Shapes and colors · 6:46am Jul 24th, 2020
I find myself fascinated by coloring problems. There must be something interesting going on if you can color the shapes in a picture just as you can color your words with emotion, or color someone with your opinions.
I think it’s worth investigating!
If you go deep into the forest of mathematics, you’ll soon discover a creature colloquially known as a morphism. You can’t see a morphism the same way you can see an object, but at the same time, you can’t see an object without a morphism.
Morphisms are transformations. You don’t observe any physical object directly. You observe the vaguely object-shaped light that physical objects emit. There’s a transformation from the object’s shape to the light it emits, and that transformation retains the outline somehow. There’s a lot more to physical objects than just the colors they emit, but the colors are one thing we have to work with.
You can see the color of lots of things because you can transform lots of shapes into lots of observations. You can add color to lots of things because you can tune what people observe when they look at objects. And every time you sit back and view the colors, you’re getting some sense of the shape of what’s beneath.
- If you color a sculpture, then the paint on the sculpture reflects the shape of the sculpture.
- If you color a story with emotion, then the emotions reflect the shape of the story.
My instinct at this point is to note down a few techniques on how to use this fact to become better at seeing colors and shapes or to become better at adding colors to shapes, but I don’t want to fall into a pattern with that. If you want to post your ideas in the comments, I can help expand them, give them shape (recursion intended), and maybe make them more intuitive.
Since you can talk about that, I’ll instead quickly point out one of my personal favorite things to do with colors: strip them away.
While colors are useful for a lot of things, colors are fickle. They change as the person viewing them changes, and they change as the lighting (context) changes. The underlying shape does not.
“The necklace hung proudly on Trixie’s neck. Victory never tasted so sweet.”“The necklace hung proudly on Trixie’s neck. Was it really worth her soul?”The shape of that first sentence captures a lot less than you might intuitively believe.
You can identify shapes as the things that don’t vary with context. They’re the things that, if you change them, they’re just not the same anymore. In the same sense that a sphere and a cylinder have some shape in common (a circle), different sentences can have some shapes in common.
One easy way to figure out whether two sentences have some shapes in common is to see if you can play around with the context to make the two sentences feel the same.
“Fluttershy sunk her teeth into the apple. She breathed a sigh of contentment, wanting never to let go.”“She took her first step into the shadow. Away from the Sun’s judging eye, at last she felt free.”
Somehow those first sentences can be used interchangeably to mean the same thing (“Fluttershy released her inhibitions”), as long as you adjust the surrounding sentences appropriately. This is similar to how viewing two objects under different lighting and from different angles can reveal their commonalities.
I’ll note that you can’t do this with all pairs of sentences — a hint that there really is something other than context that distinguishes sentences, at least within our Western framing.
“The necklace hung proudly on Trixie’s neck.”“Rarity ate lunch with Fluttershy.”There are no contexts that make these two sentences mean the same thing.
I leave you with that observation. I find this to be a fascinating tool for understanding all sorts of things more mathematically, including language. Maybe you will too.
OMG you just applied category theory to literary device.
You really need more followers. Hmm.
Huh. Fascinating way of looking at mood and phrasing. Thanks to 5320587 for pointing me to this.
"The Nobull prize hung proudly around Trixie's neck on a golden chain, much like an anchor would hang on a leaky rowboat, threatening to drag all it touched to the ocean floor and certain death."
5320587 5320709 Ditto here.
5320587
If you think of anything else that people generally believe is completely outside the realm of abstract math, I'd like to hear it. Whatever it is, I'll see if I can show that the two are deeply and inextricably connected.
5320709
Thanks!
5320748
This is unreasonably fun.
"It's just turtles all the way down."
"It's just sets all the way down."
I daresay you're right, they are interchangeable.
...
Filly, on failed algebra exam a few months later "Hence we see we can endow the turtle with a replication operator, forming a reptile group..."
"The necklace hung proudly on Trixie's neck. As yet, its commands were trivial, but it felt sure that, given a little time to work on her mind, it would be able to direct her to just about any task… for good, or for ill."
See, you can have a bit of fun by taking the sentence literally
ohhhh, nooo. I am so terribly sorry.
"Rarity ate lunch with Fluttershy. Picking yellow feathers from her teeth, she bowed her head and accepted the Order Of The Pegasus Nommers, a piece of tacky jewelry awarded by the Overly Edgy Bureau to honor services to terrible and hypothetical examples. She looked up, hearing the trotting of hooves, as another unicorn entered the room."
"The necklace hung proudly on Trixie's"
no no oh HELL no. I regret accepting this challenge, even if it wasn't a challenge. whoof.
...Yes, I do believe I shall be following Trick Question's advice and following you. :)
You may or may not find the Watson Tone Analyzer interesting
Ages ago I ran it on the opening para of one of my stories:
drive.google.com/uc?id=0B_m5Oeb6ax3-STdvYy1MdEVLRkE
I don't think it understood bore.
5321378
I do find it interesting! I don't see documentation on how its innards work, but I can guess based on its results.
When you ran it back then, it associated each word with a sentiment. Bore is often used to mean stare intently, which I'd guess is why it's classified as a negative emotion. It didn't look at context at all to understand how the word was used. This used to be common when analyzing things like tweets and news articles. It does a really bad job on a word-by-word basis, but it does passably well on the aggregate (for things like tweets and news articles). By "passably well," I mean it's something like 70% accurate (i.e., a bit better than chance) at stating whether a message is positive or negative. It was used for things like market research and reputation monitoring, where getting something statistically correct is good enough.
They actually messed up the implementation when you ran it the first time. They should have removed words like the before running their algorithm. I'm surprised they didn't catch that because it's very obviously just adding noise to the results...
The state-of-the-art has gotten way better in the last few years. People figured out how to represent sentences rather than words, include contextual information properly and build on existing tools more intelligently. The caveat is that the newer techniques no longer give concrete word-by-word information.
I don't know how much of the state-of-the-art the current tone analyzer uses. The good techniques are very expensive, so I would guess that it uses a stripped-down version of them. I tried running the same text through the tone analyzer just now and got these results.
It's much better now than it was when you first ran it, but the results still don't look that good. It mainly suffers with Joy and Sadness. If anyone here has the time and motivation, I'm curious to know how well https://github.com/huggingface/torchMoji does on the same task. I expect it will do much better, and that it will give much more precise tone information.
5322302
Joy/sadness: I was shooting for a wabi-sabi mood, so maybe it’s not that far off when taken as a whole. Of the two, it missed the mark on joy, for both sentences tagged solely with joy are, or my intent was, more about the inevitability of death; hardly joyous.
Glad you found it stimulating.
Glad to see you getting more of the attention you deserve homie.