# [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
```