Monthly Archives: August 2023

Sideband #78: Watch Compass

Long ago (in the first year of this blog), I posted Sideband #34: The North Star, which was about how sighting on the North Star (Polaris) gives you your latitude. Simply put, the elevation of the star is your latitude. My Twin Cities are at 45° north, so Polaris is 45° above my northern horizon. Simple!

In this Sideband, I’ll explain how you can use your wristwatch as a compass. Assuming your watch is an analog one with hands. And assuming you can see the Sun (so this doesn’t work at night).

But, unlike North Star navigation, this one does work in the southern hemisphere.

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Musical Scale Modes

Mathematician and educator John Baez has been putting out an excellent series of posts about music theory on his blog. The most recent, the seventh, is about how you can generate scales by picking out piano notes in intervals of fifths. What’s interesting is that you can generate all seven major scale modes in each of the twelve keys (a total of 84 scales).

It’s very cool (and new to me how this works out), and John asked if any of his readers would be interested in creating a table of all 84 rows. That’s exactly the sort of little project that often catches my eye.

A new and different problem to solve!

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Friday Notes (Aug 18, 2023)

We’re about to enter a new phase of Friday Notes. I’ve cleared most of the primary pile of notes for blog posts. What remains are notes that still might lead to posts if I find the motivation. There is also a thick sheaf of much older more ambitious notes, most of which are probably past their Use-By date by now.

The destiny of that thick sheaf remains to be seen, but I recently dug out an even older set of notes. Two old spiral-bound half-sized notebooks… from the late 1970s and early 1980s! One contains thoughts and ideas, the other fragments of song lyrics.

I haven’t looked at this stuff in years. Going through it, I decided to record some of the more interesting in blog posts before I toss those notebooks.

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X to the Zero Power

At some point in our early math education, we’re told that anything to the power of zero evaluates to one. 1°=1 and 5°=1 and 99°=1. Basically, x°=1 for all x. It’s typically presented as just a rule about taking anything to the power of zero, but it’s actually derived from a more basic rule about exponents.

Thinking about x° in connection with something else recently, it occurred to me there’s a second way to justify the notion that anything to the power of zero is one.

It also occurred to me 0 might be an implementation of the Dirac delta.

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The Dozen Year Charts

Last month when I published the Blog Anniversary post I lamented how yet another WordPress “update” had made it harder for me to copy the monthly post hit stats to my SelectedPosts database so I could make charts. The new table widget doesn’t allow selecting and copying [big frown].

Turns out my browser can be cajoled into making a screen grab that successfully interprets the image as a table with text, so it’s possible to capture the data, but looks to be a royal PITA, so it may be that the monthly hit stat ship has sailed.

But then I realized I had yearly hit stat data readily available.

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