Grothendieck starts by asserting that the experimental-deductive method has been spectacularly successful for four hundred years. His article never gets round t

Grothendieck starts by asserting that the experimental-deductive method has been spectacularly successful for four hundred years. His article never gets round to revisiting this. He never notices the bi-modal quality of the successes. Some truly spectacular successes, quite a lot of knowledge that hints weakly, and a rather empty middle ground. Think about gyroscopes. Newton invents classical mechanics, with no specific rules for rotating objects. You get a top mathematician, Euler, to work out the implications for rotating objects. The implications are weird and implausible. But it turns out that they are spot on. People invent gyroscopes and exploit the truly spectacular success of the experimental-deductive method. Another example could be James Clerk-Maxwell building on the work of Faraday and Ampere to come up with Maxwell's Equations. The equations predict electro-magnetic radiation, so Hertz goes looking and, yes, it is really there! I want a name for this kind of truly spectacular success. I'll build on the gyroscope example and call it Gyro-gnosis. But think instead of Hook's law. Spring force is proportional to extension. Kind of. It is useful enough if you don't pull too hard on your spring, but it is not fundamental. Or think of animal testing in medicine. There is some theory. All life on Earth today is based on DNA. We know the branching of the tree of life; mice are mammals, so mouse research should link up with human health, sometimes, a little bit. But theory and experiment combine to give us hints rather than wisdom. I want a name for this kind of weak knowledge that so often leads to disappointment. Stealing the T from Theory, taking the whole of hint, and the end of wisdom, I'm going to write Thintdom. By page six, Grothendieck is on to his manifesto "Fighting Scientism". We are certainly in trouble, due to thintdom being granted the prestige of gyrognosis. But if you want to push back, you have to drive a wedge between thintdom and gyrognosis. Since gyrognosis is truly spectacularly successful, fighting against it is just banging your head against a brick wall. One needs to separate out the weaker forms of knowledge so that one can criticize thintdom without its proponent being able to use gyrognosis as a shield. If you let thintdom and gyrognosis be joined together as empiricism, your criticism cannot be made to stick because the parts of empiricism that work well, work far to well to be criticized. It is now commonplace to notice the depth of the technology stack, from applications, down through compilers, assemblers, the block diagram level of hardware, the register level, the logic gate level, the transistor level, circuits with parasitic inductance and capacitance, doping and migration, statistical effects,... When you build up the way, some of the lower level features are preserved, such as conservation of momentum. And some of the lower level features help with understanding the higher levels. But medicine offers a clear warning that Nature's stack is too deep. Four hundred years of "success" have taught us what that leads to. Sometimes you get gyrognosis. Sometimes you get thintdom. By the end of his piece Grothendieck is pining his hopes on "inner class contradiction" within the scientific caste. Maybe. I think the most promising starting point is to push back against linguist poverty. We have only one word, empiricism for, err, empiricism, so the four hundred year old empirical lesson that the successes of empiricism are bimodal goes unnoticed.