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cousin_it comments on The Correct Contrarian Cluster - Less Wrong
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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.)
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.