Mir comments on Subscripts for Probabilities

[Mir]

here’s the non-quantified meaning in terms of wh-movement from right to left:

$S:\underset{\text{image: rain inside your prospective thoughts}}{\underset{}{\underset{\text{image: you thinking}}{\underset{}{\text{I think}\underset{–}{\text{what}}}}\underset{\text{(circumfix time operator)}}{\underset{}{\text{it'll}\underset{–}{\text{what}}\text{tomorrow}}}\underset{\text{image: rain}}{\underset{}{\text{rain}}}}}$

for conlanging, i like${}_{95\%}$ this set of principles:

1. minimise total visual distance between operators and their arguments

2. minimise total novelty/​complexity/​size of all items the reader is forced to store in memory while parsing

   1. every argument in memory shud find its operator asap, and vice versa

   2. some items are fairly easy to store in memory (aka active context)

      1. like the identity of the person writing this comment (me)

      2. or the topic of the post i’m currently commenting on (clever ways to weave credences into language)

   3. other items are fairly hard

      1. often the case in mathy language, bc several complex-and-specific-and-novel items are defined at the outset, and are those items are not given intuitive anaphora.

      2. another way to use sentence-structure to offload memory-work is by writing hierarchical lists like this, so you can quickly switch gaze btn ii., c, and 2—allowing me to leverage the hierarchy anaphorically.

so to quantify sentence $S$, i prefer ur suggestion “I think${}_{55\%}$ it’ll rain tomorrow”. the percentage is supposed to modify “I think” anyway, so it makes more sense to make them adjacent. it’s just more work bc it’s novel syntax, but that’s temporary.

$S^{\prime }:\underset{\text{image: rain inside your tentetative prospective thoughts}}{\underset{}{\underset{\text{(quantifier)}}{\underset{}{{\underset{–}{\text{what}}}_{55\%}}}\underset{\text{image: you thinking}}{\underset{}{\text{I think}\underset{–}{\text{what}}}}\underset{\text{(circumfix time operator)}}{\underset{}{\text{it'll}\underset{–}{\text{what}}\text{tomorrow}}}\underset{\text{image: rain}}{\underset{}{\text{rain}}}}}$

otoh, if we’re specifying that subscripts are only used for credences anyway, there’s no reason for us to invoke the redundant “I think” image. instead, write

it’ll rain tomorrow${}_{55\%}$

in fact, the whole circumfix operator is gratuitously verbose!^[1] just write:

rain tomorrow${}_{55\%}$

$S^{\prime \prime }:\underset{\text{image: rain inside your tentetative prospective thoughts}}{\underset{}{\underset{\text{image: you tentatively thinking}}{\underset{}{{\underset{–}{\text{what}}}_{55\%}}}\underset{\text{(time operator)}}{\underset{}{\text{tomorrow}\underset{–}{\text{what}}}}\underset{\text{image: rain}}{\underset{}{\text{rain}}}}}$

1. ^

   natlangs smh…^[2]

2. ^

   tbh i wish we had an editor w optimised LaTeX keyboard shortcuts so we cud effortlessly use $\underset{\text{or undersets!}}{\text{underbraces}}$ wherever we fancy.^[3]

3. ^

   additionally, we should just make much more use the dimensionality afforded to us by the editors we have.

   it’s free cheap $\stackrel{\text{semiotic}}{\underset{\text{syntactic}}{\text{semantic}}}$ real-estate.

[niplav]

so to quantify sentence S, i prefer ur suggestion “I think${}_{55\%}$ it’ll rain tomorrow”. the percentage is supposed to modify “I think” anyway, so it makes more sense to make them adjacent. it’s just more work bc it’s novel syntax, but that’s temporary.

The principles you propose make a lot of sense! Dropping “I think” or “My best guess” is then for the best${}_{80\%}$.

Also, the underset/​underbraces stuff is promising${}_{55\%}$ but too much to spend weirdness points on${}_{70\%}$.

[gwern]

but too much to spend weirdness points on_70%.

FWIW, I too worried that it would be just too weird, but I’ve been surprised how little pushback, criticism, or even notice has been taken of using subscripts for years on Gwern.net. I see more comments about my using fully-justified text!

[Mir]

did you know that, if you’re a hermit, you get infinite weirdness points?

✧*｡ヾ( >﹏< )ﾉﾞ✧*。