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1. Although as I think about it, this may only be valid on the right side of the spectrum given the data points.
9,977 karma · joined October 22, 2010
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1. Although as I think about it, this may only be valid on the right side of the spectrum given the data points.
These sorts of things are loads of fun to implement to get a closer feel to bare-metal programming. XKCD published a 16-bit “CPU” machine language 15ish years ago and I remember everyone was rushing to do code golf implementations of it, although I think a slower-paced approach to the project is better for the educational aspects.
When you read about people coming to California in the 60s and 70s (and somewhat in the 80s), it had that same magical quality that Burning Man had in the early years and has suffered the same kinds of changes. I wonder what the 2026 equivalent of going to California is now, if such a thing even exists or can exist.
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1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
And for all the people who are concerned about how sin' 2πx = 2π cos 2πx, in actual code, it doesn’t matter. Let’s say that I’m writing a basic graphing function and I want to be able to display the slope of the sin curve at any point.
I am not going to expose the turn-based units to the user. Caring about slopes implies that I’m doing calculus and thus assuming radians. So even though my internal values are [0,1], I will label them as [0, 2π] (and the actual numeric values on the display may actually be something like [50,450] which is yet another numeric value we don’t display). So to get the slope at π/4, I’ll calculate cos_t 0.125 and display that value.
We do all kinds of unit translations in computing without worrying about it. This is just another case of that which observes that numerically speaking, using turns is better aligned with the underlying numerical algorithm for calculating trig values.
It’s not a call for someone doing calculus or solving differential equations to abandon radians, just for the particular case of getting a numerical value for sin, cos, etc. from a library, having direct access to a turns-based function would produce faster code and also avoid some of the rounding errors that come from that π/π not to mention the imprecision of any angle that isn’t 0.
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1. I know at least one of these came from porting lesser-known utilities to VM/CMS. By that time, DEK already had adopted a practice of having his secretary print his emails and he’d hand-write a reply and you’d get it in the mail.
I’m still annoyed that thanks to a missed payment, I lost quixote.com.
It would also be nice to have a configurable transportation choice for the time to leave notice. Because some things I’ll walk to, some I’ll take transit and some I’ll drive and Apple seems to want be to just pick one and only use that.
My other map complaint is that there’s no indication of how much tolls are when comparing toll vs non-toll routes. Because if it’s $5 to save ten minutes, no thanks but for a buck, maybe I’ll do it.
Improvisation goes back as far as music and even some classical music has improvised elements (cadenzas were traditionally improvised before they became commonly notated, Baroque music scored for continuo essentially provides a bassline and chord changes, albeit the chords given in an archaic form (figured bass) that is not widely known by contemporary musicians.
The most amazing improvisers, it turns out, are professional church organists (think the ones who work for the largest churches/cathedrals, not the grandmas playing a church warbler at the corner parish, but sometimes them too). When I auditioned for the Holy Name Cathedral Choir, I wanted to sing a piece by Massenet, but I had lost my original sheet music halfway through trying to transcribe a cleaner copy so I had a melody line and only a few parts of the piano accompaniment. The (assistant!) organist who accompanied me at my audition site-improvised an accompaniment for the piece that was, in my opinion, actually better than the written accompaniment I had lost.
That said, being able to read music can be a sort of superpower. So many times on church gigs, I’ve had guitar players be astonished by my ability to pull chord changes out of piano/organ parts without notated chords. Certainly, some aspects of music are hard to convey in notation. Swung rhythm is a particularly notable case where you’re playing something halfway between a triplet rhythm of ♩♪ and a dotted rhythm (insufficient Unicode to write a dotted eighth followed by a sixteenth). The early transmission of jazz music to European composers by way of sheet music led to them missing out on the rhythmic aspects but picking up some of the harmonic novelties. A common injunction to musicians is to play the music, not the notes.
It’s kind of weird that this area that I was only aware of because I like studying maps has popped up a whole bunch in the last few weeks.