Rationality Quotes May 2013
Here's another installment of rationality quotes. The usual rules apply:
- Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote from Less Wrong itself, Overcoming Bias, or HPMoR.
- No more than 5 quotes per person per monthly thread, please.
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Eliezer Yudkowsky, ‘Cognitive Biases Potentially Affecting Judgement of Global Risks’, in Nick Bostrom and Milan M. Ćirković (eds.), Global Catastrophic Risks, Oxford, 2008, p. 114
Retracted because it violates the spirit of one of the section rules.
Thou shalt not quote Yudkowsky.
Understood.
...how are we supposed to tell people about this rule?
Edit: Aw, I thought it was funny.
"We don't put quotes from Eliezer in the Rationality Quotes thread" seems to work. Quoting the expression of an authority is a way to lend persuasiveness to your rule assertion but it is not intrinsic to the process of rule explaining.
I can tell people "Don't drive through intersections when the lights are red" and I'm telling someone about the rule without quoting anything.
-- Eric Hoffer
Perhaps, but absolute power tends to be the more relevant one, as it definitionally also includes the means to persue the goals derived from absolute corruption.
I wonder where one could apply "Absolute" and not come up with a scary sounding conclusion. Absolute skepticism seems it would turn one into a gibbering madman. Absolute logic--well what is a dangerous AI but absolute logic plus power?
Absolute knowledge also seems like it'd leave you gibbering... Just think about it: knowledge of everything, that is to say every atom of every single object in the universe.
I can only say Ouch
Absolute non-contradiction? Since anything else (that is, any contradictory statement) is absolutely horrible, if absolute non-contradiction is also horrible then nothing good exists.
edit: s/than nothing/then nothing/
Absolute goodness?
Anything else would be problematic. Making people smile is good. Tiling the universe with microscopic smiley faces is not.
Absolute goodness seems tautalogically good. If you pick any one good trait or action and maximize it it grows ominous again.
That's why I chose it.
Like the smiling example I gave.
-Congressman Frank Underwood in the TV series House of Cards
More from Scott Aaronson:
Replying to a many-world-like question
While the linked to blog post discussion is somewhat interesting it seems misleading to call it a 'many-world-like question'. In trying to extract the 'rationalist moral' from the link perhaps the best quote that I can extract is the preceding sentence:
At a stretch the 'rationalist moral' could be the general principle 'Don't make logical errors just because infinity confuses you'. (I'd certainly endorse that as an often neglected insight!)
Dupe: http://lesswrong.com/lw/8n9/rationality_quotes_december_2011/5erg
From Richard Feynman one last letter to his first wife, over a year after her death from TB (incidentally, antibiotics had been discovered and were being tested on humans a few months before her death; a year sooner, and she would have had a good chance of recovery):
Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard P. Feynman.
The whole letter and the rest of the book is well worth reading.
(I found this interesting, given that Feynman was likely the most instrumentally rational physicist ever, and definitely did not believe in any kind of afterlife -- he surely knew he was writing it for himself.)
That's not true at all. It's those who made up their minds to be good but aren't who do the most evil.
I'm not sure that's true in aggregate. I think most of the evil is done by people going along with things - like, if you talked to them about it for a while they'd concede that some aspects of what they were going along with were sort of questionable and maybe a bit bad, but they don't think about that spontaneously.
Right, sure, every evil overlord needs a group of willing henchmen and an army of reluctant-to-object enablers. So, the original quote is probably right "in aggregate", though not in the amount of evil per person. Even then, how do you attribute/distribute the amount of evil between, say, Pol Pot ordering the destruction of intelligentsia and the genocide of the Chinese minority and a peasant working his rice field in the countryside, occasionally affirming his allegiance to the regime, as required? Hmm, I recall HPMoR!Quirrell talking about it, but I'm not sure how much of it is author tract.
I saw the quote as an allusion to friendly/unfriendly AI.
Even more from the same source:
Daniel Dennett
Does Dennett offer supporting arguments for this assertion?
Illustration of availability bias:
http://www.youtube.com/watch?v=LVM4jR3TZsU
Johann Wolfgang von Goethe, Hermann und Dorothea, IX. 303.
Can someone please explain to me how this is a rationality quote? (not sarcastic)
George Bernard Shaw
--Scott Aaronson, D-Wave: Truth finally starts to emerge
Well, academia itself has been attempting to get away from doing the opposite. This is most noticeable in fields like medicine and especially psychology, where anyone disagreeing with whatever the consensus is at the moment is considered an anti-scientific flat-earther, whereas the fact that this consensus itself nearly reverses every couple decades is rarely brought up. Furthermore, on the occasions when someone does bring it up, the standard response is to say that the strength of science is that it can change it's consensus.
Which vicennial cycles of academic consensus have you found most noticeable?
Well, the standard example is nutrition advice. Other reasonably well-known examples include whether post-menopausal women should take estrogen supplements, and how dangerous marijuana is. An example with a longer period is the whole issue with eugenics.
How many times has the academic consensus on those reversed, and does that match your original claim that for these century-plus old fields like medicine,
?
EDIT: feel free to reply to my challenge any time, Eugine.
This is technically true for inclusive definitions of 'want' but highly misleading. There is a world of difference between "I want X but the opportunity cost (Y) is too great" and "I actively prefer !X". X and Y may be the prevention of parasitic worm infections and combating malaria. Precisely which limited resource is being allocated (time or money) changes little.
If "I don't have time" is to be replaced with an expression which conveys more personal acceptance of responsibility then it would be reasonable to translate it to "I have other priorities" but verging on disingenuous to translate it into "I don't want to".
I think you're reading this too literally. To my mind this says "You have the power to allocate your time" which is a non-trivial realization to some people. You can also understand this as saying "You allocate time to tasks according to how much you want to do them", an observation which also does not always rise to the conscious level.
This also requires a strange definition of "want" in order to become correct. Actions chosen for instrumental reasons sometimes differ from both the emotional urge and the all-else-equal reasoned preference, and so it's not particularly natural to include them under the label of "wanting".
Citation? I've read the Tao Teh Ching in a few translations and I don't recognize that at all; a Google and Google Books makes it sound like the usual apocrypha.
Yeah, I could only find it in Google so I don't know the actual source. Lao Tzu is as good as any name, I suppose, if the name is translated literally.
http://www.youtube.com/watch?v=rMXs1C434B8
"If you are too different, you're probably going to break up" is not so groundbreaking that it's worth three minutes of your readers' lives.
-Arabian proverb
...this seems exactly, diametrically wrong.
I would have said merely wrong. ie. When reversed it would still be stupidity. There seem to be both advantages and disadvantages to public expression with respect to it influencing you. Something along the lines of identity commitments on one side and the potential for denial, hypocrisy and lack of feedback on the other.
A not-entirely-different quote has been posted in the past
–A.L. Kitselman
I'm not sure what that means.
Kevin Warwick
-Marcus Aurelius
That's actually kind of sad. Hopefully times have changed since then.
It's my understanding that Marcus Aurelius no longer voices this opinion.
And the people who preserved his words to reach us were more like wise men who watched the skies and solved the puzzle of cheaply distributing text, than like emperors or philosophers.
Observing the sky is good and productive science. Perhaps he meant that as an emperor (or responsible senator, etc) he should not have been drawn into a serious scientific or philosophical career, but for those who can afford the time and effort, it's a fine pursuit.
I was told that that part was actually a reference to astrology.
--Clue (1985)
Hunter Felt
Witty to be sure, but obviously false. The causal connection between baseball and the content (as opposed to the name) of the law is probably fairly tenuous. The number three is ubiquitous in all areas of human culture.
I think further investigation would reveal that is at most a Western cultural thing, not a hardwired human universal. Elsewhere in time and place, 4 has been the important number -- e.g. recurrences of 4 and 40 in the Hebrew scriptures; the importance of 4 and (negatively) 8 in Chinese culture, etc.. Possibly some other digits have performed similarly in other places as well.
We can still blame the propaganda for helping make the laws appealing and getting them to pass
And given the popularity of things named after people like "Laura's Law" or "Megan's Law", it wouldn't surprise me if the popularity was due to the rhetorical effect on the average voter.
Lee Kelly.
Warren Buffet on proponents of the efficient market hypothesis
-Paul Graham
-- Byron Katie, Loving What Is
To recognize that some of the things our culture believes are not true imposes on us the duty of finding out which are true and which are not.
--Allan Bloom, Giants and Dwarfs, "Western Civ"
-- Byron Katie, Loving What Is
The naive application of that is to go around thinking "I shouldn't be thinking about 'should' all the time! I should stop doing that! I'm not thinking like I should!".
I have not found that this actually helps.
As Jamie Zawinski might put it, "Now you have two problems."
This doesn't really make sense. Just because the mice can't be coached for success, aren't aware of corporate goals, etc., it does not follow that they are one's "real bosses". Can the mice fire you? Can they give you a raise? Can they write you up for violations of corporate protocol? If you are having trouble with a coworker, can you appeal to the mice to resolve the issue? Do the mice, finally, decide what you work on? Your actual boss can take the mice away from you! Can the mice reassign you to a different boss?
Yes, and yes. This is spelled out in the original post.
I read the original post. The mice are not giving anyone any raises. The mice are not capable of human-level cognition, and do not occupy positions of administrative power in the company. The mice are just mice.
Your actual, human boss decides whether to give you a raise, what you work on, etc. He or she might choose to implement a policy that ties your assigment and your compensation package, in some indirect way, to the behavior of the mice (although to be more accurate, to what you do with the mice), but to insist that it is therefore accurate to say that the mice are your bosses and are making the decisions that control your career, is absurd.
There is, perhaps, a word missing from the English language. If Derek Lowe were speaking, instead of writing, he would put an exaggerated emphasis on the word real and native speakers of English would pick up on a special, metaphorical meaning for the word real in the phrase real boss. The idea is that there are hidden, behind the scenes connections more potent (more real?) than the overt connections.
There is a man in a suit, call him the actual boss, who issues orders. Perhaps one order is "run the toxicology tests". The actual boss is the same as the real boss so far. Perhaps another order is "and show that the compound is safe." Now power shifts to the mice. If the compound poisons the mice and they die, then the compound wasn't safe. The actual boss has no power here. It is the mice who are the real boss. They have final say on whether the compound is safe, regardless of the orders that the actual boss gave.
Derek Lowe is giving us an offshoot of an aphorism by Francis Bacon: "Nature, to be commanded, must be obeyed." Again the point is lost if one refuses to find a poetic reading. Nature accepts no commands; there are no Harry-Potter style spells. Nature issues no commands; we do not hear and obey, we just obey. (So why is Bacon advising us to obey?)
I'm afraid I just don't buy it. The distinguishing feature of one's boss is that this person has certain kinds of (formally recognized) power over you within your organization's hierarchy. No one thinks that their boss has the power to rearrange physical reality at a whim.
My objection to the quote as a rationality quote is that it reads like this: "Because my job performance may be affected by the laws of physical reality, which my boss is powerless to alter, he (the boss) in fact has no power over me!" Which is silly. It's a sort of sounds-like-wisdom that doesn't actually have any interesting insight. By this logic, no one has any legal/economic/social power over anyone else, and no one is anyone's boss, ever, because anything that anyone can do to anyone else is, in some way, limited by the laws of physics.
P.S. I think the Francis Bacon quote is either not relevant, or is equally vacuous (depending on how you interpret it). I don't think Bacon is "advising" us to obey nature. That would be meaningless, because we are, in fact, physically incapable of not obeying nature. We can't disobey nature — no matter how hard we try — so "advising" us to obey it is nonsense.
In a similar vein, saying that the mice have "the final say" on whether the compound is safe is nonsensical. The mice have no say whatsoever. The compound is either safe or not, regardless of the mice's wishes or decisions. To say that the have "the final say" implies that if they wished, they might say differently.
In short, I think a "poetic reading" just misleads us into seeing nonexistent wisdom in vacuous formulations.
Bo Dahlbom
-Adam Stark
-- Paul Crowley
This is a claim about reality. Do we actually know that pulling numbers out of your arse actually does produce better results than pulling the decisions out directly? Or does it just feel better, because you have a theory now?
Well at least if you pull numbers out of your arse and then make a decision based explicitly on the assumption that they are valid, the decision is open to rational challenge by showing that the numbers are wrong when more evidence comes in. And who knows, the real numbers may be close enough to vindicate the decision.
If you just pull decisions out of your arse without reference to how they relate to evidence (even hypothetically), you are denying any method of improvement other than random trial and error. And when the real numbers become available, you still don't know anything about how good the original decision was.
That's a good point.
Plugging gut assumptions into models to make sure that the assumptions line up with each other generally produces better results for me. Beyond it just feeling better, it gives me things I can go away and test that I'd never have got otherwise.
Like if I think something's 75% likely to happen in X period and I think that something else is more likely to happen than that - do I think that the second thing is 80% likely to happen? And does that line up with information that I already have? Numbers force you to think proportionally. They network your assumptions together until you can start picking out bits of data that you have that are testable.
Intuitions aren't magic, of course, but they're rarely completely baseless.
Years later, this unsurprising intuition is spectacularly confirmed by the Good Judgement Project; details in "Superforecasting".
-- Devo, on the value of confronting problems rather than letting them fester
-- René Descartes
-- Walter Russell Mead, describing someone else's failure to understand what a desperate effort actually looks like.
-- Teddy Atlas
This is a wild guess, but (on the assumption that you endorse this quote) is the thought that MWI stands in relation to experimentally testable physics as something like a metaphysical thesis, and that instrumentalism doesn't lack metaphysical theses of this kind, but simply refuses to acknowledge and examine them?
Anyway, a related quote, and so far as I know the oldest of this kind:
Reminds me of Popper (World of Parmenides):
Actually, it was someone asking what the heck I meant by "reality fluid", to which the answer is that I don't know either which is why I always call it "magical reality fluid". I mean, I could add in something that sounded impressive and might to some degree be helpful along the lines of "It's the mind-projection-fallacy conjugate of 'probability' as it appears inside hypotheses about collections of real things in which some real things are more predicted to happen to me than others for purposes of executing post-observation Bayesian updates, like, if the squared modulus rule appearing in the Born statistics reflected the quantity present of an actual kind of stuff" but I think saying, "It's magic, which is the mind-projection-fallacy conjugate of 'I'm confused'" would be wiser in a conversation like that. I think it's very important not to create the illusion of knowing more than you do, when you try to operate at the frontiers of your own ability to be coherent. At the same time, refusing to digress into metaphysics even to demarcate the things that confuse you, even to form ideas which can be explicitly incoherent rather than implicitly incoherent, is indeed to become the slave of the unexamined thought.
I wonder if others find the notion of "magical reality fluid" a useful moniker for "I have no clear idea of what's going on here, but something does, so I cannot avoid thinking about it". I confess it does nothing for me.
Hypothesis: Whether or not a readers finds that useful correlates with whether or not they've read this.
FWIW, it does a fine job for me of conveying "I don't quite know what I'm talking about here."
Some people do (I have already received multiple comments to this effect). Mileage possibly varies.
Signalling sophistication and confidence when there is no object level reason for such confidence is one of the more destructive of human social incentives. I heartily endorse measures to prevent this. Seeing that someone is willing to admit uncertainty at the expense of their dignity increases the confidence I can have that their other expressions of confidence are more than social bullshit.
I would of course encourage you to stop using "magical reality fluid" as soon as possible. That is, after someone figures the philosophy (or epistemology or physics) out with something remotely approaching rigour.
Much as I love the idea of this and would like it to work for me, unfortunately as far as I can tell my brain simply treats "magical reality fluid" the same way as it would something bland like "degree of reality".
Though come to think of it, I'm not actually sure whether or not I've really been saying the magical part to myself all this time. I'll try to make sure I don't leave it out in the future, and see whether it makes a difference.
Thanks for the explanation.
Aristotle
-- aristosophy
However, equivalences are also the bread and butter of inference. Distinguishing more than you need to will slow you down.
Unfortunately I only have a finite amount of storage available, so I can only do that up to a certain point.
-- Matthew Leifer
I like the quote, but I have a nitpick:
When I've lost in the first round of single-elimination tournaments, I've found myself hoping that the person who beat me would prove skilled enough to win the entire tournament. That way, my loss wouldn't mean that I totally sucked, but only that I wasn't the best. So I think the quoted observation fails to account for nuances relating to how losses inform us about our skill level.
Daniel Dennett
Dan Ariely, Predictably Irrational: The Hidden Forces that Shape Our Decisions, New York, 2008, pp. 138-139
The Vulcan your Vulcan could sound like if he wasn't made of straw, I guess? Link
You shouldn't trust people who claim to know 4 digits of accuracy for a forcast like this. The uncertainity involved in the calcuation has to be greater.
You shouldn't trust a human person who makes that claim. But if we are using 'person' in a way that includes the steel-Vulcan from the quote then yes, you should.
It is all uncertainty. There is no particular reason to doubt the steel-Vulcan's ability to calibrate 'meta' uncertainties too.
In the face of all the other evidence about the relative capabilities of the species in question that the character in question is implied to have it would be an error to overvalue the heuristic "don't trust people who fail to signal humility via truncating calculations". The latter is, after all, merely a convention. Given the downsides of that convention (it inevitably makes predictions worse) it is relatively unlikely that the Vulcans would have the same traditions regarding significant figure expression.
There inherent uncertainity in the input. The steel-Vulcan in question counted one specifc case as being 24% relevant to the current question. That's two digits of accuracy.
If many of your input variables only have two digits of accuracy the end result shouldn't have four digits of accuracy.
And lo, Wedrifid did invent the concept of Steel Vulcan and it was good.
Do we actually have enough fictional examples of this to form a trope? (At least 3, 5 would be better.)
Perhaps, but on the off chance that the captain doesn't listen, giving the exact probability increases the chances of success. The Vulcan mentioned that.
What I find curious about StarTrek models of... well, intelligence, if starship building is any indication of it... is that Romulans are on the same page as Vulcans. Forget 'Vulcans are more rational/logical/... then Humans'; they haven't outstripped the other subspecies! How have they been using their philosophy since Surak?
Surak's philosophy was never about improving scientific progress. Surak's philosophy was all about shutting down all hints of emotion, with the explicit intention of shutting down anger specifically, and thus preventing the entire Vulcan species from blowing itself up in a massively destructive civil war.
Vulcans, and by exension Romulans, are significantly more intelligent than humans; this is an advantage that both subspecies hold, and Surak's philosophies don't change that. Surak's philosophies speak of the inappropriateness of any sort of emotional reaction, and praise slow, careful, methodical progress, in which every factor is taken into account from all possible angles before the experiment is begun. Surak's philosophies speak out against such emotional weaknesses as enjoying one's work; a Vulcan who enjoys science may very well decide to move into a different field instead, one in which there is less danger of committing the faux pas of actually smiling. (Surak's philosophies go perhaps rather too far - to the point where a close association with a risk-taking species like humanity is probably a good thing for the Vulcans - but they do accomplish their aim of preventing extinction via civil war).
Romulans, on the other hand, have no difficulty showing emotions. Some of them will enjoy their science, they'll take risks, they'll occasionally accidentally blow themselves up with dangerous experiments (or lose their tempers and blow up other Romulans on purpose). Somehow, they've managed to avoid suicidal, self-destructive civil war so far... but I'm somehow not surprised that the Vulcans have failed to outstrip them.
And yet it is still so easy to imagine such an outcome. Actually, I am more surprised that they chose such similar roads more than they are close in achievements. For example, maybe Vulcans would have made breakthroughs in areas that have no value for Romulans, and viva a versa.
That the Vulcans and the Romulans have incredibly close levels of technology is surprising, yes; but not nearly as surprising as the idea that the Humans, the Klingons, the Betazoids, and about a hundred or so other species all have such incredibly similar technology levels, and all without any hint of shared history before they developed their seperate warp drives.
What does it mean to beat the odds by X percent?
My first thought is that it means that the number of successes is (1+X) * the expected number of successes. If so, then beating a single 1-in-a-million shot means having 1 success where 1/1000000 success is expected, then X is 99999900 percent. That's an awful lot more than 29.2%. It's also strange because the exact number is affected by adding additional missions with 100% survivability--if you have 100 missions, one of which is 1 in a million odds and the rest of which are certain, and you beat them all, the number of successes is 100 while the expected number is 99.000001, and you only beat the odds by about 1%.
Joseph Heller, Catch-22
explaining /= explaining away
-- Doug McDuff, M.D., and John Little, Body by Science, pp. ix-x
I've never seen the Icarus story as a lesson about the limitations of humans. I see it as a lesson about the limitations of wax as an adhesive, - Randall Munroe.
Rodger Cotes defending Newton from the charge that his theory treats gravity as an occult cause:
When it comes to understanding how our universe evolves, religion and theology have been at best irrelevant. They often muddy the waters, for example, by focusing on questions of nothingness without providing any definition of the term based on empirical evidence. While we do not yet fully understand the origin of our universe, there is no reason to expect things to change in this regard. Moreover, I expect that ultimately the same will be true for understanding of areas that religion now considers its own territory, such as human morality.
Science has been effective at furthering our understanding of nature because the scientific ethos is based on three key principles: (1) follow the evidence wherever it leads; (2) if one has a theory, one needs to be willing to try to prove it wrong as much as one tries to prove that it is right; (3) the ultimate arbiter of truth is experiment, not the comfort one derives from one's a priori beliefs, nor the beauty or elegance one ascribes to one's theoretical models.
Lawrence M. Krauss, A Universe from Nothing, xvi
--from the ongoing animation xkcd: Time, dialogue transcript found here
--Clyde Coombs, A theory of data 1964, pg284,488
That really asks for the Samuel Johnson's refutation...
Daniel Dennett
William James
Daniel Dennett
Is this from the new book?
Yes.
And yes, it's great.
Marcel Kinsbourne, quoted in Dennett (2013)
Matthew 7:13-14
-- Lou Scheffer
(Most recent example from my own life that springs to mind: "It seems incredibly improbable that any Turing machine of size 100 could encode a complete solution to the halting problem for all Turing machines of size up to almost 100... oh. Nevermind.")
That does (did?) seem improbable to me. I'd have expected n needed to be far larger than 100 before the overhead became negligible enough for 'almost n' to fit (ie. size 10,000 gives almost 10,000 would have seemed a lot more likely than size 100 gives almost 100). Do I need to update in the direction of optimal Turing machine code requiring very few bits?
I mentally replaced “100” with “N” anyway (and interpreted “almost N” in the obvious-in-the-context way).
You mentally threw away relevant information. ie. You merely made yourself incapable of thinking about what is claimed about the size of c relative to 100. That's fine but ought to indicate to you that you have little useful information to add in response to a comment that amounts to an expression of curious surprise that (c << 100).
Where the context suggests it can be interpreted as an example of the Eliezer's-edits bug?
I hadn't read the before-the-edit version of the comment.
In general, probably yes. Have you checked out the known parts of the Busy Beaver sequence? Be sure to guess what you expect to see before you look.
In specific, I don't know the size of the constant c.
Pretty sure that also happens in fields other than the hard sciences. For example, it is said that converts to a religion are usually much more fervent than people who grew up with it (though there's an obvious selection bias).
(The advanced, dark-artsy version of this is claiming with a straight face to never have believed A in the first place, and hope the listener trusts what you're saying now more than their memory of what you said earlier, and if it doesn't work, claim they had misunderstood you. My maternal grandpa always tries to use that on my father, and almost always fails, but if he does that I guess it's because it does work on other people.)
The operative glory is doing it in five seconds.
And, being right.
That's harder to distinguish from the outside.
I've also found this to be medium evidence that I'm not as informed about the subject as I thought that I was, so I back down by confidence somewhat. If I recently made an error that would have resulted in something very bad happening, I should be very careful about thinking that my next design is safe.
So what's the program? Is it the one that runs every turing machine up to length 100 for BusyBeaver(100) steps, and gets the number BusyBeaver(100) by running the BusyBeaver_100 program whose source code is hardcoded into it? That would be of length 100+c for some constant c, but maybe you didn't think the constant was worth mentioning.
Well, it's still encoded. But I actually meant to say "almost 100" in the original. And yes, that's the answer.
David Eagleman, Incognito, p. 71
Minor nitpick:
The reason we can learn the local language is that languages are memetically selected for learnability by humans.
So is everything else except biology and physics.
The memetic evolution of baroque music in Europe is a development towards learnability? There are probably no more than 100 people alive that can make their way through Bach's 2nd Partita for violin.
I'm pretty sure you're underestimating that by...a lot. Fermi estimate time:
Bach's sonatas and partitas for solo violin are a cornerstone of the violin repertory. We may therefore assume that every professor of violin at a major university or conservatory has performed at least one of them at least once, just like we may assume that every professor of mathematics has studied the Lebesgue dominated convergence theorem. How many professors of violin are there? Let's just consider one country, the United States. Each state in the U.S. has at least two major public universities (typically "University of X" and "X State University", where X is the state); some have many more, and this doesn't even count private universities. Personal experience suggests that the average big state university has about one professor of violin. There are 50 states in the U.S., so that's 100 people already right there. And we have yet to count:
Thus, it wouldn't surprise me at all if there were at least 10,000 people alive who have performed one of the sonatas and partitas (to say nothing of those who would be capable of performing them). There are six of these works in total, so we can divide this already-conservative estimate by six to (under)estimate the number who have performed the Second Partita in particular. (This is likely an underestimate because many of them will have performed more than one -- indeed, all six, in a fair number of cases.)
A glance at the recordings available on Amazon, sorted by release date may help put things into perspective.
The estimate "no more than 100 alive who can make it through" would be much more appropriate for a difficult contemporary work (like, say, Melismata by Milton Babbitt) than a 300-year-old standard.
It might be more accurate to say that pretty much everything, including what we call biology and physics -- humans are the ones codifying it -- is memetically selected to be learnable by humans. Not that it all develops towards being easier to learn.
Ever notice how you never hear humans playing music that humans aren't capable of learning to play? I think there may be some selection effects at play here...
Well, I never notice the satisfaction of that contradiction, quite, but I do notice that the history of baroque music includes the steady achievement of theretofore unreached technical difficulty.
Leibniz in Neal Stephenson's The Confusion
Huh, I thought the point of atoms is that they're not infinitely small.
Daniel Waterhouse says to Hooke in Neal Stephenson's Quicksilver
-- Megan McArdle, trying to explain Bayesian updates and the importance of making predictions in advance, without referring to any mathematics.
The value of health insurance isn't that it keeps you from getting sick. It's that it keeps you from getting in debt when you do get sick.
That's why McArdle recommended getting only catastrophic coverage.
It does help you to pay for (say) blood-pressure medication. This might be expected to result in more people with medical aid and blood-pressure problems taking their medication.
It also helps to pay for doctors. This leads to more people going to the doctor with minor complaints, and increased chances of catching something serious earlier.
Er, yes, fine, but... to the extent that the study shows anything, it shows that the positive results of these effects, if they exist, are consistent with zero. Can we please discuss the data, now that we have some, and not theory?
This annoys me because she doesn't talk at all about the power of the study. Usually, when you see statistically insignificant positive changes across the board in a study without much power, its a suggestion you should hesitantly update a very tiny bit in the positive direction, AND you need another study, not a suggestion you should update downward.
When ethics prevent us from constructing high power statistical studies, we need to be a bit careful not to reify statistical significance.
If the effect is so small that a sample of several thousand is not sufficient to reliably observe it, then it doesn't even matter that it is positive. An analogy: Suppose I tell you that eating garlic daily increases your IQ, and point to a study with three million participants and P < 1e-7. Vastly significant, no? Now it turns out that the actual size of the effect is 0.01 points of IQ. Are you going to start eating garlic? What if it weren't garlic, but a several-billion-dollar government health program? Statistical significance is indeed not everything, but there's such a thing as considering the size of an effect, especially if there's a cost involved.
Moreover, please consider that "consistent with zero" means exactly that. If you throw a die ten times and it comes up heads six, do you "hesitantly update a very tiny bit" in the direction of the coin being biased? Would you do so, if you did not have a prior reason to hope that the coin was biased?
I respectfully suggest that you are letting your already-written bottom line interfere with your math.
Such a study might show that it doesn't matter on average. But you'd need those numbers to see if it's increasing the spread of values. That would mean that it really helps some and hurts others. If you can figure out which is which, then it'll end up being useful. Heck, this applies even if the average effect is negative.
I don't know how often bio-researchers treat the standard deviation as part of their signal. I suspect it's infrequent.
How large was your prior for "insurance helps some and harms others, and we should try to figure out which is which" before that was one possible way of rescuing insurance from this study? That sort of argument is, I respectfully suggest, a warning signal which should make you consider whether your bottom line is already written.
I wasn't even thinking of insurance here. You were talking about garlic. I was thinking about my physics experiments where the standard deviation is a very useful channel of information.
I strongly disagree.
An old comment of mine gives us a counterexample. A couple of years ago, a meta-analysis of RCTs found that taking aspirin daily reduces the risk of dying from cancer by ~20% in middle-aged and older adults. This is very much a practically significant effect, and it's probably an underestimate for reasons I'll omit for brevity — look at the paper if you're curious.
If you do look at the paper, notice figure 1, which summarizes the results of the 8 individual RCTs the meta-analysis used. Even though all of the RCTs had sample sizes in the thousands, 7 of them failed to show a statistically significant effect, including the 4 largest (sample sizes 5139, 5085, 3711 & 3310). The effect is therefore "so small that a sample of several thousand is not sufficient to reliably observe it", but we would be absolutely wrong to infer that "it doesn't even matter that it is positive"!
The heuristic that a hard-to-detect effect is probably too small to care about is a fair rule of thumb, but it's only a heuristic. EHeller & Unnamed are quite right to point out that statistical significance and practical significance correlate only imperfectly.
That's a curious metric to choose. By that standard taking aspirin is about as healthy as playing a round of Russian Roulette.
I'd assume they mean something like the per-year risk of dying from cancer conditional on previous survival -- if they indeed mean the total lifetime risk of dying from cancer I agree it's ridiculous.
It's a fairly natural metric to choose if one wishes to gauge aspirin's effect on cancer risk, as the study's authors did.
Fortunately, the study's authors and I also interpreted the data by another standard. Daily aspirin reduced all-cause mortality, and didn't increase non-cancer deaths (except for "a transient increase in risk of vascular death in the aspirin groups during the first year after completion of the trials"). These are not results we would see if aspirin effected its anti-cancer magic by a similar mechanism to Russian Roulette.
Pardon me. Mentioning only curiosity was politeness. The more significant meanings I would supplement with are 'naive or suspicious'. By itself that metric really is worthless and reading this kind of health claim should set off warning bells. Lost purposes are a big problem when it comes to medicine. Partly because it is hard, mostly because there is more money in the area than nearly anywhere else.
And this is the reason low dose asprin is part of my daily supplement regime (while statins are not).
"All cause mortality" is a magical phrase.
Am I missing a subtlety here, or is it just that cancer is usually one of those things that you hope to live long enough to get?
Yeah, pretty much. There are other examples of this where something harmful appears to be helpful when you don't take into account possible selection biases (like being put into the 'non-cancer death' category); for example, this is an issue in smoking - you can find various correlations where smokers are healthier than non-smokers, but this is just because the unhealthier smokers got pushed over the edge by smoking and died earlier.
tl;dr: NHST and Bayesian-style subjective probability do not mix easily.
Another example of this problem: http://slatestarcodex.com/2014/01/25/beware-mass-produced-medical-recommendations/
Does vitamin D reduce all-cause mortality in the elderly? The point-estimates from pretty much all of the various studies are around a 5% reduction in risk of dying for any reason - pretty nontrivial, one would say, no? Yet the results are almost all not 'statistically significant'! So do we follow Rolf and say 'fans of vitamin D ought to update on vitamin D not helping overall'... or do we, applying power considerations about the likelihood of making the hard cutoffs at p<0.05 given the small sample sizes & plausible effect sizes, note that the point-estimates are in favor of the hypothesis? (And how does this interact with two-sided tests - vitamin D could've increased mortality, after all. Positive point-estimates are consistent with vitamin D helping, and less consistent with no effect, and even less consistent with it harming; so why are we supposed to update in favor of no help or harm when we see a positive point-estimate?)
If we accept Rolf's argument, then we'd be in the odd position of, as we read through one non-statistically-significant study after another, decreasing the probability of 'non-zero reduction in mortality'... right up until we get the Autier or Cochrane data summarizing the exact same studies & plug it into a Bayesian meta-analysis like Salvatier did & abruptly flip to '92% chance of non-zero reduction in mortality'.
If I throw a die and it comes up heads, I'd update in the direction of it being a very unusual die. :-)
Have you read the study in question? The treatment sample is NOT several thousand, its about 1500. Further, the incidence of the diseases being looked at are only a few percent or less, so the treatment sample sizes for the most prevalent diseases are around 50 (also, if you look at the specifics of the sample, the diseased groups are pretty well controlled).
I suggest the following exercise- ask yourself what WOULD be a big effect, and then work through if the study has the power to see it.
Yes, but in this case, the sample sizes are small and the error bars are so large that consistent with zero is ALSO consistent with 25+ % reduction in incidence (which is a large intervention). The study is incapable from distinguishing hugely important effect from 0 effect, so we shouldn't update much at all, which is why I wished Mcardle had talked about statistical power. Before we ask "how should we update", we should ask "what information is actually here?"
Edit: If we treat this as an exploration, it says "we need another study"- after all the effects could be as large as 40%! Thats a potentially tremendous intervention. Unfortunately, its unethical to randomly boot people off of insurance so we'll likely never see that study done.
Health is extremely important - the statistical value of a human life is something like $8 million - so smallish looking effects can be practically relevant. An intervention that saves 1 life out of every 10,000 people treated has an average benefit of $800 per person. In this Oregon study, people who received Medicaid cost an extra $1,172 per year in total health spending, so the intervention would need to save 1.5 lives per 10,000 person-years (or provide an equivalent benefit in other health improvements) for the health benefits to balance out the health costs. The study looked at fewer than 10,000 people over 2 years, so the cost-benefit cutoff for whether it's worth it is less than 3 lives saved (or equivalent).
So "not statistically significant" does not imply unimportant, even with a sample size of several thousand. An effect at the cost-benefit threshold is unlikely to show up in significant changes to mortality rates. The intermediate health measures in this study are more sensitive to changes than mortality rate, but were they sensitive enough? Has anyone run the numbers on how sensitive they'd need to be in order to find an effect of this size? The point estimates that they did report are (relative to control group) an 8% reduction in number of people with elevated blood pressure, 17% reduction in number of people with high cholesterol, and 18% reduction in number of people with high glycated hemoglobin levels (a marker of diabetes), which intuitively seem big enough to be part of an across-the-board health improvement that passes cost-benefit muster.
This would be much more convincing if you reported the costs along with the benefits, so that one could form some kind of estimate of what you're willing to pay for this. But, again, I think your argument is motivated. "Consistent with zero" means just that; it means that the study cannot exclude the possibility that the intervention was actively harmful, but they had a random fluctuation in the data.
I get the impression that people here talk a good game about statistics, but haven't really internalised the concept of error bars. I suggest that you have another look at why physics requires five sigma. There are really good reasons for that, you know; all the more so in a mindkilling-charged field.
I was responding to the suggestion that, even if the effects that they found are real, they are too small to matter. To me, that line of reasoning is a cue to do a Fermi estimate to get a quantitative sense of how big the effect would need to be in order to matter, and how that compares to the empirical results.
I didn't get into a full-fledged Fermi estimate here (translating the measures that they used into the dollar value of the health benefits), which is hard to do that when they only collected data on a few intermediate health measures. (If anyone else has given it a shot, I'd like to take a look.) I did find a couple effect-size-related numbers for which I feel like I have some intuitive sense of their size, and they suggest that that line of reasoning does not go through. Effects that are big enough to matter relative to the costs of additional health spending (like 3 lives saved in their sample, or some equivalent benefit) seem small enough to avoid statistical significance, and the point estimates that they found which are not statistically significant (8-18% reductions in various metrics) seem large enough to matter.
My overall conclusion about the (based on what I know about it so far) study is that it provides little information for updating in any direction, because of those wide error bars. The results are consistent with Medicaid having no effect, they're consistent with Medicaid having a modest health benefit (e.g., 10% reduction in a few bad things), they're consistent with Medicaid being actively harmful, and they're consistent with Medicaid having a large benefit (e.g. 40% reduction in many bad things). The likelihood ratios that the data provide for distinguishing between those alternatives are fairly close to one, with "modest health benefit" slightly favored over the more extreme alternatives.
Again, the original point McArdle is making is that "consistent with zero" is just completely not what the proponents expected beforehand, and they should update accordingly. See my discussion with TheOtherDave, below. A small effect may, indeed, be worth pursuing. But here we have a case where something fairly costly was done after much disagreement, and the proponents claimed that there would be a large effect. In that case, if you find a small effect, you ought not to say "Well, it's still worth doing"; that's not what you said before. It was claimed that there would be a large effect, and the program was passed on this basis. It is then dishonest to turn around and say "Ok, the effect is small but still worthwhile". This ignores the inertia of political programs.
Most Medicaid proponents did not have expectations about the statistical results of this particular study. They did not make predictions about confidence intervals and p values for these particular analyses. Rather, they had expectations about the actual benefit of Medicaid.
You cite Ezra Klein as someone who expected that Medicaid would drastically reduce mortality; Klein was drawing his numbers from a report which estimated that in the US "137,000 people died from 2000 through 2006 because they lacked health insurance, including 22,000 people in 2006." There were 47 million uninsured Americans in 2006, so those 22,000 excess deaths translate into 4.7 excess deaths per 10,000 uninsured people each year. So that's the size of the drastic reduction in mortality that you're referring to: 4.7 lives per 10,000 people each year. (For comparison, in my other comment I estimated that the Medicaid expansion would be worth its estimated cost if it saved at least 1.5 lives per 10,000 people each year or provided an equivalent benefit.)
Did the study rule out an effect as large as this drastic reduction of 4.7 per 10,000? As far as I can tell it did not (I'd like to see a more technical analysis of this). There were under 10,000 people in the study, so I wouldn't be surprised if they missed effects of that size. Their point estimates, of an 8-18% reduction in various bad things, intuitively seem like they could be consistent with an effect that size. And the upper bounds of their confidence intervals (a 40%+ reduction in each of the 3 bad things) intuitively seem consistent with a much larger effect. So if people like Klein and Drum had made predictions in advance about the effect size of the Oregon intervention, I suspect that their predictions would have fallen within the study's confidence interval.
There are presumably some people who did expect the results of the study to be statistically significant (otherwise, why run the study?), and they were wrong. But this isn't a competition between opponents and proponents where every slipup by one side cedes territory to the other side. The data and results are there for us to look at, so we can update based on what the study actually found instead of on which side of the conflict fought better in this battle. In this case, it looks like the correct update based on the study (for most people, to a first approximation) is to not update at all. The confidence interval for the effects that they examined covers the full range of results that seemed plausible beforehand (including the no-effect-whatsoever hypothesis and the tens-of-thousands-of-lives-each-year hypothesis), so the study provides little information for updating one's priors about the effectiveness of Medicaid.
For the people who did make the erroneous prediction that the study would find statistically significant results, why did they get it wrong? I'm not sure. A few possibilities: 1) they didn't do an analysis of the study's statistical power (or used some crude & mistaken heuristic to estimate power), 2) they overestimated how large a health benefit Medicaid would produce, 3) the control group in Oregon turned out to be healthier than they expected which left less room for Medicaid to show benefits, 4) fewer members of the experimental group than they expected ended up actually receiving Medicaid, which reduced the actual sample size and also added noise to the intent-to-treat analysis (reducing the effective sample size).
I do want to point out that, while I agree with your general points, I think that unless the proponents put numerical estimates up beforehand, it's not quite fair to assume they meant "it will be statistically significant in a sample size of N at least 95% of the time." Even if they said that, unless they explicitly calculated N, they probably underestimated it by at least one order of magnitude. (Professional researchers in social science make this mistake very frequently, and even when they avoid it, they can only very rarely find funding to actually collect N samples.)
I haven't looked into this study in depth, so semi-related anecdote time: there was recently a study of calorie restriction in monkeys which had ~70 monkeys. The confidence interval for the hazard ratio included 1 (no effect), and so they concluded no statistically significant benefit to CR on mortality, though they could declare statistically significant benefit on a few varieties of mortality and several health proxies.
I ran the numbers to determine the power; turns out that they couldn't have reliably noticed the effects of smoking (hazard ratio ~2) on longevity with a study of ~70 monkeys, and while I haven't seen many quoted estimates of the hazard ratio of eating normally compared to CR, I don't think there are many people that put them higher than 2.
When you don't have the power to reliably conclude that all-cause mortality decreased, you can eke out some extra information by looking at the signs of all the proxies you measured. If insurance does nothing, we should expect to see the effect estimates scattered around 0. If insurance has a positive effect, we should expect to see more effect estimates above 0 than below 0, even though most will include 0 in their CI. (Suppose they measure 30 mortality proxies, and all of them show a positive effect, though the univariate CI includes 0 for all of them. If the ground truth was no effect on mortality proxies, that's a very unlikely result to see; if the ground truth was a positive effect on mortality proxies, that's a likely result to see.)
Incidentally, how did you do that?
It is of course very difficult to extract any precise numbers from a political discussion. :) However, if you click through some of the links in the article, or have a look at the followup from today, you'll find McArdle quoting predictions of tens of thousands of preventable deaths yearly from non-insured status. That looks to me like a pretty big hazard rate, no?
No. The Oracle says there're about 50 million Americans without health insurance. The predictions you quoted refer to 18,000 or 27,000 deaths for want of insurance per year. The higher number implies only a 0.054% death rate per year, or a 3.5% death rate over 65 years (Americans over 65 automatically get insurance). This is non-negligible but hardly huge (and potentially important for all that).
Edit: and I see gwern has whupped me here.
If I throw a die once and it comes up heads I'm going to be confused. Now, assuming you meant "toss a coin and it comes up heads six times out of ten".
What is your intended 'correct' answer to the question? I think I would indeed hesitantly update a very (very) tiny bit in the direction of the coin being biased but different priors regarding the possibility of the coin being biased in various ways and degrees could easily make the update be towards not-biased. I'd significantly lower p(the coin is biased by having two heads) but very slightly raise p(the coin is slightly heavier on the tails side), etc.
My intended correct answer is that, on this data, you technically can adjust your belief very slightly; but because the prior for a biased coin is so tiny, the update is not worth doing. The calculation cost way exceeds any benefit you can get from gruel this thin. I would say "Null hypothesis [ie unbiased coin] not disconfirmed; move along, nothing to see here". And if you had a political reason for wishing the coin to be biased towards heads, then you should definitely not make any such update; because you certainly wouldn't have done so, if tails had come up six times. In that case it would immediately have been "P-level is in the double digits" and "no statistical significance means exactly that" and "with those errors we're still consistent with a heads bias".
I would think that our prior for "health care improves health" should be quite a bit larger than the prior for a coin to be biased.
That depends on how long "we" have been reading Overcoming Bias.
Hanson's point is that we often over-treat to show we care- not that 0 health care is optimal. Medicaid patients don't really have to worry about overtreatment.
I was interpreting "health care improves health" as "healthcare improves health on the margin." Is this not what was meant?
As someone who has a start-up in the healthcare industry, this runs counter to my personal experience. Also, currently "medicaid overtreatment" is showing about 676,000 results on Google (while "medicaid undertreatment" is showing about 1,240,000 results). Even if it isn't typical, it surely isn't an unheard-of phenomenon.