Oblique request made without any explanation: can anyone provide examples of beliefs that are incontrovertibly incorrect, but which intelligent people will nonetheless arrive at quite reasonably through armchair-theorising?
I am trying to think up non-politicised, non-controversial examples, yet every one I come up with is a reliable flame-war magnet.
ETA: I am trying to reason about disputes where on the one hand you have an intelligent, thoughtful person who has very expertly reasoned themselves into a naive but understandable position p, and on the other hand, you have an individual who possesses a body of knowledge that makes a strong case for the naivety of p.
What kind of ps exist, and do they have common characteristics? All I can come up with are politically controversial ps, but I’m starting my search from a politically-controversial starting point. The motivating example for this line of reasoning is so controversial that I’m not touching it with a shitty-stick.
That “0.99999....” represents a concept that evaluates to 1 is a question of notation, not mathematics. 0.99999… does not inherently equal 1; rather, by convention, it is understood to mean 1. The debate is not about the territory, it is about what the symbols on the map mean.
Where does one draw the line, if at all? “1+1 does no inherently equal 2; rather, by convention, it is understood to mean 2. The debate is not about the territory, it is about what the symbols on the map mean.” It seems to me like that—very ‘mysteriously’—people who understand real analysis never complain “But 0.999… doesn’t equal 1″; sufficient mathematical literacy seems to kill any such impulse, which seems very telling to me.
Yes, and that’s a case of “you don’t understand mathematics, you get used to it.” Which applies exactly to notation and related conventions.
Edit:
More specifically, if we let a_k=9/10^k, and let s_n be the sum from k=1 to n of a_k, then the limit of s_n as n goes to infinity will be 1, but 1 won’t be in {s_n|n in R}.
When somebody who is used to calculus sees ”.99...” What they are thinking of is the limit, which is 1.
But before you get used to that, most likely what you think of is some member of {s_n|n in R} with an n that’s large enough that you can’t be bothered to write all the nines, but which is still finite.
Exactly. The arguments about whether 0.99999.… = 1 are lacking a crucial item: a rigorous definition of what “0.9999...” refers to. The argument isn’t “Is the limit as n goes to infinity of sum from 1 to n of 9*10^-n equal to 1?” It’s “Here’s a sequence of symbols. Should we assign this sequence of symbols the value of 1, or not?” Which is just a silly argument to have. If someone says “I don’t believe that 0.9999.… = 1“, the correct response (unless they have sufficient real analysis background) is not “Well, here’s a proof that of that claim”, it’s “Well, there are various axioms and definitions that lead to that being treated as being equal to 1”.
It’s “Here’s a sequence of symbols. Should we assign this sequence of symbols the value of 1, or not?” Which is just a silly argument to have.
It’s not. The “0.999… doesn’t equal 1” meme is largely crackpottery, and promotes amateur overconfidence and (arguably) mathematical illiteracy.
Terms are precious real estate, and their interpretations really are valuable. Our thought processes and belief networks are sticky; if someone has a crap interpretation of a term, then it will at best cause unnecessary friction in using it (e.g. if you define the natural numbers to include −1,...,-10 and have to retranslate theorems because of this), and at worst one will lose track of the translation between interpretations and end up propagating false statements (“2^n can sometimes be less than 2 for n natural”)
the correct response (unless they have sufficient real analysis background) is not “Well, here’s a proof that of that claim”, it’s “Well, there are various axioms and definitions that lead to that being treated as being equal to 1″.
It would be an accurate response (even if not the most pragmatic or tactful) to say, “Sorry, when you pin down what’s meant precisely, it turns out to be a much more useful convention to define the proposition 0.999...=1 such that it is true, and you basically have to perform mental gymnastics to try to justify any usage where it’s not true. There are technically alternative schemas where this could fail or be incoherent or whatever, but unless you go several years into studying math (and even then maybe only if you become a logician or model theorist or something), those are not what you’ll be encountering.”
One could define ‘marble’ to mean ‘nucleotide’. But I think that somebody who looked down on a geneticist for complaining about people using ‘marble’ as if it means ‘nucleotide’, and who said it was a silly argument as if the geneticist and the person who invented the new definition were Just As Bad As Each Other, would be mistaken, and I would suspect they were more interested in signalling their Cleverness via relativist metacontrarianism than getting their hands dirty figuring out the empirical question of which definitions are useful in which contexts.
Actually, I could imagine you reading that comment and feeling it still misses your point that 0.999… is undefined or has different definitions or senses in amateur discussions. In that case, I would point to the idea that one can makes propositions about a primitive concept that turn out to be false about the mature form of it. One could make claims about evidence, causality, free will, knowledge, numbers, gravity, light, etc. that would be true under one primitive sense and false under another. Then minutes or days or month or years or centuries or millennia later it turns out that the claims were false about the correct definition.
It would be a sin of rationality to assume that, since there was a controversy over definitions, and some definitions proved the claim and some disproved it, that no side was more right than another. One should study examples of where people made correct claims about fuzzy concepts, to see what we might learn in our own lives about how these things resolve. Were there hints that the people who turned out to be incorrect ignored? Did they fail to notice their confusion? Telltale features of the problem that favoured a different interpretation? etc.
It’s not. The “0.999… doesn’t equal 1” meme is largely crackpottery
A lot (in fact, all of them that don’t involve a rigorous treatment of infinite series) of the “proofs” that it does equal 1 are fallacious, and so the refusal to accept them is actually a reasonable response.
You seem to making an assertion about me in your last paragraph, but doing so very obliquely. Your analogy is not very good, as people do not try to argue that one can logically prove that “marble” does not mean “nucleotide”, they just say that it is defined otherwise.
If we’re analogizing ”.9999… = 1″ to “marble doesn’t mean’t nucleotide”, then ”
You seem to making an assertion about me in your last paragraph, but doing so very obliquely.
Apologies for that. I don’t think that that specific failure mode is particularly likely in your case, but it seems plausible to me that other people thinking in that way has shifted the terms of discourse such that that form of linguistic relativism is seen as high-status by a lot of smart people. I am more mentioning it to highlight the potential failure mode; if part of why you hold your position is that it seems like the kind of position that smart people would hold, but I can account for those smart people holding it in terms of metacontrarianism, then that partially screens off that reason for endorsing the smart people’s argument.
It looks like you submitted your comment before you meant to, so I shall probably await its completion before commenting on the rest.
I thought about this on & off over the last couple of days and came up with more candidates than you can shake a shitty stick at. Some of these are somewhat political or controversial, but I don’t think any are reliable flame-war magnets. I expect some’ll ring your cherries more than others, but since I can’t tell which, I’ll post ’em all and let you decide.
The answer to the Sleeping Beauty puzzle is obviously1⁄2.
Rational behaviour, being rational, entails Pareto optimal results.
Food availability sets a hard limit on the number of kids people can have, so when people have more food they have more kids.
Truth is an absolute defence against a libel accusation.
If a statistical effect is so small that a sample of several thousand is insufficient to reliably observe it, the effect’s too small to matter.
Controlling for an auxiliary variable, or matching on that variable, never worsens the bias of an estimate of a causal effect.
Human nature being as brutish as it is, most people are quite willing to be violent, and their attempts at violence are usually competent.
In the increasingly fast-paced and tightly connected United States, residential mobility is higher than ever.
The immediate cause of death from cancer is most often organ failure, due to infiltration or obstruction by spreading tumours.
Aumann’s agreement theorem means rationalists may never agree to disagree.
Friction, being a form of dissipation, plays no role in explaining how wings generate lift.
Seasons occur because Earth’s distance from the Sun changes during Earth’s annual orbit.
Given the rise of online piracy, the ridiculous cost of tickets, and the ever-growing convenience of other forms of entertainment, cinema box office receipts must be going down & down.
Looking at voting in an election from the perspective of timeless decision theory, my voting decision is probably correlated and indeed logically linked with that of thousands of people relatively likely to agree with my politics. This could raise the chance of my influencing an election above negligibility, and I should vote accordingly.
The countries with the highest female life expectancies are approaching a physiologically fixed hard limit of 65 — sorry, 70 — sorry, 80 — sorry, 85 years.
The answer to the Sleeping Beauty puzzle is obviously1⁄3.
The limiting of birth rates can last for a very long time as long as you stay at replacement rates. I don’t think “obvious evolutionary reasons” apply to humans any more, it’s not likely another species will outcompete us by breeding faster.
In the “long-long run”, given ad hoc reproductive patterns, yeah, I’d expect evolution to ratchet average human fertility higher & higher until much of humanity slammed into the Malthusian limit, at which point “when people have more food they have more kids” would become true.
Nonetheless, it isn’t true today, it’s unlikely to be true for the next few centuries unless WWIII kicks off, and may never come to pass (humanity might snuff itself out of existence before we go Malthusian, or the threat of Malthusian Assured Destruction might compel humanity to enforce involuntary fertility limits). So here in 2014 I rate the idea incontrovertibly false.
Noticing that people who are the best in any sport practice the most and concluding that being good at a sport is simply a matter of practice and determination. Tabula Rasa in general.
The supply-demand model of minimum wage? Is this political? I’m not saying minimum wage is good or bad, just that the supply-demand model can’t settle the question yet people learning about economics tend to be easily convinced by the simple explanation.
That thermodynamics proves that weight loss + maintenance is simply a matter of diet and exercise (this is more Yudkowsky’s fight than mine).
I doubt it is possible to find non-controversial examples of anything, and especially of things plausible enough to be believed by intelligent non-experts, outside of the hard sciences.
If this is true, the only plausible examples would be such as “an infinity cannot be larger than another infinity”, “time flows uniformly regardless of the observer”, “biological species have unchanging essences”, and other intuitively plausible statements unquestionably contradicted by modern hard sciences.
Intelligent people make theories about how a drug is supposed to work and think it would help to cure some illness. Then when the drug is brought into clinical trials more than 90% of new drugs still fail to live up to the theoretical promise that the drug held.
A fun one which came up recently on IRC: everyone thinks that how your parents raise you is incredibly important, this is so obvious it doesn’t need any proof and is universal common sense (how could influencing and teaching a person from scratch to 18 years old not have deep and profound effects on them?), and you can find extended discussions of the best way to raise kids from Plato’s Republic to Rousseau’s Emile to Spock.
Except twin studies consistently estimate that the influence of ‘shared environment’ (the home) is small or near-zero for many traits compared to genetics and randomness/nonshared-environment.
If you want to predict whether someone will be a smoker or smart, it doesn’t matter whether they’re raised by smokers or not (to borrow an example from The Nurture Assumption*); it just matters whether their biological parents were smokers and whether they get unlucky.
This is so deeply counterintuitive and unexpected that even people who are generally familiar with the relevant topics like IQ or twin studies typically don’t know about this or disbelieve it.
(Another example is probably folk physics: Newtonian motion is true, experimentally confirmed, mathematically logical, and completely unintuitive and took millennia to be developed after the start of mechanics.)
But this interpretation foolishly neglects to consider the genetic component of parent-child similarity. Table 7.2 summarizes reports of two twin studies, an adoptive study, and a family study. In all these studies, the offspring of smokers were adults at the time they were surveyed. Smoking’s heritability averaged 43%, whereas smoking’s rearing environmental variation was close to zero. [Shared rearing variation (c^2): N/A (family, Eysenck (1980)); <0% (Twin, Cannelli, Swan, Robinette, & Fabsilz (1990)); <0% (Twin, Swan, Carmelli, Rosenman, Fabsitz, & Christian (1990)); <0% (Adoptive, Eysenck (1980)); mean: 0%] In other words, effects of rearing variation (e.g. parents’ lighting up or not, or having cigarettes in the home or not) were nil by the time the children had reached adulthood. In Eysenck’s (1980) report on adoptees, the smoking correlation of biologically unrelated parent-child pairs was essentially zero (r = -.02). Parental smoking may influence a childs risk through genetic inheritance: The role of parents is a passive one-providing a set of genes at loci relevant to smoking risk, but not SOCially influencing their offspring.
A fun one which came up recently on IRC: everyone thinks that how your parents raise you is incredibly important, this is so obvious it doesn’t need any proof and is universal common sense, and you can find extended discussions of the best way to raise kids from Plato’s Republic to Rousseau’s Emile to Spock.
Except twin studies consistently estimate that the influence of ‘shared environment’ (the home) is small or near-zero for many traits compared to genetics and randomness/nonshared-environment.
This is quite possibly the most comforting scientific result ever for me as a parent, by the way.
Whereas for me, it’s horrifying, given that my ex-spouse turned out to be an astonishingly horrible person.
I seem to recall Yvain posting a link to something he referred to as the beginnings of a possible rebuttal to The Nurture Assumption; I suppose I shall have to hang my hopes on that.
It may or may not be comforting to reflect that your ex-spouse is probably less horrible than s/he seems to you. (Just on general outside-view principles; I have no knowledge of your situation or your ex.)
‘Shh, kemo sabe—you hear that?’ ‘No; the jungle is silent tonight.’ ‘Yes. The silence of the p-values. A wild publication bias stalks us. We must be cautious’.
So… does it mean that it’s completely irrelevant who adopted Harry Potter, because the results would be the same anyway?
Or is the correct model something like: abuse can change things to worse, but any non-abusive parenting simply means the child will grow up determined by their genes? That is, we have a biologically set “destiny”, and all the environment can do is either help us reach this destiny or somehow cripple us halfway (by abuse, by lack of nutrition, etc.).
Or is the correct model something like: abuse can change things to worse, but any non-abusive parenting simply means the child will grow up determined by their genes? That is, we have a biologically set “destiny”, and all the environment can do is either help us reach this destiny or somehow cripple us halfway (by abuse, by lack of nutrition, etc.).
In an home environment within the normal range for a population, the home environment will matter little in a predictable sense on many traits compared to the genetic legacy, and random events/choices/biological-events/accidents/etc. There are some traits it will matter a lot on, and in a causal sense, the home environment may determine various important outcomes but not in a way that is predictable or easily measured. The other category of ‘nonshared environment’ is often bigger than the genetic legacy, so speaking of a biologically set destiny is misleading: biologically influenced would be a better phrase.
Has this been demonstrated for home environments in the developing world or sub-middle class home environments in the developed world? My prior understanding was that it had not been.
There are serious restriction of range problems with the literature. I believe that there is one small French adoption study with unrestricted range which produced 1 sigma IQ difference between the bottom and top buckets (deciles?) of adopting families.
I wonder if this what Shalizi alludes to when he says that IQ is closer to that of the adoptive parents than that of the biological parents.
I believe that there is one small French adoption study which produced 1 sigma IQ difference between the bottom and top buckets (deciles?) of adopting families.
(Both references describe the same study.) Capron & Duyme found 38 French children placed for adoption before age 2, 20 of them to parents with very high socioeconomic status (operationalized as having 14-23 years of education and working a profession) and 18 to parents with very low socioeconomic status (unskilled & semi-skilled labourers or farmers, with 5-8 years of education). When the kids took the WISC-R IQ test, those adopted into the high-SES families had a mean IQ of 111.6, while those in the low-SES families had a mean IQ of 100.0, for a difference of 0.77 sigma.
So… does it mean that it’s completely irrelevant who adopted Harry Potter, because the results would be the same anyway?
In the context of IQ I’ve seen it claimed that normal variation in parenting doesn’t do much, but extreme abuse can still have a substantial effect. So parenting quality would only make a difference at the tails of the parenting quality distribution, but there it would make quite a difference.
In “No Two Alike” Harris argues that the biggest non-shared environment personality determinant is peer group. So Harry Potter style “Lock him up in a closet with no friends” would actually have a huge effect.
And it should be noted that parents do have control over peer group: where to live, public school vs. private school vs. homeschooling, getting children to join things, etc. So parenting still matters even if it’s all down to genetics and non-shared environment.
Also, has anyone investigated whether the proper response to publicized social-science answers/theories/whatever you want to call them is to assume they’re true or just wait for them to be rejected? That is: how many publicized social-science answers [the same question could be asked for diet-advice answers conflicting with pre-nutrition-studies received wisdom, etc.] were later rejected? It could well be that the right thing to do in general is stick with common sense...
And it should be noted that parents do have control over peer group: where to live, public school vs. private school vs. homeschooling, getting children to join things, etc.
Exactly! If you have something to protect as a parent, then after hearing “parents are unimportant, the important stuff is some non-genetic X” the obvious reaction is: “Okay, so how can I influence X?” (Instead of saying: “Okay, then it’s not my fault, whatever.”)
For example, if I want my children to be non-smokers, and I learn that whether I am smoking or not has much smaller impact than whether my children’s friends are smoking… the obvious next question is: What can I do to increase the probability that my children’s friends will be non-smokers? There are many indirect methods like choosing the place to live, choosing the school, choosing free-time activities, etc. I would just like to have more data on what smoking correlates with; where should I send my children and where should I prevent them from going, so that even if they “naturally” pick their peer group in that place, they will more likely pick non-smokers. (Replace non-smoking with whatever is your parenting goal.)
Shortly, when I read “parenting” in a study, I mentally translate it as: “what an average, non-strategic parent does”. That’s not the same as: “what a parent could do”.
Except twin studies consistently estimate that the influence of ‘shared environment’ (the home) is small or near-zero for many traits compared to genetics and randomness/nonshared-environment.
As Protagoras points out here there are systematic problems with twin studies.
There are problems, but I don’t think they are large, I think they are brought up mostly for ideological reasons (Shalizi is not an unbiased source and has a very big axe to grind), and a lot of the problems also cut the other way. For example, measurement error can reduce estimates of heritability a great deal, as we see in twin studies which correct for it and as predicted get higher heritability estimates, like “Not by Twins Alone: Using the Extended Family Design to Investigate Genetic Influence on Political Beliefs”, Hatemi et al 2010 (this study, incidentally, also addresses the claim that twins may have special environments compared to their non-twin siblings and that will bias results, which has been claimed by people who dislike twin studies; there’s no a priori reason to think this, and Hatemi finds no evidence for it, yet they had claimed it).
Shalizi is not an unbiased source and has a very big axe to grind
Do you mean more by this than that he has very strong opinions on this topic? I would guess you do—that you mean there’s something pushing him towards the opinions he has, that isn’t the way it is because those opinions are right. But what?
Shalizi is somewhere around Marxism in politics. This makes his writings on intelligence very frustrating, but on the other hand, it also means he can write very interesting things on economics at times—his essay on Red Plenty is the most interesting thing I’ve ever seen on economics & computational complexity. Horses for courses.
Shalizi states at least part of his position as follows:
“Market socialism” is a current of ideas [...] for how to make extensive use of markets without thereby creating gross economic and political inequality. [...] On the other hand, modern states are powerful enough as things stand; to turn the economy wholly over to them is a bad idea. To combine markets with socialism seems like an elegant and feasible solution, at least technically, and it’s one which I support [...]
and on the same page says these things:
Incredible things were done in the name of [the political control of economic life], some of them noble and heroic (like resistance to Fascism, and the creation of democratic welfare states), others scarcely matched for wickedness (like Stalin’s purges and deliberate famines) and stupidity (like Mao’s Great Leap Forward and apparently unintentional but highly foreseeable famines).
and
The history of socialist movements is [...] bound up with the histories of organized labour, of economics and left-wing politics and general, and, less honourably, with that of revolutions and totalitarianism. [...] it had become clear [...] that they [sc. the Soviets] were far, far worse than capitalist democracies [...]
I have to say that none of this sounds very Marxist to me. Shalizi apparently finds revolutions dishonourable; the most notable attempts at (nominally) Marxist states, the USSR and the PRC, he criticizes in very strong terms; he wants most prices to be set by markets (at least this is how I interpret what he says on that page and others it links to).
Sometime between [1956] and 1968 [...] he [sc. Kolakowski] stopped considering himself a Marxist, even a revisionist one [...] though still a socialist and (I think) an atheist.
followed in the next paragraph by
I think his views of socialism and Marxism are absolutely on-target
which seems to me to imply, in particular, that Shalizi doesn’t consider himself “a Marxist, even a revisionist one”.
He’s certainly a leftist, certainly considers himself a socialist, but he seems quite some way from Marxism. (And further still from, e.g., any position taken by the USSR or the PRC.)
[The ideas of the Frankfurt School] are very extreme examples of ways of thinking about society, both normatively and descriptively, for which I have very little sympathy, yet are closely affiliated to ideas I am receptive to. (E.g.: so far as I can see, they were all what Marxists would call “idealists”, which is not a compliment, yet they claimed to be Marxists, even historical materialists!) My interest in them is thus interest in my notorious and embarrassing ideological cousins...
Not that I think pigeon-holing him is very useful for determining his views on economics or politics, let alone IQ.
This makes his writings on intelligence very frustrating
Does having political views that approximate Marxism imply irrationally-derived views on intelligence? I don’t see why it should, but this may simply be a matter of ignorance or oversight on my part.
I am not an expert on Marx but would be unsurprised to hear that he made a bunch of claims that are ill-supported by evidence and have strong implications about intelligence—say, that The Proletariat is in no way inferior in capabilities, even statistically, to The Bourgeoisie. But to me “somewhere around Marxism in politics” doesn’t mean any kind of commitment to believing everything Marx wrote. It isn’t obvious to me why someone couldn’t hold pretty much any halfway-reasonable opinions about intelligence, while still thinking that it is morally preferable for workers to own the businesses they work for and the equipment they use, that we would collectively be better off with much much more redistribution of wealth than we currently have (or even with the outright abolition of individual property), etc.
In another comment I’ve given my reasons for doubting that Shalizi is even “somewhere around Marxism in politics”. But even if I’m wrong about that, I’m not aware of prior commitments he has that would make him unable to think rationally about intelligence.
Of course it needn’t be a matter of prior commitments as such. It could, e.g., be that he is immersed in generally-very-leftist thought (this being either a cause or a consequence of his own leftishness), and that since for whatever reason there’s substantial correlation between being a leftist and having one set of views about intelligence rather than another, Shalizi has just absorbed a typically-leftist position on intelligence by osmosis. But, again, the fact that he could have doesn’t mean he actually has.
I think the guts of what you’re claiming is: Shalizi’s views on intelligence are a consequence of his political views; either his political views are not arrived at rationally, or the way his political views have given rise to his views on intelligence are not rational, or both. -- That could well be true, but so far what you’ve given evidence for is simply that he holds one particular set of political views. How do you get from there to the stronger claim about the relationship between his views on the two topics?
I think the guts of what you’re claiming is: Shalizi’s views on intelligence are a consequence of his political views; either his political views are not arrived at rationally, or the way his political views have given rise to his views on intelligence are not rational, or both. -- That could well be true, but so far what you’ve given evidence for is simply that he holds one particular set of political views. How do you get from there to the stronger claim about the relationship between his views on the two topics?
At least part of it was reading his ‘Statistical Myth’ essay, being skeptical of the apparent argument for some of the reasons Dalliard would lay out at length years later, reading all the positive discussions of it by people I was unsure understood either psychometrics or Shalizi’s essay (which he helpfully links), and then reading a followup dialogue http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/495.html where—at least, this is how it reads to me—he carefully covers his ass, walks back his claims, and quietly concedes a lot of key points. At that point, I started to seriously wonder if Shalizi could be trusted on this topic; his constant invocation of Stephen Jay Gould (who should be infamous by this point) and his gullible swallowing of ‘deliberate practice’ as more important than any other factor which since has been pretty convincingly debunked (both on display in the dialogue) merely reinforce my impression and the link to Gould (Shalizi’s chief comment on Gould’s Mismeasure of Man is apparently solely “I do not recommend this for the simple reason that I read it in 1988, when I was fourteen. I remember it as a very good book, for whatever that’s worth.”; no word on whether he is bothered by Gould’s fraud) suggests it’s partially ideological. Another revealing page: http://vserver1.cscs.lsa.umich.edu/~crshalizi/notebooks/iq.html I can understand disrecommending Rushton, but disrecommending Jensen who invented a lot of the field and whose foes even admire him? Recommending a journalist from 1922? Recommending some priming bullshit? (Where’s the fierce methodologist statistician when you need him...?) There’s one consistent criterion he applies: if it’s against IQ and anything to do with it, he recommends it, and if it’s for it, he disrecommends it. Apparently only foes of it ever have any of the truth.
I believe his political views are somewhere between way to the left of the Democratic Party and socialism. He dislikes the entire field of intelligence research in psychology because it’s ideologically inconvenient. He criticises anything that he can find to criticise about it. Think of him as Stephen Jay Gould, but much smarter and more honest.
See, this is a place where the US is different from Europe. Because over here (at least in the bit of Europe I’m in), being “somewhere to the right of socialism” isn’t thought of as the kind of crazy extremism that ipso facto makes someone dangerously biased and axe-grindy.
Now, of course politics is what it is, and affiliation with even the most moderate and reasonable political position can make otherwise sensible people completely blind to what’s obvious to others. So the fact that being almost (but not quite) a socialist looks to me like a perfectly normal and sensible position is perfectly compatible with Shalizi being made nuts by it. But to me “he’s somewhere to the left of Barack Obama” doesn’t look on its own like something that makes someone a biased source and explains what their problem is.
Yup, that’s a good point. (Though it depends on what “local” means. I have the impression that academics in the US tend to be leftier than the population at large.)
Academia in the US is much leftier than the population at large. I believe it was Jonathan Haidt who went looking for examples of social conservatives in his field and people kept nomimating Philip Tetlock who would not describe himself thus. At a conference Dr.Haidt was looking for a show of hands for various political positions. Republicans were substantially less popular than Communists. Psychology is about as left wing as sociology and disciplines vary but academia is a great deal to the left of the US general population.
collecting published results in medicine, psychology, epidemiology & economics journals gives an unbiased idea of the sizes of the effects they report
which is wrong at least twice over (publication bias and correlation-causation confusion) but is, I suspect, an implicit assumption made by lots of people who only made it to the first stage of traditional rationality (and reason along the lines of “normal people are full of crap, scientists are smarter and do SCIENCE!, so all I need to do to be correct is regurgitate what I find in scientific journals”).
I’d generalize that to something like X which is wrong at least twice over
Then don’t.
I point is more that if you only have theory and no empiric evidence, then it’s likely that you are wrong. That doesn’t mean that having a bit of empiric evidence automatically means that you are right.
I also would put more emphasis on having empiric feedback loops than at scientific publications. Publications are just one way of feedback. There a lot to be learned about psychology by really paying attention on other people with whom you interact.
If I interact with a person who has a phobia of spider and solve the issue and afterwards put a spider on his arm and the person doesn’t freak out, I have my empiric feedback. I don’t need a paper to tell me that the person doesn’t have a phobia anymore.
I point is more that if you only have theory and no empiric evidence, then it’s likely that you are wrong. That doesn’t mean that having a bit of empiric evidence automatically means that you are right.
Yes, I agree. To clarify, I was neither condoning the belief in my bullet point, nor accusing you of believing it. I just wanted to tip my hat to you for inspiring my example with yours.
I remember reading this in other places I don’t remember, and it seems to inspire furious arguments despite being non-political and not very controversial.
That’s a great example. If I recall, people who get worked up about it generally feel that the answer is obvious and the other side is stupid for not understanding the argument.
As I remember the problem, the plane’s wheels are supposed to be frictionless so that their rotation is uncoupled from the rest of the plane’s motion. Hence the speed of the conveyor belt is irrelevant and the plane always takes off. Now, if you had a helicopter on a turntable...
What I mean is, on hearing that I thought of a conveyor belt whose top surface was moving at a speed -x with respect to the air, and a plane on top of it moving at a speed x with respect to the top of the conveyor belt, i.e. the plane was stationary with respect to the air. But on reading the Snopes link what was actually meant was that the conveyor belt was moving at speed -x and the plane’s engines were working as hard as needed to move at speed x on stationary ground with no wind.
While at the same time the rolling speed of the plane, which is the sum of it’s forward movement and the speed of the treadmill, is supposed to be equal to the speed of the treadmill. Which is impossible if the plane moves forward.
I’m not sure what you mean by “rolling speed of the plane”, “it’s forward movement”, and “speed of the treadmill”. The phrase “rolling speed” sounds like it refers to the component of the plane’s forward motion due to the turning of its wheels, but that’s not a coherent thing to talk about if one accepts my assumption that the wheels are uncoupled from the plane.
Rolling speed = how fast the wheels turn, described in terms of forward speed. So it’s the circumference of the wheels multiplied by their angular speed. And the wheels are not uncoupled from the plane they are driven by the plane. It was only assumed that the friction in the wheel bearings is irrelevant.
Forward movement of the plane = speed of the plane relative to something not on the treadmill. I guess I should have called it airspeed, which it would be if there is no wind.
Speed of the treadmill = how fast the surface of the treadmill moves.
And that is more time than I wanted to spend rehashing this old nonsense. The grandparent was only meant to explain why the great grandparent would not have settled the issue, not to settle it on its own. The only further comment I have is the whole thing is based on an unrealistic setup, which becomes incoherent if you assume that it is about real planes and real treadmills.
And that is more time than I wanted to spend rehashing this old nonsense.
Fair enough. I have to chip in with one last comment, but you’ll be happy to hear it’s a self-correction! My comments don’t account for potential translational motion of the wheels, and they should’ve done. (The translational motion could matter if one assumes the wheels experience friction with the belt, even if there’s no internal wheel bearing friction.)
That’s different though. The Plane on a Treadmill started with somebody specifying some physically impossible conditions, and then the furious arguments were between people stating the implication of the stated conditions on one side and people talking about the real world on the other hand.
I think you may have expressed this one the wrong way around; the way you’ve phrased it (“can make you better off”) is the surprising truth, not the surprising untruth.
If your twin flies through space for 20 years at close to the speed of light, they’ll be 20 years older when they come back.
They will. I think you mean: If your twin flies through space at close to the speed of light and arrives back 20 years later, they’ll be 20 years older when they come back. That one’s false.
To be more explicit: What is needed to make the statement interestingly wrong is for the two 20-year figures to be in different reference frames. If your twin does something for 20 years, then they will be 20 years older; but if they do something for what you experience as 20 years they may not be.
Take, for example, the proposition: “Two straight lines cannot enclose a space, and with these alone no figure is possible,” and try to deduce it from the conception of a straight line and the number two; or take the proposition: “It is possible to construct a figure with three straight lines,” and endeavour, in like manner, to deduce it from the mere conception of a straight line and the number three. All your endeavours are in vain, and you find yourself forced to have recourse to intuition, as, in fact, geometry always does.
Geometry, nevertheless, advances steadily and securely in the province of pure a priori cognitions, without needing to ask from philosophy any certificate as to the pure and legitimate origin of its fundamental conception of space.
I agree that Kant doesn’t seem to have ever considered non-euclidean geometry, and thus can’t really be said to be making an argument that space is flat. If we could drop an explanation of general relativity, he’d probably come to terms with it. On the other hand, he just assumes that two straight lines can only intersect once, and that this describes space, which seems pretty much what he was accused of.
On the other hand, he just assumes that two straight lines can only intersect once, and that this describes space,
I don’t see this in the quoted passage. He’s trying to illustrate the nature of propositions in geometry, and doesn’t appear to be arguing that the parallel postulate is universally true. “Take, for example,” is not exactly assertive.
Also, have a care: those two paragraphs are not consecutive in the Critique.
This isn’t very interesting, but I used to believe that the rules about checkmate didn’t really change the nature of chess. Some of the forbidden moves—moving into check, or failing to move out if possible—are always a mistake, so if you just played until someone captured the king, the game would only be different in cases where someone made an obvious mistake.
But if you can’t move, the game ends in stalemate. So forbidding you to move into check means that some games end in draws, where capture-the-king would have a victor.
There are many beliefs that people will arrive at through armchair theorizing, but only until they are corrected. If you came up with the idea that the Earth was flat a long time ago, nobody would correct you. If you did that today, someone would correct you; indeed, society is so full of round-Earth information that it’s hard for anyone to not have heard of the refutation before coming up with the idea, unless they’re a young child.
Does that count as something arrived at through armchair theorizing? People would, after all, come up with it by armchair theorizing if they lived in a vacuum. They did come up with it through armchair theorizing back when they did live in a vacuum.
That’s why there are tons of historical examples and not so many modern examples. A modern example has to be something where the refutation is well known by experts, but the refutation hasn’t made it down to the common person, because if the refutation did make it down to the common person that would inhibit them from coming up with the armchair theory in the first place.
(For historical examples,
It’s possible that the refutation is known by our experts, but not by contemporary experts, or
because of the bad state of mass communication in ancient times, the refutation simply hasn’t spread enough to reach most armchair theorists.)
Something from the modern day, yes. The people arriving at the naive belief, and the people with the ability to demonstrate its incorrect status, should coexist.
Sorry to keep going on this, but would looking at a historical example of a group of intelligent people arriving at a naive belief, even though there was plenty of evidence available at the time that this is a naive belief work?
According to Bell, he surveyed his colleagues at CERN (clearly a group of intelligent, qualified people) about this question, and most of them got it wrong. Although, to be fair, the conflict here is not between expert reasoning and domain knowledge, since the physicists at CERN presumably possessed all the knowledge you need (basic special relativity, really) to get the right answer.
Generalising from ‘plane on a treadmill’; a lot of incorrect answers to physics problems and misconceptions of physics in general. For any given problem or phenomenon, one can guess a hundred different fake explanations, numbers, or outcomes using different combinations of passwords like ‘because of Newton’s Nth law’, ‘because of drag’, ‘because of air resistance’, ‘but this is unphysical so it must be false’ etc. For the vast majority of people, the only way to narrow down which explanations could be correct is to already know the answer or perform physical experiments, since most people don’t have a good enough physical intuition to know in advance what types of physical arguments go through, so should be in a state of epistemic learned helplessness with respect to physics.
I have a strange request. Without consulting some external source, can you please briefly define “learned helplessness” as you’ve used it in this context, and (privately, if you like) share it with me? I promise I’ll explain at some later date.
There will probably be holes and not quite capture exactly what I mean, but I’ll take a shot. Let me know if this is not rigorous or detailed enough and I’ll take another stab, or if you have any other follow-up. I have answered this immediately, without changing tab, so the only contamination is saccading my LW inbox beforing clicking through to your comment, the titles of other tabs, etc. which look (as one would expect) to be irrelevant.
Helplessness about topic X—One is not able to attain a knowably stable and confident opinion about X given the amount of effort one is prepared to put in or the limits of one’s knowledge or expertise etc. One’s lack of knowledge of X includes lack of knowledge about the kinds of arguments or methods that tend to work in X, lack of experience spotting crackpot or amateur claims about X, and lack of general knowledge of X that would allow one to notice one’s confusion at false basic claims and reject them. One is unable to distinguish between ballsy amateurs and experts.
Learned helplessness about X—The helplessness is learned from experience of X; much like the sheep in Animal Farm, one gets opinion whiplash on some matter of X that makes one realise that one knows so little about X that one can be argued into any opinion about it.
(This has ended up more like a bunch of arbitrary properties pointing to the sense of learned helplessness rather than a slick definition. Is it suitable for your purposes, or should I try harder to cut to the essence?)
Rant about learned helplessness in physics: Puzzles in physics, or challenges to predict the outcome of a situation or experiment, often seem like they have many different possible explanations leading to a variety of very different answers, with the merit of these explanations not being distinguishable except to those who have done lots of physics and seen lots of tricks, and maybe even then maybe you just need to already know the answer before you can pick the correct answer.
Moreover, one eventually learns that the explanations at a given level of physics instruction are probably technically wrong in that they are simplified (though I guess less so as one progresses).
Moreover moreover, one eventually becomes smart enough to see that the instructors do not actually even spot their leaps in logic. (For example, it never seemed to occur to any of my instructors that there’s no reason you can’t have negative wavenumbers when looking at wavefunctions in basic quantum. It turns out that when I run the numbers, everything rescales since the wavefunction bijects between -n and n and one normalizes the wavefunction anyway, so that it doesn’t matter, but one could only know this for sure after reasoning it out and justifying discarding the negative wavenumbers. It basically seemed like the instructors saw an ‘n’ in sin(n*pi/L) or whatever and their brain took it as a natural number without any cognitive reflection that the letter could have just as easily been a k or z or something, and to check that the notation was justified by the referent having to be a natural.)
Moreover, it takes a high level of philosophical ability to reason about physics thought experiments and their standards of proof. Take the ‘directly downwind faster than the wind’ problem. The argument goes back and forth, and, like the sheep, at every point the side that’s speaking seems to be winning. Terry Tao comes along and says it’s possible, and people link to videos of carts with propellers apparently going downwind faster than the wind and wheels with rubber bands attached allegedly proving it. But beyond deferring to his general hard sciences problem-solving ability, one has no inside view way to verify Tao’s solution; what are the standards of proof for a thought experiment? After all, maybe the contraptions in the video only work (assuming they do work as claimed, which isn’t assured) because of slight side-to-side effects rather than directly down wind or some other property of the test conditions implicitly forbidden by the thought experiment.
Since any physical experiment for a physics thought experiment will have additional variables, one needs some way to distinguish relevant and irrelevant variables. Is the thought experiment the limit as extraneous variables become negligible, or is there a discontinuity? What if different sets of variables give rise to different limits? How does anyone ever know what the ‘correct’ answer is to an idealised physics thought experiment of a situation that never actually arises? Etc.
Thanks for that. The whole response is interesting.
I ask because up until quite recently I was labouring under a wonky definition of “learned helplessness” that revolved around strategic self-handicapping.
An example would be people who foster a characteristic of technical incompetence, to the point where they refuse to click next-next-finish on a noddy software installer. Every time they exhibit their technical incompetence, they’re reinforced in this behaviour by someone taking the “hard” task away from them. Hence their “helplessness” is “learned”.
It wasn’t until recently that I came across an accurate definition in a book on reinforcement training. I’m pretty sure I’ve had “learned helplessness” in my lexicon for over a decade, and I’ve never seen it used in a context that challenged my definition, or used it in a way that aroused suspicion. It’s worth noting that I probably picked up my definition through observing feminist discussions. Trying a mental find-and-replace on ten years’ conversations is kind of weird.
I am also now bereft of a term for what I thought “learned helplessness” was. Analogous ideas come up in game theory, but there’s no snappy self-contained way available to me for expressing it.
I am also now bereft of a term for what I thought “learned helplessness” was. Analogous ideas come up in game theory, but there’s no snappy self-contained way available to me for expressing it.
Schelling does talk about strategic self-sabotage, but it captures a lot of deliberated behaviour that isn’t implied in my fake definition.
Also interesting to note, I have read that Epistemic Learned Helplessness blog entry before, and my fake definition is sufficiently consistent with it that it doesn’t stand out as obviously incorrect.
Also interesting to note, I have read that Epistemic Learned Helplessness blog entry before, and my fake definition is sufficiently consistent with it that it doesn’t stand out as obviously incorrect.
Now picturing a Venn diagram with three overlapping circles labelled “epistemic learned helplessness”, “what psychologists call ‘learned helplessness’”, and “what sixes_and_sevens calls ‘learned helplessness’”!
An example would be people who foster a characteristic of technical incompetence, to the point where they refuse to click next-next-finish on a noddy software installer. Every time they exhibit their technical incompetence, they’re reinforced in this behaviour by someone taking the “hard” task away from them. Hence their “helplessness” is “learned”.
Making up a term for this...”reinforced helplessness”? (I dunno whether it’d generalize to cover the rest of what you formerly meant by “learned helplessness”.)
The earth revolving around the sun was also armchair reasoning, and refuted by empirical data like the lack of observable parallax of stars. Geocentrism is a pretty interesting historical example because of this: the Greeks reached the wrong conclusion with right arguments. Another example in the opposite direction: the Atomists were right about matter basically being divided up into very tiny discrete units moving in a void, but could you really say any of their armchair arguments about that were right?
It is not clear that the Greeks rejected heliocentrism at all, let alone any reason other than heresy. On the contrary, Hipparchus refused to choose, on the grounds of Galilean relativity.
The atomists got the atomic theory from the Brownian motion of dust in a beam of light. the same way that Einstein convinced the final holdouts thousands of years later.
It is not clear that the Greeks rejected heliocentrism at all, let alone any reason other than heresy. On the contrary, Hipparchus refused to choose, on the grounds of Galilean relativity.
Lucretius talks about the motion of dust in light, but he doesn’t claim that it is the origin of the theory. When I google “Leucippus dust light” I get lots of people making my claim and more respectable sources making weaker claims, like “According to traditional accounts the philosophical idea of simulacra is linked to Leucippus’ contemplation of a ray of light that made visible airborne dust,” but I don’t see any citations to where this tradition is recorded.
The Greeks cover hundreds of years. They made progress! You linked to a post about the supposed rejection of Aristarchus’s heliocentric theory. It’s true that no one before Aristarchus was heliocentric. That includes Aristotle who died when Aristarchus was 12. Everyone agrees that the Hellenistic Greeks who followed Aristotle were much better at astronomy than the Classical Greeks. The question is whether the Hellenistic Greeks accepted Aristarchus’s theory, particularly Archimedes, Apollonius, and Hipparchus. But while lots of writings of Aristotle remain, practically nothing of the later astronomers remain.
It’s true that secondary sources agree that Archimedes, Apollonius, and Hipparchus were geocentric. However, they give no evidence for this. Try the scholarly article cited in the post you linked. It’s called “The Greek Heliocentric Theory and Its Abandonment” but it didn’t convince me that there was an abandonment. That’s where I got the claim about Hipparchus refusing to choose.
I didn’t claim that there was any evidence that it was respectable, let alone dominant, only that there was no evidence that it was rejected. The only solid evidence one way or the other is the only surviving Hellenistic astronomy paper, Archimedes’s Sandreckoner, which uses Aristarchus’s model. I don’t claim that Archimedes was heliocentric, but that sure sounds to me like he respected heliocentrism.
Maybe heliocentrism survived a century and was finally rejected by Hipparchus. That’s a world of difference from saying that Seleucus was his only follower. Or maybe it was just the two of them, but we live in a state of profound ignorance.
As for the ultimate trajectory of Greek science, that is a difficult problem. Lucio Russo suggests that Roman science is all mangled Greek science and proposes to extract the original. For example, Seneca claims that the retrograde motion of the planets is an illusion, which sounds like he’s quoting someone who thinks the Earth moves, even if he doesn’t. More colorful are Pliny and Vitruvius who claim that the retrograde motion of the planets is due to the sun shooting triangles at them. This is clearly a heliocausal theory, even if the authors claim to be geocentric. Less clear is Ruso’s interpretation, that this is a description of a textbook diagram that they don’t understand.
So, you just have an argument from silence that heliocentrism was not clearly rejected?
I didn’t claim that there was any evidence that it was respectable, let alone dominant, only that there was no evidence that it was rejected. The only solid evidence one way or the other is the only surviving Hellenistic astronomy paper, Archimedes’s Sandreckoner, which uses Aristarchus’s model. I don’t claim that Archimedes was heliocentric, but that sure sounds to me like he respected heliocentrism.
I just read through the bits of Sand Reckoner referring to Aristarchus (Mendell’s translation), and throughout Archimedes seems to be at pains to distance himself from Aristarchus’s model, treating it as a minority view (emphasis added):
You grasp [King Gelon, the recipient of Archimedes’s letter The Sand Reckoner] that the world is called by most astronomers the sphere whose center is the center of the earth and whose line from the center is equal to the straight-line between the center of the sun and the center of the earth, since you have heard these things in the proofs written by the astronomers. But Aristarchus of Samos produced writings of certain hypotheses in which it follows from the suppositions that the world is many times what is now claimed.
Not language which suggests he takes it particularly seriously, much less endorses it.
In fact, it seems that the only reason Archimedes brings up Aristarchus at all is as a form of ‘worst-case analysis’: some fools doubt the power of mathematics and numbers, but Archimedes will show that even under the most ludicrously inflated estimate of the size of the universe (one implied by Aristarchus’s heliocentric model), he can still calculate & count the number of grains of sands it would take to fill it up; hence, he can certainly calculate & count the number for something smaller like the Earth. From the same chapter:
[1] Some people believe, King Gelon, that the number of sand is infinite in multitude. I mean not only of the sand in Syracuse and the rest of Sicily, but also of the sand in the whole inhabited land as well as the uninhabited. There are some who do not suppose that it is infinite, and yet that there is no number that has been named which is so large as to exceed its multitude.
[2] It is clear that if those who hold this opinion should conceive of a volume composed of the sand as large as would be the volume of the earth when all the seas in it and hollows of the earth were filled up in height equal to the highest mountains, they would not know, many times over, any number that can be expressed exceeding the number of it.
[3] I will attempt to prove to you through geometrical demonstrations, which you will follow, that some of the numbers named by us and published in the writings addressed to Zeuxippus exceed not only the number of sand having a magnitude equal to the earth filled up, just as we said, but also the number of the sand having magnitude equal to the world.
...[7] In fact we say that even if a sphere of sand were to become as large in magnitude as Aristarchus supposes the sphere of the fixed stars to be, we will also prove that some of the initial numbers having an expression (or: “numbers named in the Principles,” cf. Heath, Archimedes, 222, and Dijksterhuis, Archimedes, 363) exceed in multitude the number of sand having a magnitude equal to the mentioned sphere, when the following are supposed.
[18] … Thus, it is obvious that the multitude of sand having a magnitude equal to the sphere of the fixed stars which Aristarchus supposes is smaller than 1000 myriads of the eighth numbers.
[19] King Gelon, to the many who have not also had a share of mathematics I suppose that these will not appear readily believable, but to those who have partaken of them and have thought deeply about the distances and sizes of the earth and sun and moon and the whole world this will be believable on the basis of demonstration. Hence, I thought that it is not inappropriate for you too to contemplate these things.
All I have ever said is that you should stop telling fairy tales about why the Greeks rejected heliocenrism. If the Sandreckoner convinces you that Archimedes rejected heliocentrism, fine, whatever, but it sure doesn’t talk about parallax.
I listed several pieces of positive evidence, but I’m not interested in the argument.
If the Sandreckoner convinces you that Archimedes rejected heliocentrism, fine, whatever, but it sure doesn’t talk about parallax.
The Sand Reckoner implies the parallax objection when it uses an extremely large heliocentric universe! Lack of parallax is the only reason for such extravagance. Or was there some other reason Aristarchus’s model had to imply a universe lightyears in extent...?
Aristarchus using a large universe is evidence that he thought about parallax. It is not evidence that his opponents thought about parallax.
You are making a circular argument: you say that the Greeks rejected heliocentrism for a good reason because they invoked parallax, but you say that they invoked parallax because you assume that they had a good reason.
There is a contemporary recorded reason for rejecting Aristarchus: heresy. There is also a (good) reason recorded by Ptolemy 400 years later, namely wind speed.
Aristarchus using a large universe is evidence that he thought about parallax. It is not evidence that his opponents thought about parallax.
Uh… why would the creator of the system consider parallax an issue, and the critics not consider parallax an issue?
And you still haven’t addressed my quotes from The Sand Reckoner indicating Archimedes considered heliocentrism dubious and a minority view, which should override your arguments from silence.
You are making a circular argument: you say that the Greeks rejected heliocentrism for a good reason because they invoked parallax, but you say that they invoked parallax because you assume that they had a good reason.
No. I said parallax is why they rejected it in part because to save the model one has to make the universe large, then you said ‘look! Archimedes uses a large universe!’, and I pointed out this is 100% predicted by the parallax-rejection theory. So what? Where is your alternate explanation of why the large-universe—did Archimedes just make shit up?
There is a contemporary recorded reason for rejecting Aristarchus: heresy. There is also a (good) reason recorded by Ptolemy 400 years later, namely wind speed.
Uh… why would the creator of the system consider parallax an issue, and the critics not consider parallax an issue?
The very question is whether the critics made good arguments. You are assuming the conclusion. People make stupid arguments all the time. Anaxagoras was prosecuted for heresy and Aristarchus may have been. How many critics of Copernicus knew that he was talking about what happens over the course of a year, not what happens over the course of a day?
Yes, Archimedes says that Aristarchus’s position is a minority. Not dubious. I do not see that in the quotes at all. Yes, Archimedes probably uses Aristarchus’s position for the purposes of worst-case analysis to get numbers as large as possible; indeed, they are larger than the numbers Ptolemy attributes to Aristarchus. As I said at the beginning, I do not claim that he endorsed heliocentrism, only that he considered it a live hypothesis. One mystery is what is the purpose of the Sandreckoner. Is it just about large numbers? Or is it also about astronomy? Is Archimedes using exotic astronomy to justify his interest in exotic mathematics? Or is he using his public venue to promote diversity in astronomy?
The very question is whether the critics made good arguments. You are assuming the conclusion.
It’s assuming the conclusion to think critics agreed with Aristarchus’s criticism of a naive heliocentric theory?
Yes, Archimedes says that Aristarchus’s position is a minority. Not dubious. I do not see that in the quotes at all.
I disagree strongly. I don’t see how you could possibly read the parts I quoted, and italicized, and conclude otherwise. Like, how do you do that? How do you read those bits and read it as anything else? What exactly is going through your head when you read those bits from Sand Reckoner, how do you parse it?
One mystery is what is the purpose of the Sandreckoner. Is it just about large numbers? Or is it also about astronomy? Is Archimedes using exotic astronomy to justify his interest in exotic mathematics? Or is he using his public venue to promote diversity in astronomy?
Gee, if only I had quoted the opening and ending bits of the Sand Reckoner where Archimedes explained his goal...
Many people object to Copernicus on the grounds that Joshua made the Sun stand still, or on grounds of wind, without seeming to realize that they object to the daily rotation of the Earth, not to his special suggestion of the yearly revolution of the Earth about the Sun. If Copernicus had such lousy critics, why assume Aristarchus had good critics who were aware of his arguments? Maybe they objected to heresy, like (maybe) Cleanthes. Archimedes was a smart guy who understood what Aristarchus was saying. He seems to accept Aristarchus’s argument that heliocentrism implies a large universe. If (if!) he rejects the premise, that does not tell us why. Maybe because he rejects the conclusion. Or maybe he rejects the premise for completely different consequences, like wind. Or maybe he is not convinced by Aristarchus’s main argument (whatever that was) and doesn’t even bother to move on to the consequences.
Ptolemy does give a reason: he says wind. He has the drawback of being hundreds of years late, so maybe he is not representative, but at least he gives a reason. If you extract any reason, that is the one to pick.
The principal purpose of the Sandreckoner is to investigate infinity, to eliminate the realm of un-nameable numbers, thus to eliminate the confusion between un-nameably large and infinite. But there are many other choices that go into the contents, and they may be motivated by secondary purposes. Physical examples are good. Probably sand is a cliche. But why talk about astronomy at all? Why not stop at all the sand in the world? Or fill the sphere of the sun with sand, stopping at Aristarchus’s non-controversial calculation of that distance? Such choices are rarely explained. I offered two possibilities and the text does not distinguish them.
If Copernicus had such lousy critics, why assume Aristarchus had good critics who were aware of his arguments? Maybe they objected to heresy, like (maybe) Cleanthes.
You have not explained why Aristarchus would make his universe so large if the criticisms were as bogus as some of Copernicus’s critics. Shits and giggles?
If (if!) he rejects the premise, that does not tell us why. Maybe because he rejects the conclusion. Or maybe he rejects the premise for completely different consequences, like wind. Or maybe he is not convinced by Aristarchus’s main argument (whatever that was) and doesn’t even bother to move on to the consequences.
If he rejects heliocentrism, as he clearly does, it does not matter for your original argument why exactly.
You still have not addressed the quotes from Sand Reckoner I gave which clearly show Archimedes rejects heliocentrism and describes it as a minority rejected position and he only draws on Aristarchus as a worst-case a fortiori argument. Far from being a weak argument from silence (weak because while we lack a lot of material, I don’t think we lack so much material that they could have seriously maintained heliocentrism without us knowing; absence of evidence is evidence of absence), your chosen Sand Reckoner example shows the opposite.
If this is the best you can do, I see no reason to revise the usual historical scenario that heliocentrism was rejected because any version consistent with observations had absurd consequences.
Aristarchus made the universe big because he himself thought about parallax. Maybe some critic first made this objection to him, but such details are lost to time, and uninteresting to compared to the question of the response to the complete theory.
As to the rest, I abandon all hope of convincing you. I ask only that any third parties read the whole exchange and not trust Gwern’s account of my claims.
Atoms can actually be divided into parts, so it’s not clear that the atomists where right. If you would tell some atomist about quantum states, I would doubt that they would find that to be a valid example of what they mean with “atom”.
The atomists were more right than the alternatives: the world is not made of continuously divisible bone substances, which are bone no matter how finely you divide them, nor is it continuous mixtures of fire or water or apeiron.
How about “human beings only use 10% of their brains”? Not political, not flamebait, but possibly also “a lot of people say it and sounds plausible” rather than armchair theorizing. “Everyone should drink eight glasses of water a day” is probably in the same category.
I looked through Wikipedia’s list of common misconceptions for anything that people might arise independently in lots of people through reasonable reflection, rather than just “facts” that sneak into the public consciousness, but none of them really qualify.
Why not also spend an equally amount of time searching for examples that prove the opposite of the point you’re trying to make? Or are you speaking to an audience that doesn’t agree this is possible in principle?
Oblique request made without any explanation: can anyone provide examples of beliefs that are incontrovertibly incorrect, but which intelligent people will nonetheless arrive at quite reasonably through armchair-theorising?
I am trying to think up non-politicised, non-controversial examples, yet every one I come up with is a reliable flame-war magnet.
ETA: I am trying to reason about disputes where on the one hand you have an intelligent, thoughtful person who has very expertly reasoned themselves into a naive but understandable position p, and on the other hand, you have an individual who possesses a body of knowledge that makes a strong case for the naivety of p.
What kind of ps exist, and do they have common characteristics? All I can come up with are politically controversial ps, but I’m starting my search from a politically-controversial starting point. The motivating example for this line of reasoning is so controversial that I’m not touching it with a shitty-stick.
Mathematical arguments happen all the time over whether 0.99999...=1 but I’m not sure if that’s interesting enough to count for what you want.
That “0.99999....” represents a concept that evaluates to 1 is a question of notation, not mathematics. 0.99999… does not inherently equal 1; rather, by convention, it is understood to mean 1. The debate is not about the territory, it is about what the symbols on the map mean.
Where does one draw the line, if at all? “1+1 does no inherently equal 2; rather, by convention, it is understood to mean 2. The debate is not about the territory, it is about what the symbols on the map mean.” It seems to me like that—very ‘mysteriously’—people who understand real analysis never complain “But 0.999… doesn’t equal 1″; sufficient mathematical literacy seems to kill any such impulse, which seems very telling to me.
Yes, and that’s a case of “you don’t understand mathematics, you get used to it.” Which applies exactly to notation and related conventions.
Edit:
More specifically, if we let a_k=9/10^k, and let s_n be the sum from k=1 to n of a_k, then the limit of s_n as n goes to infinity will be 1, but 1 won’t be in {s_n|n in R}.
When somebody who is used to calculus sees ”.99...” What they are thinking of is the limit, which is 1.
But before you get used to that, most likely what you think of is some member of {s_n|n in R} with an n that’s large enough that you can’t be bothered to write all the nines, but which is still finite.
Exactly. The arguments about whether 0.99999.… = 1 are lacking a crucial item: a rigorous definition of what “0.9999...” refers to. The argument isn’t “Is the limit as n goes to infinity of sum from 1 to n of 9*10^-n equal to 1?” It’s “Here’s a sequence of symbols. Should we assign this sequence of symbols the value of 1, or not?” Which is just a silly argument to have. If someone says “I don’t believe that 0.9999.… = 1“, the correct response (unless they have sufficient real analysis background) is not “Well, here’s a proof that of that claim”, it’s “Well, there are various axioms and definitions that lead to that being treated as being equal to 1”.
It’s not. The “0.999… doesn’t equal 1” meme is largely crackpottery, and promotes amateur overconfidence and (arguably) mathematical illiteracy.
Terms are precious real estate, and their interpretations really are valuable. Our thought processes and belief networks are sticky; if someone has a crap interpretation of a term, then it will at best cause unnecessary friction in using it (e.g. if you define the natural numbers to include −1,...,-10 and have to retranslate theorems because of this), and at worst one will lose track of the translation between interpretations and end up propagating false statements (“2^n can sometimes be less than 2 for n natural”)
It would be an accurate response (even if not the most pragmatic or tactful) to say, “Sorry, when you pin down what’s meant precisely, it turns out to be a much more useful convention to define the proposition 0.999...=1 such that it is true, and you basically have to perform mental gymnastics to try to justify any usage where it’s not true. There are technically alternative schemas where this could fail or be incoherent or whatever, but unless you go several years into studying math (and even then maybe only if you become a logician or model theorist or something), those are not what you’ll be encountering.”
One could define ‘marble’ to mean ‘nucleotide’. But I think that somebody who looked down on a geneticist for complaining about people using ‘marble’ as if it means ‘nucleotide’, and who said it was a silly argument as if the geneticist and the person who invented the new definition were Just As Bad As Each Other, would be mistaken, and I would suspect they were more interested in signalling their Cleverness via relativist metacontrarianism than getting their hands dirty figuring out the empirical question of which definitions are useful in which contexts.
Actually, I could imagine you reading that comment and feeling it still misses your point that 0.999… is undefined or has different definitions or senses in amateur discussions. In that case, I would point to the idea that one can makes propositions about a primitive concept that turn out to be false about the mature form of it. One could make claims about evidence, causality, free will, knowledge, numbers, gravity, light, etc. that would be true under one primitive sense and false under another. Then minutes or days or month or years or centuries or millennia later it turns out that the claims were false about the correct definition.
It would be a sin of rationality to assume that, since there was a controversy over definitions, and some definitions proved the claim and some disproved it, that no side was more right than another. One should study examples of where people made correct claims about fuzzy concepts, to see what we might learn in our own lives about how these things resolve. Were there hints that the people who turned out to be incorrect ignored? Did they fail to notice their confusion? Telltale features of the problem that favoured a different interpretation? etc.
A lot (in fact, all of them that don’t involve a rigorous treatment of infinite series) of the “proofs” that it does equal 1 are fallacious, and so the refusal to accept them is actually a reasonable response.
You seem to making an assertion about me in your last paragraph, but doing so very obliquely. Your analogy is not very good, as people do not try to argue that one can logically prove that “marble” does not mean “nucleotide”, they just say that it is defined otherwise.
If we’re analogizing ”.9999… = 1″ to “marble doesn’t mean’t nucleotide”, then ”
Apologies for that. I don’t think that that specific failure mode is particularly likely in your case, but it seems plausible to me that other people thinking in that way has shifted the terms of discourse such that that form of linguistic relativism is seen as high-status by a lot of smart people. I am more mentioning it to highlight the potential failure mode; if part of why you hold your position is that it seems like the kind of position that smart people would hold, but I can account for those smart people holding it in terms of metacontrarianism, then that partially screens off that reason for endorsing the smart people’s argument.
It looks like you submitted your comment before you meant to, so I shall probably await its completion before commenting on the rest.
And yet I somehow doubt most of these people reject connectedness.
I thought about this on & off over the last couple of days and came up with more candidates than you can shake a shitty stick at. Some of these are somewhat political or controversial, but I don’t think any are reliable flame-war magnets. I expect some’ll ring your cherries more than others, but since I can’t tell which, I’ll post ’em all and let you decide.
The answer to the Sleeping Beauty puzzle is obviously 1⁄2.
Rational behaviour, being rational, entails Pareto optimal results.
Food availability sets a hard limit on the number of kids people can have, so when people have more food they have more kids.
Truth is an absolute defence against a libel accusation.
If a statistical effect is so small that a sample of several thousand is insufficient to reliably observe it, the effect’s too small to matter.
Controlling for an auxiliary variable, or matching on that variable, never worsens the bias of an estimate of a causal effect.
Human nature being as brutish as it is, most people are quite willing to be violent, and their attempts at violence are usually competent.
In the increasingly fast-paced and tightly connected United States, residential mobility is higher than ever.
The immediate cause of death from cancer is most often organ failure, due to infiltration or obstruction by spreading tumours.
Aumann’s agreement theorem means rationalists may never agree to disagree.
Friction, being a form of dissipation, plays no role in explaining how wings generate lift.
Seasons occur because Earth’s distance from the Sun changes during Earth’s annual orbit.
Beneficial mutations always evolve to fixation.
Multiple discovery is rare & anomalous.
The words “male” & “female” are cognates.
Given the rise of online piracy, the ridiculous cost of tickets, and the ever-growing convenience of other forms of entertainment, cinema box office receipts must be going down & down.
Looking at voting in an election from the perspective of timeless decision theory, my voting decision is probably correlated and indeed logically linked with that of thousands of people relatively likely to agree with my politics. This could raise the chance of my influencing an election above negligibility, and I should vote accordingly.
The countries with the highest female life expectancies are approaching a physiologically fixed hard limit of 65 — sorry, 70 — sorry, 80 — sorry, 85 years.
The answer to the Sleeping Beauty puzzle is obviously 1⁄3.
Language in general might be a rich source of these, between false etymologies, false cognates, false friends, and eggcorns.
Thanks for that list. I believed (or at least, assigned a probability greater than 0.5 to) about five of those.
Thanks for this. These are all really good.
Now I just need to think of another 21 and I’ll have enough for a philosophy article!
… don’t they? (in the long run)
No, they don’t—look at contemporary Western countries and their birth rates.
Oh yes I know that, I just meant in the long-long run. This voluntary limiting of birth rates can’t last for obvious evolutionary reasons.
I have no idea about the “long-long” run :-)
The limiting of birth rates can last for a very long time as long as you stay at replacement rates. I don’t think “obvious evolutionary reasons” apply to humans any more, it’s not likely another species will outcompete us by breeding faster.
Any genes that make people defect by having more children are going to be (and are currently being) positively selected.
Besides, reducing birthrates to replacement isn’t anything near a universal phenomenon, see the Mormons and Amish.
It’s got nothing to do with another species out-competing us—competition between humans is more than enough.
This observation should be true throughout the history of the human race, and yet the birth rates in the developed countries did fall off the cliff...
And animals don’t breed well in captivity.
Until they do.
This happened barely half a generational cycle ago. Give evolution time.
So what’s your prediction for what will happen when?
In the “long-long run”, given ad hoc reproductive patterns, yeah, I’d expect evolution to ratchet average human fertility higher & higher until much of humanity slammed into the Malthusian limit, at which point “when people have more food they have more kids” would become true.
Nonetheless, it isn’t true today, it’s unlikely to be true for the next few centuries unless WWIII kicks off, and may never come to pass (humanity might snuff itself out of existence before we go Malthusian, or the threat of Malthusian Assured Destruction might compel humanity to enforce involuntary fertility limits). So here in 2014 I rate the idea incontrovertibly false.
That’s a tall order. I’ll try:
Noticing that people who are the best in any sport practice the most and concluding that being good at a sport is simply a matter of practice and determination. Tabula Rasa in general.
The supply-demand model of minimum wage? Is this political? I’m not saying minimum wage is good or bad, just that the supply-demand model can’t settle the question yet people learning about economics tend to be easily convinced by the simple explanation.
That thermodynamics proves that weight loss + maintenance is simply a matter of diet and exercise (this is more Yudkowsky’s fight than mine).
I doubt it is possible to find non-controversial examples of anything, and especially of things plausible enough to be believed by intelligent non-experts, outside of the hard sciences.
If this is true, the only plausible examples would be such as “an infinity cannot be larger than another infinity”, “time flows uniformly regardless of the observer”, “biological species have unchanging essences”, and other intuitively plausible statements unquestionably contradicted by modern hard sciences.
Most drug new drugs fail clinical trials.
Intelligent people make theories about how a drug is supposed to work and think it would help to cure some illness. Then when the drug is brought into clinical trials more than 90% of new drugs still fail to live up to the theoretical promise that the drug held.
A fun one which came up recently on IRC: everyone thinks that how your parents raise you is incredibly important, this is so obvious it doesn’t need any proof and is universal common sense (how could influencing and teaching a person from scratch to 18 years old not have deep and profound effects on them?), and you can find extended discussions of the best way to raise kids from Plato’s Republic to Rousseau’s Emile to Spock.
Except twin studies consistently estimate that the influence of ‘shared environment’ (the home) is small or near-zero for many traits compared to genetics and randomness/nonshared-environment.
If you want to predict whether someone will be a smoker or smart, it doesn’t matter whether they’re raised by smokers or not (to borrow an example from The Nurture Assumption*); it just matters whether their biological parents were smokers and whether they get unlucky.
This is so deeply counterintuitive and unexpected that even people who are generally familiar with the relevant topics like IQ or twin studies typically don’t know about this or disbelieve it.
(Another example is probably folk physics: Newtonian motion is true, experimentally confirmed, mathematically logical, and completely unintuitive and took millennia to be developed after the start of mechanics.)
* Rich’s citation is to Rowe 1994, The Limits of Family Influence: Genes, Experience, and Behavior; from pg204:
This is quite possibly the most comforting scientific result ever for me as a parent, by the way.
Whereas for me, it’s horrifying, given that my ex-spouse turned out to be an astonishingly horrible person.
I seem to recall Yvain posting a link to something he referred to as the beginnings of a possible rebuttal to The Nurture Assumption; I suppose I shall have to hang my hopes on that.
It may or may not be comforting to reflect that your ex-spouse is probably less horrible than s/he seems to you. (Just on general outside-view principles; I have no knowledge of your situation or your ex.)
You feared more than you hoped, eh?
Old epi jungle saying: “the causal null is generally true.”
‘Shh, kemo sabe—you hear that?’ ‘No; the jungle is silent tonight.’ ‘Yes. The silence of the p-values. A wild publication bias stalks us. We must be cautious’.
What is IRC?
Get off my lawn
http://en.wikipedia.org/wiki/Internet_relay_chat
So… does it mean that it’s completely irrelevant who adopted Harry Potter, because the results would be the same anyway?
Or is the correct model something like: abuse can change things to worse, but any non-abusive parenting simply means the child will grow up determined by their genes? That is, we have a biologically set “destiny”, and all the environment can do is either help us reach this destiny or somehow cripple us halfway (by abuse, by lack of nutrition, etc.).
In an home environment within the normal range for a population, the home environment will matter little in a predictable sense on many traits compared to the genetic legacy, and random events/choices/biological-events/accidents/etc. There are some traits it will matter a lot on, and in a causal sense, the home environment may determine various important outcomes but not in a way that is predictable or easily measured. The other category of ‘nonshared environment’ is often bigger than the genetic legacy, so speaking of a biologically set destiny is misleading: biologically influenced would be a better phrase.
Has this been demonstrated for home environments in the developing world or sub-middle class home environments in the developed world? My prior understanding was that it had not been.
There are serious restriction of range problems with the literature. I believe that there is one small French adoption study with unrestricted range which produced 1 sigma IQ difference between the bottom and top buckets (deciles?) of adopting families.
I wonder if this what Shalizi alludes to when he says that IQ is closer to that of the adoptive parents than that of the biological parents.
Christiane Capron & Michel Duyme (1989), “Assessment of effects of socio-economic status on IQ in a full cross-fostering study”, Nature, 340, 552-554
Christiane Capron & Michel Duyme (1996), “Effect of Socioeconomic Status of Biological and Adoptive Parents on WISC-R Subtest Scores of their French Adopted Children”, Intelligence, 22, 259-275
(Both references describe the same study.) Capron & Duyme found 38 French children placed for adoption before age 2, 20 of them to parents with very high socioeconomic status (operationalized as having 14-23 years of education and working a profession) and 18 to parents with very low socioeconomic status (unskilled & semi-skilled labourers or farmers, with 5-8 years of education). When the kids took the WISC-R IQ test, those adopted into the high-SES families had a mean IQ of 111.6, while those in the low-SES families had a mean IQ of 100.0, for a difference of 0.77 sigma.
Thanks!
In the context of IQ I’ve seen it claimed that normal variation in parenting doesn’t do much, but extreme abuse can still have a substantial effect. So parenting quality would only make a difference at the tails of the parenting quality distribution, but there it would make quite a difference.
In “No Two Alike” Harris argues that the biggest non-shared environment personality determinant is peer group. So Harry Potter style “Lock him up in a closet with no friends” would actually have a huge effect.
And it should be noted that parents do have control over peer group: where to live, public school vs. private school vs. homeschooling, getting children to join things, etc. So parenting still matters even if it’s all down to genetics and non-shared environment.
Also, has anyone investigated whether the proper response to publicized social-science answers/theories/whatever you want to call them is to assume they’re true or just wait for them to be rejected? That is: how many publicized social-science answers [the same question could be asked for diet-advice answers conflicting with pre-nutrition-studies received wisdom, etc.] were later rejected? It could well be that the right thing to do in general is stick with common sense...
Exactly! If you have something to protect as a parent, then after hearing “parents are unimportant, the important stuff is some non-genetic X” the obvious reaction is: “Okay, so how can I influence X?” (Instead of saying: “Okay, then it’s not my fault, whatever.”)
For example, if I want my children to be non-smokers, and I learn that whether I am smoking or not has much smaller impact than whether my children’s friends are smoking… the obvious next question is: What can I do to increase the probability that my children’s friends will be non-smokers? There are many indirect methods like choosing the place to live, choosing the school, choosing free-time activities, etc. I would just like to have more data on what smoking correlates with; where should I send my children and where should I prevent them from going, so that even if they “naturally” pick their peer group in that place, they will more likely pick non-smokers. (Replace non-smoking with whatever is your parenting goal.)
Shortly, when I read “parenting” in a study, I mentally translate it as: “what an average, non-strategic parent does”. That’s not the same as: “what a parent could do”.
Fictional evidence, etc. Also, HPMOR has confounders, like a differing mechanism for Horcruxes.
As Protagoras points out here there are systematic problems with twin studies.
There are problems, but I don’t think they are large, I think they are brought up mostly for ideological reasons (Shalizi is not an unbiased source and has a very big axe to grind), and a lot of the problems also cut the other way. For example, measurement error can reduce estimates of heritability a great deal, as we see in twin studies which correct for it and as predicted get higher heritability estimates, like “Not by Twins Alone: Using the Extended Family Design to Investigate Genetic Influence on Political Beliefs”, Hatemi et al 2010 (this study, incidentally, also addresses the claim that twins may have special environments compared to their non-twin siblings and that will bias results, which has been claimed by people who dislike twin studies; there’s no a priori reason to think this, and Hatemi finds no evidence for it, yet they had claimed it).
Do you mean more by this than that he has very strong opinions on this topic? I would guess you do—that you mean there’s something pushing him towards the opinions he has, that isn’t the way it is because those opinions are right. But what?
Shalizi is somewhere around Marxism in politics. This makes his writings on intelligence very frustrating, but on the other hand, it also means he can write very interesting things on economics at times—his essay on Red Plenty is the most interesting thing I’ve ever seen on economics & computational complexity. Horses for courses.
Shalizi states at least part of his position as follows:
and on the same page says these things:
and
I have to say that none of this sounds very Marxist to me. Shalizi apparently finds revolutions dishonourable; the most notable attempts at (nominally) Marxist states, the USSR and the PRC, he criticizes in very strong terms; he wants most prices to be set by markets (at least this is how I interpret what he says on that page and others it links to).
Oh, here’s another bit of evidence:
followed in the next paragraph by
which seems to me to imply, in particular, that Shalizi doesn’t consider himself “a Marxist, even a revisionist one”.
He’s certainly a leftist, certainly considers himself a socialist, but he seems quite some way from Marxism. (And further still from, e.g., any position taken by the USSR or the PRC.)
How about this?
Not that I think pigeon-holing him is very useful for determining his views on economics or politics, let alone IQ.
Suggests that Marxism is an idea Shalizi is “receptive to” but not (at least to me) that he’s actually a Marxist as such.
Does having political views that approximate Marxism imply irrationally-derived views on intelligence? I don’t see why it should, but this may simply be a matter of ignorance or oversight on my part.
I am not an expert on Marx but would be unsurprised to hear that he made a bunch of claims that are ill-supported by evidence and have strong implications about intelligence—say, that The Proletariat is in no way inferior in capabilities, even statistically, to The Bourgeoisie. But to me “somewhere around Marxism in politics” doesn’t mean any kind of commitment to believing everything Marx wrote. It isn’t obvious to me why someone couldn’t hold pretty much any halfway-reasonable opinions about intelligence, while still thinking that it is morally preferable for workers to own the businesses they work for and the equipment they use, that we would collectively be better off with much much more redistribution of wealth than we currently have (or even with the outright abolition of individual property), etc.
In another comment I’ve given my reasons for doubting that Shalizi is even “somewhere around Marxism in politics”. But even if I’m wrong about that, I’m not aware of prior commitments he has that would make him unable to think rationally about intelligence.
Of course it needn’t be a matter of prior commitments as such. It could, e.g., be that he is immersed in generally-very-leftist thought (this being either a cause or a consequence of his own leftishness), and that since for whatever reason there’s substantial correlation between being a leftist and having one set of views about intelligence rather than another, Shalizi has just absorbed a typically-leftist position on intelligence by osmosis. But, again, the fact that he could have doesn’t mean he actually has.
I think the guts of what you’re claiming is: Shalizi’s views on intelligence are a consequence of his political views; either his political views are not arrived at rationally, or the way his political views have given rise to his views on intelligence are not rational, or both. -- That could well be true, but so far what you’ve given evidence for is simply that he holds one particular set of political views. How do you get from there to the stronger claim about the relationship between his views on the two topics?
At least part of it was reading his ‘Statistical Myth’ essay, being skeptical of the apparent argument for some of the reasons Dalliard would lay out at length years later, reading all the positive discussions of it by people I was unsure understood either psychometrics or Shalizi’s essay (which he helpfully links), and then reading a followup dialogue http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/495.html where—at least, this is how it reads to me—he carefully covers his ass, walks back his claims, and quietly concedes a lot of key points. At that point, I started to seriously wonder if Shalizi could be trusted on this topic; his constant invocation of Stephen Jay Gould (who should be infamous by this point) and his gullible swallowing of ‘deliberate practice’ as more important than any other factor which since has been pretty convincingly debunked (both on display in the dialogue) merely reinforce my impression and the link to Gould (Shalizi’s chief comment on Gould’s Mismeasure of Man is apparently solely “I do not recommend this for the simple reason that I read it in 1988, when I was fourteen. I remember it as a very good book, for whatever that’s worth.”; no word on whether he is bothered by Gould’s fraud) suggests it’s partially ideological. Another revealing page: http://vserver1.cscs.lsa.umich.edu/~crshalizi/notebooks/iq.html I can understand disrecommending Rushton, but disrecommending Jensen who invented a lot of the field and whose foes even admire him? Recommending a journalist from 1922? Recommending some priming bullshit? (Where’s the fierce methodologist statistician when you need him...?) There’s one consistent criterion he applies: if it’s against IQ and anything to do with it, he recommends it, and if it’s for it, he disrecommends it. Apparently only foes of it ever have any of the truth.
Informative. Thanks! Though I must admit that my reaction to the pages of Shalizi that you cite isn’t the same as yours.
I believe his political views are somewhere between way to the left of the Democratic Party and socialism. He dislikes the entire field of intelligence research in psychology because it’s ideologically inconvenient. He criticises anything that he can find to criticise about it. Think of him as Stephen Jay Gould, but much smarter and more honest.
See, this is a place where the US is different from Europe. Because over here (at least in the bit of Europe I’m in), being “somewhere to the right of socialism” isn’t thought of as the kind of crazy extremism that ipso facto makes someone dangerously biased and axe-grindy.
Now, of course politics is what it is, and affiliation with even the most moderate and reasonable political position can make otherwise sensible people completely blind to what’s obvious to others. So the fact that being almost (but not quite) a socialist looks to me like a perfectly normal and sensible position is perfectly compatible with Shalizi being made nuts by it. But to me “he’s somewhere to the left of Barack Obama” doesn’t look on its own like something that makes someone a biased source and explains what their problem is.
Being an extremist by local standards may be more relevant than actual beliefs.
Yup, that’s a good point. (Though it depends on what “local” means. I have the impression that academics in the US tend to be leftier than the population at large.)
Academia in the US is much leftier than the population at large. I believe it was Jonathan Haidt who went looking for examples of social conservatives in his field and people kept nomimating Philip Tetlock who would not describe himself thus. At a conference Dr.Haidt was looking for a show of hands for various political positions. Republicans were substantially less popular than Communists. Psychology is about as left wing as sociology and disciplines vary but academia is a great deal to the left of the US general population.
I’d generalize that to something like
collecting published results in medicine, psychology, epidemiology & economics journals gives an unbiased idea of the sizes of the effects they report
which is wrong at least twice over (publication bias and correlation-causation confusion) but is, I suspect, an implicit assumption made by lots of people who only made it to the first stage of traditional rationality (and reason along the lines of “normal people are full of crap, scientists are smarter and do SCIENCE!, so all I need to do to be correct is regurgitate what I find in scientific journals”).
Then don’t.
I point is more that if you only have theory and no empiric evidence, then it’s likely that you are wrong. That doesn’t mean that having a bit of empiric evidence automatically means that you are right.
I also would put more emphasis on having empiric feedback loops than at scientific publications. Publications are just one way of feedback. There a lot to be learned about psychology by really paying attention on other people with whom you interact.
If I interact with a person who has a phobia of spider and solve the issue and afterwards put a spider on his arm and the person doesn’t freak out, I have my empiric feedback. I don’t need a paper to tell me that the person doesn’t have a phobia anymore.
Yes, I agree. To clarify, I was neither condoning the belief in my bullet point, nor accusing you of believing it. I just wanted to tip my hat to you for inspiring my example with yours.
Ah, okay.
If a plane is on a conveyor belt going at the same speed in the opposite direction, will it take off?
I remember reading this in other places I don’t remember, and it seems to inspire furious arguments despite being non-political and not very controversial.
That reminds me of the question of whether hot water freezes faster than cold water.
That’s a great example. If I recall, people who get worked up about it generally feel that the answer is obvious and the other side is stupid for not understanding the argument.
Same speed with respect to what? This sound kind of like the tree-in-a-forest one.
As I remember the problem, the plane’s wheels are supposed to be frictionless so that their rotation is uncoupled from the rest of the plane’s motion. Hence the speed of the conveyor belt is irrelevant and the plane always takes off. Now, if you had a helicopter on a turntable...
What I mean is, on hearing that I thought of a conveyor belt whose top surface was moving at a speed -x with respect to the air, and a plane on top of it moving at a speed x with respect to the top of the conveyor belt, i.e. the plane was stationary with respect to the air. But on reading the Snopes link what was actually meant was that the conveyor belt was moving at speed -x and the plane’s engines were working as hard as needed to move at speed x on stationary ground with no wind.
While at the same time the rolling speed of the plane, which is the sum of it’s forward movement and the speed of the treadmill, is supposed to be equal to the speed of the treadmill. Which is impossible if the plane moves forward.
I’m not sure what you mean by “rolling speed of the plane”, “it’s forward movement”, and “speed of the treadmill”. The phrase “rolling speed” sounds like it refers to the component of the plane’s forward motion due to the turning of its wheels, but that’s not a coherent thing to talk about if one accepts my assumption that the wheels are uncoupled from the plane.
Rolling speed = how fast the wheels turn, described in terms of forward speed. So it’s the circumference of the wheels multiplied by their angular speed. And the wheels are not uncoupled from the plane they are driven by the plane. It was only assumed that the friction in the wheel bearings is irrelevant.
Forward movement of the plane = speed of the plane relative to something not on the treadmill. I guess I should have called it airspeed, which it would be if there is no wind.
Speed of the treadmill = how fast the surface of the treadmill moves.
And that is more time than I wanted to spend rehashing this old nonsense. The grandparent was only meant to explain why the great grandparent would not have settled the issue, not to settle it on its own. The only further comment I have is the whole thing is based on an unrealistic setup, which becomes incoherent if you assume that it is about real planes and real treadmills.
Fair enough. I have to chip in with one last comment, but you’ll be happy to hear it’s a self-correction! My comments don’t account for potential translational motion of the wheels, and they should’ve done. (The translational motion could matter if one assumes the wheels experience friction with the belt, even if there’s no internal wheel bearing friction.)
That’s different though. The Plane on a Treadmill started with somebody specifying some physically impossible conditions, and then the furious arguments were between people stating the implication of the stated conditions on one side and people talking about the real world on the other hand.
If your twin’s going away for 20 years to fly around space at close to the speed of light, they’ll be 20 years older when they come back.
A spinning gyroscope, when pushed, will react in a way that makes sense.
If another nation can’t do anything as well as your nation, there is no self-serving reason to trade with them.
You shouldn’t bother switching in the Monty Hall problem
The sun moves across the sky because it’s moving.
EDIT Corrected all statements to be false
I think you may have expressed this one the wrong way around; the way you’ve phrased it (“can make you better off”) is the surprising truth, not the surprising untruth.
They will. I think you mean: If your twin flies through space at close to the speed of light and arrives back 20 years later, they’ll be 20 years older when they come back. That one’s false.
Reversed polarity on a few statements. Thanks.
Your first statement is still correct.
To be more explicit: What is needed to make the statement interestingly wrong is for the two 20-year figures to be in different reference frames. If your twin does something for 20 years, then they will be 20 years older; but if they do something for what you experience as 20 years they may not be.
Edited to more firmly attach “for 20 years” to the earth.
Rephrased to more explicitly place “for 20 years” in the earth’s reference frame.
Would wrong scientific theories qualify? E.g. phlogiston or aether.
Downwind faster than the wind. See seven pages of posts here for examples of people getting it wrong.
Kant was famously wrong when he claimed that space had to be flat.
As discussed previously, this exact claim seems suspiciously absent from the first Critique.
I agree that Kant doesn’t seem to have ever considered non-euclidean geometry, and thus can’t really be said to be making an argument that space is flat. If we could drop an explanation of general relativity, he’d probably come to terms with it. On the other hand, he just assumes that two straight lines can only intersect once, and that this describes space, which seems pretty much what he was accused of.
I don’t see this in the quoted passage. He’s trying to illustrate the nature of propositions in geometry, and doesn’t appear to be arguing that the parallel postulate is universally true. “Take, for example,” is not exactly assertive.
Also, have a care: those two paragraphs are not consecutive in the Critique.
This isn’t very interesting, but I used to believe that the rules about checkmate didn’t really change the nature of chess. Some of the forbidden moves—moving into check, or failing to move out if possible—are always a mistake, so if you just played until someone captured the king, the game would only be different in cases where someone made an obvious mistake.
But if you can’t move, the game ends in stalemate. So forbidding you to move into check means that some games end in draws, where capture-the-king would have a victor.
(This is still armchair theorising on my part.)
Does it have to be something from the modern day? Because there are tons of historical examples.
There are many beliefs that people will arrive at through armchair theorizing, but only until they are corrected. If you came up with the idea that the Earth was flat a long time ago, nobody would correct you. If you did that today, someone would correct you; indeed, society is so full of round-Earth information that it’s hard for anyone to not have heard of the refutation before coming up with the idea, unless they’re a young child.
Does that count as something arrived at through armchair theorizing? People would, after all, come up with it by armchair theorizing if they lived in a vacuum. They did come up with it through armchair theorizing back when they did live in a vacuum.
That’s why there are tons of historical examples and not so many modern examples. A modern example has to be something where the refutation is well known by experts, but the refutation hasn’t made it down to the common person, because if the refutation did make it down to the common person that would inhibit them from coming up with the armchair theory in the first place.
(For historical examples,
It’s possible that the refutation is known by our experts, but not by contemporary experts, or
because of the bad state of mass communication in ancient times, the refutation simply hasn’t spread enough to reach most armchair theorists.)
Something from the modern day, yes. The people arriving at the naive belief, and the people with the ability to demonstrate its incorrect status, should coexist.
Sorry to keep going on this, but would looking at a historical example of a group of intelligent people arriving at a naive belief, even though there was plenty of evidence available at the time that this is a naive belief work?
Possibly, yes. I’d love to hear whatever you’ve got in mind.
The Conservative obsession with a non-existent link between abortion and breast cancer.
That hardly satisfies any of the desiderata! It’s political, controversial, and it’s hard to see how armchair reasoning would lead you to believe it.
Bell’s spaceship paradox.
According to Bell, he surveyed his colleagues at CERN (clearly a group of intelligent, qualified people) about this question, and most of them got it wrong. Although, to be fair, the conflict here is not between expert reasoning and domain knowledge, since the physicists at CERN presumably possessed all the knowledge you need (basic special relativity, really) to get the right answer.
When I was ~16, I came up with group selection to explain traits like altruism.
Generalising from ‘plane on a treadmill’; a lot of incorrect answers to physics problems and misconceptions of physics in general. For any given problem or phenomenon, one can guess a hundred different fake explanations, numbers, or outcomes using different combinations of passwords like ‘because of Newton’s Nth law’, ‘because of drag’, ‘because of air resistance’, ‘but this is unphysical so it must be false’ etc. For the vast majority of people, the only way to narrow down which explanations could be correct is to already know the answer or perform physical experiments, since most people don’t have a good enough physical intuition to know in advance what types of physical arguments go through, so should be in a state of epistemic learned helplessness with respect to physics.
I have a strange request. Without consulting some external source, can you please briefly define “learned helplessness” as you’ve used it in this context, and (privately, if you like) share it with me? I promise I’ll explain at some later date.
There will probably be holes and not quite capture exactly what I mean, but I’ll take a shot. Let me know if this is not rigorous or detailed enough and I’ll take another stab, or if you have any other follow-up. I have answered this immediately, without changing tab, so the only contamination is saccading my LW inbox beforing clicking through to your comment, the titles of other tabs, etc. which look (as one would expect) to be irrelevant.
Helplessness about topic X—One is not able to attain a knowably stable and confident opinion about X given the amount of effort one is prepared to put in or the limits of one’s knowledge or expertise etc. One’s lack of knowledge of X includes lack of knowledge about the kinds of arguments or methods that tend to work in X, lack of experience spotting crackpot or amateur claims about X, and lack of general knowledge of X that would allow one to notice one’s confusion at false basic claims and reject them. One is unable to distinguish between ballsy amateurs and experts.
Learned helplessness about X—The helplessness is learned from experience of X; much like the sheep in Animal Farm, one gets opinion whiplash on some matter of X that makes one realise that one knows so little about X that one can be argued into any opinion about it.
(This has ended up more like a bunch of arbitrary properties pointing to the sense of learned helplessness rather than a slick definition. Is it suitable for your purposes, or should I try harder to cut to the essence?)
Rant about learned helplessness in physics: Puzzles in physics, or challenges to predict the outcome of a situation or experiment, often seem like they have many different possible explanations leading to a variety of very different answers, with the merit of these explanations not being distinguishable except to those who have done lots of physics and seen lots of tricks, and maybe even then maybe you just need to already know the answer before you can pick the correct answer.
Moreover, one eventually learns that the explanations at a given level of physics instruction are probably technically wrong in that they are simplified (though I guess less so as one progresses).
Moreover moreover, one eventually becomes smart enough to see that the instructors do not actually even spot their leaps in logic. (For example, it never seemed to occur to any of my instructors that there’s no reason you can’t have negative wavenumbers when looking at wavefunctions in basic quantum. It turns out that when I run the numbers, everything rescales since the wavefunction bijects between -n and n and one normalizes the wavefunction anyway, so that it doesn’t matter, but one could only know this for sure after reasoning it out and justifying discarding the negative wavenumbers. It basically seemed like the instructors saw an ‘n’ in sin(n*pi/L) or whatever and their brain took it as a natural number without any cognitive reflection that the letter could have just as easily been a k or z or something, and to check that the notation was justified by the referent having to be a natural.)
Moreover, it takes a high level of philosophical ability to reason about physics thought experiments and their standards of proof. Take the ‘directly downwind faster than the wind’ problem. The argument goes back and forth, and, like the sheep, at every point the side that’s speaking seems to be winning. Terry Tao comes along and says it’s possible, and people link to videos of carts with propellers apparently going downwind faster than the wind and wheels with rubber bands attached allegedly proving it. But beyond deferring to his general hard sciences problem-solving ability, one has no inside view way to verify Tao’s solution; what are the standards of proof for a thought experiment? After all, maybe the contraptions in the video only work (assuming they do work as claimed, which isn’t assured) because of slight side-to-side effects rather than directly down wind or some other property of the test conditions implicitly forbidden by the thought experiment.
Since any physical experiment for a physics thought experiment will have additional variables, one needs some way to distinguish relevant and irrelevant variables. Is the thought experiment the limit as extraneous variables become negligible, or is there a discontinuity? What if different sets of variables give rise to different limits? How does anyone ever know what the ‘correct’ answer is to an idealised physics thought experiment of a situation that never actually arises? Etc.
Thanks for that. The whole response is interesting.
I ask because up until quite recently I was labouring under a wonky definition of “learned helplessness” that revolved around strategic self-handicapping.
An example would be people who foster a characteristic of technical incompetence, to the point where they refuse to click next-next-finish on a noddy software installer. Every time they exhibit their technical incompetence, they’re reinforced in this behaviour by someone taking the “hard” task away from them. Hence their “helplessness” is “learned”.
It wasn’t until recently that I came across an accurate definition in a book on reinforcement training. I’m pretty sure I’ve had “learned helplessness” in my lexicon for over a decade, and I’ve never seen it used in a context that challenged my definition, or used it in a way that aroused suspicion. It’s worth noting that I probably picked up my definition through observing feminist discussions. Trying a mental find-and-replace on ten years’ conversations is kind of weird.
I am also now bereft of a term for what I thought “learned helplessness” was. Analogous ideas come up in game theory, but there’s no snappy self-contained way available to me for expressing it.
Good chance you’ve seen both of these before, but:
http://en.wikipedia.org/wiki/Learned_helplessness and http://squid314.livejournal.com/350090.html
Damn, if only someone had created a thread for that, ho ho ho
Strategic incompetence?
I’m not sure if maybe Schelling uses a specific name (self-sabotage?) for that kind of thing?
Schelling does talk about strategic self-sabotage, but it captures a lot of deliberated behaviour that isn’t implied in my fake definition.
Also interesting to note, I have read that Epistemic Learned Helplessness blog entry before, and my fake definition is sufficiently consistent with it that it doesn’t stand out as obviously incorrect.
Now picturing a Venn diagram with three overlapping circles labelled “epistemic learned helplessness”, “what psychologists call ‘learned helplessness’”, and “what sixes_and_sevens calls ‘learned helplessness’”!
Making up a term for this...”reinforced helplessness”? (I dunno whether it’d generalize to cover the rest of what you formerly meant by “learned helplessness”.)
The sun revolves around the earth.
The earth revolving around the sun was also armchair reasoning, and refuted by empirical data like the lack of observable parallax of stars. Geocentrism is a pretty interesting historical example because of this: the Greeks reached the wrong conclusion with right arguments. Another example in the opposite direction: the Atomists were right about matter basically being divided up into very tiny discrete units moving in a void, but could you really say any of their armchair arguments about that were right?
It is not clear that the Greeks rejected heliocentrism at all, let alone any reason other than heresy. On the contrary, Hipparchus refused to choose, on the grounds of Galilean relativity.
The atomists got the atomic theory from the Brownian motion of dust in a beam of light. the same way that Einstein convinced the final holdouts thousands of years later.
Eh? I was under the impression that most of the Greeks accepted geocentrism, eg Aristotle. Double-checking https://en.wikipedia.org/wiki/Heliocentrism#Greek_and_Hellenistic_world and https://en.wikipedia.org/wiki/Ancient_Greek_astronomy I don’t see any support for your claim that heliocentrism was a respectable position and geocentrism wasn’t overwhelmingly dominant.
Cite? I don’t recall anything like that in the fragments of the Pre-socratics, whereas Eleatic arguments about Being are prominent.
Lucretius talks about the motion of dust in light, but he doesn’t claim that it is the origin of the theory. When I google “Leucippus dust light” I get lots of people making my claim and more respectable sources making weaker claims, like “According to traditional accounts the philosophical idea of simulacra is linked to Leucippus’ contemplation of a ray of light that made visible airborne dust,” but I don’t see any citations to where this tradition is recorded.
The Greeks cover hundreds of years. They made progress! You linked to a post about the supposed rejection of Aristarchus’s heliocentric theory. It’s true that no one before Aristarchus was heliocentric. That includes Aristotle who died when Aristarchus was 12. Everyone agrees that the Hellenistic Greeks who followed Aristotle were much better at astronomy than the Classical Greeks. The question is whether the Hellenistic Greeks accepted Aristarchus’s theory, particularly Archimedes, Apollonius, and Hipparchus. But while lots of writings of Aristotle remain, practically nothing of the later astronomers remain.
It’s true that secondary sources agree that Archimedes, Apollonius, and Hipparchus were geocentric. However, they give no evidence for this. Try the scholarly article cited in the post you linked. It’s called “The Greek Heliocentric Theory and Its Abandonment” but it didn’t convince me that there was an abandonment. That’s where I got the claim about Hipparchus refusing to choose.
I didn’t claim that there was any evidence that it was respectable, let alone dominant, only that there was no evidence that it was rejected. The only solid evidence one way or the other is the only surviving Hellenistic astronomy paper, Archimedes’s Sandreckoner, which uses Aristarchus’s model. I don’t claim that Archimedes was heliocentric, but that sure sounds to me like he respected heliocentrism.
Maybe heliocentrism survived a century and was finally rejected by Hipparchus. That’s a world of difference from saying that Seleucus was his only follower. Or maybe it was just the two of them, but we live in a state of profound ignorance.
As for the ultimate trajectory of Greek science, that is a difficult problem. Lucio Russo suggests that Roman science is all mangled Greek science and proposes to extract the original. For example, Seneca claims that the retrograde motion of the planets is an illusion, which sounds like he’s quoting someone who thinks the Earth moves, even if he doesn’t. More colorful are Pliny and Vitruvius who claim that the retrograde motion of the planets is due to the sun shooting triangles at them. This is clearly a heliocausal theory, even if the authors claim to be geocentric. Less clear is Ruso’s interpretation, that this is a description of a textbook diagram that they don’t understand.
So, you just have an argument from silence that heliocentrism was not clearly rejected?
I just read through the bits of Sand Reckoner referring to Aristarchus (Mendell’s translation), and throughout Archimedes seems to be at pains to distance himself from Aristarchus’s model, treating it as a minority view (emphasis added):
Not language which suggests he takes it particularly seriously, much less endorses it.
In fact, it seems that the only reason Archimedes brings up Aristarchus at all is as a form of ‘worst-case analysis’: some fools doubt the power of mathematics and numbers, but Archimedes will show that even under the most ludicrously inflated estimate of the size of the universe (one implied by Aristarchus’s heliocentric model), he can still calculate & count the number of grains of sands it would take to fill it up; hence, he can certainly calculate & count the number for something smaller like the Earth. From the same chapter:
And he triumphantly concludes in ch4:
All I have ever said is that you should stop telling fairy tales about why the Greeks rejected heliocenrism. If the Sandreckoner convinces you that Archimedes rejected heliocentrism, fine, whatever, but it sure doesn’t talk about parallax.
I listed several pieces of positive evidence, but I’m not interested in the argument.
The Sand Reckoner implies the parallax objection when it uses an extremely large heliocentric universe! Lack of parallax is the only reason for such extravagance. Or was there some other reason Aristarchus’s model had to imply a universe lightyears in extent...?
Aristarchus using a large universe is evidence that he thought about parallax. It is not evidence that his opponents thought about parallax.
You are making a circular argument: you say that the Greeks rejected heliocentrism for a good reason because they invoked parallax, but you say that they invoked parallax because you assume that they had a good reason.
There is a contemporary recorded reason for rejecting Aristarchus: heresy. There is also a (good) reason recorded by Ptolemy 400 years later, namely wind speed.
Uh… why would the creator of the system consider parallax an issue, and the critics not consider parallax an issue?
And you still haven’t addressed my quotes from The Sand Reckoner indicating Archimedes considered heliocentrism dubious and a minority view, which should override your arguments from silence.
No. I said parallax is why they rejected it in part because to save the model one has to make the universe large, then you said ‘look! Archimedes uses a large universe!’, and I pointed out this is 100% predicted by the parallax-rejection theory. So what? Where is your alternate explanation of why the large-universe—did Archimedes just make shit up?
And how do these lead to a large universe...?
The very question is whether the critics made good arguments. You are assuming the conclusion.
People make stupid arguments all the time. Anaxagoras was prosecuted for heresy and Aristarchus may have been. How many critics of Copernicus knew that he was talking about what happens over the course of a year, not what happens over the course of a day?
Yes, Archimedes says that Aristarchus’s position is a minority. Not dubious. I do not see that in the quotes at all. Yes, Archimedes probably uses Aristarchus’s position for the purposes of worst-case analysis to get numbers as large as possible; indeed, they are larger than the numbers Ptolemy attributes to Aristarchus. As I said at the beginning, I do not claim that he endorsed heliocentrism, only that he considered it a live hypothesis.
One mystery is what is the purpose of the Sandreckoner. Is it just about large numbers? Or is it also about astronomy? Is Archimedes using exotic astronomy to justify his interest in exotic mathematics? Or is he using his public venue to promote diversity in astronomy?
It’s assuming the conclusion to think critics agreed with Aristarchus’s criticism of a naive heliocentric theory?
I disagree strongly. I don’t see how you could possibly read the parts I quoted, and italicized, and conclude otherwise. Like, how do you do that? How do you read those bits and read it as anything else? What exactly is going through your head when you read those bits from Sand Reckoner, how do you parse it?
Gee, if only I had quoted the opening and ending bits of the Sand Reckoner where Archimedes explained his goal...
Many people object to Copernicus on the grounds that Joshua made the Sun stand still, or on grounds of wind, without seeming to realize that they object to the daily rotation of the Earth, not to his special suggestion of the yearly revolution of the Earth about the Sun.
If Copernicus had such lousy critics, why assume Aristarchus had good critics who were aware of his arguments? Maybe they objected to heresy, like (maybe) Cleanthes.
Archimedes was a smart guy who understood what Aristarchus was saying. He seems to accept Aristarchus’s argument that heliocentrism implies a large universe. If (if!) he rejects the premise, that does not tell us why. Maybe because he rejects the conclusion. Or maybe he rejects the premise for completely different consequences, like wind. Or maybe he is not convinced by Aristarchus’s main argument (whatever that was) and doesn’t even bother to move on to the consequences.
Ptolemy does give a reason: he says wind. He has the drawback of being hundreds of years late, so maybe he is not representative, but at least he gives a reason. If you extract any reason, that is the one to pick.
The principal purpose of the Sandreckoner is to investigate infinity, to eliminate the realm of un-nameable numbers, thus to eliminate the confusion between un-nameably large and infinite. But there are many other choices that go into the contents, and they may be motivated by secondary purposes. Physical examples are good. Probably sand is a cliche. But why talk about astronomy at all? Why not stop at all the sand in the world? Or fill the sphere of the sun with sand, stopping at Aristarchus’s non-controversial calculation of that distance? Such choices are rarely explained. I offered two possibilities and the text does not distinguish them.
You have not explained why Aristarchus would make his universe so large if the criticisms were as bogus as some of Copernicus’s critics. Shits and giggles?
If he rejects heliocentrism, as he clearly does, it does not matter for your original argument why exactly.
You still have not addressed the quotes from Sand Reckoner I gave which clearly show Archimedes rejects heliocentrism and describes it as a minority rejected position and he only draws on Aristarchus as a worst-case a fortiori argument. Far from being a weak argument from silence (weak because while we lack a lot of material, I don’t think we lack so much material that they could have seriously maintained heliocentrism without us knowing; absence of evidence is evidence of absence), your chosen Sand Reckoner example shows the opposite.
If this is the best you can do, I see no reason to revise the usual historical scenario that heliocentrism was rejected because any version consistent with observations had absurd consequences.
Aristarchus made the universe big because he himself thought about parallax. Maybe some critic first made this objection to him, but such details are lost to time, and uninteresting to compared to the question of the response to the complete theory.
As to the rest, I abandon all hope of convincing you.
I ask only that any third parties read the whole exchange and not trust Gwern’s account of my claims.
Atoms can actually be divided into parts, so it’s not clear that the atomists where right. If you would tell some atomist about quantum states, I would doubt that they would find that to be a valid example of what they mean with “atom”.
The atomists were more right than the alternatives: the world is not made of continuously divisible bone substances, which are bone no matter how finely you divide them, nor is it continuous mixtures of fire or water or apeiron.
You could say the same of Dalton.
How about “human beings only use 10% of their brains”? Not political, not flamebait, but possibly also “a lot of people say it and sounds plausible” rather than armchair theorizing. “Everyone should drink eight glasses of water a day” is probably in the same category.
I looked through Wikipedia’s list of common misconceptions for anything that people might arise independently in lots of people through reasonable reflection, rather than just “facts” that sneak into the public consciousness, but none of them really qualify.
Of course, false “facts” can also easily sneak into less trafficked Wikipedia pages, such as its list of common misconceptions.
Perhaps “The person who came out of the teleporter isn’t me, because he’s not made of the same atoms”?
Why not also spend an equally amount of time searching for examples that prove the opposite of the point you’re trying to make? Or are you speaking to an audience that doesn’t agree this is possible in principle?
Edit: Might Newtonian physics be an example?