Thinking with constraints

Constraints an essential precursor

Here the trouble with cause and effect is that it is a story-telling mechanism, and the telling of a story depends on taking a personal point of view: it depends on a narrative structure. Such structures are great for explaining 'how something goes' to ourselves but have their limitations, and different story-tellers may choose a different cause. Philosophers have explored such problems down the ages, with Hume being a very significant inflexion point. You could borrow a metaphor from the internet, – often accounts in physics are not best structured as a set of 'if this then that' because this relies on many un-explicated necessary conditions. As anyone who codes will realise, there are auxiliary assumptions behind the correct functioning of a piece of code.

To put it another way, any assertion of cause relies on a host of ceteris paribus conditions, which are often unexamined. Physics has developed to be more concerned with the "how" and not with the "why", so with stating correlations. The relationship a=F/m is of this kind: there is no arrow of time, no before and after, hidden in the assertion of equality. It is not, in short, a causal relationship, at least in the way that story-tellers, and perhaps, therefore, any natural language-users want to use cause and effect. Instead, it is a constraint relationship, describing a possibility space. It and many other relationships in physics have this in common with energy descriptions.

So to try to decide whether acceleration causes force or force causes acceleration is to conflate two different story-telling traditions( and why does no one speak up for mass?).

Similarly, for I = VR. Maybe it's worth thinking about why no one even thinks about launching a discussion about cause and effect for the relationship density = massvolume.

Most relationships in elementary physics are like this, comparing the values of physical quantities before a change with those afterwards and in other words, constraining the possible values between a pair of snapshots.

(These are different from accumulation relationships: there are good arguments for preferring to focus on accumulation relationships in introductory kinematics)