Using the number of length and time factors in a type of unit to place that unit type horizontally and vertically respectively in a table, and creating a table for each of the five other factors, about fifty classes of units or physical quantities can be arranged in a stack of tables whose geometric relationships define algebraic relations and possible classes of dimensionally valid physical equations.

Here are two single-page versions of this arrangement of physical unit classes:

Physical Units Factor Tables / Large Print

Physical Units Factor Tables

Thermal units don’t fit neatly into this scheme, but I have noted some of the more important ones in a text box.

The names of the unit classes are from Alan Eliasen’s physically typed language / Swiss-Army-chainsaw desk calculator Frink. Names in parentheses are not defined in Frink, but still work in calculations.

]]>Is my understanding correct?

Yes, that’s right.

There are many things to say here, but I’ll just say three.

1) For the circuits we’re talking about now, the directions on the edges are not really important, since resistors, capacitors and inductors don’t have a built-in directionality. For diodes the direction would be important: if you turn around a diode on an edge you get a different circuit. But it would never make sense, for electrical circuits, to require that output terminals have no outgoing edges and input terminals have no incoming edges. For diodes this restriction would actually eliminate some interesting circuits.

2) For the circuits we’re talking about now, the distinction between inputs and outputs is purely conventional; the categories we’ll be talking about are all dagger-categories, meaning we can switch what we call the input and what we call the output. Later in the seminar, when we get to control theory, we may meet some categories where the inputs are truly different from the outputs.

3) It’s tempting to use zero-resistance wires as identity morphisms. However, we’re avoiding zero-resistance wires in our formalism because they behave in a singular way (a ‘short circuit’). We can avoid zero-resistance wires without loss of generality because whenever you have a zero-resistance wire in an electrical circuit, you can collapse that edge in your graph and get rid of it, obtaining a circuit that behaves the same way.

But if you allow zero-resistance wires, you can take any electrical circuit, add extra zero-resistance wires at the input and output terminals, and get an electrical circuit that behaves in the same way but obeys the restriction you mention.

(Later I’ll make the concept of ‘behavior’ precise; for now people can read about it in the paper Brendan and I are writing.)

]]>This suggests to me that your resulting category will be quite different from the various operads of wiring diagrams that David has been studying. He has several.

]]>https://plus.google.com/102162264382073173725/posts/3BcdQCdYz1U ]]>

With luck, this video will be the first of a series. I’m giving a seminar on network theory at U.C. Riverside this fall. I’ll start by sketching the results in this new paper:

• John Baez and Brendan Fong, A compositional framework for passive linear networks.

It’s a big paper, and I also want to talk about other papers, so I certainly won’t explain *everything* in here—just enough to help you get started! If you have questions, don’t be shy about asking them.

In this first seminar, I start with a quick overview of network theory, and then begin building a category where the morphisms are electrical circuits. Here are some lecture notes to go along with the video:

• Network theory (part 30).

]]>* Some problems in integral geometry and some related problems in microlocal analysis *, Am. J. Math. 101 (1979) 915–955, MR 0536046.

Weinstein seems to have published the idea only in 1981:

*Symplectic geometry*, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 1, 1–13.