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Mathematics and Plausible Reasoning [Two Volumes in One]

George Polya · 3 HN comments
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Amazon Summary
2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics". This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.
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came here to ask the same thing! :D

"How to solve it" [1] was helpful for me in this regard, but it isn't really condensed like this blog post.

After you finish "how to solve it", you can read the more advanced "Mathematics and Plausible Reasoning" [2]

[1] https://www.amazon.com/How-Solve-Mathematical-Princeton-Scie... [2] https://www.amazon.com/Mathematics-Plausible-Reasoning-Two-V...

Something I found useful and related was George Polya's book series "Mathematics and Plausible Reasoning" [1]. It goes into how we make "good" guesses in mathematics and how to improve the way we recognize patterns. If you are curious about this subject and want to improve your "mathematical intuition", this series helped me tremendously.

[1] https://www.amazon.com/Mathematics-Plausible-Reasoning-Two-V...

> how empirical work destroys blackboard economics

The value of empirical work hinges on the assumption that the economic environment you're modeling is ergodic, or at the very least stationary AND that you have enough data of good enough quality.

If those conditions are not given, then you need theory. To establish relationships, not just time-series properties, this needs to hold for all variables separately as well as their copula, else you need theory. If one of the ingredients in your model is not observable, you need theory.

I am really tired of all this post-adolescent posturing by "hard scientists" who haven't thought things through. Maybe the relevant distinction is not between "real world" and "imaginary world" but between mirage and best-you-can-do-under-the-circumstances. (Then again, I am a theorist so perhaps I am overly harsh.)

I suggest Polya's Plausible Reasoning [1] as a better guide to "economic epistemology". Maybe look into Rational Belief theory (key reference: M. Kurz's 1994 papers [2,3]) for a "compromise" in modeling. Also, Fischer Black: Estimating Expected Return [4].

_________

[1] https://www.amazon.com/Mathematics-Plausible-Reasoning-Two-V...

[2] http://web.stanford.edu/~mordecai/OnLinePdf/03.OnRBE_ET_1994...

[3] http://link.springer.com/article/10.1007/BF01213817

[4] http://www.cfapubs.org/doi/abs/10.2469/faj.v51.n1.1873

qntty
thanks for the Polya recommendation
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