Author Archives: Anton

toon trek

A few years ago I decided, having got behind and lost the thread of my favorite webcomics, to start them over; and then developed a more quixotic ambition: to sample as many webcomics as I can find and, more daunting, to catch up (eventually) on the good ones.

I sort the bookmarks by date, and read the oldest first. (I conceived that practice in the early days when crossovers were common.) At the moment I’m twenty years behind; if I can maintain a pace of three days per day, I’ll catch up in ten years.

sic transit

A recent update of WordPress has broken a few things around here. Noticed so far: the Classic Editor can no longer save or preview (error 406); and the sidebar does not show up in single-article display.

(later) And the comment form is gone. Argh. Time to look for a theme that I don’t hate, until I get around to learning how to make one properly.

31 frets

Here is the neck of a guitar that I’d like to have made someday, if I should ever develop the dexterity to make it worthwhile. The blue stripes show where standard frets would be, for comparison.

The tuning is my tweaked version of meantone: compared to just intonation, each factor of 2 is sharp by 1/16 comma, each factor of 3 is flat by 1/8 comma, and each factor of 5 is sharp by 1/4 comma. (A comma is the difference between 64:81, the Pythagorean major third derived from compounding fifths, and the more harmonious 4:5.) This makes the thirds and sixths much truer than in equal temperament, and the fifths slightly truer than in traditional meantone, which puts all the error in the 3s.

This design has 31 frets in the first octave: 12 flats, 7 naturals, 12 sharps. The bent frets span the difference (~151:152) between 18 of my sharp octaves and 31 of my flat fifths.

To reduce crowding, the second octave has only three flats and three sharps. The bent frets span the difference (~50:51) between G♯ and A♭.

The charts below should look familiar to players, if you squint a little.

coming in the side door

Spam comments on this blog have always been concentrated on a few old posts, so I tried disabling comments on some that look unlikely to ever attract legitimate comments.

Didn’t work. I guess all that happens when I unclick “Allow comments” is that the comment form goes away, without closing whatever channel the bots use.

how to enact a balanced budget

(Moving here from a separate file for greater visibility.)


Suppose each member of Congress were to name a budget amount, and the median number is made law. Why the median? Because this is a number such that half the members have approved at least that number.

Of course, this number is likely to include a deficit. What to cut?

There are 435 numbers for each budget item. Let B(i,m) be mth-lowest amount chosen for budget item i; let T(m) be the sum over i of B(i,m). Let k be the highest number such that T(k) < revenue. If each budget item is enacted as B(i,k), then the budget is balanced. (Of course, if B(i,k) is higher than the median in one house or the other, it must be lowered.) This rule has the effect of temporarily requiring a supermajority for spending. Congressmen won't gain by inflating their numbers; that would just lower k. Pork-barrels would be highly vulnerable to clipping, while programs backed by a consensus would be immune.