Group: meaning and truth
Group: philosophy of mathematics
Topic: abstraction
Topic: data acquisition
Topic: digital measurement
Topic: empirical truth
Topic: general relativity
Topic: geometry
Topic: history of science
Topic: information as facts
Topic: knowledge representation
Topic: law of nature
Topic: models of reality
Topic: Newtonian physics
Topic: physics
Topic: physics as computation
Topic: problems with empirical truth
Topic: quantum mechanics
Topic: real numbers and floating point numbers
Topic: science as experiment
Topic: science as mathematics
Topic: scientific method
Topic: software metrics
Topic: statistics
Topic: units
Topic: value as an abstraction
Topic: what is truth
 
Summary
Measurement is the reduction of reality to numbers. It is an abstraction. A tally is a simply measurement. It counts the size the set. Length is more complex, especially if the frame of reference is moving rapidly relative to the object. Einstein realized that if gravity is the same as acceleration, the geometry of spacetime must be curved, changing measurements near heavy objects.
Galileo pioneered the use of measurement in science. He measured how far a ball rolled down an inclined plane in how much time. He then discovered the law that fit these measurements. By ignoring everything else, he discovered a simple law. This was the start of the scientific method, leading to the successes of Newton and other scientists.
As noted above, classical measurement breaks down at high speed. It also breaks down at atomic scales where the act of measurement changes what is being measured. Within the atom, accuracy is uncertain and measurement is probabilistic. (cbb 4/06)
Subtopic: science as geometry
Quote: because the geometrical behaviour of real solid bodies depends on conditions, geometric predicates and physical laws about reality are conventions. They are selected so that geometry and all of physical law are in accord with experience [»einsA_1923]
 Quote: fourdimensional spacetime, the effect of motion on bodies and clocks, and the equivalence of energy and inert mass, follow from the interpretation of coordinates and time as products of measurement [»einsA_1934]
 Quote: the gravitational field determines the metrical laws of the spacetime continuum; only infinitesimal regions are nongravitational with Euclidean geometry [»einsA_1956, OK]
 Subtopic: science as measurement
Quote: measurement belongs to science while eternal truth belongs to faith; e.g., Ptolemy's astronomy vs. Plato's philosophy
 Quote: physics is predominant because it is based on measurement [»campNR_1919, OK]
 Quote: physics is those sciences expressible in mathematical terms and measurements; wide application [»einsA5_1940]
 Quote: only with quantitative observations can one arrive at quantitative relationships
 Quote: before Galileo, the study of motion was based on ideas and arguments; Galileo was skeptical; he measured how far a ball rolled in how long a time [»feynRP_1963]
 Quote: Galileo's mathematical physics was an application of proportionality to accurate measurements [»drakS_1980]
 Quote: describe electrical phenomena in terms of measurements, methods of measurement, and standards
 Quote: measurable quantities are the most important aspect of any phenomenon from a mathematical viewpoint [»maxwJC_1891, OK]
 Subtopic: mathematical laws
Quote: it is by definition that 'f=ma', that action and reaction are equal and opposite, that objects remain in uniform motion [»poinH_1902, OK]
 Quote: a law found by measurement is necessarily mathematical, with mathematical consequences [»drakS_1980]
 Quote: Galileo's father discovered a mathematical law about the lengths and tensions of musical strings [»drakS_1980]
 Subtopic: what is length, energy, number
Quote: the central notion of length is "just as long as"
 Quote: since distance measures depend on simultaneous events; length depends on the frame of reference [»einsA_1916b]
 Quote: we can measure distance with light only if we suppose that the velocity of light is constant for all observers [»poinH_1908, OK]
 Quote: a distance must be measured so there is no abstract distance; a property of straight lines includes the measurement [»poinH_1902, OK]
 Quote: we do not know what energy is; energy is just a calculated number that is always the same for a given system [»feynRP_1963]
 Quote: a data type indicates how something is measured, its set of possible values, and its set of possible operations [»handP_1981]
 Quote: use twin tally sticks to record sums owed and settled; marked together with a saw [»ifraG_2000]
 Subtopic: quantity as matrix
Quote: quantumtheoretical quantity is a matrix whose diagonal is the classical value with nondiagonal terms as the uncertainty [»heisW_1927]
 Subtopic: quantum mechanics
Quote: any ordering in spacetime requires an exchange of energy and momentum between the observed and observer; thus breaking the measurement [»bohrN_1934]
 Quote: in a hydrogen atom, the uncertainty of the electron's position is as large as the atom itself; an electron is like a cloud representing its probability density
 Quote: under quantum mechanics, all measurement irreversibly changes a process, and the only stability is statistical [»thomR_1975]
 Quote: physics should only describe the correlation of observations; there is no real world with causality [»heisW_1927]
 Subtopic: measurement as theory
Quote: only the theory itself can decide what is and is not observable [»heisW_1927]
 Subtopic: frame of reference
Quote: we impose the frames of time and space on nature because we find them convenient [»poinH_1905, OK]
 Quote: observation depends on coincidence in space and time, independent of a frame of reference; fundamental idea of relativity [»bohrN_1934]
 Subtopic: units
Quote: specify units for data types for consistency checks; e.g., height vs. weight, radians vs. degrees [»hoarCA_1974]
 Quote: can remove the speed of light from physical equations by defining the unit of time as the time in which light travels 1cm [»einsA_1949]
 Quote: every quantitative expression consists of a unit or standard of reference and a magnitude [»maxwJC_1891, OK]
 Quote: algorithms to convert units of measurement and perform dimensional analysis [»novaGS8_1995]
 Subtopic: precision of measurement
Quote: measurement is inheritently imprecise, as are the results of experiments [»drakS_1980]
 Quote: Galileo sought reasonable agreement with observation rather than Aristotle's incontrovertible evidence
 Quote: a mathematical scientist must deduct material hindrances just as a merchant computer must discount the boxes from the weight of sugar [»galiG_1632]

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Topic: abstraction (62 items)
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