Subject: [HM] Ye Age of Reason, in America too
From: Ralph A. Raimi (rarm@math.rochester.edu)
Date: Thu Jan 27 2000 - 03:33:16 EST
John Adams, second president of the United States under the
Constitution, was graduated from Harvard College, where he learned little
if any mathematics. For the next few years he "kept school" in Worcester,
a town about 50 miles west of Boston. It was famously said of Boston
matriarchs of the era that when planning travel to China they went "by way
of the Worcester Turnpike". The Diaries of Adams that I have read contain
two entries indicative of the state of his mathematical knowledge at that
time. Soon thereafter he seriously took up the study of law, via which he
entered politics and diplomacy, and I have never heard that he paid much
attention to mathematics thereafter. His son, John Quincy Adams, who
later himself became President, was much more the scientist and had much
influence on American standards for weights and measures, as well as
geographic surveys. It is not clear from John Adams's text just where he
learned such Euclidean geometry as he indicates, and surely the arithmetic
"real-life" problem he set himself a couple of years later is a come-down
from the philosophical vision that so briefly attracted him in 1756.
Two Entries from the Diaries of John Adams (1735-1826)
[These are the complete entries for the two dates given.]
June 1, 1756 Drank Tea at the Majors. The Reasoning of Mathemati-
cians is founded on certain and infallible Principles. Every Word
they Use, conveys a determinate Idea, and by accurate Definitions
they excite the same Ideas in the mind of the Reader that were in the
mind of the Writer. When they have defined the Terms they intend to
make use of, they premise a few Axioms, or Self evident Principles,
that every man must assent to as soon as proposed. They then take
for granted certain Postulates, that no one can deny them, such as,
that a right Line may be drawn from one given Point to another, and
from these plain simple Principles, they have raised most astonishing
Speculations, and proved the Extent of the human mind to be more
spacious and capable than any other Science.
May 28, 1760 Loitered the forenoon away upon this Question in
Arithmetic. 3 men give 20 shillings for a Bushell of Corn. A pays
in the Proportion of one half, B in the Proportion of 1/3 and C in
the Proportion of 1/4. Now how many shillings and Pence does each
one pay? I put x, an Algebraicall Expression, for that unknown
Quantity, whose 1/2 1/3 and 1/4 added together would make 20 shil-
lings.
And then formed this Equation. x/2 + x/3 + x/4 = 20.
Then to free the Equation of fractions. x + 2x/3 + 2x/4 = 40.
Then 3x + 2x + 6x/4 = 120.
Then 12x + 8x + 6x = 480
____
26x = 480 26)480(18&12/26 s = 18s. 5&14/26 d.
26_
220 12
208 _12
12 26)144(5
130
14
_4
56
In the afternoon, Zab and I wandered down to Germantown on
foot--running a Parrallell between the Pleasures, Profits, freedoms,
Ease and Uses of the several Professions, especially Physick and
Divinity.
Ralph A. Raimi Tel. 716 275 4429 or (home) 716 244 9368
Dept. of Mathematics FAX 716 244 6631
University of Rochester Webpage http://www.math.rochester.edu/u/rarm
Rochester, NY 14627 (Webpage contains links to papers)
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