Category: Science, Physics, and Philosophy of Science

He demonstrates why geometry must remain the basis for mathematics, else it becomes ordinary language with all it’s faults – long standing complaint – and primary pre-war concern of mathematicians who were concerned by the restoration of mysticism in mathematics by empty verbalisms like ‘multiple infinities’ vs ‘pairing off at different rates’. This restoration of mysticism (Cantor, Bohr, and to some degree Keynes) reversed the restoration of mathematics to geometry by Descartes. He does a great job of demonstrating anchoring in any academic endeavor. And that some scientific half-solutions are sources of ignorance. And that generations of malinvested academics have to die off before their sources of ignorance can be overcome. His interjection with illustrations are a romantic cultural indulgence that distracts from his argument. He missed the point on Hilbert – that Einstein created an obstacle by half-finishing the theory and hilbert wouldn’t have. His logic is elegant, interesting, and thorough. And easier to follow than I expected. He does not make the transition from point-geometry to shape geometry. He does not make the connection between the problem of protein folding and the problem of particles producing waves. He identifies an avenue for investigation but he does not get to the point where he grasps that the reason his theory is correct but limited is that the information is insufficient to deduce from the top down or competition between formulae because we cannot measure. And so he doesn’t get to the point of working with primitives (operations) to produce wave forms (aggregates). So he doesn’t get to the point where math might be the wrong tool per se, and that simulations are necessary – by trial and error – to produce the underlying geometry. It’s not obvious that the sub-quantum (statistical) would logically operate by the same rules as chemistry and bio chemistry, molecular biology, and genetics etc – by an operational grammar. So, my suspicion is that “You can’t get there from here”. There is no means of anticipating the grammar (referent, logic, operations, transformations). All we are left with is trial and error. (My sympathies since I had to work outside the academy as well – there is no way to put a dissertation committee together for my work either.) — Curt Doolittle

He demonstrates why geometry must remain the basis for mathematics, else it becomes ordinary language with all it’s faults – long standing complaint – and primary pre-war concern of mathematicians who were concerned by the restoration of mysticism in mathematics by empty verbalisms like ‘multiple infinities’ vs ‘pairing off at different rates’. This restoration of mysticism (Cantor, Bohr, and to some degree Keynes) reversed the restoration of mathematics to geometry by Descartes. He does a great job of demonstrating anchoring in any academic endeavor. And that some scientific half-solutions are sources of ignorance. And that generations of malinvested academics have to die off before their sources of ignorance can be overcome. His interjection with illustrations are a romantic cultural indulgence that distracts from his argument. He missed the point on Hilbert – that Einstein created an obstacle by half-finishing the theory and hilbert wouldn’t have. His logic is elegant, interesting, and thorough. And easier to follow than I expected. He does not make the transition from point-geometry to shape geometry. He does not make the connection between the problem of protein folding and the problem of particles producing waves. He identifies an avenue for investigation but he does not get to the point where he grasps that the reason his theory is correct but limited is that the information is insufficient to deduce from the top down or competition between formulae because we cannot measure. And so he doesn’t get to the point of working with primitives (operations) to produce wave forms (aggregates). So he doesn’t get to the point where math might be the wrong tool per se, and that simulations are necessary – by trial and error – to produce the underlying geometry. It’s not obvious that the sub-quantum (statistical) would logically operate by the same rules as chemistry and bio chemistry, molecular biology, and genetics etc – by an operational grammar. So, my suspicion is that “You can’t get there from here”. There is no means of anticipating the grammar (referent, logic, operations, transformations). All we are left with is trial and error. (My sympathies since I had to work outside the academy as well – there is no way to put a dissertation committee together for my work either.) — Curt Doolittle