I think there are so many disconnects between what formulas describe and what they’re used for, once you see it, you’ll wonder why we have not noticed the defect in thinking of ‘everything’ in terms of formulas right from the start. How we’ve made use of formulas has never been to actually follow them.
Their best use is always as learning tools. That’s how we test them too, but then seem to ignore how critically important the learning process is to making them work. Take the problem of sitting at dinner and picking up a glass of water to drink. We have a ‘formula’ for where the glass should be, at the upper right of the place.
We have to look at the actual environment, though, in which we are attempting to use the formula, to not make a complete mess of the operation as a rule. The formula does not give you a useful location for the glass, but a useful start to reaching out for it.
Similarly you could ask how it would work to shake someone’s hand if all you had was a statistical representation of where the other person’s hand sould be. You’d simply never get a good firm handshake out of it even if waving your hand around in the ’statistical phase space’ of your model eventually resulted in your hand bumping into the other person’s hand.
That very traditional relationship between ‘theory’ and ‘practice’ (i.e. science and engineering) has been traditionally ignored by the theorists it seems… The theory guys like to think that they were the ‘priests’ of knowledge or something, with invented abstractions being somehow superior to direct learning experience… The truth seems to be that theory comes from, and is only useful as an extension of, the learning methods of practice, and has no inherent value at all.
The tricky places are where there’s no theory, where nature is inventing whole new ways of behaving that only learning experience will expose at all. It’s those, along with a practical way of organizing historical data, I’m mostly talking about with my ‘bump on a curve’ model for questions to ask about what’s ‘happening’ in developmental change… (¸¸.•´ ¯ `•.¸¸) I describe one example as a metaphor for others in the first 3 paragraphs of my main web page.
Does that help?