-polar conversion equations to get the values of the coordinates of the same point in the polar coordinate system, and vice versa. Ditto the Jacobian equations. Operationally, use ONE of the pair as a definition and then think of the other of the pair as the inversion of the definition, that is, the solution of an equation. Since these coordinate transformations are one-to-one and "onto" functions; that is bijections; that is invertable (except at singularities), then you can invert these equations almost everywhere on a manifold, so it doesn't matter which of the pair you pick as the "definition". Hope that helps!

  • That does help a lot - thank you!

  • Thanks for this wonderful lecture.


    As a side effect  Wink , the lecture and the paper gave me a good enough refresher on derivatives that I was able to solve project Euler’s problem 262. http://projecteuler.net/index.php?section=problems&id=262


  • Brian,


    Have you seen Conal Elliot's paper "Beautiful Differnetation"? It doesn't talk about co- or contra-variance, but he does go over a lot of the same differentation you & Erik covered in your paper:





  • Thanks for the link, Justin. I haven't seen that paper and will take a look!

  • Uplifting experience to see concepts the software engineering  which is more than bunch of   “if thens  and while loop”. Thank you  Brain  and Charles

  • Pascal De Laetpaxal Pascal


    Can you satisfy my curiosity on this point ?

    Can I supose that programming without Monad(s) is like using a "flat space"  (in your universe) ?

    (The deal with "the gravitation and the relativity theory" seems like the  deal with "an effect/Rx system and a pure functional programming style").




  • This is great, but is there any way to read the supporting document on a Mac? Word 2008 complains it has "Word 2007 for Windows" equations in it, so it doesn't display the equations. PDF? Word 2008? 

  • Alex WykelProtoBytes Proto-Bytes of AW Proto Code, Inc

    Today7 the spacks jumped circuits and crosss polinated.  See my opst at: http://tinyurl.com/34eqrjv relateds to my unifide thery ofquantium tansidential fluid space mathematics.,




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