I observed some doublecruxes on AI safety topics that were about an hour long, and they didn't seem very different from ordinary attempts to resolve disagreement or seem to produce a higher than normal amount of progress towards resolving disagreement. I wonder if the participants didn't do them optimally, and whether there are recorded examples of doublecruxing I should watch instead.
My guess is that two things were going on (this is based in part on observing some recent doublecruxes at the Intellectual Internet Infrastructure Retreat, where I had a similar sense of "This doesn't seem especially different or more effective from 'just talking.'")
The main observation that I'd use to distinguish 'doublecrux' from 'disagreement' is whether the participants are saying things like 'hmm. would that actually change my mind?', and whether they're talking about events they could imagine observing. (if both participants are skilled at doublecrux, this might be going on under-the-hood rather than spoken aloud, but you should at least hear them say words about observations that might shift their perspective)
When I say "doublecrux is the fastest way for two people to resolve disagreement", I'm making a strong-confidence claim, a medium claim, and a weak claim:
I believe all three claims. Perhaps ironically (and maybe this should be a red flag that makes me reconsider?), I believe the first claim the strongest for first-principles reasons. It just seems like "well, obviously if two people want to resolve their disagreement the fastest, they'll want to focus on what would actually change their mind.' I can imagine it turning out to be that people's psychological is weird and confusing such that this isn't true, but it'd be very surprising to me.
What is the lowest cost way for someone to learn "real doublecruxing" at this point? For someone who can't do that, does it make sense to pay attention to these doublecruxing-related posts?
Strong Claim: the fastest way for two people to resolve disagreements is to focus directly on what would change their mind, without regard for legibility to anyone else, or PR, or whatnot.
This seems to imply that doublecruxing isn't optimized for being observed by an audience. Does this mean that maybe people who are trying to resolve a disagreement in front of and for the benefit of an audience (like the AI safety ones I saw) should do something else instead?
This seems to imply that doublecruxing isn't optimized for being observed by an audience. Does this mean that maybe people who are trying to resolve a disagreement in front of and for the benefit of an audience (like the AI safety ones I saw) should do something else instead?
Well, there are two different concerns – what's the optimal way to doublecrux, and what's the optimal way to do a public disagreement. I think optimal public disagreements are still better if they're more doublecrux-esque, although I think it might be better not to call them "doublecruxes" unless it's expected for the primary interaction to be the core doublecrux loop of "check for what my cruxes are."
(In general public disagreements are locally worse for the two people's ability to update than private disagreements, but you sometimes want public disagreement anyway to get common knowledge of their positions)
What is the lowest cost way for someone to learn "real doublecruxing" at this point? For someone who can't do that, does it make sense to pay attention to these doublecruxing-related posts?
The point of the first few posts in this sequence is to build common knowledge (or at least mutual knowledge) of when and why doublecrux is useful. My hope is that then,
The next few posts in this sequence will delve into "how to doublecrux on things that are deeply, confusingly hard to doublecrux about." I think this requires some background knowledge, but if you've never doublecruxed before it'll probably still be useful to read them.
I think if you've read following:
Then you probably have most of what you need to practice, and the core thing is just a) actually having someone you disagree with where the disagreement matters, b) remembering the core habits of 'operationalize' and 'what would actually change my mind'?
(There's a doublecrux format where you have a moderator who's only job is to say, after each exchange "okay, cool, but is that a crux? What would actually change your mind? How would you operationalize this?" because people tend to default to explaining why they're right rather than figuring out why they'd change their mind.)
I do think you can practice asking 'what would actually change my mind?' on your own without a partner, whenever you notice yourself believing something strongly.
While reading through your links (BTW the fourth link doesn't go where it's supposed to go), I came across this comment by Duncan Sabien:
But what I, at least, meant to convey was something like “so, there are all these really good epistemic norms that are hard to lodge in your S1, and hard to operationalize in the moment. If you do this other thing, where you talk about cruxes and search for overlap, somehow magically that causes you to cleave closer to those epistemic norms, in practice.” [...] But I claim that we’re basically saying “Do X” because of a borne-out-in-practice prediction that it will result in people doing Y, where Y are the good norms you’ve identified as seemingly unrelated to the double crux framework.
Is this something you'd endorse? If so, it seems like someone who already has these good epistemic norms might not get much out of double crux. Do you agree with that, and if so do you agree with G Gordon Worley III that I'm such a person?
I do think you can practice asking ‘what would actually change my mind?’ on your own without a partner, whenever you notice yourself believing something strongly.
I feel like my answer to that question would usually be "an argument that I haven't heard yet, or have heard but forgot, or have heard but haven't understood yet". My preferred mode of "doing disagreement" is usually to exchange arguments, counter-arguments, counter-counter-arguments, ..., questions and explanations of such arguments, etc., similar to a traditional adversarial debate, but with a goal of finding the truth for myself, the other person, and the audience, instead of trying to convince the other person or the audience of my position. E.g., I want to figure out if there's any important arguments that I don't yet know or understand, any flaws in my arguments that the other person can point out, and similarly if there's any important arguments/flaws that I can point out to the other person or to the audience.
If your answer to my question above is "no" (i.e., there's still something I can get out of learning "real doublecrux") I'd be interested in further explanation of that. For example, are there any posts that compare the pros/cons of double crux with my way of "doing disagreement"?
Short answer is "if you don't feel like you're running into intractable disagreements that are important, and that something about your current conversational style is insufficient, I wouldn't worry about doublecrux."
In particular, I suspect in your case it'd be more valuable to spend marginal effort doing distillation work (summarizing conversations), then on doing conversations better.
I *do* [weakly] expect doublecrux to also be relevant to AI Alignment debates, and think there might be things going on there that make it an improvement over "good faith adversarial debate." (Once we're not so behind on distillation, this might make sense to prioritize)
As noted earlier, doublecrux usually starts with model sharing, and I think "good faith adversarial debate" is a pretty fine format for model sharing. The main advantage of doublecrux over adversarial debate is
a) focusing on the parts that'd actually change your mind (i.e. if you detect someone posing a series of arguments that you predict won't be persuasive to you, say 'hey, my crux is more like this' and switch to another topic entirely)
b) after you've completed the model sharing and all the relevant considerations, if you find yourselves staring at each other saying 'but obviously these considerations add up to position X" vs "obviously position Y", then it becomes more important to focus on cruxes.
Thanks, this is really helpful for me to understand what doublecrux is for.
In particular, I suspect in your case it’d be more valuable to spend marginal effort doing distillation work (summarizing conversations), then on doing conversations better.
I can't think off the top of my head what conversations would be valuable to summarize. Do you have any specific suggestions?
(More directly addressing the Duncan Sabien quote: I roughly agree with the quote in terms of the immediate value of doublecrux. This sequence of posts was born from 2 years of arguing with LessWrong team members who had _something_ like 'good faith' and even 'understanding of doublecrux in particular', who nonetheless managed to disagree for months/years on deep intractable issues. And yes I think there's something directly valuable about the doublecrux framework, when you find yourself in that situation)
There is a trivial way how to get a really fast disagreement resolving. Just agree to the other person. One line disagreement resolving. But it seems there are other interesting constraints to addhere to such as having beliefs that are effective for manipulating the worlds etc. If you readily agree to falsehoods you are technically faster.
I mean, the sort of "resolve" I mean here is "the people change their minds", not "the people say they agree". (The previous post in the sequence goes into "you can resolve decisions with 'the boss says so', but this doesn't necessarily solve the relevant problem")
I am meaning the more radical version. If you genuinely are 100% suggestionable to adopt the viewpoint of others you would be superior in speed in conflict resolution. This seems like it has obvious other problems. But it reveals that the interestign challeneg is to keep within the unstated presuppositions. Presumably making the presumtions explicit would allow for a more detailed analysis how much cornercutting is still possible. "fastest possible" is really empty if we don't specify what things are allowed or not allowed.
The restrictions are something like "real humans who generally want to be effective should want to use the method".
I think it's worth pointing out that there's nothing all that special about double crux if you're used to having discussions with people on the order of being professional philosophers; double crux is just a fancy name for what I would have previously called arguing in good faith. It is special though in that many people are neither naturally shaped such that they naturally disagree with others that way or have no been trained in the method, so giving it a special name and teaching it as a technique seems worthwhile since the alternative is you know there is a "right" way to argue that converges towards truth and a "wrong" way that doesn't and teaching people to do the move where they find the beliefs their ideas hinge on and analyze that hinge in a way that might alter it and thus the entire belief network is hard if you can't precisely describe how to do it.
I feel quite confident that you already know the skill being called double crux based on the conversations I've seen you participate in LW, though I also understand how it can look like there is some "magic" in the technique you're not getting because it feels pretty magical if you learn it late in life and are then like "oh, that's why all my disagreements never go anywhere".
Something I'm unsure about (not having spent extensive time among professional philosophers) is whether they specifically do the thing where you try to change your own mind (contrasted with debate, where you try to change each other's mind, good-faith-or-no). I'm not sure this is officially what doublecrux is supposed to be, but it's how I've personally been conceiving of "Strong Form Doublecrux".
I have some skepticism because it seems like philosophy as a field hasn't converged on positions much so they can't be that good at it.
I think philosophers who are good at philosophy do change their own minds and do seek out ways to change their own minds to match what they know and reason (they, if nothing else, strive for reflective equilibrium). This is of course not what everyone does, and academic philosophy is, in my opinion, suffering from the disease of scholasticism, but I do think philosophers on the whole are good at the weaker form of double crux that takes two people and that they remain open to having their mind changed by the other person.
Philosophy mmight not have the goal of converging. It can be more valuable to generate all the possible options and to preserve solution prototypes. If everybody was using the same framework you would have effectively cut the growth space for new frameworks to zero. I philosopher is much happier that you have thought throught the problem rather than that you have come to the right conclusion.
Part of the reason why phisophy makes use of doublke cruching is precisely the presence of multiple frameworks. What passes as proof in one framework does not in the other. Another is accceptance of interest in forms of arguments whose strength is unknown. It's perfectly reasonable to explore what kind of arguments we can make if we accept ad hominem as a valid argument even if we don't know whether that is a good standard or even if we know that is a bad standard. Thus reading a philosphical literature it's likely that somebody in the discussion shares your starting point which makes their processing relevant to your private one. And if you change principles and lose interest in one author it's likely that another one is closer to your new position.
One relevant option is that philosophers think in terms of worldviews. Since single discusser have relatively random viewpoints what is socially established on what kinds of arguments fly with what kinds of groups. thus a working argument is one that is compliant to the groups axioms.
I'm not necessarily arguing doublecrux is better than whatever philosophers are doing for the purposes philosophers are doing it. Just, it seems (probably?) like it's actually different to me.
[note that in the next few posts in this sequence I'll be going into how to use doublecrux when in different worldviews, based on my experience so far. Which Vanilla Doublecrux doesn't obviously handle, but I think the extension is relatively straightforward, and also important]
I think you should link to something to do with double crux the first time you mention it; it took me a while to track down a page explaining it.
Nod. I had meant the first link in the post to establish the context (I had attempted to write the post I linked to there as a good first-introduction to doublecrux, which in turn linked to the original document you linked to here. But, seems good to go ahead and link directly here too.
Something I noticed while in a recent argument – it's hard to find cruxes for... negative or null options? Or something? (I don't know what the right words to use here)
I was debating with a friend whether we should host a party soon. My take was "I dunno, I'm not excited for a party right now." We actually agreed that at the meta level that we wanted to hold some kind of event. We had a product to build together. But when I queried "what would make me excited about holding a party" the answer was "I dunno, a vision for a particular party that felt exciting", which wasn't a very doublecruxy answer.
As it turns out, a short while later I came up with a spin on the potential party that I was excited about. It came to me fairly abruptly without much deliberateness. This was great for the purpose of solving the object level conversation, but dissatisfying from the standpoint of "right now I'm very interested in building deep knowledge of how to resolve dissagreements, and I don't feel like I figured anything out as a result of this."
I'm noting this here to help flesh out some of the open problems in disagreement resolution.
I was the friend in the story. Here's something which might be part of the picture of resolving this. I had an argument for wanting a party with the structure: A -> B, I also believed A, so I concluded B was true.
We could have double-cruxed over the entailment A -> B or if you already agreed to that, then over the truth of A, where A can be made up of many propositions.
The shift is perhaps going from the double-crux being about a conclusion of what action to take to being about whether an argument (entailment) plus its premises are true. These of course are my cruxes once/if I can uncover my beliefs to this structure (which seems like you should be able to).
Overall though, I'm a bit confused by "negatives" and "null options". In all cases you're arguing about how the world is. You can just always say "what is my crux the world is not that way?", "what are the positive beliefs that cause me to think the world is not the way my interlocutor does?"
Note: seems important to notice if it turns out doublecrux stops being the best frame. Currently I don't have strong reason to suspect that but it seems like a good hypothesis to note.
So, sometimes it seems like my reason for not believing something is "I dunno, that seems like a random hypothesis privileged, and I don't precisely have a reason to disbelieve it other than base rates or something. So the crux is "I don't see a good reason to privilege it", and it's hard to pluck a reason to privilege the hypothesis out of nowhere.
Not saying this is necessarily a good metaphor for the party conversation, but for a different illustration of the point I'm mulling over: if you say 'Do you think I should quite my job and start selling balloons on the streets of Guatamala?' I might say 'um, probably not?', and if you ask for my crux there it's like 'I dunno man, just seems like a kinda weird thing to do, why would you want to do that?'. It just feels like there's more model-sharing that needs to be done before I have anything concrete to consider.
And maybe it turns out a) you hate your job, b) you like balloons, c) you like the streets of Guatamala. In which case, okay cool, I guess that it is now a reasonable hypothesis to consider (maybe weighed against your current social life and other goals). But if those are all new facts for me it's not something I could have generated in advance.
Note: I'm pretty behind on sleep. This writing quality is likely sub-par for me.
Yeah, that picture seems correct. I think you do need to do a bunch of model sharing as the first stage in a double-crux like that, and that related to this you can't have your cruxes (your **substantive** cruxes) prepared in advance and likely can't even generate them on your own even given hours to prepare (or days or weeks or months given upon the thing).
It's not obvious that if I see no reason for the improbable position I will get much from reflecting on my own "signgle-player" cruxes before the model sharing. For the balloons example, sure, I could try to imagine from scratch (but I don't know much about the person, Guatemala, etc., so I might not do a very good job without more research). It certainly seems unlikely any cruxes I might generate will coincide with theirs and up being double-cruxes. Seems best to quickly get to the part where they explain their reasoning/models and I see whether I'm convinced / we talk about what would convince me that their reasoning is/isn't correct.
If the majority of double-cruxes are actually like this (that is, I see a reason for something that to you seems low-probability), then that means for those disagreements you won't be able to have cruxes prepared in advance beyond the generic "I don't have models that would suggest this at all, perhaps because I have little info on the target domain". It perhaps means that for all instances where you believe something that other people reasonably have a low prior on, you alone should be prepared with your cruxes, and this basically means there's asymmetrical preparedness except when people are arguing about two specific "low prior probability/complex" beliefs, e.g. minimalism vs information-density.
In the double-crux workshops I've attended, there were attempts to find people who had strong disagreements (clashes of models) about given topics, but this struggled because often one person would believe a strange/low-prior probability thing which others haven't thought about and so basically no one had pre-existing models to argue back with.
(hard to measure the length of a disagreement that you cannot voice, or you cannot voice anymore; which persists for years or decades and never gets anywhere except "I'm younger, I'll get to dance on his grave".)
Alas, double-cruxing is a two-person game; you can't make another person do it, you can only do it with someone who genuinely wants to. For everyone else, the best related trick I know is nonviolent communication.
Another issue I've run into, somewhat confused about the right way to think about:
Recently, jimrandomh and I were having a debate about the new shortform features. I was in favor of a quick, hacky solution that just automated the system we were already using (i.e. "shortform" just means "you create a post called 'shortform' and then write comments on it). I expected to spend maybe 3 days on it, and then move onto other things. I mostly wanted to create features for it that would also be useful for non-shortform things (i.e. I wanted people to be able to subscribe to shortform feeds, but I also wanted people to be able to subscribe to posts generally).
Jim wanted to treat shortform more as a first class feature, with special UI and care taken to make it seem like not a random hacked together thing.
The conversation ended up touching on many things including:
We ended up successfully coming to a compromise on how to move forward, but not really resolving any of those issues.
And, a few weeks later... I have moved closer to Jim's position. But mostly for reasons unrelated to anything we talked about. (I'd summarize the change as mostly "hmm, now that I see shortform in action and how people are relating to it, it seems useful to lean in harder towards making it good." I still think hacked-together-looking features are fine, but it seems more strategically valuable to lean into it, hacky or no. We've spent 4 weeks on it instead of 3 days and I think it makes sense to spend more. Partly the shift is about the relative-value of the "push shortform" strategy vs the "open questions" strategy (which is what I would have previously pushed)
Now, doublecrux is ideally supposed to result in an experiment you can run. "Actually build the feature and see how you feel" is sort of obvious as an experiment to run. But, also an expensive one.
I feel like I'm supposed to learn some sort of lesson from this but not sure which one. "Start building a feature and see how you feel" seems a pretty okay, practical strategy. But I'm dissatisfied with it for purposes of developing good disagreement-resolution skills. Sometimes there won't be a 'fairly reasonable experiment'.
I have some sense that in the moment, it was possible for me to do some kind of "Step backwards and think about what might actually change my mind about the original disagreement, *without* getting bogged down in the weeds of Jim's sub-cruxes."
Pedantic correction: We didn't spend 4 weeks on it; while 4 weeks did pass, there was a lot of other stuff going on during that interval.
(Meanwhile, doublecrux is not guaranteed to be faster for 3+ people to converge but I still expect it to be faster for smallish groups with particularly confusing disagreements)
Conjecture: The amount of time it takes to use double crux as a group can be lower bounded by the amount of time it takes every pair to double crux. If we assume the amount of time for every pair is the same (which it isn't), and call that amount of time t, then the lower bound is t*n(n-1)/2. (Because n choose 2 = n(n-1)/2.)
If 10 people tried this and 6 of them told me it didn't feel useful, even superficially, I'd probably change my mind significantly. If they tried it continuously for a year and there weren't at least 3 of them that could point to transparently useful outcomes, (such as disagreements taking much less time than they'd naively predict), I'd also significantly change my beliefs here.
There's also the possibility that it turns out to be a) useful for some people, but not others, b) useful**, but for something other than double crux*, c) this is an area where gains take time - perhaps past some threshold of low hanging fruit.
*Perhaps calibration, or understanding one's own beliefs better.
**The real question is if the effects are strong enough to be useful.
EDIT: I meant to write "upper bound".
To me that n choose 2 is more of an upper bound. If each 1-on-1 didn't hear each other and they were not ordered then the time to do those would be the same as randomly picking people to discuss. But in a group discussion the discussion can hear each others. In a simple case where there are only 2 true factions but each faction has 50 members you could have the whole group crux if 1 member from different factions cruxed and others listened and the chosen ones were perfectly representative of their factions. To the extent there is faction internal strife you can't reuse per se the previous discussion. The least copyfriendly case is when everything needs to be done fresh for each member in which case it doesn' t matter if 1-on-1 discussion do not hear the group discussion.
On one hand adding additonal participant means it's another dice throw from what random position they start from which can be in additional dimensions not yet exhibited. On the other hand each thing said can be listened multiple times in the same time frame (or reverse each listener can only receive 1/n amount of talk that is relevant to their beliefs).
Conjecture: The amount of time it takes to use double crux as a group can be lower bounded by the amount of time it takes every pair to double crux. If we assume the amount of time for every pair is the same (which it isn't), and call that amount of time t, then the lower bound is t*n(n-1)/2. (Because n choose 2 = n(n-1)/2.)
"How much time it'd take to pairwise doublecrux" seems like a useful detail, but doesn't seem like either an upper or lower bound. (I think it works as "this is approximately how long you should expect things to take on average", with some debates taking longer and some shorter)
Things might take longer, because maybe if everyone pairwise doublecruxes, each pair ends up disagreeing with other pairs due to idiosyncratic beliefs or personal-history that other pairs didn't share.
Things might take less time, because multiple people in the group might share enough beliefs that they can functionally share updates.
i.e. if Alice, Bob, Catherine and Doug all doublecrux, it might be that once Alice and Bob have doublecruxed, Alice can easily say to Catherine (who has a similar worldview 'Bob explained this to me, it works like X', where X uses some shorthand that Alice and Catherine already share.
There's also the possibility that it turns out to be a) useful for some people, but not others, b) useful**, but for something other than double crux*, c) this is an area where gains take time - perhaps past some threshold of low hanging fruit.
Yup. The cruxes I listed there would not shift me to "this is useless", but they would shift me to "I retract my blanket endorsement of this strategy for everyone who reads LessWrong."
By useful I primarily* meant "worth a blanket endorsement of this strategy for everyone who reads LessWrong" but for different reasons.
*This was "b"
Previously in sequence: Doublecrux is for building products.
To recap – you might want to doublecrux if either:
Regardless, you might find yourself with the problem:
Doublecruxing takes a lot of time.
For a 'serious' disagreement, it frequently takes a least an hour, and often much longer. Habryka and I once took 12 hours over the course of 3 days to make any kind of progress on a particularly gnarly disagreement. And sometimes disagreements can persist for years despite significant mutual effort.
Now, doublecruxing is faster than many other forms of truth-aligned-disagreement resolution. I actually it's helpful to think of doublecrux as "the fastest way for two disagreeing-but-honest-people to converge locally towards the truth", and if someone came up with a faster method, I'd recommend deprecating doublecrux in favor it that. (Meanwhile, doublecrux is not guaranteed to be faster for 3+ people to converge but I still expect it to be faster for smallish groups with particularly confusing disagreements)
Regardless, multiple hours is a long time. Can we do better?
I think the answer is yes, and it basically comes in the form of:
Those are all things you can do unilaterally. If you get buy-in from your colleagues, you might also try something like "develop culture that encourages people to do those four things, and help each other to do so."
I'd summarize all of that as "develop the skill and practice of keeping your beliefs cruxy."
By default, humans form beliefs for all kinds of reasons, without regard for how falsifiable they are. The result is a tangled, impenetrable web. Productive disagreement takes a long time because people are starting from the position of "impenetrable web."
If you make a habit of asking yourself "what observations would change my mind about this?", then you gain a few benefits.
First, your beliefs should (hopefully?) be more entangled with reality, period. You'll gain the skill of noticing how your beliefs should constrain your anticipations, and then if they fail to do so, you can maybe update your beliefs.
Second, if you've cultivated that skill, then during a doublecrux discussion, you'll have an easier time engaging with the core doublecrux loop. (So, a conversation that might have taken an hour takes 45 minutes – your conversation partner might still take a long time to figure out their cruxes, but maybe you can do your own much faster)
Third, once you gotten into this habit, this will help your beliefs form in a cleaner, more reality-entangled fashion in the first place. Instead of building an impenetrable morass, you'll be building a clear, legible network. (So, you might have all your cruxes full accessible from the beginning of the conversation, and then it's just a matter of stating them, and then helping your partner to do so)
[Note: I don't think you should optimize directly for your beliefs being legible. This is a recipe for burying illegible parts of your psyche and missing important information. But rather, if you try to actually understand your beliefs and what causes them, the legibility will come naturally as a side benefit]
Finally, if everyone around you is doing, this radically lowers the cost of productive-disagreement. Instead of taking an hour (or three days), as soon as you bump into an important disagreement you can quickly navigate through your respective belief networks, find the cruxes, and skip to the part where you actually Do Empiricism.
I think (and here we get into speculation), that this can result in a phase shift in how disagreement works, enabling much more powerful discourse systems than we currently have.
I think keeping beliefs cruxy is a good example of a practice that is both a valuable "Rabbit Strategy", as well as something worth Stag Hunting Together on. (In Rabbit/Stag parlance, a Rabbit strategy is something you can just do without relying on anyone else to help you, that will provide benefit to you. A Stag strategy is something with a larger payoff, but only actually works if you've coordinated with people to do so)
If you have an organization, community, or circle of friends where many people have practiced keeping-beliefs-cruxy, I predict you will find individuals benefiting, as well as creating a truthseeking culture more powerful than the sum of its parts.
Hopefully obvious addenda, operationalizing:
My crux for all this is that I think this is locally tractable.
My recommendation is not that you go out of your way to practice this all the time – rather, that you spend some time on-the-margin practicing the "look-for-cruxes" whenever you actually have a noteworthy disagreement.
If you practice crux-finding whenever you have such a disagreement, and find that it isn't locally useful, I probably wouldn't recommend continuing.
If 10 people tried this and 6 of them told me it didn't feel useful, even superficially, I'd probably change my mind significantly. If they tried it continuously for a year and there weren't at least 3 of them that could point to transparently useful outcomes, (such as disagreements taking much less time than they'd naively predict), I'd also significantly change my beliefs here.
This operationalization has some important caveats, such as "I don't necessarily expect this to work for people who haven't read the sequences or some equivalent. I also think it might require some skills that I haven't written up explanations for yet –which I hope to do soon as I continue this sequence."