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Napoleon asked him, where is God in your system? Laplace answered, I had no need of that hypothesis.

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This was the man who completed Newton's work, founded probability theory, and imagined an

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intelligence that could predict the entire future of the universe. Pierre-Simon Laplace,

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the Newton of France. Last time we met Joseph Louis Lagrange, who transformed mechanics into

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pure algebra with his Lagrangian method. His work contained not a single figure,

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the triumph of analysis over geometry. Welcome back to Men of Mathematics.

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Today we meet the man who took mathematics further into the cosmos than anyone before,

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Pierre-Simon Laplace. He proved the solar system is stable, founded modern probability,

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and articulated the deterministic vision that defined classical physics.

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Pierre-Simon Laplace was born on March 23, 1749, to a farming family in Normandy.

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His mathematical abilities attracted patronage that sent him to Paris,

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where by age 24 he was presenting papers to the Academy of Sciences.

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D'Alembert recognized his genius and helped launch his career.

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Within a few years, Laplace was tackling the most difficult problems in celestial mechanics.

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Laplace navigated the French Revolution, Napoleon's Empire, and the Bourbon Restoration

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with remarkable political dexterity. He served Napoleon briefly as Minister of the Interior.

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Napoleon later said he brought the spirit of infinitesimals into government. Not a compliment.

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He was made a count under Napoleon, then a Marquis under the restored monarchy.

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Laplace's books are notorious for the phrase, il est-ezé avoir, it is easy to see, followed

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by pages of difficult derivations.

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When a student asked him to explain one such passage Laplace reportedly spent an hour working it out then confirmed yes it is easy to see Newton Principia explained planetary motion

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but left a crucial question open. Is the solar system stable? Small perturbations from planet

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to planet gravitational attraction might accumulate until planets collide or escape.

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Laplace proved the system is stable, irregularities are periodic, and bounded.

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His five-volume Mechanique Celeste, published between 1799 and 1825,

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systematized everything known about planetary motion.

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How did the solar system form?

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Laplace proposed that it condensed from a rotating cloud of gas,

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as a success on the next trial.

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Laplace-derived, the probability equals s plus 1 divided by n plus 2.

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This Bayesian approach smooths estimates.

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With zero successes and zero trials, it gives one-half, complete uncertainty.

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With many observations, it approaches the observed rate.

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Consider the sunrise problem.

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If the sun has risen every day for a million days, what's the probability it rises tomorrow?

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Naive answer, 100%.

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Laplace, 1000

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Million days, what's the probability it rises tomorrow?

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Naive answer, 100%.

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Laplace, 1,000, and 1, over 1,012, approximately 99.99999%.

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The plus 1 accounts for our residual uncertainty.

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In regions without sources, gravitational and electric potentials satisfy Laplace's equation.

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the second partial derivatives with respect to x, y, and z, summed together, equal zero.

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Solutions are harmonic functions with beautiful smoothness properties.

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This equation appears throughout physics, electrostatics, fluid flow, heat conduction.

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Laplace developed a powerful technique for solving differential equations.

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The Laplace transform converts differential equations into algebraic equations,

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making them much easier to solve. It's essential in engineering and physics.

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Laplace articulated the ultimate deterministic vision, an intelligence that knew the position

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and momentum of every particle could predict the entire future and reconstruct the entire past.

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In his famous passage, an intellect which at a certain moment would know all forces,

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and all positions of all items of which nature is composed.

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For such an intellect, nothing would be uncertain,

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and the future, just like the past, would be present before its eyes.

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This Laplace's demon represents classical determinism.

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Randomness is just ignorance.

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Twentieth century physics challenged this vision.

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Quantum mechanics, Heisenberg's uncertainty principle, limits what can be known simultaneously.

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Chaos theory, tiny uncertainties in initial conditions grow exponentially.

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Computational limits some systems are inherently unpredictable Laplace demon is dead but understanding why took two centuries Laplace calculated that a star 250 times the sun diameter but same density would trap its own

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light. These dark stars anticipated black holes, though the mechanism, general relativity, was

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unknown. Laplace developed the mathematics of functions on spheres, essential for geophysics,

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quantum mechanics, and modern computer graphics.

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Pierre-Simon Laplace completed Newton's program for celestial mechanics,

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founded modern probability theory,

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and articulated classical determinism in its purest form.

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His mathematics described the cosmos from nebulae to planetary orbits.

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His probability described everything from coin flips to scientific inference.

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I had no need of that hypothesis wasn't arrogance.

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It was a statement of method.

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Laplace's universe ran on mathematics alone. Bell notes Laplace often failed to credit others'

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work. He absorbed results and presented them as his own. Yet his achievement is undeniable,

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taking all mathematics and astronomy for his province and cultivating it royally.

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His final words, what we know is not much. What we do not know is immense.

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As E.T. Bell wrote, Laplace was the complete mathematical physicist.

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He took all mathematics and theoretical astronomy for his province and cultivated it royally.

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Next time on Men of Mathematics, we enter the revolutionary era with Gaspar Mange,

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the man who invented descriptive geometry and organized science for Napoleon's armies.

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From the siege of Mezières to the expedition to Egypt,

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Mange combined mathematical brilliance with practical engineering.

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Thank you for joining us on this journey through mathematical history.

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If you're fascinated by the Newton of France, subscribe and hit the notification bell.

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New episodes release every week.

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I'll see you next time.