Okay. In this instance I can't actually follow your example without understanding what you mean by 'related', but presumably the meaning is such that what you

Okay. In this instance I can't actually follow your example without understanding what you mean by 'related', but presumably the meaning is such that what you are saying is true. The word 'correlate' predates the definition that you are familiar with, however. I would ask you to consider that it may often be used differently by people who lack the knowledge or cause to preserve it for the exclusive meaning with which you are familiar. This is what I meant. I wasn't arguing that your vector example was perhaps somehow in error. It actually seemed pretty clear and convincing to me that what I was saying was absolutely not true of correlations thusly defined. If (1) there is a rate 'a' that always and only increased when a rate 'b' increased, and always and only decreased whenever that rate 'b' decreased, then perhaps we could describe that as a correlation between the two rates. If, in turn, (2) there was a rate 'c' that always and only increased when the rate 'b' increased, and always and only decreased when the rate 'b' decreased, then this would be a second relation which was the same kind as the first. It seems clear to me that lemmas 1&2 above imply the existence of a third relationship, between 'a' and 'c', which will also be of the same sort as the relations a<->b and b<->c. If this is in error, then I am extremely surprised and concerned about my mental faculties, so please be kind and demonstrate the error. I need to know, and go see a doctor. If this is not in error, then this type of relationship will have a property which we might or might not be able to describe as transitivity. I have a long-ago grounding in logic and set theory, but my understanding of mathematics is largely casual. It is entirely possible that I am using the word "correlation" in a place where a different word would better serve my meaning. I am satisfied that my use of the word is not compatible with your own understanding, so I imagine such a word must exist. In my response, I had been asking you what that word was. It is also possible that I am misusing the concept of transitivity, although in that case, again, I really am quite taken aback, and I am certainly not meaning to ask you to undertake what would then be a significant chore of remedial education.