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Is "statistical dependences need to be explained causally" an accurate depiction of Reichenbach's Principle? (Rob Spekkens https://youtu.be/n8NRSPCekmI?t=1575)

Does one need to accept this principle to do science?

And by causal, I assume that rules out things like the block universe or the mathematical universe because relations are not causes. Just like for a patterned rug, one patch does not cause the next patch - it is the timeless/static patterns that describes the areas around the patch. Same for the block universe. Not causes, just relations.

But then how do we ever arrive at an actual causal story using mathematics? Isn't math always going to leave the door open as to whether anything is actually happening? Mathematical descriptions are essentially timeless relations are they not?

Does this principle actually work and make sense? Explained causally how, not mathematically...

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I can see how the saying, "correlation is not causation," might make you think that causation is not mathematical. Nothing could be further from the truth. Correlation is not causation, but statistics encompasses more than mere correlation.

Judea Pearl's approach to causation is a successful one, and I'd recommend checking out his book.

In statistics, we can build non-causal models, and we can build causal models. A typical Bayesian network, or a linear regression, is an example of a non-causal model. What Pearl calls a "causal Bayesian network" is an example of a causal model. An example of a causal model that is not probabilistic is Conway's game of life. What causal models have in common is that you begin with some initial conditions, and deduce immediate effects of those conditions, and then deduce effects of the effects, and so on. Deduction in a causal model doesn't usually go "backwards" - it can go backwards, but there is a preferred forward direction from causes to effects, which lines up with the temporal order of events, with causes happening prior to effects.

So to find a "causal story," you build a model of a process, where the model is - by design - causal. Then you check how well the model fits the observations. If the model fits well, then you have a causal story. You can try this for many different causal models to find the ones that fit the best without being too complicated (Occam's razor).

One way to distinguish causation from correlation is by looking at what kind of questions you can ask and answer. If you have a non-causal model, you can ask and answer questions of the form, "If X had been observed to take the value x, what would the distribution over Y be?" If you have a causal model, you can also ask and answer questions of the form, "if X had been set to the value x, what would the distribution over Y be?" Pearl's causal Bayesian networks allow for this second kind of query.

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  • I will take a look at Judea Pearl thanks. But if " distinguish causation from correlation" really always works, why are there people who believe the block spacetime model over the causal flow of time and becoming model. Isn't the point it's the same math, different stories - one causal one, one not. Why does positing causality help us if we just have math and observed correlations. Why assume it? Since we can't tell the difference why do we need it.
    – J Kusin
    Commented Jul 29, 2021 at 18:50
  • @JKusin There's no reason why the "block model" can't be causal. There's no operational difference between the "block model" and "causal flow" - it's just a difference in what mental picture you make, not a difference in what inferences you draw about events. Conway's game of life has a causal update rule, but we can just as easily think of time as a "block" if we imagine stacking many timesteps of the game on top of one another. The update rules are still causal if we do that.
    – causative ♦
    Commented Jul 29, 2021 at 18:53
  • @JKusin Non-causal rules are possible, but don't have anything to do with whether we think of "block time" or not. An example of a non-causal rule would be the laws of physics describing what happens in a closed timelike curve (if they exist). Or rules that don't involve time at all are non-causal, like the rules describing what a circle is or what the integers are.
    – causative ♦
    Commented Jul 29, 2021 at 18:56
  • But what about the rug example (I stole it from Harvey Brown a phil of physics)? The pattern of a rug has mathematical correlations but you would never say the left side of the pattern caused the right side. I don't feel you've addressed this key point. If I can have a mathematical description without causality, why gravitate toward causal models. Especially in reference to R's principle - why do we need causal explanations? I don't think causation is non mathematical, that's not quite my question. Now switch rug for spacetime
    – J Kusin
    Commented Jul 29, 2021 at 19:04
  • @JKusin Causal models allow us to evaluate the effect of an intervention. If you want to know if a certain drug works to cure a certain disease, what you really need is a causal model, not a correlation. Causal models are more useful to guide our decisions if you can get them. The pattern of the rug is not causal because the rules that describe the pattern of the rug are not the kind of rules that will be captured well by a causal model. (Also the left to right direction across the rug is spatial, not temporal. Whether a dimension is spatial or temporal does not depend on how we picture it.)
    – causative ♦
    Commented Jul 29, 2021 at 19:09

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