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Eliezer_Yudkowsky comments on Rationality Quotes February 2013 - Less Wrong
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--Tom Chivers
I agree subject to the specification that each such observation must look substantially more like the absence of a duck then a duck. There are many things we see which are not ducks in particular locations. My shoe doesn't look like a duck in my closet, but it also doesn't look like the absence of a duck in my closet. Or to put it another way, my sock looks exactly like it should look if there's no duck in my closet, but it also looks exactly like it should look if there is a duck in my closet.
If your sock does not have feathers or duck-shit on it, then it is somewhat more likely that it has not been sat on by a duck.
Insufficiently more likely. I've been around ducks many times without that happening to my socks. Log of the likelihood ratio would be close to zero.
You originally were talking about a duck in your closet, which isn't the same as thing as being around ducks.
The discussion reminds me of this, which makes the point that, while corelation is not causation, if there's no corelation, there almost certainly isn't causation.
This is completely wrong, though not many people seem to understand that yet.
For example, the voltage across a capacitor is uncorrelated with the current through it; and another poster has pointed out the example of the thermostat, a topic I've also written about on occasion.
It's a fundamental principle of causal inference that you cannot get causal conclusions from wholly acausal premises and data. (See Judea Pearl, passim.) This applies just as much to negative conclusions as positive. Absence of correlation cannot on its own be taken as evidence of absence of causation.
It depends. While true when the signal is periodic, it is not so in general. A spike of current through the capacitor results in a voltage change. Trivially, if voltage is an exponent (V=V0exp(-at), then so is current (I=C dV/dt=-aCV0 exp(-at)), with 100% correlation between the two on a given interval.
As for the Milton's thermostat, only the perfect one is uncorrelated (the better the control system, the less the correlation), and no control system without complete future knowledge of inputs is perfect. Of course, if the control system is good enough, in practice the correlation will drown in the noise. That's why there is so little good evidence that fiscal (or monetary) policy works.
I skipped some details. A crucial condition is that the voltage be bounded in the long term, which excludes the exponential example. Or for finite intervals, if the voltage is the same at the beginning and the end, then over that interval there will be zero correlation with its first derivative. This is true regardless of periodicity. It can be completely random (but differentiable, and well-behaved enough for the correlation coefficient to exist), and the zero correlation will still hold.
For every control system that works well enough to be considered a control system at all, the correlation will totally drown in the noise. It will be unmeasurably small, and no investigation of the system using statistical techniques can succeed if it is based on the assumption that causation must produce correlation.
For example, take the simple domestic room thermostat, which turns the heating full on when the temperature is some small delta below the set point, and off when it reaches delta above. To a first approximation, when on, the temperature ramps up linearly, and when off it ramps down linearly. A graph of power output against room temperature will consist of two parallel lines, each traversed at constant velocity. As the ambient temperature outside the room varies, the proportion of time spent in the on state will correspondingly vary. This is the only substantial correlation present in the system, and it is between two variables with no direct causal connection. Neither variable will correlate with the temperature inside. The temperature inside, averaged over many cycles, will be exactly at the set point.
It's only when this control stystem is close to the limits of its operation -- too high or too low an ambient outside temperature -- does any measurable correlation develop (due to that approximation of the temperature ramp as linear breaking down). The correlation is a symptom of its incipient lack of control.
Knowledge of future inputs does not necessarily allow improved control. The room thermostat (assuming the sensing element and the heat sources have been sensibly located) keeps the temperature within delta of the set point, and could not do any better given any information beyond what it has, i.e. the actual temperature in the room. It is quite non-trivial to improve on a well-designed controller that senses nothing but the variable it controls.
Exponential decay is a very very ordinary process to find a capacitor in. Most capacitors are not in feedback control systems.
The capacitor is just a didactic example. Connect it across a laboratory power supply and twiddle the voltage up and down, and you get uncorrelated voltage and current signals.
Somewhere at home I have a gadget for using a computer as a signal generator and oscilloscope. I must try this.
False. Here (second graph) is an example of a real-life thermostat. The correlation between inside and outside temperatures is evident when the outside temperature varies.
The thermostat isn't actually doing anything in those graphs from about 7am to 4pm. There's just a brief burst of heat to pump the temperature up in the early morning and a brief burst of cooling in the late afternoon. Of course the indoor temperature will be heavily influenced by the outdoor temperature. It's being allowed to vary by more than 4 degrees C.
I wonder why EY didn't make an example of that in Stuff That Makes Stuff Happen.
Examples like the ones I gave are not to be found in Pearl, and hardly at all in the causal analysis literature.
Sorry, can you clarify what you mean by "like the ones". What is the distinguishing feature?
Dynamical dependencies -- one variable depending on the derivative or integral of another. (Dealing with these by discretising time and replacing every variable X by an infinite series X0,X1,X2... does not, I believe, yield any useful analysis.) The result is that correlations associated with direct causal links can be exactly zero, yet not in a way that can be described as cancellation of multiple dependencies. The problem is exacerbated when there are also cyclic dependencies.
There has been some work on causal analysis of dynamical systems with feedback, but there are serious obstacles to existing approaches, which I discuss in a paper I'm currently trying to get published.
Yes, this is completely wrong. There is frequently no correlation but strong causation due to effect cancellation (homeostasis, etc.)
Here's a recent paper making this point in the context of mediation analysis in social science (I could post many more):
http://www.quantpsy.org/pubs/rucker_preacher_tormala_petty_2011.pdf
Nancy, I don't mean to jump on you specifically here, but this does seem to me to be a special instance of a general online forum disease, where people {prefer to use | view as authoritative} online sources of information (blogs, wikipedia, even tvtropes, etc.) vs mainstream sources (books, academic papers, professionals). Vinge calls it "the net of a million lies" for a reason!
I didn't feel jumped on, though I still don't have a feeling for how common causation without corelation is.
The common example I go on about is any situation where a system generally succeeds at achieving a goal. This is a very large class. In such situations there will tend to be an absence of correlation between the effort made and the success at achieving it. The effort will correlate instead with the difficulties in the way. Effort and difficulty together cause the result; result and goal together cause effort.
A few concrete examples. If my central heating system works properly and I am willing to spend what it takes to keep warm, the indoor temperature of my house will be independent of both fuel consumption and external temperature, although it is caused by them.
If a government's actions in support of some policy target are actually effective, there may appear to be little correlation between actions and outcome, creating the appearance that their actions are irrelevant.
An automatic pilot will keep an aircraft at a constant heading, speed, and altitude. Movements of the flight controls will closely respond to external air currents, even if those currents are not being sensed. Neither need correlate with such variations as remain in the trajectory of the plane, although these are caused by the flight controls and the external conditions.
"The carpets are so clean, we don't need janitors!"
"When you do things right, people won't be sure you've done anything at all."
Not disagreeing, but just wanted to mention the useful lesson that there are some cases of causation without correlation. For example, the fuel burned by a furnace is uncorrelated with the temperature inside a home. (See: Milton Friedman's thermostat.)
I'm not sure I understand this. Do you mean that the way your shoe looks is not evidence for the presence or absence of a duck somewhere in your closet?
I think the original quote was meant to imply that as long as your shoe doesn't have the properties that differentiate ducks from non-ducks then your shoe possesses the absence of duck properties and should be assumed to be a non-duck. In other words, for a given object each property must have a binary value for duckness and when all properties have non-duckness values, you should conclude that the object as a whole has a non-duckness property.
I get confused by too many negatives and ducks.