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The 10 key ideas

1. Key idea 1 · free to read

   Chance is only a measure of our ignorance

   Laplace begins with a firm claim. Every event follows from the laws of nature as surely as the sun follows its course. People speak of chance only when they cannot see the causes. As knowledge grows, those imaginary causes fade away.

   Then comes his best-known picture. Imagine an intelligence that knows all the forces of nature and the positions of all things at one instant, and that can analyze them. It would express in one formula the motion of the largest bodies and the lightest atom. For it, the future would be as present as the past.

   Astronomy gives a faint copy of that mind. Halley saw that the comets of 1531, 1607 and 1682 were one body and announced its return. Clairaut worked out the pull of Jupiter and Saturn, and the comet passed the sun in April 1759, just as he had fixed it. Chance names our ignorance, and probability is the tool for working inside it.

2. 2

   Probability is favorable cases over equally possible cases

   Laplace defines probability in one sentence.

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3. 3

   Combine chances by multiplying, and watch them shrink

   The third principle covers joined events.

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4. 4

   Learn about causes by working backward from events

   The most original part of the book concerns reasoning from effects to causes.

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5. 5

   Fair value is probability times gain, adjusted by wealth

   Laplace calls the worth of an uncertain prize its mathematical hope.

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6. 6

   Large numbers bring order out of chaos

   Among the changing causes we call chance, a striking regularity appears when events multiply.

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7. 7

   Probability sharpens measurement and sets astronomy in order

   No observation is exact, so scientists must combine many of them.

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8. 8

   Weigh testimony by how extraordinary the claim is

   Most of our beliefs rest on the word of others, so Laplace tests testimony with urns.

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9. 9

   Votes, courts, life tables and insurance follow the same math

   Laplace treats group decisions with the same tools.

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10. 10

    Distrust first impressions, and use method to approach truth

    Laplace calls the mind prone to illusions that only reflection can correct.

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