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Measurement. By: Daniel Cornelius. Long, long ago.. Before “numbers”. 9 th Millennium BC: Different types of clay tokens were used to tally agricultural products in Mesopotamia. Use of written symbols to represent tallies. Euclid(280BC) defined a number as a ‘multitude composed of units”.

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  1. Measurement By: Daniel Cornelius

  2. Long, long ago.. Before “numbers” • 9th Millennium BC: Different types of clay tokens were used to tally agricultural products in Mesopotamia. • Use of written symbols to represent tallies. • Euclid(280BC) defined a number as a ‘multitude composed of units”

  3. Counting leads to.. Measuring! • Cubit: The length from the elbow to the end of the middle finger. (3rd millennium BC) • ‘Sacred’ Cubit: Inscribed on monuments as a standardized length for building and surveying Egypt. • Evolved (…somehow…) into the ‘foot’ and the ‘inch’

  4. Activity

  5. …and the mile! • The Romans introduced the ‘mile passus’ which consists of 1000 paces, or double-steps. A pace equal to five (Roman) feet. (so, 5000 ‘feet’) • Mile changed to 5280 Feet by Queen Elizabeth I, so that 1 mile=40 Furlongs.

  6. English Measurements • Most English units developed from using Barley length to measure. • An early Welsh law defines a “natural foot” as 27 barley corns laid end to end. • Standardized in the early 14th century. “Be it remembered, That the Iron Yard of our Lord the King, containeth three Feet and no more. And a foot ought to contain Twelve Inches… It is ordained that three grains of Barley dry and round do make an inch; Twelve inches make a foot; Three feet make a yard.:

  7. Wait… what about weight!? • One of the oldest (known) standards of weight is the Beqa shekel(~13g) which was used in ancient Eqypt. • Greek- AegerinaStater(~12.5g) and Athenian Stater(~8.5-8.9g) • 1 Stater= 1 Drachmas • 100 Drachmas= 1 Mina (like the pound) • Roman- “pound” or Libra was about 327g. • Libra was subdivided into 12 Unciae(twelfths)

  8. Variety “Tends of thousands of new units were introduced and hundreds of thousands of local variations emerged from the Atlantic seaboard to central and Eastern Europe” – Ronald Zupko • Did anything have a standardized unit?

  9. Astronomers • Apparently, it was the guys (and gals) who liked to stare off into space(literally) who got the whole measurement thing right! ‘The degree of arc and its sexagesimal subdivions together with the equinoctial hour and its sexagesimal subdivions.’ (Roche) • The Babylonians divided the circle into twelve 30-degree intervals. The Greek astronomers innovated the use of angular measure by using 1/360-th of a circle to denote 1 degree.

  10. Time • While not entirely obvious, measuring time is a milestone of measurement in itself. (So, if this presentation isn’t long enough, I argue that your time system is flawed) • The Eqyptian priests dived day and night into 10 equal periods, which did not include the twilights at dawn and dusk(two hours a piece) • Before the widespread availability of mechanical clocks, the lengths of the hours in the day varied with the season (as there is more daylight in the summer, the day’s ‘hours’ would be longer than the night’s)

  11. Temperature • Temperature was one of the first things to be thought of as quantitative. • Claudius Galen defined a medical scale of temperature in terms of four ‘degrees’ of hot/warm/cool/cold (more or less), with the center of the scale being the theoretical temperature achieved by mixing equal amounts of boiling water and ice.

  12. Reform • “It is quite evident that the diversity of weights and measures of different countries, and frequently in the same province, are a source of embarassment in commerce, in the study of physics, in history, and even in politics itself; the unknown names of foreign measures, the laziness or difficulty in relating them to our own give rise to confusion in our ideas and leave us in ignorance of facts which could be useful to us.” • Charles de La Condamine 1747

  13. Metric System • France’s troubled measurement system(s) • Spain adopted France’s measurement system • Russia adopted England’s measurement system • French Revolution(1789)- Nobility forfeited their right to control local weights/measures • 1793- Decimal time introduced • 1795- Draft Metric System • 1806- Decimal time discarded

  14. Draft Metric System • Meter defined as (1/10,000,000) of the distance between the north pole and the equator (going through Paris) (problematic) • Liter defined as 1 dm3 for the volume of liquid • Gram defined as the mass of one cubic centimeter of water (more problematic) • Multiples to be named with Greek prefixes (kilo, deka, hecta, deci, centi, milli)

  15. “New” Measures • With science exploding, new things needed measured, and new measuring techniques were needed. Things like Joules, Watts, Ohms, ampere, candela, mole, etc. • These along with the other measures came with a strong desire to “define” a base unit which was based on something in nature, instead of some arbitrary value.

  16. Metric Problems • Even after some of the world’s greatest scientists, mathematicians, and politicians put their brains together to come together with one unified system for measurements, there were still problems. • Although the definition of a meter was very clear, the miniscule error in recording the actual distance between the North Pole and the Equator become significant when looking at (1/10,000,000)th of that distance. • Using water to define mass is great in theory, but not in practice. Water fluctuates density at different temperatures (and obviously at different purities)

  17. Expansion to the World • The Metric System spread through Europe quickly. • France in 1812 • Italy in 1860 • Spain in 1849 • Germany in 1871 • Great Britain in … well… not so much • United States in … see Great Britain

  18. Imperical/English System • The use of the ‘foot/inch/yard/mile’, the ‘pound/ounce’ and the ‘gallon/quart/ pint/cup/ounce’ (etc) are primarily used only in Great Britain and the United States. • Both countries have discussed ‘metricating’ for centuries, and have even passed bills with the plan to convert to the metric system. • The real irony is that currently we define our units in terms of their metric counterparts. • 1 lb = 453.59237 (exactly)

  19. SI • Committee held every 4-6 years to improve, through better standardization, the metric system • 1960- Definition of the meter was changed to reflect a wavelength of light • Kilogram: The lone remaining measurement which still has an arbitrary definition (the kg prototype)

  20. SI Definitions • http://physics.nist.gov/cuu/Units/current.html

  21. Work Cited • Roche, John. “The Mathematics of Measurement.” London: The Athelone Press, 1998. • http://physics.nist.gov/cuu/Units/current.html • http://www.sciencemadesimple.com/metric_system.html

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