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Do not quote yourself.
Do not quote comments or posts from Less Wrong itself or from Overcoming Bias.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Do not quote yourself.
Do not quote comments or posts from Less Wrong itself or from Overcoming Bias.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.

the voltage across a capacitor is uncorrelated with the current through it

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.

It depends. While true when the signal is periodic, it is not so in general.

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 ... (read more)