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Information Theory is the ur-science. It's the theory of mapping observed data onto models. In other words, it's how to fuse inductive logic into deductive logi

Information Theory is the ur-science. It's the theory of mapping observed data onto models. In other words, it's how to fuse inductive logic into deductive logic. In physics, this is especially salient, since many of the models are of low-information systems. See, e.g. Wootter's paper "Statistical Distance and Hilbert Space" [1], which gets pretty close to deriving the Dirac formulation fo quantum mechanics as the physics of low information systems in those explicit terms. (It doesn't seem to explain why it's a complex Hilbert space.) [1] https://journals.aps.org/prd/abstract/10.1103/PhysRevD.23.357 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.23.35...

a1369209993 6y ago
> It doesn't seem to explain why it's a complex Hilbert space. It's surprisingly difficult to motivate complex- (rather than real-) valued quantum mechanics. See eg https://www.scottaaronson.com/blog/?p=4021 https://www.scottaaronson.com/blog/?p=4021, for example. (As they point out, though, motivating "not quaternions" is pretty easy at least.)
gnulinux 6y ago
> Information Theory is the ur-science. Eh, this can be said about a lot of foundational disciplines/studies/theories. Philosophy of science (or philosophy of mathematics), logic, category theory, model theory etc would all fit the description. I'm not saying you're wrong, it's just that information theory isn't unique in this respect.
- thisiscorrect 6y ago
  All other possible ur-sciences you list are purely deductive. But the natural sciences have an element of inference, or inductive reasoning, to them as well. To the extent that scientists aim to capture all observed phenomena into a theory which is capable of making predictions and otherwise performing deduction, they need to bridge that gap. Category theory, e.g., does not do this.
  - salawat 6y ago
    ...Not at all? The very definition and distinction between deductive and inductive reasoning is in and of itself a matter firmly tread in the annals of philosophy. Every realized science is just a topical offshoot of natural philosophy, where the corpus of the eventually named science are all the axioms and techne that the particular field concerns itself with. Even the distinction between that most vaunted science, physics, and it's far more fluid, subjective sibling, metaphysics is squarely settled in the philosopher's forum rather than the scientist's academy. To the scientist, the epistemic question is settled by your choice of field by necessity. Another way to think of it: The Art to good Philosophy is to learn to cope with and identify those patterns of reasoning that degenerate down to navel gazing. It is why the very tool by which we interlocute and communicate is in and of itself a matter of great philosophical concern. The ability to elicit a shared understanding of a purportedly common world phenomema is still hotly debated within philosophical circles. The question of what the essence of meaning is and what it means to be all happen far outside the borders of any science's capability to operate or even exist as standalone rational framework. A science is a rational workshop, which is what is because of the collection tools and products of philosophically established ground states that render the space conducive to ongoing thought and reasoning. Seriously. If yoy think philosophy is all deductive, crack open some books. Enrich thyself, and marvel.

a1369209993 6y ago

> It doesn't seem to explain why it's a complex Hilbert space. It's surprisingly difficult to motivate complex- (rather than real-) valued quantum mechanics. See eg https://www.scottaaronson.com/blog/?p=4021 https://www.scottaaronson.com/blog/?p=4021, for example. (As they point out, though, motivating "not quaternions" is pretty easy at least.)

gnulinux 6y ago

> Information Theory is the ur-science. Eh, this can be said about a lot of foundational disciplines/studies/theories. Philosophy of science (or philosophy of mathematics), logic, category theory, model theory etc would all fit the description. I'm not saying you're wrong, it's just that information theory isn't unique in this respect.

thisiscorrect 6y ago
All other possible ur-sciences you list are purely deductive. But the natural sciences have an element of inference, or inductive reasoning, to them as well. To the extent that scientists aim to capture all observed phenomena into a theory which is capable of making predictions and otherwise performing deduction, they need to bridge that gap. Category theory, e.g., does not do this.
- salawat 6y ago
  ...Not at all? The very definition and distinction between deductive and inductive reasoning is in and of itself a matter firmly tread in the annals of philosophy. Every realized science is just a topical offshoot of natural philosophy, where the corpus of the eventually named science are all the axioms and techne that the particular field concerns itself with. Even the distinction between that most vaunted science, physics, and it's far more fluid, subjective sibling, metaphysics is squarely settled in the philosopher's forum rather than the scientist's academy. To the scientist, the epistemic question is settled by your choice of field by necessity. Another way to think of it: The Art to good Philosophy is to learn to cope with and identify those patterns of reasoning that degenerate down to navel gazing. It is why the very tool by which we interlocute and communicate is in and of itself a matter of great philosophical concern. The ability to elicit a shared understanding of a purportedly common world phenomema is still hotly debated within philosophical circles. The question of what the essence of meaning is and what it means to be all happen far outside the borders of any science's capability to operate or even exist as standalone rational framework. A science is a rational workshop, which is what is because of the collection tools and products of philosophically established ground states that render the space conducive to ongoing thought and reasoning. Seriously. If yoy think philosophy is all deductive, crack open some books. Enrich thyself, and marvel.