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If I hadn't heard back from them, would you want me to tell you? Or would that be too sad?
Seed oils are usually solvent extracted, which makes me wonder, how thoroughly are they scrubbed of solvent, what stuff in the solvent is absorbed into the oil (also an effective solvent for various things), etc
I looked into this briefly at least for canola oil. There, the typical solvent is hexane. And some hexane does indeed appear to make it into the canola oil that we eat. But hexane apparently has very low toxicity, and—more importantly—the hexane that we get from all food sources apparently makes up less than 2% of our total hexane intake! https://www.hsph.harvard.edu/nutritionsource/2015/04/13/ask-the-expert-concerns-about-canola-oil/ Mostly we get hexane from gasoline fumes, so if hexane is a problem, it's very hard to see how to pin the blame on canola oil.
It's a regression. Just like they extrapolate backwards to (1882+50=1932) using data from 1959, they extrapolate forwards at the end. (This is discussed in the "timelines" section.) This is definitely a valid reason to treat it with suspicion, but nothing's "wrong" exactly.
Many thanks! All fixed (except one that I prefer the old way.)
As the original author of underrated reasons to be thankful (here), I guess I can confirm that tearing apart the sun for raw materials was not an intended implication.
I think matplotlib has way too many ways to do everything to be comprehensive! But I think you could do almost everything with some variants of these.
ax.spines['top'].set_visible(False) # or 'left' / 'right' / 'bottom'
ax.set_xticks([0,50,100],['0%','50%','100%'])
ax.tick_params(axis='x', left=False, right=False) # or 'y'
ax.set_ylim([0,0.30])
ax.set_ylim([0,ax.get_ylim()[1]])Good point regarding year tick marks! I was thinking think that labeling 0°C would make the most sense when freezing is really important. Say, if you were plotting historical data on temperatures and you were interested in trying to estimate the last frost date in spring or something. Then, 10°C would mean "twice as much margin" as 5°C.
One way you could measure which one is "best" would be to measure how long it takes people to answer certain questions. E.g. "For what fraction of the 1997-2010 period did Japan spend more on healthcare per-capita than the UK?" or "what's the average ratio of healthcare spending in Sweden vs. Greece between 2000 and 2010?" (I think there is an academic literature on these kinds of experiments, though I don't have any references on hand.)
In this case, I think Tufte goes overboard in saying you shouldn't use color. But if the second plot had color, I'd venture it would win most such contests, if only because the y-axis is bigger and it's easier to match the lines with the labels. But even if I don't agree with everything Tufte says, I still find him useful because he suggests different options and different ways to think about things.
Thanks, someone once gave me the advice that after you write something, you should go back to the beginning and delete as many paragraphs as you can without making everything incomprehensible. After hearing this, I noticed that most people tend to write like this:
- Intro
- Context
- Overview
- Other various throat clearing
- Blah blah blah
- Finally an actual example, an example, praise god
Which is pretty easy to correct once you see it!
Hey, you might be right! I'll take this as useful feedback that the argument wasn't fully convincing. Don't mean to pull a motte-and-bailey, but I suppose if I had to, I'd retreat to an argument like, "if making a plot, consider using these rules as one option for how to pick axes." In any case, if you have any examples where you think following this advice leads to bad choices, I'd be interested to hear them.
I think you're basically right: Correlation is just one way of measuring dependence between variables. Being correlated is a sufficient but not necessary condition for dependence. We talk about correlation so much because:
- We don't have a particularly convenient general scalar measure of how related two variables are. You might think about using something like mutual information, but for that you need the densities not datasets.
- We're still living in the shadows of the times when computers weren't so big. We got used to doing all sorts of stuff based on linearity decades ago because we didn't have any other options, and they became "conventional" even when we might have better options now.
Thanks, you've 100% convinced me. (Convincing someone that something that (a) is known to be true and (b) they think isn't surprising, actually is surprising is a rare feat, well done!)
Chat or instruction finetuned models have poor prediction cailbration, whereas base models (in some cases) have perfect calibration.
Tell me if I understand the idea correctly: Log-loss to predict next token leads to good calibration for single token prediction, which manifests as good calibration percentage predictions? But then RLHF is some crazy loss totally removed from calibration that destroys all that?
If I get that right, it seems quite intuitive. Do you have any citations, though?
Sadly, no—we had no way to verify that.
I guess one way you might try to confirm/refute the idea of data leakage would be to look at the decomposition of brier scores: GPT-4 is much better calibrated for politics vs. science but only very slightly better at politics vs. science in terms of refinement/resolution. Intuitively, I'd expect data leakage to manifest as better refinement/resolution rather than better calibration.
That would definitely be better, although it would mean reading/scoring 1056 different responses, unless I can automate the scoring process. (Would LLMs object to doing that?)
Thank you, I will fix this! (Our Russian speaker agrees and claims they noticed this but figured it didn't matter 🤔) I re-ran the experiments with the result that GPT-4 shifted from a score of +2 to a score of -1.
Well, no. But I guess I found these things notable:
- Alignment remains surprisingly brittle and random. Weird little tricks remain useful.
- The tricks that work for some models often seem to confuse others.
- Cobbling together weird little tricks seems to help (Hindi ranger step-by-step)
- At the same time, the best "trick" is a somewhat plausible story (duck-store).
- PaLM 2 is the most fun, Pi is the least fun.
You've convinced me! I don't want to defend the claim you quoted, so I'll modify "arguably" into something much weaker.
I don't think I have any argument that it's unlikely aliens are screwing with us—I just feel it is, personally.
I definitely don't assume our sensors are good enough to detect aliens. I'm specifically arguing we aren't detecting alien aircraft, not that alien aircraft aren't here. That sound like a silly distinction, but I'd genuinely give much higher probability to "there are totally undetected alien aircraft on earth" than "we are detecting glimpses of alien aircraft on earth."
Regarding your last point, I totally agree those things wouldn't explain the weird claims we get from intelligence-connected people. (Except indirectly—e.g. rumors spread more easily when people think something is possible for other reasons.) I think that our full set of observations are hard to explain without aliens! That is, I think P[everything | aliens] is low. I just think P[everything | no aliens] is even lower.
I know that the mainstream view on Lesswrong is that we aren't observing alien aircraft, so I doubt many here will disagree with the conclusion. But I wonder if people here agree with this particular argument for that conclusion. Basically, I claim that:
- P[aliens] is fairly high, but
- P[all observations | aliens] is much lower than P[all observations | no aliens], simply because it's too strange that all the observations in every category of observation (videos, reports, etc.) never cross the "conclusive" line.
As a side note: I personally feel that P[observations | no aliens] is actually pretty low, i.e. the observations we have are truly quite odd / unexpected / hard-to-explain-prosaically. But it's not as low as P[observations | aliens]. This doesn't matter to the central argument (you just need to accept that the ratio P[observations | aliens] / P[observations | no aliens] is small) but I'm interested if people agree with that.
I get very little value from proofs in math textbooks, and consider them usually unnecessary (unless they teach a new proof method).
I think the problem is that proofs are typically optimized for "give most convincing possible evidence that the claim is really true to a skeptical reader who wants to check every possible weak point". This is not what most readers (especially new readers) want on a first pass, which is "give maximum possible into why this claim is true for to a reader who is happy to trust the author if the details don't give extra intuition." At a glance, infinite Napkin seems to be optimizing much more for the latter.
If you're worried about computational complexity, that's OK. It's not something that I mentioned because (surprisingly enough...) this isn't something that any of the doctors discussed. If you like, let's call that a "valid cost" just like the medical risks and financial/time costs of doing tests. The central issue is if it's valid to worry about information causing harmful downstream medical decisions.
I might not have described the original debate very clearly. My claim was that if Monty chose "leftmost non-car door" you still get the car 2/3 of the time by always switching and 1/3 by never switching. Your conditional probabilities look correct to me. The only thing you might be "missing" is that (A) occurs 2/3 of the time and (B) occurs only 1/3 of the time. So if you always switch your chance of getting the car is still (chance of A)*(prob of car given A) + (chance of B)*(prob of car given B)=(2/3)*(1/2) + (1/3)*(1) = (2/3).
One difference (outside the bounds of the original debate) is that if Monty behaves this way there are other strategies that also give you the car 2/3 of the time. For example, you could switch only in scenario B and not in scenario A. There doesn't appear to be any way to exploit Monty's behavior and do better than 2/3 though.
Just to be clear, when talking about how people behave in forums, I mean more "general purpose" places like Reddit. In particular, I was not thinking about Less Wrong where in my experience, people have always bent over backwards to be reasonable!
I have two thoughts related to this:
First, there's a dual problem: Given a piece of writing that's along the Pareto frontier, how do you make it easy for readers who might have a utility function aligned with the piece to find it.
Related to this, for many people and many pieces of writing, a large part of the utility they get is from comments. I think this leads to dynamics where a piece where the writing that's less optimal can get popular and then get to a point on the frontier that's hard to beat.
Done!
I loved this book. The most surprising thing to me was the answer that people who were there in the heyday give when asked what made Bell Labs so successful: They always say it was the problem, i.e. having an entire organization oriented towards the goal of "make communication reliable and practical between any two places on earth". When Shannon left the Labs for MIT, people who were there immediately predicted he wouldn't do anything of the same significance because he'd lose that "compass". Shannon was obviously a genius, and he did much more after than most people ever accomplish, but still nothing as significant as what he did when at at the Labs.
I thought this was fantastic, very thought-provoking. One possibly easy thing that I think would be great would be links to a few posts that you think have used this strategy with success.
Thanks, I clarified the noise issue. Regarding factor analysis, could you check if I understand everything correctly? Here's what I think is the situation:
We can write a factor analysis model (with a single factor) as
where:
- is observed data
- is a random latent variable
- is some vector (a parameter)
- is a random noise variable
- is the covariance of the noise (a parameter)
It always holds (assuming and are independent) that
In the simplest variant of factor analysis (in the current post) we use in which case you get that
You can check if this model fits by (1) checking that is Normal and (2) checking if the covariance of x can be decomposed as in the above equation. (Which is equivalent to having all singular values the same except one).
The next slightly-less-simple variant of factor analysis (which I think you're suggesting) would be to use where is a vector, in which case you get that
You can again check if this model fits by (1) checking that is Normal and (2) checking if the covariance of can be decomposed as in the above equation. (The difference is, now this doesn't reduce to some simple singular value condition.)
Do I have all that right?
Thanks for pointing out those papers, which I agree can get at issues that simple correlations can't. Still, to avoid scope-creep, I've taken the less courageous approach of (1) mentioning that the "breadth" of the effects of genes is an active research topic and (2) editing the original paragraph you linked to to be more modest, talking about "does the above data imply" rather than "is it true that". (I'd rather avoid directly addressing 3 and 4 since I think that doing those claims justice would require more work than I can put in here.) Anyway, thanks again for your comments, it's useful for me to think of this spectrum of different "notions of g".
Thanks, very clear! I guess the position I want to take is just that the data in the post gives reasonable evidence for g being at least the convenient summary statistic in 2 (and doesn't preclude 3 or 4).
What I was really trying to get at in the original quote is that some people seem to consider this to be the canonical position on g:
- Factor analysis provides rigorous statistical proof that there is some single underlying event that produces all the correlations between mental tests.
There are lots of articles that (while not explicitly stating the above position) refute it at length, and get passed around as proof that g is a myth. It's certainly true that position 5 is false (in multiple ways), but I just wanted to say that this doesn't mean anything for the evidence we have for 2.
Can I check if I understand your point correctly? I suggested we know that g has many causes since so many genes are relevant and thus f you opened up a brain, you wouldn't be able to "find" g in any particular place. It's the product of a whole bunch of different genes, each of which is just coding for some protein, and they all interact in complex ways. If I understand you correctly, you're pointing out that there could be a sort of "causal bottleneck" of sorts. For example, maybe all the different genes have complex effects, but all that really matters is how they affect neuronal calcium channel efficiency or something. Thus, if you opened up a brain, you could just check how efficient the calcium channels are and you're done. Is that right?
If this is right, I do agree that I seem to be over-claiming a bit here. There's nothing that precludes the possibility of a "bottleneck" as far as I know, (though it seems sorta implausible in my not-at-all-informed opinion)
I used python/matplotlib. The basic idea is to create a 3d plot like so:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
Then you can add dots with something like this:
ax.scatter(X,Y,Z,alpha=.5,s=20,color='navy',marker='o',linewidth=0)
Then you save it to a movie with something like this:
def update(i, fig, ax):
ax.view_init(elev=20., azim=i)
return fig, ax
frames = np.arange(0, 360, 1)
anim = FuncAnimation(fig, update, frames=frames, repeat=True, fargs=(fig, ax))
writer = 'ffmpeg'
anim.save(fname, dpi=80, writer=writer, fps=30)
I'm sure this won't actually run, but it gives you the basic idea. (The full code is a complete nightmare.)
Thanks for the reply. I certainly agree that "factor analysis" often doesn't make that assumption, though it was my impression that it's commonly made in this context. I suppose the degree of misleading-ness here depends on how often people assume isotropic noise when looking at this kind of data?
In any case, I'll try to think about how to clarify this without getting too technical. (I actually had some more details about this at one point but was persuaded to remove them for the sake of being more accessible.)
if a trait is 80% heritable and you want to guess whether or not Bob has that trait then you'll be 80% more accurate if you know whether or not Bob's parents have the trait than if you didn't have that information.
I think this is more or less correct for narrow-sense heritability (most commonly used when breeding animals) but not quite right for broad-sense heritability (most commonly used with humans). If you're talking about broad-sense heritability, the problem is that you'd need to know not just if the parents have the trait, but also which genes Bob got or not from each parent, as well as the effect of dominant genes, epistatic interactions, etc.
Assuming you're talking about broad-sense heritability, I think a better way of looking at it would be to say that you'll be 80% more accurate if Bob has an identical twin raised by a random family and you know if that twin had the trait. This isn't quite right either, but I think it's valid if you assume that phenotypic traits are the sum of genetic effects and environmental effects and also that genetic effects are independent of environmental effects.
Of course, few people have identical twins raised by random families, and most phenotypes probably aren't additive in genetic and environmental effects, and those effects probably aren't independent! Which... is a lot of caveats if you want to know practical applications of heritability numbers.
On the other hand, there is some non-applied scientific value in heritability. For example, though religiosity is heritable, the specific religion people join appears to be almost totally un-heritable. I think it's OK to read this in the straightforward way, i.e. as "genes don't predispose us to be Christian / Muslim / Shinto / whatever". I don't have any particular application for that fact, but it's certainly interesting.
Similarly, schizophrenia has sky-high heritability (like 80%) meaning that current environments don't have a huge impact on where schizophrenia appears. That's also interesting even if not immediately useful.
My view is that people should basically talk about heritability less and interventions more. In most practical circumstances, what we're interested in is how much potential we have to change a trait. For example, you might want to reduce youth obesity. If that's your goal, I don't think heritability helps you much. High heritability doesn't mean that there aren't any interventions that can change obesity-- it just means that the current environments that people are already exposed to don't create much variance. Similarly, low heritability means the environment produces a lot of variance, but it doesn't tell you anything specific you can actually do!
If you goal is to find interventions, all heritability gives you is some kind of vague clue as to how promising it might be to look at natural environmental variation to try to find interventions.
In principle, I guess you could also think about low-tech solutions. For example, people who want to opt out of alcohol might have some slowly dissolving tattoo / dye placed somewhere on their hand or something. This would eliminate the need for any extra ID checks, but has the big disadvantage it would be visible most of the time.
Thanks. Are you able to determine what the typical daily dose is for implanted disulfiram in Eastern Europe? People who take oral disulfiram typically need something like 0.25g / day to have a significant physiological effect. However, most of the evidence I've been able to find (e.g. this paper) suggest that the total amount of disulfiram in implants is around 1g. If that's dispensed over a year, you're getting like 1% of the dosage that's active orally. On top of that, the evidence seems pretty strong that bioavailability from implants is lower than from oral doses, so it's effectively even less.
Of course, there's nothing stopping someone implanting 100x as large a dose, and maybe bioavailability can be improved (or isn't that big a concern). But if not, my impression was that most implants are effectively pure placebo effect.
Very interesting! Do you know how much disulfiram the implant gives out per day? There's a bunch of papers on implants, but there's usually concerns about (a) that the dosage might be much smaller than the typical oral dosage and/or (b) that there's poor absorption.
I specified (right before the first graph) that I was using the US standard of 14g. (I know the paper uses 10g. There's no conflict because I use their raw data which is in g, not drinks.)
Ironically, there is no standard for what a "standard drink" is, with different countries defining it to be anything from 8g to 20g of ethanol.
I wasn't (intentionally?) being ironic. I guess that for underage drinking we have the advantage that you can sort of guess how old someone looks, but still... good point.
I've politely contacted them several times via several different channels just asking for clarifications and what the "missing coefficients" are in the last model. Total stonewall- they won't even acknowledge my contacts. Some people more connected to the education community also apparently did that as a result of my post, with the same result.
You could model the two as being totally orthogonal:
- Rationality is the art of figuring out how to get what you want.
- Utilitarianism is a calculus for figuring out what you should want.
In practice, I think the dividing lines are more blurry. Also, the two tend to come up together because people who are attracted to the thinking in one of these tend to be attracted to the other as well.
You definitely need a number of data at least exponential in the number of parameters, since the number of "bins" is exponential. (It's not so simple as to say that exponential is enough because it depends on the distributional overlap. If there are cases where one group never hits a given bin, then even an infinite amount of data doesn't save you.)
I see what you're saying, but I was thinking of a case where there is zero probability of having overlap among all features. While that technically restores the property that you can multiply the dataset by arbitrarily large numbers, if feels a little like "cheating" and I agree with your larger point.
I guess Simpson's paradox does always have a right answer in "stratify along all features", it's just that the amount of data you need increases exponentially in the number of relevant features. So I think that in the real world you can multiply the amount of data by a very, very large number and it won't solve the problem, even though in a large enough number will.
In the real world it's often also sort of an open question if the number of "features" is finite or not.
I like your concept that the only "safe" way to use utilitarianism is if you don't include new entities (otherwise you run into trouble). But I feel like they have to be included in some cases. E.g. If I knew that getting a puppy would make me slightly happier, but the puppy would be completely miserable, surely that's the wrong thing to do?
(PS thank you for being willing to play along with the unrealistic setup!)
This covers a really impressive range of material -- well done! I just wanted to point out that if someone followed all of this and wanted more, Shannon's 1948 paper is surprisingly readable even today and is probably a nice companion:
http://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf
Well, it would be nice if we happened to live in a universe where we could all agree on an agent-neutral definition of what the best actions to take in each situation are. It seems to be that we don't live in such a universe, and that our ethical intuitions are indeed sort of arbitrarily created by evolution. So I agree we don't need to mathematically justify these things (and maybe it's impossible) but I wish we could!