Cyan comments on The Correct Contrarian Cluster - Less Wrong

38 Post author: Eliezer_Yudkowsky 21 December 2009 10:01PM

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Comment author: PhilGoetz 23 December 2009 03:57:05PM *  0 points [-]

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,

Comment author: Cyan 23 December 2009 04:43:28PM *  1 point [-]

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).

Comment author: PhilGoetz 23 December 2009 07:15:48PM -1 points [-]

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.

Comment author: Tyrrell_McAllister 23 December 2009 07:22:19PM *  1 point [-]

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.)

Comment author: PhilGoetz 23 December 2009 11:06:37PM *  -2 points [-]

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.

Comment author: Tyrrell_McAllister 23 December 2009 11:15:09PM *  2 points [-]

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.

Comment author: PhilGoetz 24 December 2009 12:13:38AM -1 points [-]

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.

Comment author: Vladimir_Nesov 23 December 2009 11:12:33PM *  0 points [-]

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]

Comment author: PhilGoetz 24 December 2009 12:14:16AM 0 points [-]

Yes, you're right.

Comment author: Cyan 23 December 2009 07:32:15PM 0 points [-]

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.

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