I was confused about what <4> = \lambda ^ 5 4 meant, since it already seemed to have a "4" in it.
The trick is that the 4 seems to be similar to a positional argument index, but numbered inside out.
IOW, in this encoding, <4> is a function that can be called 5 times (the exponent on the lambda) and upon the fifth call will resolve to whatever was passed in 1st (which because of the inside-out ordering is labeled "4").
(For a simpler example, 0 is a function that can be called once and returns its argument.)
So succ is 3-ary; it says, give me a function (index 2, outermost call); next, give me its first argument (index 1, second-outermost call); when you call that (index 0, dropped, innermost call), I'll apply the function to the argument.
But note that if index 2 is a numeral <N>, the outermost call returns a function that will "remember" the next thing passed in and return it after 1 (succ's innermost call) + N + 1 (<N>'s contract) calls.
I think in _Babel_ (and _Katabasis_ as well), Kuang is a bit more prone than Tartt to showing off legit academic tidbits, which gives a nice scholarly glint (the illusion of high-brow? authenticity, dare I say?) to the environment, while not compromising the easy fantasy reading. More details than vibes, perhaps?
(When she gets details wrong, it does break the illusion. Like a small tangent on the etymology of the Greek word for truth in _Katabasis_.)
Oxford also simply has a certain aura for me, being from the US. All in all, I think Kuang's books are great "binge" or "airplane" reads with a smack of academic authenticity.
I saw _Possession_ mentioned elsewhere, which I think does academic vibes _and_ details very and IMO resides in a more refined literary category than either of the two other books. I should reread it!
A bit of a nit, but the 17kb PNG actually looks slightly blurry, or "artifact-ed" on my MacBook screen. Happily though, the author included a section on SVG at the bottom, which was my knee-jerk reaction for the appropriate format for lettering at that scale.
Agreed, not least because:
- area-based visualizations make the effect hard to distinguish; bar charts or data clouds with numbers and confidence intervals would have been way more immediate.
- the colors make the negative group (usually) more visually prominent, since it has higher contrast with the background, exacerbating the area-estimation problem. (e.g. me wondering, "are there more overweight pink people as a fraction of pink people?")
While I agree the LSD is somewhat meaningless, I personally find it fun to test my color matching/mixing. Binary search circumvents that (at least for the most significant digit); though I agree it really only applies for the first and maybe second guess.
For instance, my initial guess was off by (+1,-1,-1,+3,-1-2) and my first impulse was to look at the target and see that I had too much red and not enough green.
That intuition makes a lot of sense to me, especially if I picture the person's frame of reference.
Kind of reminds me (a layman) of winding numbers. I suppose there are topologically inspired variations of this problem that might be even more "paradoxical" (or perhaps just silly). If you moonwalk the second half, you undo your rotation? Or if you follow specially designed subterranean tunnels, you can end up doing 0 or negative rotations!
"Travois" seemed the most interesting one. Based purely on the first page of Google images, it struck me as somewhere between a horse and a carriage, but ever more on the vehicle side.
What a great example! As a recent astronomy enthusiast, I found myself doubting this comment initially ("well, eclipses ARE related"), and this despite the fact that I have a toy tellurion right by my desk.
But hearing a particular phrase in the below video helped correct my model. One sanity check is that you can see non-full moons during the day (although I definitely would have just assumed it was still a matter of angles).
I never did math past linear algebra/real analysis, so the only concept of sizes I have are countable/uncountable infinities.
Apparently the crux of this proof was showing that "the space of all modular forms with bounded denominators" and "the space of all congruence modular forms" were the same size.
I wonder what kind of expression "size" is here. Presumably not some finite integer, nor one of the simple infinities, since their first step was showing one is "a bit bigger" than the other. I wish this article went into more detail on that.
I definitely remember nerding out about modular forms via Andrew Wiles as a younger self.
Of particular note are some reinforcements from Old Norse (circa 850s onward):
- are (displacing bēoþ, sind, and sindon)
- their (displacing heora)
- they (displacing hīe)
As a linguistic game, sounds fun. Hopefully its pupils don't take it too seriously, hem hem, e.g. William Strunk the Lesser: "Saxon is a livelier tongue than Latin, so use Anglo-Saxon words"
I'm from NYC and call it "plain" or "cheese." "Regular" makes me think too hard as to whether the "New York thing" is to say "regular" or "plain." It's also a lot of syllables.
A similar phenomenon occurs with waiting "in [a/the] line" vs "on [a/the] line." I think I say either, but I'm "supposed to" say "on line."
I see this concept often cited when mathematicians talk about how they had a breakthrough on a proof, but I have to say, I don't think I've ever noticed it in myself, sadly.
I have good ideas, and sometimes I need a break before my idea generation is back to a good state. Perhaps this is because I spend most of my time coding on complicated but not groundbreaking stuff.
But a little bit of jealousy certainly at seeing this described as a "universal human experience."
I wish it weren't song-based, though it's an understandable implementation.
As others have noted, there are often many cues 'n' clues even before a single word is uttered. But also, I have trouble enough picking out words in my native tongue, let alone when transmogrified by musical prosody and accompaniment.
Today I learned that Polish sounds nothing like what I thought it sounded like :)
Actually, Americans wouldn't say "fourth July" – that would likely connote "the fourth iteration of July" in some longer timespan (e.g. "In the fourth July of my adolescence").
"Fourth _of_ July" (or "July fourth") are the Americanisms here.
I was confused about what <4> = \lambda ^ 5 4 meant, since it already seemed to have a "4" in it.
The trick is that the 4 seems to be similar to a positional argument index, but numbered inside out.
IOW, in this encoding, <4> is a function that can be called 5 times (the exponent on the lambda) and upon the fifth call will resolve to whatever was passed in 1st (which because of the inside-out ordering is labeled "4").
(For a simpler example, 0 is a function that can be called once and returns its argument.)
So succ is 3-ary; it says, give me a function (index 2, outermost call); next, give me its first argument (index 1, second-outermost call); when you call that (index 0, dropped, innermost call), I'll apply the function to the argument.
But note that if index 2 is a numeral <N>, the outermost call returns a function that will "remember" the next thing passed in and return it after 1 (succ's innermost call) + N + 1 (<N>'s contract) calls.