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.
it has no wheels so it is just dragged, maybe behind a horse but people can drag them too. horses walk and carriages roll, so it's not really between them. it's the asymptotic limit as wheels shrink to zero.
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.