Rationality Quotes February 2013

arundelo

Another monthly installment of the rationality quotes thread. The usual rules apply:

Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself.
Do not quote comments or posts from Less Wrong itself or from Overcoming Bias.
No more than 5 quotes per person per monthly thread, please.

Another monthly installment of the rationality quotes thread. The usual rules apply:

Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself.
Do not quote comments or posts from Less Wrong itself or from Overcoming Bias.
No more than 5 quotes per person per monthly thread, please.

Sorry, confused. A function is not always uncorrelated with its derivative. Correlation is a measure of co-linearity, not co-dependence. Do you have any examples where statistical dependence does not imply causality without a faithfulness violation? Would you mind maybe sending me a preprint?

edit to express what I meant better: "Do you have any examples where lack of statistical dependence coexists with causality, and this happens without path cancellations?"

I just noticed your edit:

edit to express what I meant better: "Do you have any examples where lack of statistical dependence coexists with causality, and this happens without path cancellations?"

The capacitor example is one: there is one causal arrow, so no multiple paths that could cancel, and no loops. The arrow could run in either direction, depending on whether the power supply is set up to generate a voltage or a current.

Of course, I is by definition proportional to dV/dt, and this is discoverable by looking at the short-term transient b... (read more)

6Richard_Kennaway13y

I omitted some details, crucially that the function be bounded. If it is, then the long-term correlation with its derivative tends to zero, providing only that it's well-behaved enough for the correlation to be defined. Alternatively, for a finite interval, the correlation is zero if it has the same value at the beginning and the end. This is pretty much immediate from the fact that the integral of x(dx/dt) is (x^2)/2. A similar result holds for time series, the proof proceeding from the discrete analogue of that formula, (x+y)(x-y) = x^2-y^2. To put that more concretely, if in the long term you're getting neither richer nor poorer, then there will be no correlation between monthly average bank balance and net monthly income. [...] Don't you mean causality not implying statistical dependence, which is what these examples have been showing? That pretty much is the faithfulness assumption, so of course faithfulness is violated by the systems I've mentioned, where causal links are associated with zero correlation. In some cases, if the system is sampled on a timescale longer than its settling time, causal links are associated not only with zero product-moment correlation, but zero mutual information of any sort. Statistical dependence does imply that somewhere there is causality (considering identity a degenerate case of causality -- when X, Y, and Z are independent, X+Y correlates with X+Z). The causality, however, need not be in the same place as the dependence. [...] Certainly. Is this web page current for your email address?