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| 4. Science and Learning |
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(See 1847)| Scientific inquiry underwent great changes by the end of the 19th century. With the discoveries of Max Planck (1858–1947) and Albert Einstein (1879–1955), the older Newtonian view of the knowable universe was shaken by the new concept of randomness. Physicists demonstrated that in the small-scale world of the electron, scientists can only theorize about probabilities, not facts. Like modern art and Freud's theories of human nature, modern physics introduced feelings of uncertainty, probability, and mystery into a world early-19th-century Europeans felt confident they could conquer. | 1 |
| The major benchmarks in scientific inquiry included: | 2 |
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| a. Mathematics, Physics, and Astronomy |
| 1848 |
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| William Thomson (Lord Kelvin) (1824–1907) established the absolute thermodynamic scale of temperature, which is named after him. | 3 |
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| 1849 |
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| Armand Fizeau (1819–96) for the first time successfully measured the speed of light by observations that did not involve astronomical constants. | 4 |
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| 1849 |
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| Jean Bernard Foucault (1819–68) measured the speed of light accurately in media other than air, and thereby determined that the speed in air is greater than in water. Later, in a famous pendulum experiment, he demonstrated that the earth rotates (1851). | 5 |
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| 1850 |
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| William Cranch Bond (1789–1859), using the Harvard College Observatory's 15-inch refractor, took the first photograph of a star. | 6 |
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| 1850 |
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| Rudolph Clausius (1822–88) announced the second law of thermodynamics: heat cannot of itself pass from a colder to a warmer body. In Über die bewegende Kraft der Wärme (1865) he introduced the term entropy, stating that the entropy of the universe tends to increase. | 7 |
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| 1851 |
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| Bernhard Riemann (1826–66) introduced topological considerations into analysis. | 8 |
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| 1853 |
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| The first International Statistical Congress was held at Brussels, organized and inspired by Adolphe Quetelet. | 9 |
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| 1854 |
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| Riemann established the mathematical importance of non-Euclidean geometrics, discussing them in his general theory of manifolds. In the same year he gave the most comprehensive and general definition of the classical definite integral, since called the Riemann integral. | 10 |
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| 1854 |
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| George Boole (1815–64) published The Laws of Thought, an expansion of his 1847 work, The Mathematical Analysis of Logic, which marked the beginning of symbolic logic, that is, the attempt to express the laws of thought in algebraic symbols. | 11 |
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| 1856 |
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| Karl Weierstrass (1815–97) began to lecture at the University of Berlin. In these lectures, which spanned over 30 years, he gave the modern (delta-epsilon) definition of a limit, eliminated the remaining vagueness in the concepts of the calculus, introduced the notion of uniform convergence, and founded the theory of functions of a complex variable on power series. | 12 |
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