Ed:

The requirement of causality is to distinguish between cause (A) and effect (B) being quantities of physical entities (A, B)  differing in kind (lat. genus) like apples and pears. Whether physical entities differ in kind can be found by analyzing their dimensions. Cause A (dimension A) and effect B (dimension B) are entities with different dimensions (different entities). Consequently a mathematical law of causality (generation of effect B by a generating cause A) cannot read B = A. The only reasonable mathematical relation between such different quantities (if there is any) is a geometric proportionality according to A/B = C = constant. The dimensions of the constant C accordingly will be given [A/B].

 

Alex:

What about causality of the same kind (species) – parent to child?

Ed:

I’m arguing within the context and geometrical language of Isaac Newton’s natural philosophy. In this context, “cause” is “force”, and “force” is different from “matter”. So “parents” (matter) cannot be the “cause” of child (matter).

 

Ed:

So your “form 1” where you deal with two “events” of a same kind has nothing to do with causality.

Alex:

So, what is this? Clearly the event B that is further from the source of the step – it cannot happen before A. In fact it can only happen after event A, and moreover this “after” happens L/c  time units later – where L is the distance between points A and B in the transmission line.

Ed:

Even though every cause must precede its effect, not everything that precedes some other thing is also the cause of the latter. This is a very old philosophical problem, the “post hoc ergo propter hoc” problem of those who cannot distinguish geometrically between cause and effect, but rely on Leibniz’s absurd arithmetical identification “causa aequat effectum”, A = A.

Alex:

And we can’t deny this effect because this is what we see in the experiments.

Ed:

I do not deny the effect either, but I reject the idea that what precedes it must be its cause.

Alex:

I can interpret this as geometric proportionality with coefficient k, which is dimensionless in your terms.

The dimensionlessness of k proves that the terms you correlate are homogenes and therefore not genetically different, so that they cannot form a proportionality as required by definition. Moreover, such an interpretation is not a geometric proportionality, but rather results in an arithmetic “equation” A = B = A of the correlated homogenous terms.

Alex:

But, incidentally, who said that geometric proportionality should be defined by the algebraic division operator?

Ed:

It is Euclid who says it, in “Elements” book V, definitions of “logos” (ratio A = B) and “analogos” (proportio A/B = C = constant). And, it is Newton who also says it, in his second law (a chagne in motion is proportional to the impressed force), and in his Scholium after Lemma X (proportionality of heterogeneous entities).

Physical world can suggest us other forms of proportionality – for example, we can define proportionality in the form of a time-shift operator?

Physical world can of course suggest us other forms of interrelations, but so long as causality is defined according to natural experience and in my Newtonian context as a proportionality of force and motion (change of motion), that is, as generation of some effect by a generating cause, we cannot define it otherwise at will. By the way, just drive a nail with a hammer, and you will learn the law of proportionality of cause and effect.

Alex:

Please not that I am not dismissing your definition of causality as being limited. I am just looking for a form of expressing the event precedence effect in transmission line, which is what we see in our experiments. Ivor’s theory underpins it with the notion of “Heaviside signal” (aka “energy current”).

Ed:

Please see that I do not propose “my” definition of causality. I just refer to what natural philosophy knows under this technical term since the time of Galileo and Newton, who derived it from natural experience and experiment only. May I, by the way, recommend reading my essay “The Language of Nature is not Algebra”, which essentially is a criticism of Judea Pearl’s famous book “Causality” (Cambridge University Press 2009) ?