The National Day of Reason and Euclid
National Day of Reason: 7th May
The 947th Resolution of the 116th Congress makes May the 7th the National Day of Reason. It states “...the application of reason has been the essential precondition for humanity’s extraordinary scientific, medical, technological, and social progress since the modern Enlightenment”. This is true, because god did not build the first car, free the first slave or think the only rational thought. It was science, and it is medicine that will see us through this Lockdown. On the 1st of May, just last week, the United States Congress voted this Day in. At long last. It’s also the National Day of Prayer.
It was Euclid who created geometry, it was Euclid who said that the eye, eye vision, was rational, it was Euclid who gave number theory. Basic. Euclid was the author of Elements and coincided with Ptolemy who reigned 323-283BCE. He died in 270BCE, probably, but we know he was born mid 4th century BCE and died mid 3rd cent BCE. Rationally. We don’t know place or circumstances, but there are references to him from Archimedes onwards, 287-212BCE. He died in Alexandria, the centre of academia. He was so intelligent, or mathematical, that some say that because of the strange lack of biographical information (for the time) about him, then he is not a historical figure, so his works were instead the work of a team of mathematicians, named after Euclid of Megara, but there is little evidence for this. He was called Euclid of Alexandria, he was a mathematician, he was the founder of geometry, and his name means “renowned, glorious”
Few references survive, so we know little about his life. A few Arabian authors mention birth town of Tyre 50m from Beirut S. today in Lebanon, but he’s thought to come, originally, from Ancient Greece. The references by Proclus and one by Pappus of Alexandria 32CE who said that Apollonius 247-222BCE “spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought.”
His main work, “Elements”, was published in late 19th or early 20th cent., gave geometric theorems from axioms, a Euclidean perspective, conic sections, spherical geometry, number theory, geometric results; perfect numbers by Mersenne primes (the Euclid-Euler theorem); the infinitude of prime numbers; Euclid’s lemma on factorisation from the fundamental theorem of arithmetic on the uniqueness of prime factorisation seems; and the Euclidean algorithm for the greatest common denominator. It had mathematical rigour. Euclid was not anachronistic or non-relational to other academics of the time, he was completely rational in his writing. Anachronistic means belonging to a period other than that being portrayed, or, belonging or appropriate to an earlier period, especially so as to seem conspicuously old-fashioned e.g. "she is rebelling against the anachronistic morality of her parents". Anachronistic means that it is from a different time period from what it says, we often say today “ancient”, but Euclid was explainable by his context.
His other works were Data, On Divisions of Figures, Catoptrics, Phaenomena, Optics all known today, but Conics, Porisms, Pseudaris, Surface Loc and several works on mechanics namely On the Heavy and the Light, On the Balance and one about a moving lever, it’s circles, containing 4 propositions, are all lost. It has been suggested that the latter three on mechanics all form one work, along with more.
Data talks about the nature and implication of “given” information in geometrical problems <- the Elements. On Divisions of Figures concerns ratios, namely the division of geometrical figures into 2 or more equal parts or into parts in given ratios and has syllogism with a 1st cent CE work by Heron of Alexandria, which survives in an Arabic translation. Catoptrics is the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors, but the allegation here among former researchers is that it is anachronistic, without cause such that JJ O’Connor and EF Robertson therefore name Theon of Alexandria as a more probable author; it is still mathematical.
Phaenomena is a treatise on spherical astronomy and has syllogism with On the Moving Sphere by Autolycus of Pitane who flourished around 370BCE, and survives in Greek. Optics describes the eye and says that vision consists of discrete rays which emanate from the eye, following Ptolemy; the 4th def “Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear less”, and there are 39 propositions, <= 38 more on vision.
The lost works are conics, which is about conic sections, Porisms, whose content is controversial, Pseudaria, an elementary text about errors in reasoning which is also called Book of Fallacies, Surface Loci about loci or quadratic surfaces, maybe, and the several works on mechanics On the Heavy and the Light with 9 definitions and 5 propositions giving Aristotlean notions of moving bodies and the concept of gravity, On the Balance, with 2 axioms and 4 propositions, and the last one about a moving lever, it’s circles, containing 4 propositions.
Proclus said Euclid was Platonic, or of the Platonic “persuasion”. He believed Euclid lived during time of Ptolemy I 367-282 BCE, being mentioned by Archimedes, because Euclid wrote before Archimedes. Proclus told a story that, when Ptolemy was asked if there was a shorter way to learn geometry than Euclid’s Elements, Ptolemy said “Euclid replied there is no royal road to learning geometry”. However, this was a common thing to say, a saying, which was around regarding Menaechmus and Alexander the Great. Peter Kingsley’s relationality arguement (Ancient Philosophy, Mystery and Magic, in which all academia was relational and the purpose of which was knowledge of life, or common(ers) understanding, makes sense, and is true. All Euclid’s work was mathematical, and he indeed is the father of reason. Not Jesus or god. Religion historically was based on physicalism, or the atom, when today it is based around irrationality, faith. I say faith is irrational, because it has been found to be, not because it begs or pleas dumbness. Christian say themselves that faith is not rationality, that it is essentially incomprehensible trust, and Richard Dawkins believes it is delusion.
This is Euclid: “If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the the whole together with the square on the straight line between the points of section is equal to the square on the half” (Euclid, Book 2, 5th Proposition, trans. TL Heath).
Book 2 of Elements was unearthed at Oxyrhynchus in Middle Egypt, by Grenfell and Hunt in 1897. It was 160km S-SW of Cairo in Minya Governorate, and it is also an archeological site, “considered one of the most important ever discovered.” The digs at Oxyrhynchus found or unearthed texts from the Ptolemaic kingdom and Roman Egypt, the plays of Menander, fragments of the Gospel of Thomas, fragments of the Elements, and there was also a few vellum manuscripts (vellum is parchment made of calfskin, called membrane as single pages, scrolls, codices or books, for writing or printing on). And more recently, there were Arabic manuscripts which are on paper as the medieval P. Oxy. VI 1006. More recent scholarship dates this 2nd book of Elements to 75-125CE. This Book 2 fragment is called the Papyrus Oxyrhynchus 29 (P. Oxy. 29).
This is reason. There are fragments. Euclid’s work became Euclidean geometry, which now from the 19th century has been overtaken by non-Euclidean geometry. Let us celebrate the Day of Reason with joy and hope, because rational processes mean healthy people. You choose, prayer or reason.
The National Day of Reason:
https://youtu.be/O36L7RN6sQA
and
https://youtu.be/i9pfJxXqOTU
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