“One cannot step twice in the same river.”

1. QOTD “One cannot step twice in the same river.” Heraclitus (ca. 540 – ca. 480 BCE) • Defend/rebuke and explain your rationale. • 75+ words. • Select Team member to orally present.

2. Heraclitus (ca. 540 – ca. 480 BCE)

3. Heraclitus (ca. 540 – ca. 480 BCE) Heraclitus lived in Ephesus, an important city on the Ionian coast of Asia Minor, not far from Miletus, the birthplace of philosophy. Little is known, except from his writings.

4. Heraclitus (ca. 540 – ca. 480 BCE) Heraclitus criticizes his predecessors and contemporaries for their failure to see the unity in experience. Opposites are necessary for life, but they are unified in a system of balanced exchanges. The world itself consists of a law-like interchange of elements, symbolized by fire.

5. Heraclitus (ca. 540 – ca. 480 BCE) Thus, the world is not to be identified with any particular substance, but rather with an ongoing process governed by a law of change. The underlying law of nature also manifests itself as a moral law for human beings. Heraclitus first Western philosopher to go beyond physical theory in search of metaphysical foundations and moral applications.

6. Heraclitus (ca. 540 – ca. 480 BCE) His message: >reality is constantly changing >reality an ongoing process rather than a fixed and stable product. Buddhism shares a similar metaphysical view: >annica -- the claim that all reality is fleeting and impermanent.

7. Heraclitus (ca. 540 – ca. 480 BCE) >In modern times Henri Bergson (1859 – 1941) described time as a process that is experienced. >An hour waiting in line is different from an hour at play. >Today contemporary physics lends credence to process with the realization that even apparently stable objects, like marble statues, are actually moving, buzzing bunches of electrons and other subatomic particles.

8. QOTD Pythagoras “It is only necessary to make war with five things; with the maladies of the body, the ignorances of the mind, with the passions of the body, with the seditions of the city and the discords of families.” • Defend/rebuke and explain your rationale. • 75+ words. • Select Team member to orally present.

9. Pythagoras • Pythagoras, (b. 580B.C.-507B.C.) • ”all things are numerable & can be counted.” • e.g. in geometry, angles are measured by the number of degrees • Number is a very vital aspect of the universe & is fundamental in it. • Symmetry

10. PYTHAGORAS 580 B.C.E. - 507 B.C.E.

11. PYTHAGORAS 580 B.C.E. -507 B.C.E. Samos Thales & Anaximander Egypt Beliefs: (1) that at its deepest level, reality is mathematical in nature,(2) that philosophy can be used for spiritual purification,(3) that the soul can rise to union with the divine,(4) that certain symbols have a mystical significance, and(5) that all brothers of the order should observe strict loyalty and secrecy.

13. Philosophy: …the dependence of the dynamics of world structure on the interaction of contraries, or pairs of opposites; …the viewing of the soul as a self-moving number experiencing a form of metempsychosis, or successive reincarnation in different species until its eventual purification (particularly through the intellectual life of the ethically rigorous Pythagoreans); …understanding ...that all existing objects were fundamentally composed of form and not of material substance. Further Pythagorean doctrine ... identified the brain as the locus of the soul; and prescribed certain secret cultic practices.

14. Pythagorean Theories • (i) The sum of the angles of a triangle is equal to two right angles. Also the Pythagoreans knew the generalization which states that a polygon with n sides has sum of interior angles 2n - 4 right angles and sum of exterior angles equal to four right angles. • (ii) The theorem of Pythagoras - for a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. We should note here that to Pythagoras the square on the hypotenuse would certainly not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the side. To say that the sum of two squares is equal to a third square meant that the two squares could be cut up and reassembled to form a square identical to the third square. • (iii) Constructing figures of a given area and geometrical algebra. For example they solved equations such as a (a - x) = x2 by geometrical means.

15. Pythagorean Theories • (iv) The discovery of irrationals. This is certainly attributed to the Pythagoreans but it does seem unlikely to have been due to Pythagoras himself. This went against Pythagoras's philosophy the all things are numbers, since by a number he meant the ratio of two whole numbers. However, because of his belief that all things are numbers it would be a natural task to try to prove that the hypotenuse of an isosceles right angled triangle had a length corresponding to a number. • (v) The five regular solids. It is thought that Pythagoras himself knew how to construct the first three but it is unlikely that he would have known how to construct the other two. • (vi) In astronomy Pythagoras taught that the Earth was a sphere at the centre of the Universe. He also recognized that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realize that Venus as an evening star was the same planet as Venus as a morning star.