As pointed out in the previous blog entry, there are, in fact, no axiomatic proofs in Greek math. But there is a widespread and sticky belief to that effect.
Why is this false belief about axiomatic proofs among Greeks so widespread and sticky? In fact, Western/church education spread the false myth.
Cambridge foolishness
Thus, on (1) that false myth of axiomatic proofs among Greeks, linked to (2) the false myth about the person Euclid and his intentions, (3) the order of theorems in the Elements was regarded as very important, and the key contribution made by “Euclid”.
This third myth was so important that the Cambridge Board of Studies foolishly laid down in its exam rules in the 1880’s that students must follow that order. This Cambridge foolishness is extraordinary because the Cambridge syndics commissioned a new text, which liberally uses empirical proofs, including, of course, the empirical proof of SAS (Side angle Side or proposition 4). Order is unimportant once an empirical proof is used: for instance the Indian proof of the “Pythagorean theorem” in the युक्तिभाषा proves the theorem in one simple step, without needing 46 earlier propositions.
The Cambridge foolishness in insisting on the order of the propositions, while using a text which gives empirical proofs tells us how the education system propagates Greediotic myths for centuries, and teaches students to ignore facts.
Church hegemony over the Western mind
Even Bertrand Russell, as a product of Cambridge, continued to believe in the “Euclid” myth of axiomatic proofs, though he realized the myth did not fit the actual book. He foolishly declared it to be Euclid’s error and not the error of the false myth of Euclid and his intentions!
That is the effect of the church control over the Western education system, and consequent hegemony over the Western mind, including the minds of those opposed to the church. This church “education” from Cambridge widely spreads myths and superstitions, which were then globalised by colonial education. It created “Greediots, Greediots everywhere and not a stop to think”.
A politically convenient reinterpretation
As Proclus explains (and the reason why he wrote his Commentary on the Elements), the Elements is a “pagan” religious text, i.e. a text on Egyptian mystery geometry which is meant to arouse the soul, exactly as Plato argued in Meno. The book Elements was never intended to be about axiomatic proofs. How did “Euclid” fit church needs to a T?
The church simply re-interpreted the book to suit its politics of reason. The church was well aware that most people are gullible, because of childhood indoctrination. And such was the fear of the church (not only the Inquisition, but even in England), that the church as well aware that no one would dare to challenge its interpretation. The facts is the no one did so for centuries.
During this time the church used the Elements to teach reasoning to its priests: a special kind of metaphysical reasoning, which suited the church, since its divorced from facts, and involving faith based or axiomatic proofs.
The church monopoly on education, through the “reputed” institutions it set up and controlled, such as Oxford and Cambridge, resulted in spreading this superstition widely among Westerners.
So widely, that when the myth of axiomatic proofs in “Euclid” ultimately collapsed (among the knowledgeable), people like Russell and Hilbert created formal mathematics to save it.
The Pythagorean calculation
Curiously, Greediots and Western historians, intent on glorifying themselves, never ever speak of the “Pythagorean CALCULATION”, though a formal proof of the “Pythagorean proposition” has no practical value, and all practical value derives from the ability to use it to CALCULATE the diagonal of a rectangle whose sides are known.
Western historians are silent about the process of calculation among Greeks. Why? Because, as stated in the Manava sulba sutra 10.10, that calculation requires square roots and Greeks and Romans did not have fractions or square roots or any part of the mathematical apparatus needed to carry out that calculations as Egyptians (Ahmes papyrus), Iraqis, and Indians did. See this article in Journal of Black Studies or its manuscript version. Many non-Greeks had the “Pythagorean” calculation which was SUPERIOR since it offers practical value than the mere “Pythagorean” theorem, and its sham epistemic value.
This dishonesty of Western historians (in not comparing the calculation and the theorem) is not accidental: false history is a deep seated part of Western culture. Western culture has obvious church roots, and the church discovered long ago that lies are a terrific source of power, and can be used to rule over gullible people even without weapons. Since then, the West has been systematically writing false history in the manner of Orosius’, History Against the Pagans, with the calculated intent to glorify itself and portray all others as inferior.
It has propagated these lies through the Western education system over which it had a monopoly for centuries.
Globalisation due to colonialism
The problem is that colonialism globalised this church education system, and our children are its victims, suffering its evil consequences until today.
For example, our class X school text in math uses the term “Pythagorean theorem” 32 times to hammer the lie home in the minds of children. A thousand lies are not needed to make a truth, 32 times is quite enough.
Naturally, children start believing it to be true, and they disbelieve other ways to understand the proposition. No room is provided to students or anyone else to disagree or challenge the school text or even ask for evidence: if you do, all that NCERT does is to say that this is the way it is done in Western texts. So, we the colonised must slavishly imitate it. That is the purpose of colonial/church education: to teach slavish imitation.
To repeat, teaching the Greediotic history of the “Pythagorean theorem” is like teaching the literal belief in virgin birth: no evidence for it, it is contrary to known evidence and contrary to common sense. Yet millions of people hang on both beliefs because of childhood indoctrination through “education”.
It is high time we repaired our text books to eliminate this kind of nonsense Western history by eliminating all references to the Pythagorean theorem in them.
