1600-1699: Measurement and theory

Among the most important problems of the 17th century were those concerned with physical measurement- of time, distance, and space- for astronomy, surveying, map making, navigation and territorial expansion. This century saw great new growth in theory and the dawn of practice- the rise of analytic geometry, theories of errors of measurement and estimation, the birth of probability theory, and the beginnings of demographic statistics and "political arithmetic".

By the end of this century, the necessary elements were at hand- some real data of significant interest, some theory to make sense of them, and a few ideas for their visual representation. Perhaps more importantly, one can see this century as giving rise to the beginnings of visual thinking.

early 1600s

Tables of empirical data, published tables of numbers begin to appear. "Die Tabellen-Statistik," as a branch of statistics devoted to the numerical description of facts- Germany.

1600
Empirical data tables
Added: 2008-07-17

Tables of empirical data, published tables of numbers begin to appear. "Die Tabellen-Statistik,'' as a branch of statistics devoted to the numerical description of facts


References:
none
1603
1st world map with isogons
Added: 2007-02-01

Le Nautonier's geomagentic mapLe Nautonier's geomagentic map

Modern re-creation of the magnetic equator after Le NautonierModern re-creation of the magnetic equator after Le Nautonier

Le Nautonier portraitLe Nautonier portrait

Tables, and first world map showing lines of geomagnetism (isogons), used in work on finding longitude by means of magnetic variation. The tables give the world distribution of the variation, by latitude, along each of the meridians


References:
Nautonier:1602 MandeaMayaud:2004
1603
Pantograph
Added: 2007-02-01

Scheiner's pantographScheiner's pantograph

The pantograph was invented for mechanically copying a figure on an enlarged or reduced scale


References:
none
1610
Astronomical pictures
Added: 2007-04-06

Page 9v: craters on the moonPage 9v: craters on the moon

Cover page from Sidereus NunciusCover page from Sidereus Nuncius

The first astronomical pictures ever printed, from observations through a telescope, used to illustrate discoveries of craters on the moon, the 4 staelites of Jupiter and a vast number of stars never seen by unaided eyes


References:
Galilei:1610
1614
Logarithmic tables
Added: 2008-07-17

Two pages from Napier's table of logarithmsTwo pages from Napier's table of logarithms

Diagram of spherical triangles fromDiagram of spherical triangles from

Napier portraitNapier portrait

Linear and logarithmic scalesLinear and logarithmic scales

Invention of logarithms, and the first published tables of logarithms.


In 1617, the year of his death, Napier invented a calculating device, called "Napier's Bones," based on logarithms to facilitate multiplication and division. Napier was also the first to describe the systematic use of the decimal point in representing the result of long division.
References:
Napier:1614
1617
Trigonometric triangulation
Added: 2008-07-17

Snellius portraitSnellius portrait

First use of Frisius' method of trigonometric triangulation to produce locations of major cities in Holland; foundation of geodesy


In 1621, Willibrord Snell, in Cyclometricus, discovered the law of refraction which says that the ratio of the sines of the angles of incidence and refraction is a constant and the index of refraction varies from one transparent substance to another. This law implies that the velocity of light in a medium is inversely proportional to its refractive index. Cyclometricus was published after Snell's death by Rene' Descartes.
References:
Snell:1617
1620 to 1628
Gunter's scale
Added: 2004-11-03

Gunter's scale imageGunter's scale image

Gunter's log scaleGunter's log scale

Oughtred's dual log scaleOughtred's dual log scale

Invention of a mechanical device, containing a logarithmic scale of equal parts and trigonomic functions which, with the aid of a pair of calipers, could be used as a slide rule. This device, called "Gunter's scale,'' or the "gunter'' by seamen, was soon replaced by a true slide rule, containing two parallel logarithmic scales


References:
Babcock:1994 Gunter:1624
1623
1st adding machine
Added: 2004-06-05

reproduction of Schickard's calculating clockreproduction of Schickard's calculating clock

The first known adding machine, a mechanical calculator called the "Calculating Clock.'' It could add and subtract up to six-digit numbers, based on the movement of six dented wheels geared through a "mutilated" wheel which with every full turn allowed the wheel located at the right to rotate 1/10th of a full turn


References:
none
1626
Sunspots
Added: 2008-07-17

Apparatus for recording sunspotsApparatus for recording sunspots

Scheiner sunspot imageScheiner sunspot image

Visual representations used to chart the changes in sunspots over time. Also, the first known use of the idea of "small multiples'' to show a series of images in a coherent display


References:
Scheiner:1626
1632
Least deviations
Added: 2008-07-17

Galileo portraitGalileo portrait

Statistical analysis of observations on location of Tycho Brahe's star of 1572, based on idea that the most probable hypothesis is the one having the smallest (least absolute value) deviations


References:
Galileo:1632 Hald:1990
1637
Coordinate system
Added: 2008-07-17

Descartes portraitDescartes portrait

Coordinate system reintroduced in mathematics, analytic geometry; relationship established between graphed line and equation


About 1629, Pierre de Fermat discovered that the equation $f(x,y)=0$ represents a curve in the xy-plane. This is the fundamental principle of analytic geometry, and was first published by Descartes in 1637. He also formulated a method for determining the maximim and minimum values which give single solutions for problems which in general have two solutions. This procedure is "almost precisely that now given in the differential calculus''" ''(Boyer 1949:156).
References:
Descartes:1637
1644
1st data graph
Added: 2008-07-17

Langren imageLangren image

First visual representation of statistical data: variations in determination of longitude between Toledo and Rome


References:
Langren:1644
1646
Image projection
Added: 2008-07-17

Althanasius Kircher portraitAlthanasius Kircher portrait

Invention of the first projection lantern (the magic lantern). [Images were painted on glass and projected on walls. Kirscher, a Jesuit priest, was the last recorded ordained priest openly to concern himself with optics. Henceforth, the art of projecting images was classified as an entertainment and curtailed.]


References:
Kirscher:1646
1654
Theory of probability
Added: 2008-07-17

Pascal portraitPascal portrait

Initial statements of the theory of probability


References:
Ball:1908
1654
1st econometric survey
Added: 2004-11-03

William Petty portraitWilliam Petty portrait

The first large scale attempt at a scientific, economic survey (of the Irish estates confiscated by Oliver Cromwell), perhaps the first econometric study, leading to development of political arithmetic


References:
Petty:1665 Petty:1690
1657
1st text on probability
Added: 2008-07-17

Huygens portraitHuygens portrait

1662
Demographic statistics
Added: 2008-07-17

Mortality table, fromMortality table, from

Graunt portraitGraunt portrait

Cover page of "Natural and Political Observations..." Cover page of "Natural and Political Observations..."
Published in 1662.

Founding of demographic statistics: Development of the idea that vital statistics (records of christenings and burials in London) could be used to construct life tables. The average life expectancy in London was 27 years, with 65\% dying by age 16


Graunt's work of 1662 is often ascribed to Sir William Petty. The authorship questionhas been discussed by Wilcoxwho concludes that although a portion ofthe work was by Petty, the majority is due to Graunt.
References:
Graunt:1662 Sutherland:1963 Petty:1665 Wilcox:1937
1663
Weather clock
Added: 2008-07-17

Wren portraitWren portrait

Automatic recording device (the weather clock) producing a moving graph of temperature and wind direction (in polar coordinates)


References:
Bennett:1982 Wren:1750
1666
1st complete census
Added: 2008-07-17

First modern complete demographic census, a record of each individual by name of the 3215 inhabitants of New France


E. H. Godfrey says that this is "a date prior to any modern census, whether European or American'', seeThe returns were fairly complete, giving data on population, sexes, families, conjugal condition, age, profession and trades, and they filled 154 pages. The original copy is now in the Archives of Paris, and a transcript in the Archives of Ottawa.
References:
Godfrey:1918 JohnsonKotz:97
1669
Life table
Added: 2008-07-17

Huygens graphHuygens graph

First graph of a continuous distribution function, a graph of Gaunt's life table, and a demonstration of how to find the median remaining lifetime for a person of given age


Source: correspondence between Huygens and his brother Lodewijk.
References:
Boyer:1947
1671
Mortality table
Added: 2007-02-01

de Witt portraitde Witt portrait

First attempt to determine scientifically what should be the purchase price of annuities, using mortality tables


References:
deWitt:1671
1679
Network diagram on a map
Added: 2009-09-16

Adams1679Adams1679
This map shows the distances between cities in England.

A map of England showing distances between cities arranged for the use of travellers.


References:
Adams:1679
1686
Bivariate plot
Added: 2008-07-17

Halley's graph of change in barometric pressureHalley's graph of change in barometric pressure

Bivariate plot of a theoretical curve derived from observations (barometric pressure vs. altitude), graphical analysis based on empirical data


References:
Halley:1686
1686
1st weather map
Added: 2008-07-17

Halley's wind map, section 1 detailHalley's wind map, section 1 detail

Halley's wind map, 1686Halley's wind map, 1686

Halley portraitHalley portrait

First known weather map, showing prevailing winds on a geographical map of the Earth


References:
Halley:1686a
1687
International statistics
Added: 2008-07-17

Petty portraitPetty portrait

Use of statistics for international comparisons, e.g., London vs. Rome and London vs. Paris, compared in people, housing, hospitals, etc.


References:
Petty:1687a Petty:1687b
1693
1st mortality tables
Added: 2008-07-17

First real mortality tables, containing the ages at death of a stable sample of individuals under stable conditions (from Breslau Bills of Mortality)


References:
Halley:1693
1693
rectangles for probabilities
Added: 2008-07-17

Halley 1893 2D diagramHalley 1893 2D diagram

Halley 1893 3D diagramHalley 1893 3D diagram

Halley's diagramHalley's diagram

First use of areas of rectangles to display probabilities of independent binary events


References:
Halley:1693 Hald:1990