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The city of Miletus, situated on the coast of a Greek settlement of the landscape of Ionia (Asia Minor), gained economic importance in the 6th century B.C. through extensive trade relations. A social class developed for which "just about everything was available for comfort and a higher standard of living".The cultural milieu was marked by Orphic or Dionysian cults, stories of Homer and epics of Hesiod (born before -700); influences from Mesopotamia and Egypt, Phoenicians and Chaldeans must have been noticeable as well. But time and leisure also brought with them the attempt "to escape ignorance without expecting any benefit beyond knowledge" (Aristotle, after (Schupp, 2003a, p. 43)). Philosophy can be born in such an atmosphere.ThalesThales lived in this town from about -625 to -547. At first he was a merchant and must have been around a lot in the world at that time. He is said to have brought geometrical and astronomical knowledge from Egypt. In his later years he also interfered in politics. But we only know of all this from later sources, whose credibility is not always given.What is certain, however, is that he must have lived around 585 BC. He had predicted an eclipse of the sun, which according to modern astronomical calculations took place just in 585 BC. Babylonian astronomers already knew the cycles with which solar and lunar eclipses were repeated. Sun eclipses are not visible from every place equally well; but one knew thus when one could count on such at all. Thales had probably benefited from this knowledge, either through his earlier travels or through more recent cultural contacts. But he was also someone himself who studied the stars. Diogenes Laertius knew that Thales was said to have written two writings about solstices and equinoxes. Because of his knowledge he was also admired by later philosophers (Laertius, 2015, p. 13).Many of us can surely remember that in school they learned the SATZ OF THALES in mathematics lessons. We do not know whether Thales himself discovered this sentence. Diogenes Laertius writes only 800 years later: "In geometry, a pupil of the Egyptians, he first entered the right-angled triangle into the semicircle, as Pamphile reports. (Laertius, 2015, p. 13). There it is also mentioned that Thales in Egypt should have measured the height of the pyramids, "giving their shadow, which he measured exactly at the time when our shadow and our body have the same length" (Laertius, 2015, p. 13). (Laertius, 2015, p. 15). Thales must have been highly intelligent in any case and he knew how to use his new knowledge independently.The philosophers regard Thales of Miletus as the first of their guild. We do not know how Thales came to such thoughts, which today are called philosophical thoughts. The processes "emergence and decay" were in the foreground in the mythical narratives and on his travels Thales will not only have taken up geometrical and astronomical knowledge, but also become acquainted with the most diverse of such narratives. Since one constantly observes changes in nature, including emergence and decay, the question may arise as to whether there must not be something lasting and eternal "behind" all this. This must then be something causal and "underlying", something like a "primordial principle" or a "primordial substance", that is, something that could also be called "the One".Aristotle later wrote about the ideas Thales had developed for this:"Thales, the first representative of this direction of philosophical investigation, describes water as such a principle. He therefore taught that the land, too, rests on water. The reason for this view was probably the observation that the food of all beings is moist, that the heat itself arises from it and lives from it. But what everything becomes of, that is the principle of everything. If this was one of the reasons for his opinion, then another was probably the fact that the seeds of all beings are of moist nature, but that water constitutes the principle for the nature of wetness.It was not far-fetched that water should be the primordial cause of all things, for the Sumerians and Egyptians also spoke of an "primordial sea", and in Homer's case the inhabited world was surrounded by the Okeanos, a mighty river, which was also considered the father of the gods and the origin of the world.It is important, however, that Thales argues this way here and elsewhere: Water causes moisture, food needs water, otherwise it dries up and becomes inedible. Water can form fog and clouds, and in the last instance even air (water vapour) and fire were formed from it. Sedimentation on the coast shows how land can be removed from the water.AnaximanderThales brought a whole new way of thinking into the world. Anaximander (ca. -610 to -546), who also lived in Miletus and is regarded by many as a pupil of Thales, took up this way of thinking, but immediately showed that one can come to a different conclusion in it. For him, water was perhaps too concrete as primordial matter, and he concentrated more on one particular aspect: the One which should be a primordial reason had to be unlimited, an apeiron (from Greek ἀπέραντος=aperantos, unlimited, infinite). The Greeks had the same word for "unlimited" and "infinite", but could not yet imagine a curved space. Today we know spaces of different dimensions; a vivid example for an unlimited, but not infinite space is the surface of a sphere, a two-dimensional curved space.This is where the term "infinity" came into play, a term which subsequently occupied almost all philosophers and mathematicians and which was only learned to be dealt with consistently and formally at the end of the 19th century within the framework of the Cantor set theory. According to Anaximander, what people do not know  nor what they can imagine, should apply to the Apeiron: "The Apeiron is without age" and the "Apeiron is without death and decay" (according to Schupp, 2003a, p. 53).These were qualities that were granted only to the gods. The One was thus placed on the same level with the gods. Thus Anaximander came suspiciously close to the world of myth, but he answered the question of how the One would create multiplicity, more like a physicist: He spoke of opposing elemental forces, dry hot fire and humid cold steam, that could lie in battle with each other.In this way he had an idea of what the sun, moon and stars were made of, and even knew how to explain how solar or lunar eclipses occur. According to him, the earth was at the centre of the circles on which the celestial bodies were moving, and it was in perfect equilibrium with all the stars.  In the shape of a cylinder it was similar to a "stone column segment". Humans lived on the top of the cylinder; according to the geographer Agathemeros, Anaximander even "dared to be the first to draw the map of the inhabited world" (Mansfeld &#38; Primavesi, 2011, pp. 65, No.2). The distances of the celestial bodies from the earth were in certain proportions to each other. Thus, Hyppolyt of Rome reports in the 3rd century that according to Anaximander the circle of the moon and the sun is 19 and 27 times the diameter of the earth cylinder, respectively (Mansfeld &#38; Primavesi, 2011, pp. 75, No.20).Even a weakening of the struggle between the hot and the humid a passing of the "existing" as well as a new creation from the Apeiron was planned. For Anaximander the Apeiron is therefore not only infinite; it can also create infinite many worlds and let them pass away again. One inevitably thinks of the quantum vacuum in Stephen Hawking's M-theory and of the constant emergence of new universes from it through quantum fluctuations.For the interaction between the opposing pairs he had an answer, which again fits more to the myth and the heaven of gods: "From which things the things in existence have their origin, in these also their decay takes place, as it must be, because they do each other justice and punishment for the injustice, according to the temporal order" (Mansfeld &#38; Primavesi, 2011, pp. 71,Nr.15).The whole picture already contains astonishingly many modern aspects such as the description of spatial relations in quantitative form and the concept of infinity.AnaximenesAt Anaximenes (approx. -586 to -527) the primary substance is now something you know from everyday life: the air. Instead of an abstract, it is now something concrete again. From the Doxographen Aёtios from the 1. century we experience: "Anaximenes set as principle of the being things the air, because from this everything develops and into this everything dissolves again. Just as our soul, which is air, holds us together through its power, so also the whole cosmos includes "breath and air". (Mansfeld &#38; Primavesi, 2011, pp. 87,Nr.3).Anaximenes presumably took the air as the primary substance because he observed opposite properties in the air; it could be warm or cold, compressed or diluted. From the observation of a breath he believed he could deduce a relationship between these pairs of opposites: "For when the breath is compressed and solidified by the lips, it becomes cold, while when the mouth is open it escapes, it becomes warm through dilution". (Mansfeld &#38; Primavesi, 2011, pp. 89, No.5).So he saw compression or dilution as the basic principle for the difference in things: Clouds consist of weakly compressed air, rain of more compressed air and ice like earth of even more compressed air. The solidification of matter generally has its origin in the cold air, the thinness and looseness in the warm air. Wind was moving air. The primordial matter was now something that could also produce multiplicity. Thus, he had an idea of how the One could become the Many. The air was a primordial substance which, as a breath of life, absorbed all living beings into the unity of all things.So here we find the connection between breath and life, a thought that one encounters again and again in the intellectual history - e.g. also in the idea of Christianity that the Holy Spirit originated from the Father and Son through breathing (see Wikipedia: Hauchung).In this earliest school of the pre-Socratics, the Ionian school or the school of Miletus, the concept of "being" or "One" as a primordial substance or principle is in focus. In later schools also the "existing"  or the "Many" will become more strongly in the view and the question about which possibilities of the knowledge we can have about the being like the existing.Paradigm shiftWith the Ionic School, a world view was created that was derived from observations of nature and not from stories about interventions from a "supernatural". This was a big step for mankind. But it was only a first step in a new direction. Of course, there were no clear answers. The reasons for such statements as "Everything is water" or "Everything is air" were only more or less plausible, necessarily not at all. Later Empedocles (-490 to -430) should still claim that "everything is fire" applies. Generally one spoke of the four basic elements water, air, earth and fire.It was to take more than 2,000 years before a second step was taken in natural science, from which followed what we now call modern physics. Two new thoughts had to emerge:First: One does not immediately try to understand the world as a whole, but one has to "begin it in the small", thus with a simple and most clear phenomenon.Secondly, one should try to understand the phenomenon not only qualitatively, but also quantitatively, so that an as exact as possible examination of the reasoning becomes possible. This requires sufficiently developed mathematics.Galileo Galilei was the one to whom these thoughts came in the early 17th century and who was fully aware that he had founded a "new science" with a demonstration of the fertility of such thoughts. If one loves the term "paradigm shift", which was so unnecessarily strained by Thomas Kuhn (Kuhn, 1973), then one can say that Galileo caused a paradigm shift. It would be the second - after the first paradigm shift by Thales and the Ionian school. Perhaps today we are experiencing a third paradigm shift in artificial intelligence with data-driven machine learning.I will come back to all this in later blog posts. First of all, we must follow the path that has created all the conditions for this second and perhaps third paradigm shift. This includes, in particular, mathematics in which one learns quantitative and truth-preserving reasoning. Pythagoras (ca. -570 to after -510) is at the beginning of such a mathematics. In the next two blog posts we have to deal with him and his students.