Roderick Long defines right-conflationism as defending existing economic structures as if they were outcomes of a genuinely free market (what Kevin Carson calls vulgar libertarianism), and left-conflationism as using those outcomes to attack the concept of free markets. I hope my paraphrasing doesn’t offend either of them.

Left-conflationism asks us to believe that Big Business, through its corrupt control of legislatures, prevents political interference in the market and goes no further; that mere market freedom allows it to loot us so thoroughly that it does not seek subsidies or protection from competition.

In MacBSD, the command cal 9 1752 shows the shortening of that month in the British Empire. If I reinstall MacOS and choose Italian as its default language, will the shift show up instead in October 1582?

allRGB: images in which each of 16 million colors occurs exactly once. (Found at MathPuzzle.) I see I’m not the only one to think of the Hilbert curve idea, but I’ll post two others.

In unrelated news, I was surprised today to find some late blackberries, bland but wholesome.

My old calculus book gives a formula for the curvature of a parametric arc in the plane — that is, an arc defined by two functions (x(t),y(t)) of one variable. For thirty years I didn’t think about the derivation of that formula. Just now it hit me (and I did the algebra to confirm) that, in terms of the complex plane (z=x+iy), the curvature formula is equivalent to

Im(z″/z′) / |z′|

This should improve my cubic approximations to transcendental curves.

Read this first.

To throw for maximum distance (on an infinite plane in a vacuum), you aim at 45° elevation; in other words, split kinetic energy evenly between vertical and lateral velocity. (I dimly remember having proven that, but am not awake enough to do it again now.)
It follows that the kinetic energy of a perfect vertical throw is twice the vertical kinetic energy of a perfect distance throw.

The arc of the latter is a parabola, of course, and its height is easily found to be a quarter of its length. Double that, because with double the energy you get double the altitude; and the result is consistent with Munroe’s estimate.

What about air resistance? The vertical throw has a moment of zero speed, but the distance throw’s minimum speed is 1/√2 the maximum; so it seems to me that the vertical throw suffers less air resistance (not even considering the thinner air up there), and therefore the altitude estimate given above is low.

Each month shall have 30 days, except within a lune spanning 157°15′57″ (5.242199 × 30°) of longitude, wherein the month shall be extended by one day which shall not affect the cycle of the week. The lune so affected shall shift westward(?) each month by its own width. The phase of the lune shall be such that, in every longitude, the northward equinox shall fall on the last day of March. (During a transition of roughly two years, each month shall have 30 days without leaps, to shift the equinox from March 21 to March 30/31.)

My computer ran for eight solid days to extend this table from six rows — (2 3 7), (2 4 5), (3 3 4), (2 3 ∞), (2 ∞ ∞), (∞ ∞ ∞), each of which is (in some sense) minimal — to 106, by request. I don’t know why anyone would want all those others; I see no qualitative difference between any of them and one or more of the six.

Now that the run is done, I look again at my code and see where it could be made more efficient, by changing from complex to real arithmetic; I’ve already done that in my other hyperbolic programs, the ones that generate the ribbon patterns.