Definitions, characterizations, and hard-to-ground variables
[I am hoping this post is not too repetitive, does not spend too much time rehashing basics… also: What should this be tagged with?]
Systems are not always made to be understandable—especially if they were not designed in the first place, like the human brain. Thus, they can often contain variables that are hard to ground in an outside meaning (e.g. “status”, “gender”...). In this case, it may often be more appropriate to simply characterize how the variable behaves, rather than worry about attempting to see what it “represents” and “define” it thus. Ultimately, the variable is grounded in the effects it has on the outside world via the rest of the system. Meanwhile it may not represent anything more than “a flag I needed to make this hack work”.
I will refer to this as characterizing the object in question rather than defining it. Rather than say what something “is”, we simply specify how it behaves. Strictly speaking, characterization is of course a form of definition[0] - indeed, strictly speaking, nearly all definitions are of this form—but I expect you will forgive me if for now I allow a fuzzy notion of “characterization vs. definition” scale.
Let us consider a simple example where this is appropriate; consider the notion of “flying” in Magic: the Gathering. In this game, a player may have his creatures attack another player, who can then block them with creatures of his own. Some of these creatures have printed on them the text “flying”, which is defined by the game rules to expand to a larger block of explanatory text. What does “flying” mean? It means “this creature can’t be blocked except by creatures with flying”[1]. So the creature can only be blocked by creatures that can only be blocked by creatures that can only be blocked by… well, you see the problem. This is not the real definition at all; if you took a card with “flying” and instead actually replaced it with the text “this creature can’t be blocked except by creatures with flying”, you’d get a weaker card. (Such cards actually exist, too.)
The real definition isn’t what it nominally expands out to; really, it’s just a flag. Meanwhile it’s characterized by an external rule that says that creatures with the flag can only be blocked by other creatures with the flag. It may represent the ability to fly but that’s just a helpful reminder.
Now a description of anything is of no use unless it actually bottoms out somewhere, so such self-referential “definitions” will not typically occur by themselves in nature[2]. Once we establish our primitive physical notions by characterization, our more complex ones we should typically be able to describe by definition. And yet the fact remains that the notion of “flying” in Magic is meaningful, and does bottom out; it just didn’t appear to at first because I didn’t define it correctly. Once we have a substrate that allows us to add variables (like whether or not a creature has flying) and use these to control the actions of the system, these variables automatically obtain meaning from how they control the system. However, an attempt to define such a variable and simply state what it “is” may run into the problem of self-reference.
Typically we expect that the variables in a program correspond to some specific outside concept, that they each “represent” something. But how do you make this notion work when the program you’re analyzing has 5 distinct states, each with very distinct but seemingly arbitrary behavior? Then the central state variable represents… well, what state it’s in, and more than that is hard to say. A definition is the wrong notion to apply here.
Now perhaps that sort of thing shouldn’t occur in a well-written program, but if you’re reading an entry in an obfuscated code contest, it’ll be commonplace. And the human brain is a system that wasn’t written by an intelligent mind in the first place. So it shouldn’t be surprising that it is a mistake to attempt to define something like “status” by identifying with some outside phenomenon. Obviously this is technically possible—a meaningful notion must be grounded—but it is better to describe it in a way that takes account of the fact that status is a variable that is instantiated in human brains. As Vladimir_Nesov pointed out, status is not power, it is some sort of godshatter proxy for power. So we have to be willing to say: “Status is a variable kept track of in the human brain; it is read on the following occasions with the following effects; it is written to on the following occasions; it satisfies the following properties and invariants...”
(This is common in mathematics—what’s the tensor product of M and N? Well, it’s the thing such that a homomorphism from it is the same as a bilinear map from M×N. OK, but what is it? The answer to that question is rarely relevant.)
This is speculative, but given how transsexual people seem to talk about it I suspect something similar is true of “gender”. People report knowing from a young age that they were the “wrong” gender, they naturally imitated more closely those of this gender (the same way anyone naturally imitates more closely those of their own gender)… what does it mean that this person feels like a “female” despite being male in sex? I suspect the answer is: Nothing, it just means that the “gender” flag in her head has been set to female! A primitive “gender” flag exists, and has no intrinsic meaning except for how it influences our actions, such as by directing us to imitate more closely those who we perceive to have that flag in the same state as we do. A male imitates other males the same way a flying creature blocks other flying creatures, because there’s a computational substrate that allows us to turn these informal self-referential definitions into properly grounded characterizations. (Though obviously the statement about males should just be taken as one example statement, not a complete attempt at a characterization!) Note that this would mean that the answer to Eliezer’s question “If you know who you are apart from categorizations, why does it make so much difference whether it fits into a particular category?” is, “Well, if you’ve really pinned down everything downstream of it (which you probably haven’t), it doesn’t—but I’ve got this hanging node in my brain...”
[0]Usually; there is an exception. Whatever notions we take as primitive cannot be defined, and must be characterized instead. However these characterizations (“axiomatizations”) are not definitions because there is nothing for them to be defined on top of.
[1]Before anyone else points it out: Yes, I realize that as of Future Sight, it’s “this creature can’t be blocked except by creatures with flying or reach”. I’m keeping things simple here.
[2]Except, of course, at the level of the primitive laws of physics; at the primitive level, only characterizations can occur. What does it mean for a particle to be positively charged? It means it repels other positively charged particles and attracts negatively charged particles. You see where this is going. For this reason, ultimately we have to ground things in what we can detect and predict, rather than the fundamental laws of physics—after all, we don’t even know the latter yet!
Hah. One of my very first LW posts described just such a a recursively grounded game-theoretic concept: Re-formalizing PD. Then we went on to apply quining to decision theory in many weird and wonderful forms :-)
Minor nitpicks: “transsexual” is written with two S’s, and when writing about positive charges, you probably meant “attracts negatively charged particles”.
On to the subject:
If the “gender flag” is there for the purposes of reproduction, how can non-heterosexuals and childfree people exist?
More importantly, the “flight” flag is observable: we can look at a card and see that it reads “flying”. Assuming we could do a full brain scan, what would be your prior expectation for finding this gender flag? Would you expect to be able to identify transsexuals by this flag in close correlation to their self-reporting? What would you do about false positives and false negatives, if those turned out to exist?
Fixed, thanks.
Just because something has a purpose, doesn’t mean it necessarily achieves it. This is especially so when the designer is the blind idiot God. See Adaptation-Executers, not Fitness-Maximizers for some discussion of this phenomenon.
Yes, I agree that it’s a mistake to equate status (or gender, or etc.) with an outside phenomenon, just like it’s a mistake to equate my memory of an event with the event itself.
OTOH, there is a story to be told about why proto-humans whose brains had states homologous with the states of our brains that we label “gender,” “status,” and so forth succeeded in passing their genes along to the present day, while their siblings who lacked such states did not. (1)
Which suggests that there is—or at least was—something in the world that these brain states correlate with non-accidentally.
And if you want to understand that brain state at a functional level, you want to understand that corresponding thing-in-the-world.
So when you suggest
...well, sure, in some sense that’s true. Nothing in my brain has any intrinsic meaning, it’s all just a mechanism that influences my actions.
But I would counter-suggest that the “primitive gender flag” (assuming it actually is a simple primitive, rather than a complex contingent data structure) got that way for a reason, and that reason has to do with facts about the world, and an understanding of gender that fails to take those facts about the world into account is an importantly incomplete understanding of gender.
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(1) Well, probably. It’s possible that it was just an accident, I guess. But it doesn’t seem like the thing to bet on.
Of course. And indeed for most purposes gender can be identified with sex. However introducing reflection into the system, or keeping multiple variables all “representing” the same thing, introduces the possibility that the reflection can lose sync with what it is supposed to be reflecting, or that the various representations may lose sync with each other. If a human designed the system he’d call the resulting state “inconsistent”, but the program runs nonetheless. And so if we want to know what’s going to occur, at this point it no longer suffices to identify the reflection with the territory; we have to begin analyzing what the variable actually does; if there is more than one, we have to begin analyzing which representations the program uses for which purposes (which, if it were in a consistent state, would be irrelevant). If we are discussing gender in a context where transgendered people are relevant, we have to discuss what being set to “male” actually does, discuss the code rather than the comments. I agree though that this distinction can usually be elided.
As regards status, ISTM to just be a weird evolved system of social organization and not a reflection of anything in particular. Something like Morendil’s idea that it’s this thing that you can gain and spend, though that particular idea looks simplistic to me (ISTM high-status people can often get large things done without spending status). I’m not sure I’ve seen any proposal for what it might reflect that both avoids self-reference and is anywhere close to consistent with how it actually works. But like I said, I see no reason why self-reference need be avoided here (except that self-reference is not so good a way to state things); such systems seem to be entirely evolvable when you consider all the other complex systems of coordinated behavior that have evolved. I suppose we would expect the variables in such a system to initially correspond to real, outside, quantities, but once a whole community is using it for coordination I don’t see why such a correspondence would have to continue, especially as behaviors evolve specifically to take advantage of the system.
That story heavily involves the different roles the genders play in reproduction. In particular the something that the brain states correlate with is whether you contribute sperms or eggs to the next generation.
Sure, it would be startling if that weren’t a big part of it.
It also probably relates to whether fetuses gestate inside you or not, and to whether you lactate. It might relate to how you bond emotionally to a one-week-old, though then again it might not. It might relate to the selection criteria you use to choose mates. It might relate to the selection criteria you use to choose allies. Etc.
If we actually want to understand “what gender is,” it behooves us to understand the things that it relates to and the things that it doesn’t. And because each of those things is being altered by social changes in different ways, knowing what gender actually relates to helps us predict and understand the effects of various social changes on people of various genders.