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(This one is longer than the usual post; I recommend reading directly on Substack instead of in your inbox by clicking the title above. I’ve grouped it into sections for those who prefer reading in multiple sittings.)

As always when something is a prerequisite for itself, you have to proceed in a spiral. An approximate understanding of a small part of the subject makes it possible to grasp more of it, and thereby to revise your understanding of the initial beachhead. You need repeated passes over the topic, in increasing breadth and depth, to master it. -David Chapman, Ontological Remodeling

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I want to talk about the modern crisis of meaning. With our powerful computers and modern scientific techniques and access to all sorts of media, why is it so hard to figure out what’s actually

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? I think a major reason is a lack of emphasis on representation: that is, how we choose to describe the world in the first place. We evaluate effective representations and ineffective representations side-by-side without distinguishing between them, hoping that truthfulness for one maps to the other, and instead are left only with confusion. 

This is a hard thing to talk about, because a “representation” is a concept that I must represent effectively to you. The whole problem is that we’re not used to talking about representational issues, but talking about representational issues is an example of a representational issue. So I can’t describe the problem to you without solving it; it’s a prerequisite for itself. As such, we’ll take Chapman’s advice and proceed in a spiral, insinuating our way towards the subject rather than rushing it head-on. (I’ll also have to gently mislead you for a while, though I promise to fix it before the end.) 

. Rabbits, Adams tells us, can’t count higher than four. It’s not that they only have memory for four things; Hazel, the leader of the novel’s band of rabbits, has more than four followers, and he knows all of their names. But rabbits never

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“We’re agreed, then, that we ought to send an expedition to this warren and there’s a good chance of being successful without fighting. Do you want everyone to go?” “I’d say not, ” said Blackberry. “Two or three days journey; and we’re all in danger, both going and coming. It would be less dangerous for three or four rabbits than for hrair. Three or four can travel quickly and aren’t conspicuous: and the Chief Rabbit of this warren would be less likely to object to a few strangers coming with a civil request.”

“Everyone” is a concept Hazel understands just fine, even though more than four rabbits are part of the “everyone” that lives in his warren. But if Hazel was asked exactly how many rabbits went into this “everyone”, he couldn’t say. What matters to him here is that four rabbits can travel more carefully than

Ends up being five or ten or twenty. For the case of “how many rabbits ought to visit the other warren?”, there’s no need to count higher than four.

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Isn’t sufficient. Suppose there’s a log that could be used like a see-saw to open up a new feeding ground, but requires at least eight rabbits sitting on one end to make it move. We tell Hazel to have his rabbits sit on one end to see what happens, and he responds “I’ve already tried having

Get a group of hrair rabbits. Have each of them choose a different rabbit not already in the group. This is two- hrair.

Is a concept worth remembering.  Does this mean Hazel learned to count to eight? Not really. He can’t tell in advance whether he has two-

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Worth of rabbits, and he can’t reach the intermediate states of five to seven. But clearly, if Hazel remembers the trick of “when

The word we’re reaching for is ontology, a jargony philosophy term that can be more or less understood as “the list of things in a category” or “the list of answers to a question.” Before, Hazel’s list of options for “how many of a certain thing is there?” was this: {one, two, three, four,

Is a lot less general than the other entries on the list, because it can only apply to rabbits that are working together and following the same rule. One, two, three, and four are numbers,

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Is just a new answer that’s potentially available for questions of the form “how many—?”. Nothing says it has to behave like the other answers, or be available for all potential “how many—?” questions that come up. Take note of that asymmetry before continuing on: all numbers are answers to “how many—?” questions, but new answers to “how many—” questions don’t need to be numbers. 

Game A: Would you trade away four value-units for a 25% chance of having five value-units? Game B: Would you trade away four value-units for a 25% chance of having one thousand value-units?

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A lot of modern discussion of uncertainty works by asking these sorts of questions and finding answers that are as objectively defensible as possible. I don’t want to get into that, so I deliberately chose payoffs extreme enough that the answers are pretty obvious. Game A stinks, whether the value units are dollars or candy bars; Game B is incredible unless you only have a few value-units and will instantly die without them (vials of insulin, for example). Imagine we’re all sitting around a picnic table, coming to a quick consensus, when a couple of rabbits hop nearby. We want to get their input, so we translate our questions into Lapine:

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Game A: Would you trade away four value-units for a 25% chance of having hrair value-units? Game B: Would you trade away four value-units for a 25% chance of having hrair value-units?

They look at us with their confused little bunny eyes and ask, “Sorry, why did you describe the same game twice?” Lapine cannot

Won’t help: metaphysical value-units aren’t the same thing as conscious and cooperating rabbits, so we can’t run the process to get to two-

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If we want the rabbits to understand our question, we’ve got to teach them our sort of counting, an algorithm that can be continually re-executed to produce an infinite ontology: . What’s the incentive we can give them for learning our method of counting—the equivalent of the log and the new feeding ground we used to teach them two-

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? Can rabbits get any use out of playing these games? In what situations would they actually be offered the chance to trade away four value-units to get either five or one thousand? What are the value units in question? Do Game A and Game B show up in their lives via sufficiently different contexts that we can just refer to those contexts without teaching counting at all? Maybe something like an aphorism: “bargain a sure thing for

, not logical: since Game A and B look the same to them, the application of any rabbit-scale formal method would yield the same answer. And given how different the two games are, a method that gives the same answer for both of them can’t be all that useful. Formal methods pre-suppose that nebulous reality has been described at the level of detail the method requires. It doesn’t matter how good your math is if you’re telling it to a rabbit.

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If, for an audience of humans, I had gotten into the math of Game A vs. Game B, made their payoffs a little closer, used phrases like “expected value”, and maybe threw in an integral sign somewhere, it would have been a lot of work. So much work, in fact, that it’d be easy to imagine that pushing those numbers around is just a conscious representation of what our brains are doing subconsciously when we make decisions. But hopefully I’ve shown how a precise-enough understanding of the situation has to come first, before any sort of math. Formally solving uncertainty on

There’s another important point here, one that you might have started thinking about a couple of paragraphs back. I claimed that, in order to teach the rabbits our sort of counting, we’d have to ground it in their local context. But how did

Learn our sort of counting? Many people are comfortable reading Game A and Game B as they are, without relating them to a local context. You don’t

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To imagine dollars, or candy bars, or vials of insulin. The number “1000” feels meaningful even if it’s not 1000 of anything in particular. So saying “humans know how to count infinitely and rabbits don’t” is just kicking the can down the road as an explanation. The real difference is that humans are able to learn context-free information. Why is that?

, an essay written by a literal banana, offers us the frame we need to explore this further. It’s an essay concerning indexicality, a word that, like ontology, sounds awfully jargony but isn’t so bad once you get to know it. Indexicality is essentially the degree to which local context matters for a given concept, though I’ll let the banana

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