Subject: [HM] Euclid and USA Politics (was: "President Garfield's Proof")
From: Antreas P. Hatzipolakis (xpolakis@otenet.gr)
Date: Thu Jan 27 2000 - 07:52:24 EST
Following is an excerpt from the web page jeff_r(4).htm on Jefferson
located at:
http://www.math.virginia.edu/Jefferson/
<quote>
In the Jefferson Memorial in Washington, DC the next sentence of
the Declaration of Independence is written up on the wall: "We
hold these truths to be self-evident: . . . " Why does he say that?
You would only put it like that, you would only express your
thoughts in those precise words, if you had studied Euclid at an
impressionable age. Years later, Jefferson wrote to John Adams
of his state of mind after he had stopped being President, saying
that he was happy to have "given up newspapers in exchange for
Tacitus and Thucydides, for Newton and Euclid."-a Roman
historian, a Greek historian, and two mathematicians. His two
favorite mathematical writers were Newton and Euclid, both men
whose works he had read and studied from his days at William
and Mary College. Awareness of the strength of an axiomatic
system was firmly located in Jefferson's way of thinking, the
use of unexamined, or unexaminable, or self-evident, principles
as a solid foundation from which a complex superstructure could
be logically deduced. Of course, Euclidean axioms and Newtonian
axioms are rather different: Euclidean axioms are arguably
'self-evident' in a way that Newtonian axioms are most certainly
not. Note too from the manuscript of the Declaration of Independence
(see illustration above) that Jefferson only reached the phrase
'self-evident' truths after trying 'sacred and undeniable' truths.
So there's a lot going on here.
In evaluating the role of mathematics in American political
thought of the period we must bear in mind too that Jefferson's
colleagues and co-signatories were educated in Newtonian
science also. John Adams, who was to be the second president
(the one in between Washington and Jefferson), had been a
student at Harvard College under John Winthrop; he is the man
who memorably remarked "I must study politics and war [in order
that] my sons may have liberty to study mathematics and
philosophy". No less than four signatories of the Declaration of
Independence were educated at William and Mary College.
Another signatory was the great scientist Benjamin Franklin.
And of the younger generation James Madison, Jefferson's
successor as fourth president of the United States, studied some
mathematics and Newtonian science at Princeton. The whole
group was, as politicians go, quite remarkably characterised by
scientific awareness and a relatively deep imbibing of
Newtonian thought-patterns. Jefferson was only the most
prominent and most accomplished of a sophisticated and
scientifically literate group of men, someone particularly alert
to recent and current mathematical developments, and to the
importance of promoting mathematics and mathematics
education, which is something that Jefferson's public position
enabled him to influence.
</quote>
Antreas
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