(This blog has slept since I wrote the previous post. That post had to wait for a year to be made public! Anyway, here I go again …)
One of the ways people characterise science and technology is by saying that science is about prediction and technology is about design. This is not wrong but I feel that it misses something.
An astrologer too claims to predict the future and claims to tell you how to re-design your future. So the above explanation of science and technology could make it indistinguishable from magic!
One thing that does distinguish science is that the prediction and design is done by “calculation”; this is not restricted to mathematical calculation but includes recipes like “mix so much of this reagent with so much of that solvent”. In fact, the notion of calculation can be expanded to anything that I can teach someone else to do — even an “idiot” like a computer.
This leads us to the view that science is not only about making predictions and designing things but also about teaching others to do the same. At the very first level, this is done by providing “formulas” which other people can use to make predictions and design things.
However, this is not quite far enough, since it would still make the act of creating these formulas a magical thing! So we must take this a step further and be able to teach others how to create their own formulas. In other words, we want to provide formulas for creating new formulas.
It does look as if we could be in infinite regression here, for who will then create formulas to provide formulas for creating new formulas!
Luckily, the “monadic” thinking of Turing helps us here. He realised that “formulas for creating new formuals” are themselves just (slightly more complicated) formulas. Just as a gift-wrapped box containing a gift can be thought of as just a box containing a gift.