Canonical forms · 9:12am Jul 7th, 2020
Epistemic status: Who knows, but it settles well.
Have you ever been frustrated by the inability of other people to see the things you see so clearly? It turns out there’s sometimes a solution to that. In cases where there isn’t a solution, there’s at least an explanation, so you can comfort yourself with the knowledge that, although you’re losing the battle, it’s a battle against the fundamental principles of thought itself.
Twilight, stop! Winning that battle is worse than losing!
I would break the problem down into these sub-problems:
- Your thought process makes it easier for you to piece things together in ways that others can’t. Solution: use canonical forms.
- You pick up on concepts that others ignore. Solution: provide better context.
- You view the significance of certain information differently. Solution: use better analogies.
If you discard language problems, this list should be complete. I do discard language problems because they’re only interesting when you’re talking to robots, and talking to robots is never frustrating.
This post is about the first item on that list: canonical forms.
A canonical form of X is a standard way of representing X. That means whenever you want to describe X, if you describe it using its canonical form, you’ll always describe it the same way.
Contrast this:“I bucked 27+15+19 apple trees.” This is not in canonical form.
With this:“I bucked 62 apple trees.” This is in canonical form.
Which one requires less mental effort? Less interpretation? Less knowledge? Those are all important when you’re trying to get your message across. Those are the problems that canonical forms solve.
I liken this to the problem of seeing the world through the qualia of a bat. I guess it’s fitting that I discovered the usefulness of canonical forms while studying the Fourier Transform, which is one of the fundamental tools for studying sound. (Bat. Sound. Get it?) The Fourier Transform produces a canonical form for certain kinds of objects in certain kinds of spaces. It’s fundamental to the way we view the physical world. One might suggest that it’s fundamental to our ability to see the physical world in a common way, which in turn is fundamental to our ability to communicate with one another.
Here are some scattered cases where a canonical form would help you describe your point better:
- Your characters all sound the same. If only you could describe why!
- You keep making the same mistake. If only you could describe what it is in a more generally-recognizable form!
- All those stories have the same plot. If only you could describe it without lumping in your favorite stories!
Coming up with the right distinctions to describe your feelings can be hard, and that’s essentially what you’re trying to do. So how do you do it?
I’ll start with the suggestion that no one wants to hear. It helps a lot to know more math. Large chunks of abstract math are basically canonicalizations of common thought processes. That means if you have two thoughts, math can tell you if they’re really just one thought with two different masks.
Who’s under the mask? It’s math! Yay!
Second, don’t just think about the one thing you’re trying to say. Think about the space of things you could possibly say, and think about what makes each thing unique. Don’t think of a single character and how it speaks, think of what makes character speaking styles unique. Don’t think about a single mistake, think about what distinguishes different kinds of mistakes. Don’t think a plotline in isolation, think about what the plotline does and doesn’t encompass.
Third, think very hard about which space of things you’re talking about, and be consistent. Why?
Contrast this:Blueberries are nice because you can give them to someone you love.
Pineapples are nice because they taste like a vacation.
Which is better? Blueberries or pineapples? I need a vacation… but I also want to hang out with someone I love.
With this:Blueberries are nice because they taste like a summer day.
Apricots are nice because they taste like a spring day.
Which is better? Blueberries or apricots? It feels like a spring day.
When you put things into a common space, it’s easier to make sure your distinctions are actually distinctions and not just associations. With distinctions, you can very clearly state that you’re talking about X and not Y. With associations, everything gets muddled into heuristics.
Fourth, have fun! This is hard to do, which sucks unless it’s fun.
Yes, I know 27+15+19 isn’t equal to 62.
Thanks, B, for getting me to write this.
Useful shit. We take failure to be fated and troubles with others to be beyond us. Truth of the matter is one needs to break from the scene and analyze what happened, why others didn't get it, how you explain it to how certain people receive information, addressing every aspect in play. I would have never broken this down so technically. Which causes me to be glad in someone taking a new approach with all of this.
Feelings are clue to a deeper thought process. Characters feeling they sound the same is felt by a collection of cues. One searches and condenses to the theme holding multiple problems in a vase. You're far more concise than I ever could be on the matter. For your first blog this was quite good. Don't forget, however, to go loose from time to time. You're allowed to be experimental due to the nature of the website.
I do hope to see more from you homie.
~ Yr. Pal, B
This was the most unique way I have seen some one explain this topic.
I would like to see you continue to make blogs like this, as I enjoyed this one quite a bit.
You do plan to do more, right? Pretty please?
This is pretty smart, thank you for sharing!
Something I noticed about your examples is that the better-sounding ones are also the shorter ones, in terms of word count. Whenever I want to try and explain something to someone, I find that being as brief and concise as possible is the best way to do it. Less words = less to potentially get confused or lost about.
"Brevity is Wit" as the phrase goes.
Okay, I am home, which means I can make a more substantial comment.
The part that comes to mind in this blog is how you explain breaking down your perspective into simpler concepts. You might be right on the nail with what you're saying, but because of how it is worded, the other party will end up lost on what you're trying to say. Phrasing in your explanation is an important factor to consider. That part is what stuck out to me the most, because it is something I have been employing as of late as I do the most productive thing on the internet: debate!
I never seen a mathematical approach to it explained, and honestly it was a breath of fresh air on a well talked about topic.
As such, I implore you make more blogs about topics that interest you, as I believe you'd have a unique perspective to share that I'm interested in seeing.
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Thanks for the feedback, and that's a great point! I think that's incidentally related to canonical forms. The shorter examples tend to be shorter because they're more self-evident and require less explanation. Self-evident statements are usually a strong indication that you've found the canonical form of what you're trying to describe.
For clarity, was the fruit example the most difficult to follow? My canonical form for that one is actually a 3D picture. I'm still trying to figure out the right way to translate such thoughts into words.
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I've also been thinking a lot about how to decompose concepts and systems. That's one of the most broadly-useful techniques I've discovered. At some point, I want to make a post on why I say things like
"If you discard language problems, this list should be complete."There's a perspective from which decomposing concepts and strategies becomes way easier.And yup! I intend to write more. I have a giant (and growing) list of topics, and I want to figure out how to write about all of them. I'm going to aim for two posts a week.
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Thanks for that
. This is going to sound stupid, but that had actually slipped my mind. Now that you mention it, I want to develop a style for interleaving exposition and poetry. I think the blueberry line was my subconscious' way of getting started with that.
I want to try out a bunch of practical things too, which probably won't look experimental unless you have access to my secret document. This particular post begins with what I think of as the standard format for brainstorming, and it ends somewhere I don't quite know. This format is something I'd like to develop too, and it'll take some work.
Side note:
Those two sentences are really pretty near each other. The first one justifies and elaborates on the second. The second is also a great example of what the first is talking about. The visual of problems in a story as flowers in a vase feels right for reasons I want to understand. The notion of condensing a theme by considering multiple problems simultaneously feels like it's grounded in something very deep and very true.
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I feel like the fruit example was easy to follow! And what you say about self-evident statements makes sense, too.
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Awesome. I look forward to seeing them, bro!