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KF5JRV > TECH 13.08.16 16:27l 65 Lines 3751 Bytes #999 (0) @ WW
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Tables
In an age of Excel spreadsheets it is all too easy to underestimate the table
as an innovation with its own unique history. Though not always understood as
'instruments', tables of numerical values were, and still remain, fundamental
resources for calculation. In fact, rulers and scales are, in essence,
convenient representations of tabular information. The contents of tables
include solutions of mathematical functions, astronomical coordinates and
tax brackets.
The invention of tabular record keeping can be traced back to third-millennium
BCE Mesopotamia, where tablets using columns and rows were used to account for
the transfer of various goods and livestock. The classic tables of antiquity
could be found in the astronomer Ptolemy's Almagest, which he republished
and distributed under the name Handy Tables. Tables of mathematical and
empirical values were helpful for organizing observations and calculations,
and their clear-cut presentation made them also ideal devices for sharing
knowledge.
In early modern Europe, mathematical tables became important resources for
simplifying otherwise laborious calculations. John Napier is renowned for
his discovery of the method of logarithms, which he published as a treatise in
1614.
Logarithms allowed large values to be expressed as a standard base raised to a
power, making them easier to write down and then look up. Furthermore, they
reduced multiplication and division to simpler addition and subtraction. This
made the possession of accurate logarithm tables essential.
Entering the age of industry
Henry Briggs (1561-1630), the first professor of geometry at Gresham College
in London, was enamoured with Napier's system and worked to recalculate and
distribute his logarithm tables widely. This was the beginning of the long
tradition of checking calculations and republishing tables, often as
pocket-sized 'ready reckoners', for commercial transactions - a practice that
became more common during industrialisation.
However, accuracy was always a problem with tables calculated by human
'computers', as error could be introduced during calculation, copying, or
typesetting. It was for this reason that this era also saw the first attempts
to design and build machines capable of computing and printing tables
mechanically.
Pocket-sized reckoners had to present information selectively, and were often
made for only very specific purposes, or to accompany some other instrument.
Their small size made them more akin to handy tools than bound volumes. For
example, when it became necessary to build railroads with tighter curves to
save space, engineers had to carefully calculate curve radii so that trains
would not derail. An engineer could consult these cards from 1878 by Alexander
Beazeley, which were small enough to carry around in a pocket or lay on a
theodolite while measuring angles.
Other reckoners were used to calculate interest over time, present exchange
rates for mixed currencies, and set values on livestock and other agricultural
goods. As markets fluctuated, they were updated. In the sciences, on the other
hand, standard sets of tables played a crucial role in making experiments
legitimate. Laboratories relied on sets of standard values, like the specific
heat of a substance, for setting up an experiment as well as calculating
results. In 1938, Ronald A. Fisher and Frank Yates published the first
edition of Statistical tables for biological, agricultural and medical
research, which helped to spread the application of statistical tests to the
design of experiments and validity of results. It sold 22,000 copies by the
1960s, and became the most important statistical resource of its time.
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