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.
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.
Phil, sorry, but you’re wrong. It is possible to travel straight downwind faster than the wind. The mechanisms that Tao outlines don’t have the limitation you think they have. This quote:
But if this is the only dimension one exploits, one can only sail up to the wind speed |v_0| and no faster...
doesn’t mean what you think it means. Reread the quote carefully, paying attention to the words “the only dimension”. Then reread the paragraph that follows it in the post, then take a hard look at Figure 4 and the paragraph that follows it, then come back. You’re just embarrassing yourself.
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.
No he didn’t, as I’ve explained at least 3 times in this thread already, including in the comment you just replied to. He wrote:
“it became possible for sails to provide a lift force which is essentially perpendicular to the (apparent) wind velocity, in contrast to the drag force that is parallel to that velocity.”
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.
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.
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.
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.
How would you explain its acceleration when the vehicle is traveling at wind speed, in the vehicle’s reference frame? It seems to me — incorrectly, I assume — that the only energy available there is from the ground/vehicle difference.
Consider a thrusting rocket, looked at in a frame where its exhaust is stationary. The reaction mass is accelerated backwards from v=v_r to v=0, losing kinetic energy, which is added (together with energy supplied by the fuel) to the rocket’s KE. It seems to me that this is basically the same situation.
You’re of course right in the vehicle frame; I’m not sure yet how best to think about that.
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.)
In the simplest case, air pushes the propeller forwards, but it doesn’t significantly rotate it. The propeller is a sail. The propeller rotates in such a way that higher speed of the propeller leads to lower resistance with the air (it becomes more in sync with the wind), that is propeller rotates in the opposite direction to what one would normally expect, it “lets the wind through”. If it were a normal cart moving faster than wind with propeller not attached to anything, it would be the same direction of the rotation (but our propeller rotates faster). At the same time, the propeller is rigidly connected to the wheels, so that higher speed of the cart corresponds to faster rotation of the propeller, and, as a result, to lower pressure from the air. When the cart decelerates, the propeller rotates slower, which increases the pressure from the wind on the propeller and thus accelerates the cart.
Oops, sorry, I wrote an incorrect explanation, having relied on confabulation of fading memories too much. Here is a reworked one:
In the simplest case, air pushes the propeller forwards, but it doesn’t significantly rotate it. The propeller is a sail. If it were a normal cart moving faster than wind with propeller not attached to anything, it would be the same direction of the rotation (but our propeller rotates faster). At the same time, the propeller is rigidly connected to the wheels, which allows it to rotate faster than the headwind would make it. As a result, it is pushed by the wind from behind rather than resisted, which accelerates the cart, which lends power to the propeller to keep on rotating faster than it otherwise would.
It is a bad intuition to see propeller as throwing the air backwards at speed higher than the difference of cart’s speed and the speed of the wind, as the cart is essentially fueled by the resulting hind-wind, not the other way around. Also, the propeller only needs to go a little bit faster than it would because of the headwind.
That’s a pretty good explanation. Another way to look at it is to think what would happen if the propeller was not connected to the wheels. In that situation, the cart would travel as fast as the wind, but the propeller would spin at high speed. If you connect the propeller to the wheels that energy is used to further increase velocity.
In fact, it would work if you place a radio controlled clutch between the propeller and the wheels. First wait for the cart to accelerate to wind speed, and the propeller to rotate faster than the wheels (if it’s 1:1 ratio without gears), then engage the clutch. The end result would be that the wheels would rotate at a higher speed and thus the cart would travel faster than the wind.
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.
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.
Sailing downwind faster than the wind looks and feels like sailing upwind. How often have you, when the tell tales are streaming aft, checked to see if a stationary flag was blowing in the opposite direction?
You could also have sailed on many kinds of boats whose hulls experience too much water resistance before achieving the speed of the wind to accelerate further with the power provided by that wind.
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.
Assume a uniform wind of 20 km/h flowing in the direction from A to B and that B is 100 km from A. Fred is an expert sailor and has a top line sailboat. While Fred is stationary at A, he notices Joe floating past him in a hot air balloon going at the 20 km/h wind speed. Assuming no changes to the wind is it possible for Fred to catch up to Joe using only sailboat before Joe reaches B five hours later?
If you answer ‘no’ then you are incorrect.
If you answer ‘yes’, then understand that this is what people mean when they say it is possible to go downwind faster than the wind.
Has this actually happened? Does this prove anything if it did, given that winds at altitude and ground level are vastly different?
It is impossible for any existing sailboat to have a downwind component that is faster than the wind. If it were possible, you could sail the boat with no wind at all. (This argument does not apply to the ground vehicle under discussion.)
Will you at least agree that it is impossible to sail with the boat pointed directly downwind faster than the wind in a conventional sailboat (including racing sailboats)?
A sailboat can reach faster than the wind because the mass of the wind is greater than the mass of the sailboat, and the energy in the wind is transferred to the boat. Moving downwind faster than the wind is very different, and requires a different mechanism. And you cannot use apparent wind to explain moving downwind faster than the wind, because the apparent wind would be in the opposite direction.
Does this prove anything if it did, given that winds at altitude and ground level are vastly different?
The greater wind at higher elevation would only be an advantage to the hot air balloon.
It is impossible for any existing sailboat to have a downwind component that is faster than the wind. If it were possible, you could sail the boat with no wind at all.
No. If there is no wind at all, then if the boat moved forward in any direction, it would face an apparent direct headwind opposing its motion. But with some amount of wind, the boat can travel at some angle from dead down wind, so that the apparent wind will not be directly ahead, so that the perpendicular lift will have a forward component.
Will you at least agree that it is impossible to sail with the boat pointed directly downwind faster than the wind in a conventional sailboat (including racing sailboats)?
Yes.
A sailboat can reach faster than the wind because the mass of the wind is greater than the mass of the sailboat
Well, the total mass of all the air that was deflected by the sails as the boat accelerated past wind speed will be greater than the mass of the boat, but that does not really explain what is going on. The point is that the boat is able to continue to derive enough thrust from the apparent wind to overcome drag forces. And this continues to work even when a component of the boat’s velocity is downwind.
And you cannot use apparent wind to explain moving downwind faster than the wind, because the apparent wind would be in the opposite direction.
It is not exactly the opposite direction, and even a small deviation can be significant.
There are potential ambiguities in the language used. Considering a specific example like this allows us to establish whether we are disagreeing about the physics itself or just using different words. I get the impression that we are disagreeing on the nature of physics itself. Fred can win.
Does this prove anything if it did, given that winds at altitude and ground level are vastly different?
I didn’t want to dwell on technicalities and hoped ‘uniform’ was sufficient to convey my intended meaning.
Will you at least agree that it is impossible to sail with the boat pointed directly downwind faster than the wind in a conventional sailboat (including racing sailboats)?
Yes.
A sailboat can reach faster than the wind because the mass of the wind is greater than the mass of the sailboat, and the energy in the wind is transferred to the boat.
Hence the applicability of the ‘sailboat’ analogy to the vehicle in question.
Some people claim that a sailboat can move faster than the wind when reaching (moving perpendicular to the wind). When reaching, you let the sail out much farther than you would intuitively expect, until it’s nearly parallel to the wind. It may be operating on lift at that point.
A jumbo jet can’t take off vertically. Therefore, the thrust provided by lift from its wings is greater than the thrust provided by its engines. So perhaps a sailboat can travel faster than the wind when reaching. EDIT: No, that’s wrong. You can’t get more energy out than you put in.
Consider the problem from the frame of reference of the wind. The wind is still; you begin with the only energy source being the motion of the ground to the left, and using this energy, you are supposed to cause the vehicle to move to the right. You can’t cause rightward motion without violating the conservation of momentum unless you cause either the air to move to the left, or the ground to move faster to the left.
I just watched the video. It’s a trick, though probably not intentional. The windsock is mounted directly behind the propeller. So when the vehicle moves and the propeller turns, it blows the windsock backwards, and this is the “proof” that the vehicle is travelling faster than the wind.
ADDED: Folks. Think about it. The sock blowing backward is supposed to show that the vehicle is moving faster than the wind. It doesn’t show that; the sock would blow backwards as long as the speed of the vehicle plus the speed of air impelled from the propeller is greater than the speed of the wind. There is no evidence in the video that the vehicle is travelling faster than the wind.
Downvoting this comment is not a vote saying that travelling downwind faster than the wind is possible. This comment does not dispute that. Downvoting this comment is disagreeing with the math and claiming that watching a sock blown backwards by a propeller demonstrates movement faster than the wind.
Did you read the “Solution” post that Vladimir linked to? What about it was unconvincing? (If it’s any comfort, that guy ate enough crow for the both of you ;).)
I read the solution. I don’t need to think too deeply about his long, complicated explanation that begins with a detailed and erroneous description of the gears, because I have a short, simple explanation of how the illusion is generated in the video, and a short, simple explanation of why such a device would violate conservation laws, which I gave below.
What do you mean by that term? The post does say this:
What this all means is that you’ve essentially gotten energy from the friction of the wheels against the ground, and turned it into propulsion. The ground friction is providing a way to make the propellor “tack” against the wind. The nature of the mechanism means that the initial acceleration of the cart is slower than a pure sail-driven system, because the way the propeller spins adds resistance to the wheels via the gearing. But ignoring losses to friction, if the wind is constant, it won’t stop it from accelerating—it’ll just slow the rate of acceleration.
At this point, the pure wind force has fallen to 0, because the cart isn’t moving relative to the wind. But the propellor is still producing a force dependent on G, A, and r.
So for the right values of G, A, and r, you’ll still be accelerating.
This seems to equivocate between wind/propellor force and net force.
I just watched the video. It’s a trick, though probably not intentional. The windsock is mounted directly behind the propeller. So when the vehicle moves and the propeller turns, it blows the windsock backwards, and this is the “proof” that the vehicle is travelling faster than the wind.
The sock shows only that at the point where the sock is mounted the air is going backwards relative to the vehicle. What are the implications of that? Where is the energy required to do this coming from? As the vehicle approached the wind speed what would happen to the sock?
Where is the energy required to do this coming from?
From the wind. Which is travelling faster than the vehicle. Except in the immediate vicinity of the propeller.
As the vehicle approached the wind speed what would happen to the sock?
If the vehicle moved exactly at the speed of the wind, with the propeller moving, the air would appear dead still before taking into account the movement of the propeller, and so the sock would be blown strongly out behind the vehicle, making it look as if the vehicle were moving much faster than the wind.
From the wind. Which is travelling faster than the vehicle. Except in the immediate vicinity of the propeller.
So the parts of the vehicle that are travelling slower than the wind receive energy from the wind but not the propeller? If I took off the propeller would the vehicle go faster or slower?
The point is that the propeller blows the sock backwards, regardless of whether the vehicle is moving faster than the wind; and this is shown as proof that it’s travelling faster than the wind.
The point is that the propeller blows the sock backwards, regardless of whether the vehicle is moving faster than the wind; and this is shown as proof that it’s travelling faster than the wind.
It is a very good feature of the video (from rationality test standpoint) that this piece of evidence is compromised: you are handed a conspiracy theory right away, and so when rationalization kicks in, you know what to point to.
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.
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.
Phil, sorry, but you’re wrong. It is possible to travel straight downwind faster than the wind. The mechanisms that Tao outlines don’t have the limitation you think they have. This quote:
doesn’t mean what you think it means. Reread the quote carefully, paying attention to the words “the only dimension”. Then reread the paragraph that follows it in the post, then take a hard look at Figure 4 and the paragraph that follows it, then come back. You’re just embarrassing yourself.
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.
No he didn’t, as I’ve explained at least 3 times in this thread already, including in the comment you just replied to. He wrote:
“it became possible for sails to provide a lift force which is essentially perpendicular to the (apparent) wind velocity, in contrast to the drag force that is parallel to that velocity.”
Perpendicular to the apparent wind velocity.
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.
Tao’s discussion is not relevant to these carts, as he isn’t discussing DDFTTW.
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:
You’re right.
(Completely OT, of course.)
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.
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.
If your intuitions don’t think it will work then two options available are building the device or doing the actual math.
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.
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.
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.
How would you explain its acceleration when the vehicle is traveling at wind speed, in the vehicle’s reference frame? It seems to me — incorrectly, I assume — that the only energy available there is from the ground/vehicle difference.
In the road frame, it is.
Consider a thrusting rocket, looked at in a frame where its exhaust is stationary. The reaction mass is accelerated backwards from v=v_r to v=0, losing kinetic energy, which is added (together with energy supplied by the fuel) to the rocket’s KE. It seems to me that this is basically the same situation.
You’re of course right in the vehicle frame; I’m not sure yet how best to think about that.
The propeller cannot do both. If the wind is being accelerated backwards by the propeller, the propeller is not taking energy from the wind.
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.
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.)
In the simplest case, air pushes the propeller forwards, but it doesn’t significantly rotate it. The propeller is a sail. The propeller rotates in such a way that higher speed of the propeller leads to lower resistance with the air (it becomes more in sync with the wind), that is propeller rotates in the opposite direction to what one would normally expect, it “lets the wind through”. If it were a normal cart moving faster than wind with propeller not attached to anything, it would be the same direction of the rotation (but our propeller rotates faster). At the same time, the propeller is rigidly connected to the wheels, so that higher speed of the cart corresponds to faster rotation of the propeller, and, as a result, to lower pressure from the air. When the cart decelerates, the propeller rotates slower, which increases the pressure from the wind on the propeller and thus accelerates the cart.
That’s what I just said. But what’s the energy flow?
I concede that it works, and in basically the same way as the sailboat going downwind that I also said couldn’t work.
Oops, sorry, I wrote an incorrect explanation, having relied on confabulation of fading memories too much. Here is a reworked one:
In the simplest case, air pushes the propeller forwards, but it doesn’t significantly rotate it. The propeller is a sail. If it were a normal cart moving faster than wind with propeller not attached to anything, it would be the same direction of the rotation (but our propeller rotates faster). At the same time, the propeller is rigidly connected to the wheels, which allows it to rotate faster than the headwind would make it. As a result, it is pushed by the wind from behind rather than resisted, which accelerates the cart, which lends power to the propeller to keep on rotating faster than it otherwise would.
It is a bad intuition to see propeller as throwing the air backwards at speed higher than the difference of cart’s speed and the speed of the wind, as the cart is essentially fueled by the resulting hind-wind, not the other way around. Also, the propeller only needs to go a little bit faster than it would because of the headwind.
That’s a pretty good explanation. Another way to look at it is to think what would happen if the propeller was not connected to the wheels. In that situation, the cart would travel as fast as the wind, but the propeller would spin at high speed. If you connect the propeller to the wheels that energy is used to further increase velocity.
In fact, it would work if you place a radio controlled clutch between the propeller and the wheels. First wait for the cart to accelerate to wind speed, and the propeller to rotate faster than the wheels (if it’s 1:1 ratio without gears), then engage the clutch. The end result would be that the wheels would rotate at a higher speed and thus the cart would travel faster than the wind.
The article explicitly refers to ‘tacking sailboats’, which can in fact travel faster than the wind in the downwind direction.
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.
Well, that’s obvious. By definition of “wind power”.
The propeller is not at the same speed as the ground.
?
Sailing downwind faster than the wind looks and feels like sailing upwind. How often have you, when the tell tales are streaming aft, checked to see if a stationary flag was blowing in the opposite direction?
You could also have sailed on many kinds of boats whose hulls experience too much water resistance before achieving the speed of the wind to accelerate further with the power provided by that wind.
Assume a uniform wind of 20 km/h flowing in the direction from A to B and that B is 100 km from A. Fred is an expert sailor and has a top line sailboat. While Fred is stationary at A, he notices Joe floating past him in a hot air balloon going at the 20 km/h wind speed. Assuming no changes to the wind is it possible for Fred to catch up to Joe using only sailboat before Joe reaches B five hours later?
If you answer ‘no’ then you are incorrect.
If you answer ‘yes’, then understand that this is what people mean when they say it is possible to go downwind faster than the wind.
Has this actually happened? Does this prove anything if it did, given that winds at altitude and ground level are vastly different?
It is impossible for any existing sailboat to have a downwind component that is faster than the wind. If it were possible, you could sail the boat with no wind at all. (This argument does not apply to the ground vehicle under discussion.)
Will you at least agree that it is impossible to sail with the boat pointed directly downwind faster than the wind in a conventional sailboat (including racing sailboats)?
A sailboat can reach faster than the wind because the mass of the wind is greater than the mass of the sailboat, and the energy in the wind is transferred to the boat. Moving downwind faster than the wind is very different, and requires a different mechanism. And you cannot use apparent wind to explain moving downwind faster than the wind, because the apparent wind would be in the opposite direction.
The greater wind at higher elevation would only be an advantage to the hot air balloon.
No. If there is no wind at all, then if the boat moved forward in any direction, it would face an apparent direct headwind opposing its motion. But with some amount of wind, the boat can travel at some angle from dead down wind, so that the apparent wind will not be directly ahead, so that the perpendicular lift will have a forward component.
Yes.
Well, the total mass of all the air that was deflected by the sails as the boat accelerated past wind speed will be greater than the mass of the boat, but that does not really explain what is going on. The point is that the boat is able to continue to derive enough thrust from the apparent wind to overcome drag forces. And this continues to work even when a component of the boat’s velocity is downwind.
It is not exactly the opposite direction, and even a small deviation can be significant.
There are potential ambiguities in the language used. Considering a specific example like this allows us to establish whether we are disagreeing about the physics itself or just using different words. I get the impression that we are disagreeing on the nature of physics itself. Fred can win.
I didn’t want to dwell on technicalities and hoped ‘uniform’ was sufficient to convey my intended meaning.
Yes.
Hence the applicability of the ‘sailboat’ analogy to the vehicle in question.
Possible world too convenient!
Some people claim that a sailboat can move faster than the wind when reaching (moving perpendicular to the wind). When reaching, you let the sail out much farther than you would intuitively expect, until it’s nearly parallel to the wind. It may be operating on lift at that point.
A jumbo jet can’t take off vertically. Therefore, the thrust provided by lift from its wings is greater than the thrust provided by its engines. So perhaps a sailboat can travel faster than the wind when reaching. EDIT: No, that’s wrong. You can’t get more energy out than you put in.
It seems like you’re equating speed with energy. Since the masses are different, couldn’t the energy of the machine be less but the speed be greater?
When talking about the jet, I was talking only about force. “The masses are different”—what masses are you talking about?
Consider the problem from the frame of reference of the wind. The wind is still; you begin with the only energy source being the motion of the ground to the left, and using this energy, you are supposed to cause the vehicle to move to the right. You can’t cause rightward motion without violating the conservation of momentum unless you cause either the air to move to the left, or the ground to move faster to the left.
I just watched the video. It’s a trick, though probably not intentional. The windsock is mounted directly behind the propeller. So when the vehicle moves and the propeller turns, it blows the windsock backwards, and this is the “proof” that the vehicle is travelling faster than the wind.
ADDED: Folks. Think about it. The sock blowing backward is supposed to show that the vehicle is moving faster than the wind. It doesn’t show that; the sock would blow backwards as long as the speed of the vehicle plus the speed of air impelled from the propeller is greater than the speed of the wind. There is no evidence in the video that the vehicle is travelling faster than the wind.
Downvoting this comment is not a vote saying that travelling downwind faster than the wind is possible. This comment does not dispute that. Downvoting this comment is disagreeing with the math and claiming that watching a sock blown backwards by a propeller demonstrates movement faster than the wind.
Did you read the “Solution” post that Vladimir linked to? What about it was unconvincing? (If it’s any comfort, that guy ate enough crow for the both of you ;).)
I read the solution. I don’t need to think too deeply about his long, complicated explanation that begins with a detailed and erroneous description of the gears, because I have a short, simple explanation of how the illusion is generated in the video, and a short, simple explanation of why such a device would violate conservation laws, which I gave below.
It wouldn’t have convinced me, if I thought the thing didn’t work — it never mentions rolling resistance!
What do you mean by that term? The post does say this:
(Emphasis added.)
Okay, it does there, but I refer to this part:
This seems to equivocate between wind/propellor force and net force.
Don’t trust socks? Try this one with shoestrings instead.
I’ll have to think about that.
think think think
It appears to demonstrate the same thing, convincingly.
The sock shows only that at the point where the sock is mounted the air is going backwards relative to the vehicle. What are the implications of that? Where is the energy required to do this coming from? As the vehicle approached the wind speed what would happen to the sock?
From the wind. Which is travelling faster than the vehicle. Except in the immediate vicinity of the propeller.
If the vehicle moved exactly at the speed of the wind, with the propeller moving, the air would appear dead still before taking into account the movement of the propeller, and so the sock would be blown strongly out behind the vehicle, making it look as if the vehicle were moving much faster than the wind.
So the parts of the vehicle that are travelling slower than the wind receive energy from the wind but not the propeller? If I took off the propeller would the vehicle go faster or slower?
The point is that the propeller blows the sock backwards, regardless of whether the vehicle is moving faster than the wind; and this is shown as proof that it’s travelling faster than the wind.
It is a very good feature of the video (from rationality test standpoint) that this piece of evidence is compromised: you are handed a conspiracy theory right away, and so when rationalization kicks in, you know what to point to.