Why do some things work in theory but not in practice? Do some factors that practice include not accepted or included when forming a theory? Put simply, does putting a theory in practice always require values to be implemented, and if so, is this what can be a source of error in a theory, thus causing the disconnect?
Answer by Jürgen Lawrenz
A look at the words ‘theory’ and ‘practice’ already tells you a little about the disconnect. Theory contains the notion of ‘god’ (theos) and could be rendered in English as “through the eyes of God”. This implies a perfection of vision which we humans don’t have, but aspire to — i.e. to some truths that are immutable and forever. Whereas ‘practice’ refers to activity, things being done. It reflects the real world, of course, namely the world of randomness and chances and intrinsic uncertainty; whereas theory is the view of a world that is law-abiding, bound to cycles and causes and wholly determined.
It is among others the idea that the universe evolved from a single point-like locus of expanding energy in the midst of nothing and followed a strict and ‘in principle’ calculable chain of events to attain its present state and its eventual return to nothingness (cf. Paul Davies, About Time). However, mapping the stars, galaxies and other visible features reveals no signs at all that the present state can (‘in principle’) be reversed, so that we would watch a movie in which all this matter and energy runs back to the so-called Big Bang and just disappears.
Maybe a simpler example can illustrate this discrepancy. You can draw a perfect circle with a compass and have it touching a perpendicular at an arbitrary point. Can we express this point as a simple number? No; it cannot be done. We cannot decompose the circular and straight lines into points, so that they meet at the juncture where each line has a point in common, Indeed, that’s where the problems lies.
I have just exemplified what reality is like. Innumerable features and processes resist our notion of an exact causality or exact definition. Reality is messy; it is only the similarity between one mess and another that makes it possible for creatures to adapt, cope with and anticipate a likely outcome.
Now the point of theory: We can easily square the circle with an algebraic formula. But formulae are concepts, mental things, not things we find in the world outside of our heads. The moment we put numbers into the formula, reality bites us again!
Let me quote another typical specimen: weather prediction. Even if we could trace the trajectory of every atom in the clouds there is insufficient information to project their paths into the future with certainty, because of the complexity of their interactions. Computers add to this uncertainty with their rounding off problem (i.e. rounding up or down necessarily gives us two divergent paths at an infinitude of instants). If you attend to the weather watch you will know that you rarely read “rain coming”, but mostly “x% chance of rain”.
One could multiply examples like this from all walks of life which teach us that practical reality is full of motions and features which we can mostly grasp only in terms of probability. Our own evolutionary growth has bestowed such ‘probability instincts’ on us, enabling us to survive unpleasant surprises. But this is not theory. Theory seeks certainty; it tries to catch the eternal momentary stillness in the welter of motions and changes. Even my explanations above can do no more than convey hints. But the gist of it, I hope, comes through, that theory is important for us to understand and articulate propositions of what we are up against in the empirical world we live in. That’s excellent in terms of technological progress. But in practice we rely mostly on experience and intuition, which are not quantifiable to such exactitude that every value in our theories can be called correct. In a word, your surmise that the source of error causes the disconnect is spot on. Which assumes, of course, as in the above specimens, that error is unavoidable: Humanum errare est.