useful, thanks 

thanks for the term for this and the link

Even if shrimp consciously experience pain or suffering, my question is, why do we think electrocution is more humane than freezing?

The idea of freezing to death sounds horrible because we are warm-blooded animals. In cold blooded animals, cooling gradually slows metabolism inducing torpor. I would have thought for a shrimp, ice slurry immersion would be a gentle method of putting them under anesthesia; sounds like that takes a minute. Do they behaviorally indicate pain or aversion?  I’m more surprised that an ice slurry kills them. Apparently pink shrimp (the kind people eat) thrive best in ocean waters between 0-8C and have been found living in -2C waters (wikipedia).

(I think part of why this goes squirrelly, in practice, is that it’s easy for a certain type of person to feel like they’re engaging in a purely one-on-one interaction, in places like Facebook or Twitter or LessWrong or wherever. Like, if one is already a pays-less-attention-to-the-audience type Pokémon to begin with, then it’s easy for the audience to fall completely out of your thoughts as you tunnel-vision on the person you’re directly responding to. But I sort of can’t ever not-notice the other monkeys watching.)

This post in general, and this comment especially, was helpful in clarifying for me why I hate social media so much. (This forum being an exception).  It seems to me that people are much less rational when arguing on social media than they are in a private one-on-one conversations, because they can't help noticing the other monkeys watching -- even if they claim the contrary. This pertains to the obligation-to-respond case and a much wider set of dynamics. 

The more aggressive-seeming sorts may honestly believe they are just purists for truth and socially oblivious. For some, this may be true. But more often I notice an interesting pattern: in public online discussions, their arguments are littered with subtle rhetorical devices (argumentum ad hominem, ad populum, ad ridiculum, ad verecundium, etc.) (in english: glib, snarky, pontificating, witty banter, etc.) -- none of which are aimed at helpfully updating their own or the other person's worldview, and rather seem to be aimed at playing to the audience. Tellingly, this dimension often disappears when same person is in a one-on-one conversation, even on the identical disagreement with the same 'opponent'. The same person can be much more constructive, rational, curious, open-minded, willing to concede uncertainty, etc. when the other monkeys aren't watching.  It is also vastly more epistemically efficient to communicate, figure out common ground, and distill differences in one-on-one conversations, without the distraction of tracking what the audience might know/think as well.  

So I'm a big advocate of this: as soon as people realize they substantively disagree, assuming everyone's real motivation is to figure out what is actually true (or at least that's the motivation we all wish to honor),  work it out in a one-on-one conversation.  You might reach agreement, or reach clarity about the root disagreement. One or the other party might decide the whole question is not that important, or other person isn't arguing in good faith, or whatever, and can choose to abandon the conversation at any time -- without worrying about how that will be perceived.   In the end, if either of you think the conversation was constructive, you can always write up a distillation of the useful bits for a wider audience. (Co-authoring a disagreement distillation seems like a genre we should especially encourage).

But while you are doing hard intellectual and perhaps emotional work of wrangling with a disagreement, having an audience is generally not helpful, and often gets in the way. 

PSA for people who are interested in nutrition and health, and frustrated by the level of BS in the media surrounding these topics: I find the Nutrition Diva podcast to be exceptionally objective and rational. It’s my go to place to check for an informed take on any nutrition claim or question. She does the work of looking up and reading the original research articles, checking if the experiment is well-designed, inference valid, and if the data actually support the claims, a task I normally don’t have time for myself. She is unusually clear on epistemic status (for example, distinguishing between evidence of absence and absence of evidence; articulating uncertainty rather than burying it).  And she doesn’t seem to shy away from taking unpopular stands, if that’s where the data land.

More generally, in the very early phase of discovery in any field, when nobody has any idea what is going to turn out to be true or fruitful, insiders of a field tend to get bogged down because they have an overly correlated set of ideas. Not only the main ideas (like hypotheses, in science) but also concepts, tools, approaches, analogies, aesthetic preferences, and background knowledge.  So a vast effort gets allocated to a tiny corner of the potential search space.  This is why cross disciplinary transplants can make outsized contributions.  

This is in tension with expertise. Amateurs and beginners by definition lack a lot of existing knowledge. This is a blessing, because they don’t “know” things all the experts “know” incorrectly,  and a curse because they also don’t “know” things all the experts know correctly. In a decently rigorous and otherwise productive field, most of what experts know is in the latter category^[1].   

This leads me to a speculation: the optimal way to tap the potential contributions of field-outsiders is to pair them up with experts, or integrate them into teams of experts. That is a big investment and commitment on both parts, so a prior vetting / recruitment step is needed.

As a first step you can invite such people to participate in high level, big picture conversations on a one time or short term basis. The interaction group has to be big enough that it can accommodate a couple of wild cards, but small enough that it won’t be a huge drag on the experts to have to constantly explain basic things. That said, asking experts to explain things in plain language which they all take for granted as obvious, is often the value added. 

The outsider has to be the right sort, though. Smart enough to pick up new ideas quickly; confident enough to ask “dumb” questions or speak up in general;  articulate enough to explain their ideas to people outside their own domain of expertise; enough social intelligence to notice when it’s a good time to pipe up vs be quiet, and capacity to self-regulate accordingly.  And it takes a certain kind of creativity to be good at recognizing unseen connections or implications. 

It isn’t necessarily obvious which other disciplines have the sauce that is missing. Physics and Philosophy are often good bets. But here’s a speculation: anyone who is a seasoned expert in any completely different but rigorous and successful domain is a good bet.  (Young folks with a few years in another strong discipline also make great trainees. People who are long-established in a field that is mostly bankrupt are less likely to help than any random person on the street). 

So if you are running a workshop or conference or symposium that is not too big, where many of the participants are high-level experts within Alignment, and most others are coming up from within the field,  consider allocating a significant budget (in terms of  limited attendee slots) to inviting relatively senior people from other disciplines. Worst case, they are lost or bored or contribute useless ideas, and one slot was wasted for a few days. But if they engage well, you have a lot of information about their potential to contribute as a member of a team (hire them, collaborate, invite them to more things), and they have a lot of information about how exciting and important that might be.

Here’s the rub: people who are that senior and that good are busy and get a lot if invitations, and are selective about which to accept. So you may need to make a strong pitch explaining why alignment is an important problem and why you think their particular expertise would be valuable. The low hanging fruit is therefore to invite ones who have already expressed an interest, however tentatively. Invite pretty much all of those.

Disclosure 1: these observations are supported by my reading of history of science, my own experience switching fields, and experience in a leadership role promoting interdisciplinary collaboration in another fledgling research area.

Disclosure 2: these comments are potentially self-serving,  speaking as a relatively senior member of an outside discipline who is interested in engaging with the alignment community, but not finding opportunities to engage at this sort of level, despite the widely professed value placed on diverse perspectives.

1. ^{^}

   By the same token, the outsider brings with them a lot of other background knowledge, in quantity proportional to their maturity in the previous field, which is correct in proportion of the rigor of the previous field, and non-overlapping in proportion to the distance of the previous field.

Great post. I would have liked to see the images in this post but the links all appear to be broken. If the OP is here could you repair the links?

Based on the text alone, this strikes me as right on the mark. 

An interesting bit of history: the New York Academy (which still exists, in another form) was back in the 1980s an unaccredited graduate school and the premiere training ground for classical figurative drawing and sculpture, which were otherwise in much neglect in the Art World. From what I have heard (second-hand), there were two competing schools within the Academy at the time, one group favoring "perceptual" drawing (essentially the skill of copying a 2D image, or seeing a model as a 2D image and then drawing what you literally see); and the other favoring "conceptual" drawing, the skill of understanding how objects in three-dimensional world generate the two-dimensional projection we see, and then drawing from an understanding of that underlying cause. I think the perceptual approach is typical of photo-realist painters (and most present day portrait artists), and the conceptual approach was typical of Renaissance painters.

An anecdote I love that illustrates the contrast is: apparently one day when the class was drawing a long pose the model took a break, and when she came back the pose was slightly different such that all the shadows changed. The Perceptual students complained, whereas a Conceptual student countered: actually we should change the lights every 15 minutes. Then we can see what is actually there, and draw it from a better understanding.

For an example of what drawing looks like when approached conceptually, see the drawings of Luca Cambiaso (1527-1585). (This is not an artwork; it is a conceptual study done to figure out the scene 3-dimensionally in preparation for a classical renaissance drawing or painting).
 

in response to my remark

What has particularly struck me in reading on this topic is the degree to which statements of fact or logic are often interwoven with rhetorical style that serves to sway opinion by means other than reason [...]

@the gears to ascension wrote

There's recently been vigorous debate on lesswrong about whether that's the case.

I am not sure what "that" refers to in "whether that's the case" . Based on the segment of my post they quoted, it sounds like there's been debate about whether it's the case that facts and logic are often interwoven with rhetorical persuasion devices when making arguments.    But I suspect the commenter is referring to my wondering whether it would be advantageous to avoid mixing facts and logic with rhetorical persuasion devices when making arguments. If there has been vigorous debate on lesswrong on the latter topic, I would like to read it. Can anyone provide links or keywords?

My interpretation of the commenter's intent is supported by their further saying

the quoted claim is not clearly well enough justified to conclude the case about whether moderating impulses towards confident wording is useful.

I will note that I didn't make a claim about this, much less attempt to provide any sort of evidence.  So far I only suggested some possible arguments for and against the first thought that came to my mind.  My intention was to invite a discussion on the pros and cons of this idea.

In my opinion, this post misses the main challenge with the "platonic ideal" vision of a concept like percentage of explained variance: it's something that accidentally depends on the distribution of your variables in the sample, rather than a fundamental property of the relationship between those variables.

Perhaps we need to step back and clarify what "Platonic Explained Variance" could even mean. All knowledge is contextual; it is a mistake to expect that there is a Truth to be known devoid of context. I supposed that the OP meant by this phrase something like: the true, complete statistical dependence between X and Y in the sampled population, as against our estimate or approximation of that dependence based on a given limited sample or statistical model. In any case, I'd like to argue that such distinction makes sense, while it does not make sense to look for a statistical relationship between X and Y that is eternally and universally true, independent of a specific population.

When we are using empirical statistics to describe the relationship between measurable variables X and Y, I think the conclusions we draw are always limited to the population we sampled. That is the essential nature of the inference. Generalization to the sampled population as a whole carries some uncertainty, which we can quantify based on the size of the sample we used and the amount of variability we observed, subject to some assumptions (e.g., about the underlying distributions, or independence of our observations).

But generalization to any other population always entails additional assumptions. If the original sample was limited in scope (e.g. a particular age, sex, geographic location, time point, or subculture), generalization outside that scope entails a new conjecture that the new group is essentially the same as the original one in every respect relevant to the claim. To the extent the original sample was broad in scope, we can as you say test whether such other factors detectably modified the association between X and Y, and if so, include these effects as covariates in our statistical model. As you note, this requires a lot of statistical power. Even so, whenever we generalize outside that population, we assume the new population is similar in the ways that matter, for both the main association and the modifier effects.

A statistical association can be factually, reproducibly true of a population and still be purely accidental, in which case we don't expect it to generalize. When we generalize to a new context or group or point in time, I think we are usually relying on an (implicit or explicit) model that the observed statistical relation between X and Y is a consequence of underlying causal mechanisms. If and to the extent that we know what causal mechanisms are at play, we have a basis for predicting or checking whether the relevant conditions apply in any new context. But (1) generalization of the causal mechanism to a new condition is still subject to verification; a causal model derived in a narrow context could be incomplete, and the new condition may differ in a way that turns out to be causally important in a way we didn't suspect; and (2) even if the causal mechanism perfectly generalizes, we do not expect "the fraction of variance explained" to generalize universally. That value depends on a plethora of other random and causal factors that will in general be different between populations [^1].

Summing up, I think it's a mistake to look for the 'Platonic Variance Explained' divorced from a specific population. But we can meaningfully ask if the statistical dependence we estimated from a finite empirical sample using a particular statistical model accurately reflects the true and complete statistical dependence between the variables in the population from which we sampled.

1. This account might be particular to the branches of natural science that seek mechanistic causal models and/or fundamental theories as explanations. Other fields of research or philosophic frameworks that lack or eschew causal explanation or theory may have a different epistemic account, which I'd be interested to hear about.

Note that parts of my post are actually model-free! For example, the mathematical definition and the example of twin studies do not make use of a model

Yes, good point, I should have said "unlike regression"  rather than "unlike variance explained". I'll have to think more on how the type of analysis described in the twin example maps onto information theory.

But this is predicated on the implicit model that Y is a normally distributed variable.

I'm not aware of (implicitly) making that assumption in my post!

By "this" I meant the immediately preceding statements in my post. (Although the cartoon distributions you show do look normal-ish, so at least you invite that intuition). The idea that the mean or average is a good measure of central tendency of a distribution, or a good estimator, is so familiar we forget that it requires justification. For Normal distributions, it is the lowest MSE estimator, the maximum likelihood estimator, and is an unbiased estimator, but this isn't true of all distributions.  For a skewed, long-tailed distribution, for example, the median is a better estimator. For a binomial distribution, the mean is almost never the maximum likelihood estimator. For a Cauchy distribution, the mean is not even defined (although to be fair I'm not entirely sure entropy is well defined in that case, either). Likewise the properties of variance that make it a good estimator of dispersion for a Normal distribution don't necessarily make it good for other distributions.  

It is true that partitioning of variance and "variance explained" as such don't rely on a normality assumption, and there are non-parametric versions of regression, correlation, ANOVA etc. that don't assume normality. So I have not entirely put my finger on what the difference is.

You can measure mutual information even if the form of the relationship is unknown or complicated.

Is this so? Suppose we'd want to measure differential entropy, as a simplified example, and the true density "oscillates" a lot. In that case, I'd expect that the entropy is different than what it is if the density were smoother. But it might be hard to see the difference in a small dataset. The type of regularity/simplicity assumptions about the density might thus influence the result.

This might be a good place to mention that I work exclusively with discrete entropy, and am not very familiar with notations or proofs in differential (continuous) entropy.  So if Y is continuous, in practice this involves discretizing the value of Y (binning your histograms).  I agree the continuous case would be more directly comparable, but I don't think this is likely to be fundamentally important, do you?

In principle, conceptually, you can estimate entropy directly from the probability density function (PDF) non-parametrically as H = sum(-P log2 P), where the sum is over all possible values of Y, and P is the probability Y takes on a given value.^[1] Likewise, you can estimate the mutual information directly from the joint probability distribution between X and Y, the equation for which I won't try to write out here without an equation editor. In practice, if Y is continuous, the more data you have, the more finely you can discretize Y and the more subtly you can describe the shape of the distribution, so you converge on the true PDF and thus the true entropy as the data size goes to infinity.  

I'm not denying that it can take a lot of data to measure entropy or mutual information by brute force in this way. What is worse, these naive estimators are biased if distributions are under-sampled. So getting a good estimate of entropy or mutual information from data is very tricky, and the shape of the distribution can make the estimation more or less tricky. To the extent one relies on regularity or simplicity assumptions to overcome data limitations, these assumptions can affect your result. 

Still, if you are careful about it, an estimate based on assumptions can still be a strict bound: X removes at least z% of your uncertainty about Y.  There is a direct analogy in regression models: if Yhat=f(X) explains z% of the variance of y (assuming this is established properly), then x "Platonically" explains at least z% of the variance of y.  

Relatedly, you can pre-process X into some derived variable such as Q=f(X) or an estimator Yhat=f(X), and then measure the mutual information between the derived variable and the true value of Y.  The Data Processing Inequality states that if the derived variable contains Z amount of information about Y, the input variable X must contain at least that much information. This is very much like defining a particular regression model f(X); and in the Yhat=f(X) case, it does give you a model you can use to predict Y from X.

1. ^{^}

   sorry, I haven't figured out the equation editor yet.