Reduction’s Limit

For / the love of / all x.

Can we continue to rely on the reductionist approach? No.

From No Silver Bullet; Essence and Accident in Software Engineering. Frederick P. Brooks, Jr (1986).

Mathematics and the physical sciences made great strides for three centuries by constructing simplified models of complex phenomena, deriving properties from the models, and verifying those properties experimentally. This worked because the complexities ignored in the models were not the essential properties of the phenomena. It does not work when the complexities are the essence.

From Categorical Quantum Mechanics I: Causal Quantum Processes. Bob Coecke, Aleks Kissinger. (October 2015):

When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.

— Erwin Schrödinger, 1935.

By 1935, Schrödinger had already realised that the biggest gulf between quantum theory and our classical ways of thinking was really that, when it comes to quantum systems, the whole is more than the sum of its parts. In the classical world, for instance, it is possible to totally describe the state of two systems—say… two objects sitting on a table—by first totally describing the state of the first object then totally describing the state of the second object. This is a fundamental property one expects of a classical, or separable (or, in category-theory lingo: Cartesian) universe. However, as Schrodinger points out, there exist states predicted by quantum theory (and observed in the lab!) which do not obey this ‘obvious’ law about the physical world. Schrödinger called this new, totally non-classical phenomenon verschränkung, which later became translated to the dominant scientific language as entanglement. In contrast to this great insight, it took physicists many years to actually exploit this property and reveal the features of the quantum world that are direct consequences of it.

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