Who do we have to blame for cos⁻¹𝑥 meaning the inverse function (arc cosine), but cos²𝑥 meaning the square of the cosine?
Today I did a little reading in Florian Cajori's "A History of Mathematical Notations" and found that it's none other than William Herschel (discoverer of Uranus.) He acknowledged that that the superscript notation already meant exponentiation, and thus that cos⁻¹𝑥 already meant something different, but insisted that the right thing was to use superscripts for iteration and inverses. After all, we already used 𝑑², 𝑑³, etc. for iterated differentiation (so if you want to blame Liebniz instead, I guess that's fair.)
And so we got stuck halfway, because inverse sine is useful, and sine to a power is useful, but iterated sine not so much.
People constantly hate it but the standard has been established because alternatives are either not solving everything or only nieche cases or completely fall on their face once they encounter something they weren't designed for...
For better or worse...
Like #Tablature, the #init script of #Notation: It gets people started but fails for anything more complex.
"Bruno Le Maire retient son souffle" (BFM) "le gouvernement en apnée" (Le Parisien)... pas pour les ventes de ses bouquins mais pour la note de l'agence américaine Standard&Poor’s sur la France. Une dégradation serait un choc... surtout pour l'ambitieux ministre de l'Economie. Ces derniers jours, notre grand argentier a multiplié les annonces chocs notemment en proposant de sabrer dans le chômage des seniors. Ceci expliquant cela...
"By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect, increases the mental power." – Alfred North Whitehead (1861–1947) #quote#mathematics#math#maths#notation
One of the most frustrating things for people getting into AI is the amount of math notation involved. To make things easier, I’ve started a series where I explain math notation and show how it translates into Python!
Last week @terjefjelde asked me about my #composing techniques, use of #musicTechnology, and thoughts about #musicProduction, and I promised to reply when I had more time. Here’s a too-long thread about this and other things that came to mind…
One thing I do appreciate about #notation software is the playback feature, which can be helpful for judging questions of pacing, or identifying phrases or ideas that need a little more or less time. It also helps me protect against a worst-case, overly literal, unfeeling interpretation—by demonstrating just what that would sound like. If I can get even the #MIDI playback to sound okay, it’ll surely be safe in the hands of a sympathetic human.
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