Michael Fowler (This is a Draft Version, 10/2/07)
With Ptolemy’s Almagest giving detailed accounts and predictions of the movement of the planets, we reach the end of the great classical period in science. Let’s review what was achieved.
First, the Babylonians developed a very efficient system of
numbers and measures of all kind, primarily for business purposes. Unfortunately,
it did not pass through to the Greeks and Romans, except for measures of time
and angle, presumably those are the units relevant for recording astronomical
observations. The Babylonians kept
meticulous astronomical records over many centuries, mainly for astrological
purposes, but also to maintain and adjust the calendar. They had tables of squares they used to aid
multiplication, and even recorded solutions to word problems which were a kind
of pre-algebra, a technique broadened and developed millennia later in
The Egyptians developed geometry for land measurement (that’s what it means!), the land being measured for tax assessment.
The Greeks, beginning with Thales then Pythagoras, later Euclid, Archimedes and Apollonius, greatly extended geometry, building a logical system of theorems and proofs, based on a few axioms. An early result of this very abstract approach was the Pythagoreans’ deduction that the square root of 2 could not be expressed as a ratio of whole numbers. This was a result they didn’t want to be true, and that no-one would have guessed. Remember, they believed that God constructed the Universe out of pure numbers! Their accepting of this new “irrational” truth was a testimony to their honesty and clear mindedness.
The development of geometry took many generations: it could only happen because people with some leisure were able to record and preserve for the next generation complicated arguments and results. They went far beyond what was of immediate practical value and pursued it as an intellectual discipline. Plato strongly believed such efforts led to clarity of thought, a valuable quality in leaders. In fact, above the door of his academy he apparently wrote: “let no one who cannot think geometrically enter here.”
Over this same period, the Greeks began to think scientifically, meaning that they began to talk of natural origins for phenomena, such as lightning, thunder and earthquakes, rather than assuming they were messages from angry gods. Similarly, Hippocrates saw epilepsy as a physical disease, possibly treatable by diet or life style, rather than demonic possession, as was widely believed at the time (and much later!).
The geometric and scientific came together in analyzing the motion of the planets in terms of combinations of circular motions, an approach suggested by Plato, and culminating in Ptolemy’s Almagest. This Greek approach to astronomy strongly contrasted with that of the Babylonians, who had made precise solar, lunar and planetary observations for many hundreds of years, enough data to predict future events, such as eclipses, fairly accurately, yet they never attempted to construct geometric models to analyze those complex motions.
Why did the development of science on the ancient world
pretty much end after 800 years, around 200 AD or so? For one thing, the Romans were now dominant,
and although they were excellent engineers, building thousands of miles of
roads, hundreds of military garrisons, and so on, they did very little
science. And, the Greeks themselves lost interest: Plato’s Academy began to
concentrate on rhetoric, the art of speechmaking. Perhaps this had been found to be more
valuable for an aspiring leader than the ability to think geometrically or
scientifically—or perhaps better for winning elections and persuading people. Furthermore, with the conversion of the
"Nor need we be afraid lest the Christian should be rather ignorant of the force and number of the elements, the motion, order and eclipses of the heavenly bodies, the form of the heavens, the kinds and natures of animals, shrubs and stones ... It is enough for the Christian to believe that the cause of all created things, whether heavenly or earthly, whether visible or invisible, is none other than the goodness of the Creator, who is the one true God."
It’s a little puzzling to put this together with Botticelli’s picture, showing Augustine looking prayerful but with scientific instruments in plain sight! (Augustine was very interested in science and many other unholy things earlier in life.)
Actually, the story of the treatment of the Greek
mathematical and scientific knowledge by the early Christian church is
complicated, like the church itself.
Recall that mathematics and science effectively ended in
What has this got to do with science? It is a crucial link in the chain. In contrast to most of the rest of the
church, the Nestorians preserved and read the works of Aristotle, Plato, etc.,
and translated many of them into Syriac.
They felt that clear thinking was useful in theology. Being declared heretics meant that it was no
longer a good idea to stay in the
Let’s briefly review the extent of the
The maps below are from:
At its greatest extent, in 116 AD, pictured above, notice
that the Empire included almost all of present-day
At the time of the death of
The Nestorians found temporary refuge with Syriac speaking
(Nestor was a pupil of Theodore of Mopsuestia in
This was all during the time of the second
The Sassanid Persian kings saw an opportunity to handle
their own considerable number of Christian subjects better. They granted protection
to Nestorians in 462, then in 484, they executed the Bishop of Nisibis (37 04
N, 41 13 E) (who was anti Nestorian, pro Byzantine) and replaced him with a
Nestorian. (This is from Wikipedia.) The Nestorians settled in the
The academy at Gundishapir had Syraic as the working
language. Under a Sassanid monarch,
Khosrau I, 531 – 579 AD, it became famous
for learning. Although Khosrau I
was a Zoroastrian, the dominant Persian religion, he was tolerant of all
religions, in fact one of his sons became a Christian. He greatly improved the infrastructure,
building palaces, strong defenses, and irrigation canals. He encourages science and art, collecting
books from all over the known world, and introducing chess from
In 622, the prophet Muhammad left hostile
In 749, a second dynasty, the Abbasid caliphate,
began. In 762 the Abbasid Caliph
al-Mansur built a magnificent new capital:
Meanwhile, Gundishapur wasn’t far away: generously funded
court appointments drew physicians (including al-Mansur’s personal physician) and
Later, under the Abbasid Caliph al-Ma’mun (813 – 833), the House of Wisdom was founded (in 828): a large library and translation center into Arabic: first from Persian, then Syriac, then Greek. Many works were translated from Syriac into Arabic, including some Archimedes and all Euclid. Hunayn, a Christian, from Jundishapur, redid many translations to make them more readable.
The House of Wisdom: al-Khwarismi
Perhaps the most famous scholar from the House of Wisdom is Al-Khwarismi (780 – 850). The word algorithm, meaning some kind of computational procedure, is just a mangling of his name. This is because he wrote the book that introduced the Hindu numbering system (now known as Arabic) to the Western world, and medieval scholars used his name to refer to routines for multiplication using Arabic numbers, far more efficient than anything possible with the previously used Roman numerals!
He also wrote the book on algebra: that word is actually
“al-jabr” meaning completion. (We’ll see below why this is an appropriate
term.) Actually, he didn’t use symbols
to denote unknown quantities, now the essence of algebra. Ironically, such symbols had been used by the
Greek Diophantus, in
Let’s look at one of his examples: (OK, I’ve cheated by using x: he wrote it all out in words, but his thought process was as outlined below.)
This he thought of in terms of equating areas: a very natural approach to something beginning with a square! On the left we have a square of side x and a rectangle of sides x and 10.
His strategy is to add area to this to make it one big square—he takes the rectangle and divides it into four equal rectangles each having sides x and 10/4 = 5/2. He then glues these to the x square:
The next step is to extend this to give just one square, by adding the green bits. But to keep the equation valid, the same amount must of course be added to the other side. That is, 5/2×5/2×4 is to be added to each side. We can see that on the left we now have a square of side x + 5. on the right hand side, we have 39 + 25 = 64 = 8×8. Therefore, x + 5 = 8, and x = 3.
So by adding to both sides we have “completed the square”, and al-jabr is this adding to get completion. Negative numbers were not in use at that time, so quadratics like , for example, were treated separately, and several distinct cases had to be explained.
It’s not clear that al-Khwarismi’s own contribution, by which I mean really new mathematics, was great, but his influence was tremendous: his presentation of algebra, and of the Arab numerals, sparked much further mathematical development, both in Baghdad and, later, in the West, as we shall see.