Thales of Miletus, Part 2 of 3
Before Thales, the Greeks explained the origin and nature of the world through myths of anthropomorphic gods and heroes. Phenomena such as lightning or earthquakes were attributed to actions of the gods.
In contrast to these mythological explanations, Thales attempted to find naturalistic explanations of the world, without reference to the supernatural. He explained earthquakes by hypothesizing that the Earth floats on water, and that earthquakes occur when the Earth is rocked by waves. More specifically, a supernatural point of view presupposes the existence of passive, inanimate objects that are animated and made to do what they do by divine powers external to them. Fire, for example, is not naturally hot, but is moved to hotness by the daemon of fire.
Thales, according to Aristotle, asked what was the nature (Greek physis, Latin natura) of the object so that it would behave in its characteristic way. Physis (öýóéò) comes from phuein (öýåéí), "to grow", related to our word "be". (G)natura is the way a thing is "born", again with the stamp of what it is in itself.
Aristotle characterizes most of the philosophers "at first" (ðñ?ôïí) as thinking that the "principles in the form of matter were the only principles of all things", where "principle" is arche, "matter" is hyle ("wood") and "form" is eidos.
"Principle" translates arche, but the two words do not have precisely the same meaning. A principle of something is merely prior (related to pro-) to it either chronologically or logically. An arche (from áñ÷åéí, "to rule") dominates an object in some way. If the arche is taken to be an origin, then specific causality is implied; that is, B is supposed to be characteristically B just because it comes from A, which dominates it.
The archai that Aristotle had in mind in his well-known passage on the first Greek scientists are not necessarily chronologically prior to their objects, but are constituents of it. For example, in pluralism objects are composed of earth, air, fire and water, but those elements do not disappear with the production of the object. They remain as archai within it, as do the atoms of the atomists.
What Aristotle is really saying is that the first philosophers were trying to define the substance(s) of which all material objects are composed. As a matter of fact, that is exactly what modern scientists are trying to do in nuclear physics, which is a second reason why Thales is described as the first scientist.
Thales' most famous belief was his cosmological doctrine, which held that the world originated from water. Aristotle considered this belief roughly equivalent to the later ideas of Anaximenes, who held that everything in the world was composed of air.
The best explanation of Thales' view is the following passage from Aristotle's Metaphysics. The passage contains words from the theory of matter and form that were adopted by science with quite different meanings.
"That from which is everything that exists (?ðáíôá ô? ?íôá) and from which it first becomes (?î ï? ãßãíåôáé ðñ?ôïõ) and into which it is rendered at last (å?ò ? öèåßñåôáé ôåëåõôá?ïí), its substance remaining under it (ô?ò ì?í ï?óßáò ?ðïìåíïýóçò), but transforming in qualities (ôï?ò ä? ðÜèåóé ìåôáâáëëïýóçò), that they say is the element (óôïé÷å?ïí) and principle (?ñ÷Þí) of things that are."
And again:
"For it is necessary that there be some nature (öýóéò), either one or more than one, from which become the other things of the object being saved... Thales the founder of this type of philosophy says that it is water."
Aristotle's depiction of the change problem and the definition of substance is clear. If an object changes, is it the same or different? In either case how can there be a change from one to the other? The answer is that the substance "is saved", but acquires or loses different qualities (ðÜèç, the things you "experience").
A deeper dip into the waters of the theory of matter and form is properly reserved to other articles. The question for this article is, how far does Aristotle reflect Thales? He was probably not far off, and Thales was probably an incipient matter-and-formist.
The essentially non-philosophic Diogenes Laertius states that Thales taught as follows:
"Water constituted (?ðåóôÞóáôï, 'stood under') the principle of all things."
Heraclitus Homericus states that Thales drew his conclusion from seeing moist substance turn into air, slime and earth. It seems clear that Thales viewed the Earth as solidifying from the water on which it floated and which surrounded Ocean.
Thales applied his method to objects that changed to become other objects, such as water into earth (he thought). But what about the changing itself? Thales did address the topic, approaching it through magnets and amber, which, when electrified by rubbing, attracts also. A concern for magnetism and electrification never left science, being a major part of it today.
How was the power to move other things without the mover’s changing to be explained? Thales saw a commonality with the powers of living things to act. The magnet and the amber must be alive, and if that were so, there could be no difference between the living and the dead. When asked why he didn’t die if there was no difference, he replied “because there is no difference.”
Aristotle defined the soul as the principle of life, that which imbues the matter and makes it live, giving it the animation, or power to act. The idea did not originate with him, as the Greeks in general believed in the distinction between mind and matter, which was ultimately to lead to a distinction not only between body and soul but also between matter and energy.
If things were alive, they must have souls. This belief was no innovation, as the ordinary ancient populations of the Mediterranean did believe that natural actions were caused by divinities. Accordingly, the sources say that Thales believed all things possessed divinities. In their zeal to make him the first in everything they said he was the first to hold the belief, which even they must have known was not true.
However, Thales was looking for something more general, a universal substance of mind. That also was in the polytheism of the times. Zeus was the very personification of supreme mind, dominating all the subordinate manifestations. From Thales on, however, philosophers had a tendency to depersonify or objectify mind, as though it were the substance of animation per se and not actually a god like the other gods. The end result was a total removal of mind from substance, opening the door to a non-divine principle of action. This tradition persisted until Einstein, whose cosmology is quite a different one and does not distinguish between matter and energy.
Classical thought, however, had proceeded only a little way along that path. Instead of referring to the person, Zeus, they talked about the great mind:
"Thales", says Cicero, "assures that water is the principle of all things; and that God is that Mind which shaped and created all things from water."
The universal mind appears as a Roman belief in Virgil as well:
"In the beginning, SPIRIT within (spiritus intus) strengthens Heaven and Earth,
The watery fields, and the lucid globe of Luna, and then --
Titan stars; and mind (mens) infused through the limbs
Agitates the whole mass, and mixes itself with GREAT MATTER (magno corpore)"
Thales was known for his innovative use of geometry. His understanding was theoretical as well as practical. For example, he said:
Megiston topos: hapanta gar chorei
”Place is the greatest thing, as it contains all things”
Topos is in Newtonian-style space, since the verb, chorei, has the connotation of yielding before things, or spreading out to make room for them, which is extension. Within this extension, things have a position. Points, lines, planes and solids related by distances and angles follow from this presumption.
Some have argued that his geometry was simply a lucky happenstance resulting from empirical method worked out by the Babylonians or Egyptians and that he had no understanding of the basic principles involved. This overskeptical view neglects Thales own predilection for insight and also human nature. The mathematics of the times was not especially difficult or obscure and we have a convincing story from DL that when he had inscribed a right triangle in a circle he sacrificed an ox. According to Lonergan in his noted study called “Insight”, such behavior is a typical of insights, or sudden realizations of the truth. Better known is Archimedes’ shouting, eureka! (“I have found it!”) with reference to Archimedes’ Principle, into which he had just had an insight. Less dramatically, most of us just evidence the behavior associated with being startled.
Thales understood similar triangles and right triangles, and what is more, used that knowledge in practical ways. The story is told in DL (loc. cit.) that he measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. A right triangle with two equal legs is a 45-degree right triangle, all of which are similar. The length of the pyramid’s shadow measured from the center of the pyramid at that moment must have been equal to its height.
This story reveals that he was familiar with the Egyptian seqt, or seked, defined by Problem 57 of the Rhind papyrus as the ratio of the run to the rise of a slope, which is currently the cotangent function of trigonometry. It characterizes the angle of rise.
Our cotangents require the same units for run and rise, but the papyrus uses cubits for rise and palms for run, resulting in different (but still characteristic) numbers. Since there were 7 palms in a cubit, the seqt was 7 times the cotangent.
To use an example often quoted in modern reference works, suppose the base of a pyramid is 140 cubits and the angle of rise 5.25 seqt. The Egyptians expressed their fractions as the sum of fractions, but the decimals are sufficient for the example. What is the rise in cubits? The run is 70 cubits, 490 palms. X, the rise, is 490 divided by 5.25 or 93.33 cubits. These figures sufficed for the Egyptians and Thales. We would go on to calculate the cotangent as 70 divided by 93.33 or.75003 and looking that up in a table of cotangents find that the angle of rise is a few minutes over 53 degrees.
Whether the ability to use the seqt, which preceded Thales by about 1000 years, means that he was the first to define trigonometry is a matter of opinion. More practically Thales used the same method to measure the distances of ships at sea, said Eudemus as reported by Proclus (“in Euclidem”). According to Kirk & Raven, all you need for this feat is three straight sticks pinned at one end and knowledge of your altitude. One stick goes vertically into the ground. A second is made level. With the third you sight the ship and calculate the seqt from the height of the stick and its distance from the point of insertion to the line of sight.
The seqt is a measure of the angle. Knowledge of two angles (the seqt and a right angle) and an enclosed leg (the altitude) allows you to determine by similar triangles the second leg, which is the distance. Thales probably had his own equipment rigged and recorded his own seqts, but that is only a guess.
Thales’ Theorem is stated in another article. In addition Eudemus attributed to him the discovery that a circle is bisected by its diameter, that the base angles of an isoceles triangle are equal and that vertical angles are equal. It would be hard to imagine civilization without these theorems.
It is possible, of course, to question whether Thales really did discover these principles. On the other hand, it is not possible to answer such doubts definitively. The sources are all that we have, even though they sometimes contradict each other.
According to Diogenes Laertius, Lobon of Argos wrote that he saw a statue of Thales at Miletus with an inscription describing him as "most senior in wisdom of all the astronomers (áóôñïëïãïé)." The word, astrologoi, could mean what it does today, the divination of human affairs from the positions of the stars, but it also meant scientific astronomy, as in the case of Thales.
Thales was said to be able to predict eclipses and fix the solstices, which abilities made him a very useful man in business and politics. Whether he was the first to do these things, as the enthusiastic DL claims, is another matter.
He set the seasons of the year and divided the year into 365 days. These abilities presume that he had a - to some degree - effective theory of the path of the sun, but we don't know what it was. He estimated the size of the sun at 1/720th of its path and that of the moon at the same ratio of its smaller path. He was able to estimate the heights of the pyramids from the lengths of their shadows. He knew and taught the value of Ursa Minor to navigators, which the sources say he got from the Phoenician, but as far as they were concerned, he "discovered" it.
We know that he observed the stars, as he is related to have fallen into a ditch one night. Answering his cries for help, an old woman (in DL) wanted to know how he expected to know anything about the stars when he didn't even know what was on the Earth at his feet. Plato makes the ditch a well and questioner a witty and attractive Thracian slave girl[21], unless we presume he fell twice and elicited the same sort of comment.
In terms of modern science, Thales had as high a batting average as anyone in the ancient world. He was totally wrong about a few things. His reason for the yearly flooding of the Nile, for example, was that seasonal winds blowing upstream impeded the water.
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Thales".
Labels: Anaximenes, Aristotle, astronomy, biography, cosmology, geometry, history, metaphysics, Milesian School, Milesians, philosopher, philosophy, Pre-Socratics, Thales
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