How Classical Knowledge Reached Baghdad

Michael Fowler

The Classical Achievement in Mathematics and Science

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 Baghdad, as we shall see.

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.