I am off in a ninety minutes to spend five hours canvassing for Ryan Watts here in the NC 6th. Actually, the canvassing will only take three hours, but I live at the eastern end of the 6th and we are doing our door-to-door in Greensboro, at the western end, so it will take me an hour to get there and an hour to get home.

Meanwhile, all hell is breaking loose at the national level. I think if Dr. Blasey Ford testifies on camera, Kavanaugh will go down. As for Rosenstein, the fact that Trump has not summarily fired him says a good deal about how vulnerable Trump is.

With all of this going on, I am preparing to lecture on Tuesday about the ideological significance of linear homogeneous functions. How weird is that?

## Saturday, September 22, 2018

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## 6 comments:

I hope that the canvassing goes well.

What are linear homogeneous functions and why are they ideological?

Yes, there is an article explaining them in Wikipedia, but it's way over my non-mathematical head. So if someone could explain them to a person whose mathematical abilities haven't advanced since junior high school (and may have declined actually),

I would be very thankful.

Prof. Wolff, Ben Carson is now blaming Prof. Ford’s allegations against Judge Kavanaugh on you and other socialist sympathizers. Aren’t we fortunate to have such astute political analysts in our seat of government?

I'll take a stab at "linear homogeneous functions," which appear to be bread and butter for economic analysis (which is where I suspect we discover lurking ideological distortions). The common example is manufacturing, for which a production function determines how all inputs will produce an output. Consider input variables for manufacture of a widget, say, capital and labor. The function says some amount of capital combined with some amount of labor will produce some number of widgets. A linear homogeneous function occurs when multiplying each of the inputs by a constant--say, doubling labor and capital--increases the number of widgets by the constant--in this example resulting in twice as many widgets. The function is "linear" because the exponent of the constant is 1. If the constant were 2, then 2 raised to the power of 1 is still 2. But if the function includes an exponent greater than 1, say n, then we say the function is homogeneous of degree n. As an example, if doubling capital (C) and labor (L) produces not just double the number of widgets (W), but eight times the number, then

2C + 2L = 2^3W [This is sloppy notation, because the function doesn't literally add capital to labor. For the sake of a simple example, however, it's more clear than the notation correct notation. Here, 2^3 means 2x2x2, i.e., 8.]

...that is, n is 3, and the function is homogeneous of degree 3.

Sort of, but not quite. Maybe I need to post about this.

That would be great if you could post about it, but as the lawyer says in the movie Philadelphia (which I assume you saw), explain it as if you were explaining it to a four year child.

Yes, please do. I'm interested in both a more accurate description of the function and in its ideological aspect.

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