[lit-ideas] Re: Einstein
- From: Michael Chase <goya@xxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sun, 30 Oct 2005 11:00:31 +0100
Le 29 oct. 05, à 19:50, Eric Yost a écrit :
MC: and the best ones, like Einstein, come up with ways of looking at
milennium-year-old problems from an entirely new viewpoint
I had a similar reaction to Andy's posting that he was disappointed in
Einstein. True, Einstein had the Lorenz equations to work from,
expressing the relationship between mass and speed-of-light. Yet
Einstein's insight was something we can all admire.
My personal favorite is Archimedes. Without using zero, but using
Greek letters instead, Archimedes developed a system of scientific
notation. Less famously, Archimedes built the first planetarium and
the first ocean liner sized vessel (a gigantic ship designed to bring
the grain harvest from Egypt).
M.C. Indeed. He also appears to have developed a death ray using
mirrors (although experts still debate the veracity of this stiory),
and the recent discovery of the Archimedes palimpsest seems to show he
was well on his way to inventing calculus.
The Medieval Arabs picked up where Archimedes left off. Roshdi Rashed
has recently shown that Thabit ibn Qurra (c. 880-943) invented a
mathematical method for dealing with infinite sets, thus about a
millennium before Cantor's discovery of degrees of infinity. Here are
the postulates of Thabit's system, according to Rashed :
-. The set of whole numbers is an infinite set in actuality.
-. The infinite subsets of the set of whole numbers are comparable. For
instance, the subset of even numbers and that of odd numbers.
-. Two infinite subsets of the set of natural whole numbers have the
same number of elements, and are equipotent. This is true for the
subset of even numbers and for the subset of odd numbers.
-. The application that associates its successor to each even number is
a bijection between the two subsets.
-. Since the intersection of these two subsets is empty, and their
union is the entire set of whole numbers, then each of these two
subsets is half of the set of whole numbers. Consequently, one infinity
can be half of another infinity.
Which is just to get to this point. Anyone can criticize, blame, and
find fault. It's more rare and more important to be able to praise.
It's so hard to do new things, and it's so easy to be discouraged.
Sometimes it seems like the natural course of society is toward
discouragement, so those attainments and examples that pull away from
discouragement are all the more to be treasured.
M.C. Hear, hear.
Here in Europe, the phenomenon described by Eric is so common that
many high administrative poobahs would like to eliminate the discipline
of the history of philosophy altogether : after all, what could we
possibly learn from all those antiquated old farts?
Yet the example of Thabit, whose works have onely recently been
translated and edited, shows that we *do* still have something to learn
from the Ancients on the scientific level. And we could sometimes learn
from them as far as attitude, methodology and philosophical orientation
is concerned, too. Here's John the Scot (Johannes Scotus Eriugena)
(810-877 ; he thus died a couple of years before Thabit's birth) :
"This too is taught to us by nature, since authority came forth from
true reason, but reason by no means came forth from authority. For all
authority that is not approved by true reason is seen to be unstable ;
yet true reason, since it relies on its own powers and remains
immutable, does not need to be confirmed by the agreement of any
authority (Periphyseon 513 BC, my translation)".
M.C.: Creationists and intelligent designers take note.
Michael Chase
(goya@xxxxxxxxxxx)
CNRS UPR 76
7, rue Guy Moquet
Villejuif 94801
France
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