Wednesday, March 23, 2016

Some information transfer model basics

I do this kind of thing from time to time to make sure I have everything straight in my own head. There's no reason not to share it with you.






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10 comments:

  1. Tom BrownMarch 23, 2016 at 9:36 PM

    Good... I'm always curious what goes on inside the sausage factory. ;)

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    1. Tom BrownMarch 23, 2016 at 9:41 PM

      ...someday you might be able to scrawl "dD/dS = kD/S" on a check and be confident it'll never be cashed. I'd still contribute to your 401k though, just in case.

      Delete
    2. Todd ZorickMarch 24, 2016 at 8:58 AM

      I admire Jason's courage! Most of the time random scribblings of what is in people's heads would not be so productive.

      Delete
    3. Jason SmithMarch 24, 2016 at 5:07 PM

      I'm not sure I'd use that equation in that way because I didn't derive it -- it's Fielitz and Borchardt's.

      Delete
  2. Todd ZorickMarch 24, 2016 at 9:00 AM

    Perhaps a dumb question so that I can understand- what is the practical meaning of "amount of D" and "element of D" (and reciprocally, "amount of S" and "element of S")?

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    Replies
    1. Tom BrownMarch 24, 2016 at 9:22 AM

      Todd, those are great questions.

      Delete
    2. Jason SmithMarch 24, 2016 at 5:05 PM

      The continuous analog of number of X and unit of X.

      Sum of unit of X up to number of X equals X. Integral of differential element of D up to D equals D.

      Delete
    3. Todd ZorickMarch 24, 2016 at 5:24 PM

      Once again just so I understand the relevance to economics and supply and demand (calculus was a LOOONG time ago for me)- demand for widget (Dw) would be the number of widgets that people want to buy at a given price, and dDw would be how much that changes as a function of time, or supply? Usually the derivative is a function of time (dDw/dt), but it is not clear to me that this is the case- is it dDw/dSw?

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    4. Jason SmithMarch 24, 2016 at 6:00 PM

      With the Leibnitz notation (I.e. dy/dx) you can treat the dy and dx like they are dividend and divisor. It's frequently said it's an abuse of notation, but in most ordinary circumstances it's fine.

      But really, dx is a differential element (an infinitesimal quantity).

      And there's no "usually" for derivatives. You can take them with respect to time, space, other functions... all kinds of stuff.

      In this case you can think of dD as a single widget. But there are so many widgets that dD is infinitely small.

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    5. Jason SmithMarch 24, 2016 at 6:00 PM

      I should say demand for a single widget.

      Or demand event.

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