Science and Hypothesis excerpts

What follows are excerpts from the book Science and Hypothesis by Henri Poincaré, translated (1905) from La Science et l’hypothèse (1902). p.xxiii The latter [definitions or conventions] are to be met with especially in mathematics and in the sciences to which it is applied. From them, indeed, the sciences derive their rigour; such conventions are […]

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Two measures of motion

By common experience, we know there are three dimensions of motion. That is, space, which is the space of motion, is three dimensional. To measure the extent of motion requires comparing one motion with another, of which there are two ways: distance and duration. The distance of a motion is measured by comparing it with

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Newton’s laws and their duals

The following is based on Classical Mechanics by Kibble and Berkshire, 5th ed., Imperial College Press, 2004, with the dual version indented and changes italicized. p.2 The most fundamental assumptions of physics are probably those concerned with the concepts of space and time. We assume that space and time are continuous, that it is meaningful

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Speaking of reality

Anti-realism has been popular among the elites for some time. This has led to anti-realist speech spreading to the mass media and general culture. It has also led to much confusion and foolishness. One wonders how it will end, but reality can be averted only so long. As a start toward speaking of reality the

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Republican representation

This post builds on previous ones, such as here. In the year 507 B.C., the Athenian leader Cleisthenes introduced a system of political reforms that he called demokratia, or “rule by the people.” This system was comprised of three separate institutions: the ekklesia, a sovereign governing body that wrote laws and dictated foreign policy; the

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Dual calendar systems

The unit for all calendars is the day, the diurnal cycle of daylight and night. A lunar calendar is based on the monthly (synodic) cycle of the Moon’s phases. A solar calendar is based on the annual cycle of the Sun’s height above the horizon. A lunar-solar (lunisolar) calendar is based on the lunar month

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Contraries as duals

Contrariety is a property of pairs of propositions, but it also applies to pairs of terms or concepts. “Two general terms are contraries if and only if, by virtue of their meaning alone, they apply to possible cases on opposite ends of a scale. Both terms cannot apply to the same possible case, but neither

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Science, unity and duality

It is a Christian concept (or at least a theistic concept) that the world we inhabit is a universe. The existence of the universe requires there to be a perspective that encompasses the whole of the world, which is the perspective of a transcendent divinity. The universe is thus the whole of creation. It is

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Length and duration

Let us begin with (1) the motion of a body between two events and (2) two ways of measuring the extent of that motion: length and duration (or time). The measurement of length and duration is coordinated so that both measures are of the same motion. Length and duration are measured by a rigid rod

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