Archive for the ‘Medieval history of science’ Category

If we knew the names of the Mayan hydrologists, we would rank them among the great names in the history of technology.

The Mayans lived in a karst landscape on the Yucatan peninsula. A karst landscape is one whose bedrock is limestone rather than sandstone, shale, or some kind of igneous or metamorphic rock. The characteristic of limestone is that, while it may hold water in streams and pools, it is always eroded by the presence or passage of water. Shale repels water; we may find oil in shale, but not water. Igneous rocks – rocks from volcanoes – are too solidly constructed to allow the entrance of water into their structure. Metamorphic rocks – rocks that result from powerful compression – are also too dense to hold water.

Sandstone, however, holds water like a sponge, and the common wells, all over the world, reach into sandstone so that the water seeps from the sandstone into our pumping apparatus. No such well can be arranged in limestone. If there were to be a sandstone composed of shelly crumbs, and if water were introduced into such an environment, it would either erode the sand and carry it away in a white stream, or it would clog the crumbs with lime, and quickly close up their pores.


In that respect, limestone is like shale and the other unsandy rocks: water mostly sits on it or goes over or around it; it does not go through. However, a kind of well can be built through limestone, whereby an underground stream flowing through an eroded limestone cavern may be accessed and its water gathered for our use. alternatively, an underground lake can be accessed if you know where it is and can find a way to drill down to it.

Even so, a lake is not an infinite source of water. Every lake, above ground or below, depends on a constant water supply. Above or below, lakes are replenished by streams, which are themselves ultimately replenished by rain or snow. Stop the rain, stop the snow or stop its melting, and the lake has only a short life. The smallest lakes, ponds, fed by seasonal streams, are only seasonal for this very reason.

Now, the Yucatan has underground lakes which are called cenotes (three syllables: se-note-es) and they treated as reservoirs for use during the dry season. So much is simple enough. If you can find the lake and find a way to open a passage to it, and if you can keep the passage clean and protected, then you can use it. In the Yucatan, such discoveries were the original condition of settlement.

But it was the further genius of the Mayans – and originally, we may be sure, of a particular Mayan hydrologist – that they not only found these underground waters but they followed up by building more. In areas that lacked cenotes, they built enormous underground, stone-lined cisterns called chultuns and figured out how to replenish them with carefully collected surface waters. A chultun could hold enough water to carry an average of 25 people through the dry season. It was filled by directing water from surface spaces that look like plazas or roads of some kind, but these plazas dip just slightly, just enough to direct the seasonal rains into the chultuns. These collection spaces were kept meticulously clean; there is no trash in them, and no waste of any kind is allowed in the area. You know, when we have an archeological dig, we discover where cooking was done and where waste was collected and where things that fell were simply left where they fell. The collection spaces for the cenotes may have been used for play during the dry season, but they were not used for any purpose that left trash.

We do not know the name of the man who designed the first chultun, but this sort of thing does not spontaneously “evolve.” Somebody has to think through the entire design, the entire task of waterproofing, and the whole task of directing clean water into an access that is protected from animals, dirt, and enemies. After all that, everybody has to cooperate with the construction and maintenance of the whole system. For people who lived by the collection of seasonal rains, this was their life.

I am sure that the process was taken in steps – early chultuns were doubtless smaller, and perhaps there was a period in which existing cenotes were strengthened. In that sense, the chultun would have been the work of several inventive minds over a period of time. But I want to emphasize that an integrated vision of this sort is the work of a clear mind focused on a definite problem.

We do not know the name behind that mind – the Mayan writings do not tell us that much. We have names of kings and their children, but, at least so far, we do not have the names of the hydrologists. Still, they lived, and they had names, and at some period, long ago, those names were celebrated.


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In discussing Roger Bacon, I casually mentioned that he was the contemporary of Robert Grosseteste, as if that were a name everyone should recognize. Maybe it is, but in case you don’t, here’s the scoop.

Grosseteste lived from 1175 to 1253, entirely overlapping the life of St. Francis, whose Friars he taught at Oxford; remember, Roger Bacon was a Franciscan; he may or may not have actually met Grosseteste. He was also Bishop of Lincoln for the last 20 years of his life.

What else?

Well, it is interesting to note and he wrote an allegory about redemption called the Castle of Love. In his story, a king has four daughters, mercy, justice, truth, and peace, and they argue about the rightful fate of a guilty vassal. It’s an interesting approach to the doctrine of the atonement, and the fact that he wrote it is a measure of his desire to preach the gospel persuasively.

He was a good bishop.

He was a good statesman, which was part of the job of being a bishop in those days.

He was also an important philosopher, one who influenced Roger Bacon. Between 1230 and 1235, he wrote commentaries on Aristotle for his students, and one important aspect of this is that he certainly understood the dual path of scientific reasoning:

  1. One generalizes from observations and comes to a conclusion about universal principles.
  2. From that universal conclusion, one lays out what to expect in terms of observation and then checks whether new observations further affirm the universal principle or require its correction.

In other words, science requires both inductive reasoning, which goes from many observations to a single principle, and deductive reasoning, which goes from an abstract principle to the interpretation of many individual facts. He called inductive reasoning “resolution” since it brings many things into focus; he called deductive reasoning “composition” because it suggests how to place other physical events under the umbrella of a principle. Science consists of resolution and composition.

Seems obvious, but lesser men emphasize one path at the expense of the other. His ideas formed a tradition of placing science firmly in the realm of observation and experimental verification, and Galileo specifically built upon that tradition almost 400 years later.

Geometry and Optics

It is really impossible to think of studying optics without a knowledge of geometry. What is reflection if not geometry? Light strikes a flat surface, and the angle at which it falls is the same as the angle at which it bounces away: “the angle of incidence is equal to the angle of reflection.” Grosseteste wrote about optics and about the importance of math for good science.

He also wrote thoughtfully about the rainbow, although I don’t know exactly what he said because what I found about this quickly turned to a discussion of Roger Bacon’s development of his ideas. Nevertheless, he does seem to have understood the exciting possibilities opened up by an understanding of the principles of light:

“This part of optics, when well understood, shows us how we may make things a very long distance off appear as if placed very close, and large near things appear very small, and how we may make small things placed at a distance appear any size we want, so that it may be possible for us to read the smallest letters at incredible distances, or to count sand, or seed, or any sort of minute objects.”

In other words, he envisioned the twin invention of the telescope and microscope, still 350 years in the future.

When you notice how others have a habit of portraying the progress of scientific thought as a mental jump from the Greeks of 300 BC to the Renaissance of 1500 AD, think of Grosseteste. The medieval thinkers brought Greek thought into the Christian intellectual world, reflected on it, gave it a proper home, and developed it. They disagreed with Aristotle on some issues, but they thought about his ideas.

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