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orthonormal comments on The Correct Contrarian Cluster - Less Wrong
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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:
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.
You might have been thinking of "conflate".
Yep, that's the one. ETA: Thanks!
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.
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:
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:
Now if you'd quoted
that would have supported your assertion. But then Tao goes on to write
so you're wrong again (sort of -- the approach he's describing is of unknown practicality).
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.
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 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
Emphasis added. v_0 is the velocity of the wind. There's no room here for reading this as anything other than literal.
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.
Do you understand what Tao says in the article? With sufficiently high confidence? (Have you even read it?) Be careful. From the article:
Yes, you're right.
So you agree that my second quote is more apposite than the quote you provided. Hurray!
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.