In the vast majority of cases involving sine waves, the correlation between A and B is due to the common cause of time. Space is also a common cause of such correlations.
However, if you imagine a sine wave in time and another sine wave in space, they have no correlation until you impose a correlation between space and time (e.g., by using a mapping from x to t). In that case, Armok’s comment about a logical rather than physical cause might apply.
I started writing a reply to this comment, but as I was thinking through it I realized that the situation is actually WAY more interesting than I thought and requires a whole post. I’ve posted it in discussion:
In the vast majority of cases involving sine waves, the correlation between A and B is due to the common cause of time. Space is also a common cause of such correlations.
However, if you imagine a sine wave in time and another sine wave in space, they have no correlation until you impose a correlation between space and time (e.g., by using a mapping from x to t). In that case, Armok’s comment about a logical rather than physical cause might apply.
I don’t understand what does that mean. In which sense can time be thought of as a cause?
I started writing a reply to this comment, but as I was thinking through it I realized that the situation is actually WAY more interesting than I thought and requires a whole post. I’ve posted it in discussion:
http://lesswrong.com/r/discussion/lw/is7/the_cause_of_time/
Sorry if it’s a bit unclear right now, hopefully I’ll have time to add some diagrams this weekend.