The Correct Contrarian Cluster

Followup to: Contrarian Status Catch-22

Suppose you know someone believes that the World Trade Center was rigged with explosives on 9/11.  What else can you infer about them?  Are they more or less likely than average to believe in homeopathy?

I couldn't cite an experiment to verify it, but it seems likely that:

  • There are persistent character traits which contribute to someone being willing to state a contrarian point of view. 
  • All else being equal, if you know that someone advocates one contrarian view, you can infer that they are more likely than average to have other contrarian views.

All sorts of obvious disclaimers can be included here.  Someone who expresses an extreme-left contrarian view is less likely to have an extreme-right contrarian view.  Different character traits may contribute to expressing contrarian views that are counterintuitive vs. low-prestige vs. anti-establishment etcetera.  Nonetheless, it seems likely that you could usefully distinguish a c-factor, a general contrarian factor, in people and beliefs, even though it would break down further on closer examination; there would be a cluster of contrarian people and a cluster of contrarian beliefs, whatever the clusters of the subcluster.

(If you perform a statistical analysis of contrarian ideas and you find that they form distinct subclusters of ideologies that don't correlate with each other, then I'm wrong and no c-factor exists.)

Now, suppose that someone advocates the many-worlds interpretation of quantum mechanics.  What else can you infer about them?

Well, one possible reason for believing in the many-worlds interpretation is that, as a general rule of cognitive conduct, you investigated the issue and thought about it carefully; and you learned enough quantum mechanics and probability theory to understand why the no-worldeaters advocates call their theory the strictly simpler one; and you're reflective enough to understand how a deeper theory can undermine your brain's intuition of an apparently single world; and you listen to the physicists who mock many-worlds and correctly assess that these physicists are not to be trusted.  Then you believe in many-worlds out of general causes that would operate in other cases - you probably have a high correct contrarian factor - and we can infer that you're more likely to be an atheist.

It's also possible that you thought many-worlds means "all the worlds I can imagine exist" and that you decided it'd be cool if there existed a world where Jesus is Batman, therefore many-worlds is true no matter what the average physicist says.  In this case you're just believing for general contrarian reasons, and you're probably more likely to believe in homeopathy as well.

A lot of what we do around here can be thought of as distinguishing the correct contrarian cluster within the contrarian cluster.  In fact, when you judge someone's rationality by opinions they post on the Internet - rather than observing their day-to-day decisions or life outcomes - what you're trying to judge is almost entirely cc-factor.

It seems indubitable that, measured in raw bytes, most of the world's correct knowledge is not contrarian correct knowledge, and most of the things that the majority believes (e.g. 2 + 2 = 4) are correct.  You might therefore wonder whether it's really important to try to distinguish the Correct Contrarian Cluster in the first place - why not just stick to majoritarianism?  The Correct Contrarian Cluster is just the place where the borders of knowledge are currently expanding - not just that, but merely the sections on the border where battles are taking place.  Why not just be content with the beauty of settled science?  Perhaps we're just trying to signal to our fellow nonconformists, rather than really being concerned with truth, says the little copy of Robin Hanson in my head.

My primary personality, however, responds as follows:

  • Religion
  • Cryonics
  • Diet

In other words, even though you would in theory expect the Correct Contrarian Cluster to be a small fringe of the expansion of knowledge, of concern only to the leading scientists in the field, the actual fact of the matter is that the world is *#$%ing nuts and so there's really important stuff in the Correct Contrarian Cluster.  Dietary scientists ignoring their own experimental evidence have killed millions and condemned hundreds of millions more to obesity with high-fructose corn syrup.  Not to mention that most people still believe in God.  People are crazy, the world is mad.  So, yes, if you don't want to bloat up like a balloon and die, distinguishing the Correct Contrarian Cluster is important.

Robin previously posted (and I commented) on the notion of trying to distinguish correct contrarians by "outside indicators" - as I would put it, trying to distinguish correct contrarians, not by analyzing the details of their arguments, but by zooming way out and seeing what sort of general excuse they give for disagreeing with the establishment.  As I said in the comments, I am generally pessimistic about the chances of success for this project.  Though, as I also commented, there are some general structures that make me sit up and take note; probably the strongest is "These people have ignored their own carefully gathered experimental evidence for decades in favor of stuff that sounds more intuitive."  (Robyn Dawes/psychoanalysis, Robin Hanson/medical spending, Gary Taubes/dietary science, Eric Falkenstein/risk-return - note that I don't say anything like this about AI, so this is not a plea I have use for myself!)  Mostly, I tend to rely on analyzing the actual arguments; meta should be spice, not meat.

However, failing analysis of actual arguments, another method would be to try and distinguish the Correct Contrarian Cluster by plain old-fashioned... clustering.  In a sense, we do this in an ad-hoc way any time we trust someone who seems like a smart contrarian.  But it would be possible to do it more formally - write down a big list of contrarian views (some of which we are genuinely uncertain about), poll ten thousand members of the intelligentsia, and look at the clusters.  And within the Contrarian Cluster, we find a subcluster where...

...well, how do we look for the Correct Contrarian subcluster?

One obvious way is to start with some things that are slam-dunks, and use them as anchors.  Very few things qualify as slam-dunks.  Cryonics doesn't rise to that level, since it involves social guesses and values, not just physicalism.  I can think of only three slam-dunks off the top of my head:

These aren't necessarily simple or easy for contrarians to work through, but the correctness seems as reliable as it gets.

Of course there are also slam-dunks like:

  • Natural selection:  Yes.
  • World Trade Center rigged with explosives:  No.

But these probably aren't the right kind of controversy to fine-tune the location of the Correct Contrarian Cluster.

A major problem with the three slam-dunks I listed is that they all seem to have more in common with each other than any of them have with, say, dietary science.  This is probably because of the logical, formal character which makes them slam dunks in the first place.  By expanding the field somewhat, it would be possible to include slightly less slammed dunks, like:

  • Rorschach ink blots:  No.

But if we start expanding the list of anchors like this, we run into a much higher probability that one of our anchors is wrong.

So we conduct this massive poll, and we find out that if someone is an atheist and believes in many-worlds and does not believe in p-zombies, they are much more likely than the average contrarian to think that low-energy nuclear reactions (the modern name for cold fusion research) are real.  (That is, among "average contrarians" who have opinions on both p-zombies and LENR in the first place!)  If I saw this result I would indeed sit up and say, "Maybe I should look into that LENR stuff more deeply."  I've never heard of any surveys like this actually being done, but it sounds like quite an interesting dataset to have, if it could be obtained.

There are much more clever things you could do with the dataset.  If someone believes most things that atheistic many-worlder zombie-skeptics believe, but isn't a many-worlder, you probably want to know their opinion on infrequently considered topics.  (The first thing I'd probably try would be SVD to see if it isolates a "correctness factor", since it's simple and worked famously well on the Netflix dataset.)

But there are also simpler things we could do using the same principle.  Let's say we want to know whether the economy will recover, double-dip or crash.  So we call up a thousand economists, ask each one "Do you have a strong opinion on whether the many-worlds interpretation is correct?", and see if the economists who have a strong opinion and answer "Yes" have a different average opinion from the average economist and from economists who say "No".

We might not have this data in hand, but it's the algorithm you're approximating when you notice that a lot of smart-seeming people assign much higher than average probabilities to cryonics technology working.

229 comments, sorted by
magical algorithm
Highlighting new comments since Today at 10:39 AM
Select new highlight date
Moderation Guidelines: Reign of Terror - I delete anything I judge to be annoying or counterproductiveexpand_more

I don't understand how many worlds can be a slam dunk for someone who doesn't understand all the math behind quantum physics.

If a significant number of people who do understand this math believe that many-worlds is wrong, then no matter how convincing I find your non-mathematical arguments in favor of many-worlds isn't it rational for me to still assign a significant probability to the possibility that many worlds isn't correct?

Doesn't physics all come down to math, meaning that people who can't follow the math should put vastly more weight on polls of experts than on their own imperfect understanding of the field?

If a significant number of people who do understand this math believe that many-worlds is wrong, then no matter how convincing I find your non-mathematical arguments in favor of many-worlds isn't it rational for me to still assign a significant probability to the possibility that many worlds isn't correct?

It is. However, a useful cc-factor metric would focus on topics for which you have a confident belief. If those you get the right answer to those slam dunk topics that you do happen to be confident in then your cc-factor will be high.

The math isn't actually -that- hard. It would be far better to apply yourself to learning it.

I have been told by physicists that it is.

But even if I could understand it, do you really think someone with an IQ below 100 could? Trust me, as a college professor I know that you need an above average IQ to have a good understanding of even calculus. So I can't imagine that the math behind quantum physics is accessible to over 50% of humanity.

C.f. above: You need an above-average IQ to learn calculus in spite of the American educational system. We have no idea what genetic IQ is required to learn calculus.

I've personally lowered the IQ needed to understand Bayes's Theorem by browsing online, and if I rewrote the page today I bet I could drop it another 10 points.

From what I've seen of the actual math, if you can understand the content of a typical Calc 3 course (which covers multivariable calculus), you can understand the math of quantum mechanics. If you can get an engineering degree (which is not an easy feat, but it's something an awful lot of people manage to do), you should be smart enough to do quantum mechanics calculations.

Electrical engineering occasionally relies on quantum mechanical properties of semiconductors and other materials in their products. Then again, EE is one of the hardest engineering disciplines (or so I hear).

In many cases, engineers can get by with relatively simple empirical models to describe devices that depend on quantum mechanics to actually work. (Case in point: permanent magnets, which, according to classical electrodynamics, really shouldn't be able to exist.)

I have been told by physicists that it is.

Consider the signaling incentives they have. Do physicists look better or worse if the math they do is seen as harder or as easier?

Contrariwise, I (like many people here) associate mostly with very smart people, so greatly overestimate average intelligence.

Actually the math of quantum mechanics is much more complicated than, say, the Three Body Problem of classical mechanics, which is still unsolved today. It's not so much because calculus is that hard (assuming someone willing to spend the effort to learn it), but rather that doing any math with undefined functions doesn't work as well as you might think. What I'm trying to say is that, for all but the simplest quantum mechanics calculations, you can't actually do the math and instead need to have a computer do a huge amount of calculations for you -- and I think that qualifies as hard. (The same, of course, applies to classical problems like the Three Body Problem)

In any case, the math has nothing to do with this question, as you would know if you actually knew about the topic instead of wanting to brag. After all, the different interpretations of the model give the same predictions, and so use the same (or equivalent) math. The difference is in the assumptions behind the interpretation -- why do we need to assume a special "non-quantum reality" or worse "special observers" when we get the same results by applying the theory to the whole world such that when we observe a quantum event, we also become entangled with it (with all the usual results).

Slam dunk in reality, not in the mind. You're not looking for people who only get easy slam dunks, you're looking for people who are actually right. So you should start with items that you're sure are actually right - not that are easy. It's the respondents' job to get there, whether by choosing the right physicists to trust, or doing the math on their own... it's not your job to decide in advance how they find the truth, maybe you'll learn something! But the items you use as keys do have to be true.

Along with 99% of humanity my IQ isn't high enough for me to ever understand the math behind quantum physics. So I can't do the math myself, or figure out which physicist to trust when the physicists disagree.

Given your IQ and information set many worlds might be a slam dunk. But I submit that anyone with my IQ or lower would necessarily be irrational to think that many worlds is a slam dunk.

Along with 99% of humanity my IQ isn't high enough for me to ever understand the math behind quantum physics

This may be a tangential point, but I need to say this somewhere: claims like this are quite likely false. (Notice how rarely they're accompanied by justification.)

Quantum mechanics is new (in the scheme of things). So, of course, we see right now that the only people who understand it are very smart people: the ones who first thought of it and their students and associates. But that doesn't mean that no one else can understand it; it just hasn't had time to trickle down into everyone's general education yet.

300 years ago, you could have replaced "quantum" by "classical" in that sentence, and it would have seemed reasonable: at that time, only a few dozen people in the world understood the differential and integral calculus. Yet now this kind of mathematics is taught regularly to hordes of IQ 110 college freshmen, and (I expect) is considered elementary and routine by a majority of LW readers. Taking an Outside View approach here, I don't see any reason not to expect that the same trend will continue into the future, with quantum mechanics eventually being considered a grade-school subject (even without recourse to transhumanist solutions such as intelligence enhancement, which will immediately come to the minds of many readers).

Going back further, once upon a time literacy was an elite skill. Now we take it for granted, but how much do you really think our IQs have improved in the last couple thousand years?

And let's not forget that even now, we already know that the fundamental mathematical ideas behind quantum mechanics are actually quite simpler than you would have thought from listening to physicists -- little more than linear algebra over complex vector spaces.

Going back further, once upon a time literacy was an elite skill. Now we take it for granted, but how much do you really think our IQs have improved in the last couple thousand years?

A lot! Western IQ scores have improved by ~30 points since IQ tests were invented around a century ago. And literacy is probably part of a positive feedback loop that historically boosted IQ: increased literacy improves IQ, and higher IQ increases literacy. That feedback loop likely hasn't been going for two thousand years, but it's been going for at least two hundred years, which is more than enough time for a feedback loop to go nuts.

Still, though I suspect IQs have improved massively in the last couple thousand years, I definitely agree with your comment. I think the rise in average IQ over time doesn't mean we've gotten qualitatively smarter, more that our environment has - and one aspect of that is the trickle-down effect of mental tools like literacy, classical mechanics, and quantum mechanics.

You should look at the SAT math test to get an estimate of the percentage of Americans for which "linear algebra over complex vector spaces" can ever be simple.

I don't disagree, but keep in mind that these people went through horrible learning processes to get there.

I simply refer you again to my comment above. It applies to linear algebra as much as quantum mechanics.

Yet now this kind of mathematics is taught regularly to hordes of IQ 110 college freshmen, and (I expect) is considered elementary and routine by a majority of LW readers

This seems factually false to me. For starters, the average IQ of college freshman (all colleges, all majors) is more like 115 or 120 (choose the reference you please from Google). And math or physics majors are a cut far above that average, with GRE scores indicating an average around 130. (Prospective grad students, yes, but the ranking fits with high school SAT scores.)

I don't think very many schools make relativity-level mathematics (or even just multi-variate calculus sufficient to solve Newtonian problems) a core requirement rather than major-specific...

The number 110 was just a guess, of course, but the point clearly stands even if the average IQ of people taking business calculus is 120.

The 17th-century counterparts of these folks would have been illiterate peasants or possibly, in a few cases, local merchants; they would not have been Newton and Leibniz.

http://betterexplained.com/ may change your opinion of some of the "hard" mathematics you have learned. Teaching methods are technology and can be improved.

They don't have to think it's a slam-dunk. They just have to choose "Yes" if the choices are "Yes" or "No".

In effect, you're encouraging rationalist posers to signal agreement with you on these signature issues. By talking about the signal and its interpretation, you weaken it.

You obviously don't poll Less Wrong readers using those keys!

Does that mean you're holding some in reserve?

Another little essay on MWI. tl;dr : Eliezer is wrong on the Internet! Won't somebody please think of the mind children?...

I have spent many years studying and thinking about interpretations of quantum theory. Eliezer's peculiar form of dogmatism about many worlds is a new twist. I have certainly encountered dogmatic many-worlds supporters before. What's exceptional is Eliezer's determination to make belief in many worlds a benchmark test of rationality in general. He's not just dogmatic about it as a question of physics, but now he even calls it a rationalist "slam-dunk", a thing which should be obvious to any sufficiently informed clear thinker, and which can be used to rank a person's rationality.

My position, I suppose, is that it is Eliezer who is insufficiently informed. He has always been a wavefunction realist - a believer in the existence of the wavefunction - and simply went from a belief in collapse of the wavefunction, to a belief in no collapse. If that was the only choice, he'd have a point. But it is far from being the only choice.

One thing I wonder about (when I adopt the perspective of trying to draw lessons regarding general rationality from this affair) is whether he ought to regard himself as culpable for this error, or whether ignorance is a valid excuse. Yesterday I was promoting "quantum causal histories" as an example of an alternative class of interpretation. Those are rather obscure papers. He's certainly not at fault for not having heard of them. Yet he surely should have heard of John Cramer's transactional interpretation, and there's no trace of it in his writings on this topic.

I suspect that another factor in his thinking is a belief in the minimalism of many-worlds. All you need is the wavefunction. You even get to remove something from the theory - the collapse postulate. But the complexities reenter - and the handwaving begins - when you try to find the worlds in the wavefunction. Naive onlookers to this discussion may think of a world as a point in configuration space. But this is not the usual notion of "world" in the technical literature on many worlds. Worlds are themselves represented by lesser wavefunctions: components of the total wavefunction, or tensor factors thereof. It is a chronic question in many-worlds theory as to which such components are the worlds, or whether one even needs to specify a particular algebraic breakdown of the universal wavefunction as the decomposition corresponding to reality. I don't even know what Eliezer's position on this debate is. Is a world a point in configuration space? Is it a blob of amplitude stretching across a small contiguous region of configuration space? What about a wavefunction component which stretches across most of configuration space, and has multiple peaks - is it legitimate or not to treat that as a world? Eliezer is impressed by Robin Hanson's mangled worlds proposal; should we take Robin's definition of worlds as the one to use, if we wish to understand his thought?

I don't object to many-worlds advocates having their theoretical disputes; certainly better that they have them, than that their concepts should remain fuzzy and undeveloped! But I find it very hard to justify this harsh advocacy of many-worlds as obviously superior when the theoretical details of the interpretation remain so confused. The confusion, the unfinished work, seems comparable to that still existing with respect to the zigzag interpretations like Cramer's. And since a zigzag interpretation only requires a single, basically classical space-time, and does away with the wavefunction entirely except as the sort of probability distribution appropriate to a situation in which causality runs backwards and forwards in time, it has its own claim to elegance and minimalism.

My own position is the anodyne one that Further Research Is Required, and that theoretical pluralism should be tolerated. I respect the rigor of Bohmian mechanics; I don't believe it is the truth, but working on it might lead to the truth, and the same goes for a number of other interpretations. I tilt towards single-world interpretations because I anticipate that in most completed many-worlds theories (many-worlds theories in which the confusions have truly been resolved, by an exact theoretical framework), you will be able to find self-contained histories, akin to Bohmian trajectories but perhaps metaphorically "thicker" in cross-section. And my ultimate message for many-worlds enthusiasts is that the apparent simplicity of many worlds is an illusion because of the theoretical work necessary to finish the job. You will end up either adding lots of extra structure, or compromising on objectivity and theoretical exactness (e.g. by being blase about what is and is not a "world").

But the complexities reenter - and the handwaving begins - when you try to find the worlds in the wavefunction. ... It is a chronic question in many-worlds theory as to which such components are the worlds, or whether one even needs to specify a particular algebraic breakdown of the universal wavefunction as the decomposition corresponding to reality.

Now, I'm no quantum expert, but this seems to me to be a criticism based entirely on the name; “It's called many-worlds, so where are the worlds?” Fine. I hereby rename the theory to “much-world”.

Take “The Conscious Sorites Paradox” (thanks to Zack_M_Davis for the link) and s/person/world/.

It is a chronic question in many-worlds theory as to which such components are the worlds, or whether one even needs to specify a particular algebraic breakdown of the universal wavefunction as the decomposition corresponding to reality. I don't even know what Eliezer's position on this debate is.

Cf. "The Conscious Sorites Paradox"

If accepting Many Worlds is a slam dunk then advocating quantum monadology is surely a technical foul. +1 anecdote to cc-factoring.

Some views are contrarian in society at large, but dominant views in particular subcultures. Libertarian views aren't dominant in economics, but they're (correct me if I'm wrong) dominant in the economics department at George Mason where Robin Hanson works. Does that make Robin a contrarian, or a conformist?

I bet that most 9/11 conspiracy theorists have a lot of friends who are also conspiracy theorists. Sometimes supporting one contrarian theory (the Jews were behind 9/11) is a way of aligning with a larger, locally-conformist narrative (the Jews are behind everything).

Next thing you know, someone will say Jews are behind the Singularity Institute... um... uh-oh.

Yes, if nearly all "contrarian" views are just conformity with local groups, then there will be no c-factor - just a lot of ideologies that don't correlate with each other. This was alluded to in the OP.

This could be true of the general population but not of academia/intelligentsia, in which case polling 10,000 respondents there might still work.

This is a reason to collect data not just on what people think, but on who they know, and try to get many pairs of people who know each other to participate in your survey.

Perhaps if the poll is shared by friends on Facebook, this becomes easy?

I've read that in the 19th century, there were many people who said that iron ships couldn't possibly float. If you take a few seconds to do the math, you can quickly verify that iron ships can float. That seems like a good slam-dunk to me. Is there a modern equivalent?

Some similar, not-quite-as-obvious former popular opinions:

  • Humans can never fly.
  • Humans can never reach the moon.

(Interestingly, the much older "sailboats can never sail upwind" seems more plausible to me than any of these.)

Contemporary unpopular slam-dunk-yes views:

  • Computers will someday attain human-level performance on any task you can name.
  • Technology can enable humans to live to the age of 200.
  • Evolution. (Still unpopular worldwide.)

There are culture-specific slam-dunks. I noticed, while traveling in China, particularly during an episode when the US bombed a Chinese embassy and when discussing the Tienanmen Square massacre, that most of the Chinese people who spoke openly with me (just a few) simultaneously believe their government is corrupt and untrustworthy, yet believed everything it said about those incidents. Numerous Russians I've spoken to have a blindness reconciling their views on Stalin with their views on Putin (the same attributes that made Stalin bad make Putin good). Maybe a foreigner should help us identify our slam-dunks.

There are some slam-dunks that are popular on the low end of g, and on the high end of g, but not in the middle range of g, e.g.

  • Men and women have different distributions of preferences and cognitive aptitudes.

Using these in your survey could contaminate the results.

(Interestingly, the much older "sailboats can never sail upwind" seems more plausible to me than any of these.)

Wind-powered directly downwind faster than the wind vehicle!

Solution (spoiler).

I don't believe it.

Contrary to what the article says, sailboats can't travel downwind faster than the wind (except briefly, when the wind changes). If this were possible, I would have experienced it.

When the vehicle is moving as fast as the wind, in order to go faster, the energy output from the propeller must be more than the energy input through the wheels. The energy output of the propeller comes entirely from the energy input through the wheels, so this is impossible.

Right?

I'm feeling uncertain, because dozens of people reviewed the article and all agreed that the thing works.

I think that the sailing-faster-than-the-wind or the directly-downwind-faster-than-the-wind (DDFTTW) problems would make for a very interesting contrarian-cluster question, as it has a few features that don't often coincide in one controversy:

  • Many ordinary people claim that sailing downwind faster than the wind actually works in practice, not merely in theory.
  • This claim appears to have the form of "I don't need to check the details of your perpetual motion machine, I know right off the bat that it can't work!" It seems blindingly obvious that some principle of physics ought to prevent DDFTTW from working.
  • The amateur Youtube video for the DDFTTW machine is a very low-status means of demonstration (i.e. it's just what a crank or faker would do).
  • However, several of the smartest and most skeptical minds who did the actual computations have averred that the folk wisdom is right, and the "obvious" physics principle is mistaken in its application here!

Just having considered these data points (I haven't worked through Tao's or MarkCC's analyses), I assign very high probability (>99%) to sailing-faster-than-the-wind and DDFTTW working as described.

I expect Robin and Eliezer to agree with this assessment (and, though I expect them both to have updated in the same fashion, I suspect that Robin would have updated faster and with less effort than Eliezer in this instance— though on other types of problems I'd expect the opposite.)

Robin would've had to update pretty fast to update faster than I updated. I'm like, "Tao says it works? OK."

I don't really find it very counterintuitive. The different velocities of wind and ground are supplying free energy. Turns out you can grab a bunch of it and move faster than the wind? I don't see how that would violate thermodynamics or conservation of momentum. I haven't even checked the math; it just doesn't seem all that unlikely in the first place.

Ah: a focus on negentropy makes the idea more plausible for you at first glance. I was expecting you'd each find it counterintuitive, that Robin would be first to favor the expert consensus, and that you would wait until you'd worked through the full analysis. So I take a hit on my Bayes-score with regard to "things Eliezer finds counterintuitive".

I find it counterintuitive, but not impossible. it's this specific implementation that I have trouble with. But the "string" example does appear to work.

Moving faster than the wind is not even counterintuitive; sailboats can, because the mass of the wind is greater than the mass of the boat. Moving downwind faster than the wind is counterintuitive.

Right; I was talking about two linked problems (mentioned together by you), and linked to a discussion of each: sailboats keeling faster than the wind by Tao, and DDFTTW by Chu-Carroll. The characteristics I listed applied to each problem in much the same way, so I discussed them together.

I just worked through this stuff. Chu-Carroll and Tao describe different mechanisms of traveling faster than the wind and they're both right. Chu-Carroll gives a more detailed explanation here. In Tao's post, one only needs to parse Figure 4 to be convinced.

In this and other similar cases, restricting ourselves to only meta-level arguments seems unwise. What good is memorizing that DDFTTW is possible because Tao said it is, compared to actually understanding the matter? A good contrarian-cluster question should be more difficult on the object level.

Yes, I'm combining two distinct things here— but both problems have the same characteristics, and might separate out some clusters of contrarians by the heuristics they favor. The fact that one of these heuristics might be "sit down and actually work out the problem yourself" isn't a bad feature.

EDIT: Oops, "confute" doesn't mean "combine" at all.

Again, Tao did not say that DDFTTW is possible. Tao said that it is impossible. See my comment above. [Retracted later.]

Jump into Figure 4 in Tao's post, start from 0, follow the red vectors for a half circle in any direction, then fold up the sail, bingo - you're moving straight downwind 2x faster than the wind. Yes this assumes a pure lift sail and no friction, but you can almost-satisfy both assumptions and still outrun the wind by a big margin.

No. The black vectors show the apparent wind velocity. The red vectors, which are perpendicular to the black vectors, show the resulting boat velocity. You would have to build up speed moving (nearly) perpendicular to the apparent wind, then fold up the sail and steer downwind. Your total travel time to get downwind would be greater than the wind's travel time, so you would still not outrun the wind.

Read the caption below the figure. Neither red nor black vectors are velocities. Velocity values are denoted by points on the graph plane. The graph is in velocity space, not physical position space. The point 0 is the rest velocity, not the boat's starting point. The point v_0 means the boat is moving with the wind. The vectors show how the pilot can change the velocity of a boat already moving at a given velocity; they're acceleration vectors. Black vectors show accelerations possible with a pure-drag sail, red vectors are for a pure-lift sail.

Hmm. I think you're right. Oops. You can sail downwind faster than the wind. I tried to write up a detailed proof of why it wouldn't work, and it worked.

However, several of the smartest and most skeptical minds who did the actual computations have averred that the folk wisdom is right, and the "obvious" physics principle is mistaken in its application here!

I put the 'folk wisdom' on the side of "you can't go DDFTTW" here. It doesn't seem obvious from the perspective of physics but perhaps it does from the perspective of 'common sense'.

Tao shows how it's possible to move faster than the wind using wind power. I am not disputing this. Tao says in that very same post that it is impossible to sail downwind faster than the wind:

The most obvious dimension to exploit is the windward/leeward dimension – the direction that the wind velocity v0 is oriented in. But if this is the only dimension one exploits, one can only sail up to the wind speed |v_0| and no faster,

That's the wrong quote -- it refers to a limited situation where cross-wind forces are not being exploited. The next line after your quoted text is:

Things get more interesting when one also exploits the crosswind dimension perpendicular to the wind velocity, in particular by tacking the sail.

Now if you'd quoted

[By use of a keel], it becomes possible to sail against the wind, or faster than the wind, so long as one is moving at a non-trivial angle to the wind (i.e. v is not parallel to v _0 or - v _0).

that would have supported your assertion. But then Tao goes on to write

In theory, one can also sail at any desired speed and direction by combining the use of an air sail (or aerofoil) with the use of a water sail (or hydrofoil).

so you're wrong again (sort of -- the approach he's describing is of unknown practicality).

That's the wrong quote -- it refers to a limited situation where cross-wind forces are not being exploited.

Cross-wind forces cannot be exploited if you are travelling directly downwind. Tacking is done upwind only.

When Tao says "one can also sail at any desired speed and direction", he obviously doesn't mean that literally. Unless you also want to say Tao said that sailboats can go faster than light.

When Tao says "one can also sail at any desired speed and direction", he obviously doesn't mean that literally. Unless you also want to say Tao said that sailboats can go faster than light.

He writes, "In theory, one can also sail at any desired speed and direction" (emphasis added). And he means that quite literally. You can travel any desired speed under the theoretical framework that he's using (which doesn't take into account relativistic effects, among other things.)

You cannot travel at any desired speed! You can't travel a million miles an hour in a 5 knot wind because you desire it. And that's what the person quoting it meant to imply: "Tao says you can travel at any speed and direction; therefore, you can travel downwind faster than the wind." Correct conclusion, wrong reason.

You cannot travel at any desired speed! You can't travel a million miles an hour in a 5 knot wind because you desire it.

[. . .]

Tao simply does not say the things you people are trying to make him say. He is agreeing with me on every point I've discussed here.

You yourself quoted him as saying it. As you indicated, you can only make him agree with you by saying that he didn't "mean that literally".

At the end of the paragraph, he repeats it even more explicitly: "By alternately using the aerofoil and hydrofoil, one could in principle reach arbitrarily large speeds and directions, as illustrated by the following diagram:"

Are you saying that he didn't mean "arbitrarily large" literally?

ETA: In the next paragraph, he writes

It is reasonable (in light of results such as the Kutta-Joukowski theorem) to assume that the amount of lift provided by an aerofoil or hydrofoil is linearly proportional to the apparent wind speed or water speed. If so, then some basic trigonometry then reveals that (assuming negligible drag) one can use either of the above techniques to increase one’s speed at what is essentially a constant rate; in particular, one can reach speeds of n|v_0| for any n > 0 in time O(n).

Emphasis added. v_0 is the velocity of the wind. There's no room here for reading this as anything other than literal.

At the end of the paragraph, he repeats it even more explicitly: "By alternately using the aerofoil and hydrofoil, one could in principle reach arbitrarily large speeds and directions, as illustrated by the following diagram:"

Are you saying that he didn't mean "arbitrarily large" literally?

That was what I meant. And I see I was wrong. Sorry. It's such a shocking statement that I didn't take it seriously at first. In retrospect, the energy influx is continuous, so continuous acceleration is possible.

Tao simply does not say the things you people are trying to make him say. He is agreeing with me on every point I've discussed here.

Do you understand what Tao says in the article? With sufficiently high confidence? (Have you even read it?) Be careful. From the article:

Figure 6. By alternating between a pure-lift aerofoil (red) and a pure-lift hydrofoil (purple), one can in principle reach arbitrarily large speeds in any direction.
[...]
[O]ne can use either of the above techniques to increase one’s speed at what is essentially a constant rate; in particular, one can reach speeds of n|w| for any n > 0 in time O(n). [w is the wind speed]

Cross-wind forces cannot be exploited if you are travelling directly downwind.

So you agree that my second quote is more apposite than the quote you provided. Hurray!

Unless you also want to say Tao said that sailboats can go faster than light.

Tao obviously intends his analysis to apply whenever Newtonian dynamics is a good approximation, so bringing relativity into it is ignoratio elenchi. You asserted that Tao said that it is impossible to sail downwind faster than the wind; in fact he offered a theoretical approach for doing exactly that.

As Cyan points out, Tao is saying that you can't sail directly with the wind faster than the wind if you don't exploit more than one dimension. But the carts that started this discussion do exploit more than one dimension. Specifically, they exploit the vertical dimension by using the difference in speed between the ground and the air.

Sailboats can't travel downwind faster than the wind

Yes, they can. A boat sailing 45 degrees off of dead down wind, making downwind progress at the speed of wind (its total speed being square root of 2 times the speed of wind), will feel an apparent wind 45 degrees off its bow, from which it can generate more thrust and go even faster, until the apparent wind is much closer to directly ahead. Modern racing sailboats do this all the time.

A boat sailing 45 degrees off of dead downwind has its sail out very far to leeward, so that the apparent wind will slow it down, not speed it up. You're thinking of a boat sailing 45 degrees off of upwind. [EDIT: My mistake. When you reach the same speed in the downward direction as the wind, the apparent wind is coming entirely from a direction perpendicular to the wind, and so your sail will be trimmed in perpendicular to the wind and be receiving lift in the same direction as the wind.]

You might be able to move with a component in the downwind direction faster than the wind due to lift - but I wouldn't bet on it. I can't swear that it doesn't happen, because I try never to be in this situation. It's the easiest way to flip a boat, or to get "windlocked" (when the wind is too strong for you either to pull the sail in or to steer windward, so unless you jibe, you're stuck going the direction you're going until the wind dies down).

I always trim the sails for the apparent wind. If the apparent wind is backwinding the sails, I will trim them in, so that they work properly and provide forward thrust. As the boat accelerates on a straight line course, the apparent wind will shift forward and I will trim in the sails.

In the situation you described, the apparent wind is travelling from the tail of the sail to the front, in the opposite direction you would need for it to provide thrust. There is an apparent wind, and you do trim the sail in response to it, but it doesn't provide thrust when you're going downwind.

No, in the situation I described, the apparent wind flows from the luff (leading edge) to the leach (trailing edge) of the sail. I have actually done this. I will see if I can produce a diagram later tonight.

Edit: Here is the diagram:

(Completely OT, of course.)

When the vehicle is moving as fast as the wind, in order to go faster, the energy output from the propeller must be more than the energy input through the wheels. The energy output of the propeller comes entirely from the energy input through the wheels, so this is impossible.

Looking at it in the road's reference frame, the propeller decelerates the wind — even if the vehicle is already moving at wind speed — and takes kinetic energy from it.

The idea is that the propeller is providing thrust, not taking energy from the wind. It's rotating in the opposite direction from what you're suggesting.

The propeller does both. If the vehicle is moving at the same speed as the wind, then in the vehicle frame, the wind is being accelerated backwards (hence momentum is conserved), so in the road frame, the wind is being decelerated and donating energy to the vehicle.

The movement of the wind backwards is coupled to the movement of the vehicle forward; but that's the effect of the energy, not the source of the energy.

If your intuitions don't think it will work then two options available are building the device or doing the actual math.

The movement of the wind backwards is coupled to the movement of the vehicle forward; but that's the effect of the energy, not the source of the energy.

My intuition tells me that the source of the energy is the wind and some of that energy is removed from the wind and ends up on the cart.

The idea is that the propeller is providing thrust, not taking energy from the wind.

Think push not twist. The energy taken from the wind is not in the form of increased rotation of the blade. Rather, it is being pushed along like a sail. It just happens to put some of the energy back into increased rotational energy of the blade by means of gears connected to the ground.

For the gears connected to the ground to take energy out of the ground, it has to slow the vehicle down. You are then trying to speed the vehicle up, through the propeller, using only energy derived from the contact with the ground, which is necessarily less than or equal to the energy loss that the vehicle sustained in order to convert its forward momentum into the rotational energy to turn the propeller.

You are then trying to speed the vehicle up, through the propeller, using only energy derived from the contact with the ground, which is necessarily less than or equal to the energy loss that the vehicle sustained in order to convert that energy into rotational energy.

No, I'm not trying to do that because that wouldn't work. Energy taken from the ground/vehicle difference is not being used to accelerate the vehicle.

Gain and loss of energy are frame-dependent; in the road frame, the wind certainly is a source of energy (just as a rocket takes kinetic energy from its reaction mass, when looked at in a frame where it has a greater speed than its exhaust). I'm not sure yet how to think about the vehicle frame.

Here's where I am now:

  • Sailboats can move with a downwind component faster than the wind.

  • The first (windsock) video shows no evidence that the cart moves downwind faster than the wind.

  • The string video is more convincing, but I'm not convinced that this particular cart works as advertised. The rational offered for how it works is that when it moves at a velocity v, this causes the propeller to turn at a rate that thrusts air backwards with a velocity greater than v. Hmm... okay, maybe. The propeller blades moving perpendicular to the wind are a lot like the sails of a boat moving perpendicular to the wind.

The rational offered for how it works is that when it moves at a velocity v, this causes the propeller to turn at a rate that thrusts air backwards with a velocity greater than v. If that were the proper rational, it would be a perpetual motion machine.

This ignores mass. Thrust is (mass flow rate) * v_air, so it can get enough thrust by moving enough air at a velocity less than v_car. As for energy, power = 1/2 * F * v for air or car, so again, you can get enough thrust if v_air < v_car.

There's no perpetual motion, because as the originally linked solution says, eventually the apparent headwind becomes too strong. (The above assumes apparent wind is zero.)

Contrary to what the article says, sailboats can't travel downwind faster than the wind (except briefly, when the wind changes).

The article explicitly refers to 'tacking sailboats', which can in fact travel faster than the wind in the downwind direction.

When the vehicle is moving as fast as the wind, in order to go faster, the energy output from the propeller must be more than the energy input through the wheels. The energy output of the propeller comes entirely from the energy input through the wheels, so this is impossible.

The energy comes from harnessing the difference the difference between the velocity of the wind relative to the velocity of the ground. It may be helpful to refer to the 'propeller' as the 'propellee'. It is there to make sure the wind always has something to push on that is at roughly the same speed as the ground and only uses energy based on losses to drag and friction.

The article says: "It should be obvious that there's some way to go downwind faster than the wind, because as so many people pointed out, sailboats do it." Sailboats do not go downwind faster than the wind. I have gone downwind hundreds or thousands of times on many different types of sailboats, and I have never seen the wind indicators streaming behind me as I did so.

Tacking sailboats are going upwind, not downwind.

The energy comes from harnessing the difference the difference between the velocity of the wind relative to the velocity of the ground.

Well, that's obvious. By definition of "wind power".

It may be helpful to refer to the 'propeller' as the 'propellee'. It is there to make sure the wind always has something to push on that is at roughly the same speed as the ground

The propeller is not at the same speed as the ground.

and only uses energy based on losses to drag and friction.

?