A subjective mode of explanation/description of Nature, based on an ‘I-Thou’ intimacy with Nature; hence, a highly individual approach to phenomena concentrating on specific aspects rather than general patterns.
This approach was decisively overturned by the Pre-Socratics who developed a supposedly objective ‘I-It’ relation with Nature.
Giorgio de Santillana’s view of myth:
Many myths seem global in character, indicating that, in spite of vast geographical separation, various cultures were attempting to explain a ‘shared experience’.
This shared experience was a comprehension of large cosmic events such as the precession of the equinoxes.
The capability of ‘primitive’ cultures to comprehend such events is indicated, if Gerald Hawkins is right, by Stonehenge.
Egyptians and Babylonians:
Mathematics
The Egyptians seem to have been quite primitive in arithmetic, depending on the method of duplication both for multiplication and division. Moreover, by insisting on expressing complex fractions in unit-fraction series, they had no capability of dealing effectively with fractional computation. Geometry was perhaps more sophisticated in Egypt but was still at a crude level according to our evidence.
The Egyptians were individual-problem oriented. They made no apparent attempt to derive general cases, theorems, or proofs.
The Babylonians, because of their sexagesimal computational system (with its Place-Value Notation) as well as their simple, two-symbol numbering system, were so adept at arithmetical procedures as to be able to solve types of quadratic, quartic, etc., equations. Consequently geometry was not well developed.
The Babylonians do appear to have initiated a case-study approach to arithmetic by discussing general problems, but they did not develop a systematic approach like that of the Greeks.
Astronomy:
Egyptian astronomy was generally primitive except for a reasonably sophisticated emphasis on calendrics and subsequent attempts to reconcile solar and lunar cycles. The Egyptians developed the 365 day year as well as the 24 hour day.
Babylonian astronomy was more moon-oriented than Egyptian astronomy and was consequently more involved with eclipse cycles, etc. Through totally arithmetic means the Babylonians were able to construct tables which demonstrated a recognition of recurring, patterned variations (for example, the zig-zag function).
The Babylonians did not, however, develop any known cosmological model to systematize their observations or derived tables.
Medicine:
Both the Egyptians and Babylonians, at least in the early stages, seem to have been empirical in their approach to surgery and pharmacological lore. However, the later Babylonians (that is, Assyrians) tended to combine medicine more and more with the abstract “science” of astrology.
The Greeks:
Metaphysics–the search for ultimate Being or Reality:
From Thales onward the Greeks tended increasingly toward metaphysical and physical speculation. Metaphysically the search was for a general, eternal principle (for example, the “stuff”–physis-orthe ‘order’– logos) underlying the universe. Physically the search was for logical, causal explanations of natural phenomena within the given metaphysical framework.
Plato and Aristotle–the two most influential Greek philosophers:
Plato, in his quest for a coherent metaphysics, relied on the eternal Forms as the ultimate basis of reality. Thus, geometry was a perfect example of a real science involved with real entities (perfect, changeless circles, triangles, etc. ). In terms of our comprehension of things, the Forms are irrevocably implanted in our minds, so that we are able to recognize things by their similarity, however imperfect, to those perfect Forms. Hence, we recognize various “species” by their similarity to the universal Forms.
Aristotle, on the other hand, accepted the reality of the world as it appears here and now. For him it was only the combination of Form and Matter that gave reality (actuality) to things. Furthermore, as evidenced by his view of causality, Aristotle, unlike Plato, accepted the notion of process or change as a genuine feature of Nature. Our knowledge of forms is not prior (implanted) but comes from inductive abstraction of similarities from similar classes of things.
Astronomy–tendency toward conceptual models:
Problems encountered and described/explained:
Daily (diurnal) motion.
Periodic planetary, lunar, and solar motions in opposite direction to daily motion.
Retrograde motion.
Apparent changes in velocity.
Other, more subtle irregularities and long-term periodicities in various orbital motions.
Basic assumptions behind Greek astronomy:
Geocentricity (geocentric and geostatic):
Assumed basically because Greek physics, with no notion of inertia, could hardly deal effectively within the framework of a moving-earth system.
The notion of perfect circular motion, or compound circular motion, around a central point.
The Cosmos is finite.
Eudoxean system–further refined and modified by Aristotle:
System of nested, concentric spheres rotating in such a way as to account, through compounded motions, for gross orbital appearances.
One fatal flaw in this concentric sphere system was its inability to account for obvious variations in distance between Earth and various planets (indicated by increasing and decreasing apparent size and brightness).
Ptolemaic system–based on Hipparchus:
System of Deferents, Epicycles, and Equants, all in varying sizes and velocities depending on the complexity and irregularity of various planetary orbits (for example, the sun’s orbit was simple whereas Mercury’s was quite complex, calling for added circular motions to account for the high irregularity).
The Ptolemaic system was mathematically more accurate and was thus ultimately more acceptable to astronomers than the Eudoxean/Aristotelian model. Nonetheless, Aristotle’s system prevailed up to the 17th century for the common understanding of the cosmos.
Aristotelian Physics:
Basic Notions:
Natural Place, Natural Motion, and Violent Motion.
Four Elements: Earth, Water, Air, Fire (and the Fifth Essence: Aether).
Change, Motion, and Growth are all aspects of the same thing–that is, the actualization of the potential or, in terms of the four causes, the attaining of something to its Final Cause by the proper meshing of the Formal and Material Causes (Form + Matter) through the agency of the necessary Efficient Cause.
In terms of actual motion Aristotle believed the velocity of any object in motion was contingent on the force of propulsion as well as the resistance of the medium traversed. Thus: V = F/R
From this it is obvious that velocity in a void (where R = 0) would be infinite. Hence, the existence of void is impossible.
The ‘equation’ is not universal because it does not hold in cases where R exceeds F.
Moreover, in violent (projectile) motion it is necessary that there be a continually active propulsive force (Efficient Cause) to counteract the constant tendency of the body to seek its natural place.
Mathematics:
The Pythagoreans, steeped in number mysticism, were metaphysically rooted in number atomism.
However, the discovery of the irrationality of 2 (what G. de Santillana calls “the crisis of the irrational”) forced the Greeks to abandon the Pythagoreans’ arithmetical analysis of nature in favor of geometry.
This was aided by the development of a critical attitude toward logic fostered by the Eleatics and carried forward by Aristotle.
Thus, mathematics became a matter of developing a logical, axiomatic system of universal geometrical proofs or theorems. This was carried even into what we would consider purely arithmetical realms such as the study of ratios (fractions).
Development of methodologies:
Analysis and Synthesis
Method of Exhaustion
Hence, Euclid’s Elements, as a textbook treatment of geometry, was merely a logical compilation of theorems, many of which were developed and proven by earlier mathematicians such as Eudoxus.
In short, geometry became paramount in Greek thinking, governing not only mathematical thought but astronomical modelbuilding that emerged with Eudoxus, Aristotle, and Ptolemy in particular.
Medicine:
Hippocratic Corpus (ca. 400 B.C.): tendency toward:
Theory of the four Humors; disease was considered an imbalance in distribution–notion of disharmony as root of illness.
Clinical diagnosis and prognosis.
Dogmatists–Alexandria (Hellenistic period):
‘A reasoned theory of medicine’–overriding theoretical principles to explain diseases and facilitate cures.
Empiricists–Alexandria (Hellenistic period):
More ‘clinically’ oriented than the Dogmatists.
Galen–tended toward Dogmatism in medical explanation.
Comparative anatomy through animal dissections.
Physiology of three Spirits (pneuma) carried by the ebb and flow of venoarterial system.
Biology:
Aristotle–founded Lyceum in Athens ca. 335 B.C.
The Lyceum, for 2 generations after Aristotle, became an important center of biological (as well as physical) investigations until its transfer to the Museum of Alexandria.
Emphasis on observation–actual dissection and controlled ‘experimental’ investigations.
Taxonomy–attempts at classifications according to ‘species’ and ‘genus’ determined by certain ‘class’ characteristics (like ‘red-blooded’ and ‘non-red-blooded’).
Notion of Life as a ‘great chain of being’ graduating from less to the more ‘vital’ (for example, Plants–Animals).
Theophrastus (student of Aristotle)–Continuation of Lyceum and its investigatory goals, especially in Botany.