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Thread: 3,700-year-old Babylonian tablet rewrites the history of maths - and shows the Greeks did not develop trigonometry727 days old

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    Quote Originally Posted by ageladakos View Post
    Invented =/= developed

    Journalist AntHellinism detected.
    Righty-o dear chap. I hope my reply did yours justice in a more verbose manner.

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    Quote Originally Posted by ageladakos View Post
    Invented =/= developed
    Yeah, that's what the ancient Greeks did: they developed Mesopotamian mathematics, and improved upon it.

    Quote Originally Posted by ageladakos View Post
    Journalist AntHellinism detected.
    Not really. Find any Greek clay tablets older than 1,700 BC containing trigonometry or any other form of advanced mathematics, and then you might have a case of anti-Hellenic bias in the media. Even then, it would be pretty hard to accuse the media of an anti-Greek bias, because they're just reporting accurately here, that trigonometry -- and accurate trigonometry at that -- was known in Mesopotamia long before it was in ancient Greece.

    Quote Originally Posted by Pendragon1 View Post
    This isn't really that much of news , per se, everyone who is educated knows the Greeks got some of their ideas of mathematics from Egypt and Babylonia etc..
    No actually, the Greeks got most of their ideas from Mesopotamia. Really most. Also Egyptian influence was very limited, in Greece and elsewhere; even Michael H. Hart has argued very seriously how Egyptian civilization had little to no influence on the ancient and modern world. It's also known that a lot of those Greek philosophers used to travel to Mesopotamia and study.

    That's not to say of course, that the ancient Greeks didn't further develop mathematics and other stuff, but the 'complete package' so to say, they got it from Mesopotamia, then they added on to it and further improved it. For example the Olympic games, was originally a Sumerian religious thing, but the Greeks took it and made it into a yearly sports festival. And it goes on like that.

    Quote Originally Posted by Pendragon1 View Post
    this article completely misses the point of the Greeks' true contribution to mathematics. That the Greeks may not have 'invented' trigonometry completely misses the point.
    Not really. All science is built on the shoulders of giants. Greeks taking an already developed branch of mathematics and adding to it, is obviously not as impressive as Greeks inventing that branch of mathematics from scratch.

    Quote Originally Posted by Pendragon1 View Post
    I quote from "Mathematics for the Non-Mathematician" by Morris Klein :
    Most of the mathematics that existed in ancient Greece, was already known in ancient Mesopotamia. Also, keep in mind that a lot of Mesopotamian clay tablets have been destroyed or not even found. It's fully possible we'll see more discoveries of Mesopotamian clay tablets in the future, that show for example, how the ancient Mesopotamians knew more mathematics than we think they did.

    Quote Originally Posted by Pendragon1 View Post
    The main fault of Egyptian and Babylonian Mathematics was that is was too practical in an empirical trial and error fashion. So , the Greeks made a quantum leap over them in thinking and in mathematical methods.
    The only thing Egyptians used their mathematics for, was to build pyramids and other temples that glorified their rulers.

    Anyway, Mesopotamian civilization basically ended in 539 BC (as in the independence of Mesopotamian civilization); had it gone on uninterrupted until the Roman era, I'm sure all the mathematics stuff the Greeks perfected, would have been done by Mesopotamians. The Persians for a very long time employed Assyrian and Babylonian architects; this is why for example, Assyrian lamassu sculptures are found as far east as in Persepolis

    Quote Originally Posted by Pendragon1 View Post
    I should point out that Mathematicians still use the basics of Euclid's methods in his "Elements" in that they prove theorems from basic axioms even though only a dozen or so of Euclid's specific propositions, from "Elements", not basic method, are used in higher mathematics today as foundations that is because mathematics liquidates clumsier tools, that came before, as it gathers what is still relevant as a base.
    What makes you think Euclid didn't get his ideas from Mesopotamia?
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    Quote Originally Posted by EliasAlucard
    What makes you think Euclid didn't get his ideas from Mesopotamia?
    What differentiates Euclid's work from his predecessors in Mesopotamia is that he insisted on proof and gave proofs of his propositions starting from a few basic axioms. Also, it was highly abstracted e.g. imagining a perfect line instead of say a real line in the sand used to help build a pyramid or an ideal square instead of a set square used by Temple Architects in Mesopotamia . Mathematicians use the Greek Euclidian method to solve theorems, more or less, to prove theorems from a few basic axioms. Mathematicians today don't use practical empirical methods from Egypt and Mesopotamia . In fact most Mathematicians have a Platonic (or the philosophy of the Greek Plato) in that they believe they discover mathematics as they go along etc.. etc.. they don't rely on a philosophical outlook or methodical approach from Egypt and Babylonia.

    I'll give an Egyptian example. The priestly caste of the Egyptians on a Rhind papyrus, recorded from a scribe, had a formula for calculating the area of a circle in terms of its diameter. They had pi calculated to an error of less one percent correct to about five decimal places. What is noteworthy about this is not whether we regard this error as large or small but rather the scribe or teacher feels no compunction about handing out a rule without the slightest indication of how anyone discovered it or why anyone should take it on trust. It was same with the priestly caste of Iraq or Babylonia. So what distinquishes the Egytpians and Babylonians from the Greeks and Euclid is that they show no recognition of the need to formulate reasons for believing in the rules they used. Euclid's "Elements" was a quantum leap , in thinking, from this previous stance. The veneration of the Greeks by their successors is indeed to the fact they were the first to insist explicitly on the need for proof. Mathematicians until this very day prove theorems -- that is what they do besides teach mathematics as a professor their main function is to prove theorems not just formulate them and force them upon you as something you should just take on trust or authority like the Babylonians and Egyptians. Also, like I said most modern Mathematicians are also platonic or have the philosophy of Plato in their outlook on Mathematics.
    Last edited by Pendragon1; 2017-08-25 at 21:57.

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    *bump* I edited my above post a bunch of times to correct errors and make more sense i.e. be more lucid.

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    Quote Originally Posted by Pendragon1 View Post
    What differentiates Euclid's work from his predecessors in Mesopotamia is that he insisted on proof and gave proofs of his propositions starting from a few basic axioms.
    That's cool.

    By the way, perhaps you missed it in post #9, so I'll quote it again:

    “Mesopotamian mathematics knew the concept of zero and pi, reciprocals, powers, square and cubic roots, logarithms, numerical series, plane geometry, polynomial equations and the triangle of “Pythagoras” already a thousand years before they were transmitted to the Greeks by Pythagoras and Euclides.” ― Simo Parpola

    ^^ We can now add trigonometry to that list. And also algebra for that matter (not sure how Parpola forgot algebra). No one is denying that the Greeks improved upon and 'perfected' Mesopotamian mathematics, but the point is, the basics for Greek mathematics, most of it was already present in ancient Mesopotamia.

    Also, keep in mind that there was no real schooling or education in ancient Mesopotamia. Mainstream people were both illiterate and innumerate, and it was mainly the Mesopotamian elites (basically the priestly caste, royal scribes and such) who were literate and spent time on mathematics and stuff like that. In fact, one of the few or maybe only Mesopotamian king who was literate, was Ashurbanipal (who was one of the last Assyrian kings). This was of course also true for contemporary Greeks, so that's why Greeks from take say, 900 BC or the Homeric age, weren't developing advanced mathematics. The rise of the ancient Greeks on the other hand, came during classical antiquity (and that was mainly from 500 BC to 200 BC). This is the period that saw all those Greek mathematicians, philosophers and so on, which of course was owed to an expansion of education in Greece. Obviously education wasn't as mandatory and universal as it is today in Western countries, but the ancient Greeks enrolled education to a larger extent of the male population than Mesopotamians did. Had Mesopotamians done the same and earlier, I'm sure we'd see all sorts of complex mathematics already during the Sumerian period.

    Assyria was a true alpha male society btw: it was basically a military dictatorship, and Babylonia was a beta male society: arts, math, astronomy and so on, was what they spent most of their time on in Babylonia. Of course that stuff existed in Assyria as well, but the primary focus in Assyria was warfare and conquests, whereas the primary focus in Babylonia was art and intellectual activity.

    Anyway my point is that the ancient Greeks really got most of their mathematics and other cultural ideas, from Mesopotamia, and then they added on to it, improved it and further fine-tuned it. I'm not denying that Greeks improved on Mesopotamian mathematics, so we're not really in disagreement there. I'm just saying it came from Mesopotamia to Greece, that's all. People really don't like giving credit where it's due.

    Quote Originally Posted by Pendragon1 View Post
    *bump* I edited my above post a bunch of times to correct errors and make more sense i.e. be more lucid.
    You don't have to post a notification of every time you've edited a post
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    Quote Originally Posted by EliasAlucard
    Not really. All science is built on the shoulders of giants. Greeks taking an already developed branch of mathematics and adding to it, is obviously not as impressive as Greeks inventing that branch of mathematics from scratch.
    No mathematics is made from scratch --it sometimes liquidates some earlier mathematics, but ultimately some earlier mathematics remains in it. For instance, Isaac Newton's Calculus takes in all mathematical branches, that came before it. Also, as a base modern mathematics can be said to rest on only less 12 propositions, from the original 200, from Euclid's "Elements" as we have found more efficient or elegant ways of doing the other propositions with modern mathematics. So, that is like saying Isaac Newton's Calculus is not impressive because he did not invent it from scratch but uses Descartesian geometrical concepts, the concept of 0 from the Hindus, and ultimately about less than 12 propositions, from the original 200, from Euclid's "Elements" and could not also exist without the Arab concept of Algebra etc.. etc.. what you say doesn't make a lot of sense to anyone who understands mathematics-- which you don't. The reason why less than a dozen of Euclid's propositions form part of the base of Calculus is because the rest are more complicated ways of doing things once you know higher mathematics. However, that still means Calculus is dependent on rules of Greek geometry. Modern trigonometry , algebra and the use of graphs also rely on Greek Geometry and these dozen or less propositions of Euclid.




    Quote Originally Posted by Elias
    The only thing Egyptians used their mathematics for, was to build pyramids and other temples that glorified their rulers.

    Anyway, Mesopotamian civilization basically ended in 539 BC (as in the independence of Mesopotamian civilization); had it gone on uninterrupted until the Roman era, I'm sure all the mathematics stuff the Greeks perfected, would have been done by Mesopotamians. The Persians for a very long time employed Assyrian and Babylonian architects; this is why for example, Assyrian lamassu sculptures are found as far east as in Persepolis.
    There is nothing that suggests the Mesopotamians would have accomplished what the Greeks did in Mathematics. For instance, it took until 19th century to finally witness decisive steps in the creation of non-Euclidean geometry. So it took mankind about 2,100 years to go from Euclidian to non-Euclidian geometry. No offense, broseph, but Mathematics is not your strong suit so maybe you should stick to a topic you know more about ?
    Last edited by Pendragon1; 2017-08-25 at 23:16.

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    Quote Originally Posted by Pendragon1 View Post
    There is nothing that suggests the Mesopotamians would have accomplished what the Greeks did in Mathematics.
    Nonsense. All that was needed for that, would have been to introduce mandatory education in Mesopotamia. You can't expect revolutionary improvements in mathematics when the overwhelming majority of the population is illiterate and innumerate. Quite frankly it's impressive that the ancient Mesopotamians came as far as they did with mathematics, given how few Mesopotamians back then, there were who knew mathematics. Keep in mind that the Mesopotamian population back then was very small, I mean the largest cities were usually far below 100,000 individuals. And literacy wasn't even above 10% of the population.

    Greeks didn't have this problem, much in large thanks to the alphabet which was much easier to read than cuneiform.

    Quote Originally Posted by Pendragon1 View Post
    For instance, it took until 19th century to finally witness decisive steps in the creation of non-Euclidean geometry. So it took mankind about 2,200 years to go from Euclidian to non-Euclidian geometry.
    Why do you think that's the case? I mean why do you think it took so long? The reason it took so long was that for 2,200 years, Europeans and Middle Easterners were constantly waging war against one another, and also it was lots of Europeans vs Europeans too. Focus back then wasn't schooling, science, mathematics and shit like that. It was just non-stop tribal warfare and survival; that, was the main focus. By the time of the 19th century, education had become a big thing; that's why mathematics made big leaps, like non-Euclidian geometry, not because there's some imaginary Moore's law-like time frame that a time gap of 2,200 years is required to go from Euclidian to non-Euclidian geometry.

    The reason the ancient Greeks could focus on mathematics, philosophy, the arts and so on, was because they lived in Greece; the Aegean was relatively spared from invasions from hostile tribes. You see, the reason why Assyria developed into a military dictatorship, was because Assyria was constantly threatened by invasions from foreign tribes and such. So the focus focus in Assyria became warfare and not mathematics or schooling in general. Babylonia had the same problem, but much less so, because Babylonia was in the south, and it was mainly Assyrians who were warding off incoming tribes (usually Scythians) from the north. So that's why Babylonia was more prominent in the arts.

    Anyway, this is the same reason why Sparta made basically no contributions to the arts, philosophy, mathematics or anything else: Sparta was totally focused on warfare and a martial lifestyle; I classify Sparta as a hardcore alpha male society. Athens was the beta male society of the ancient Greeks; that's where Greeks innovated in mathematics, philosophy and other intellectual pursuits.

    It was of course the same throughout Europe in the medieval era: warfare (and religion) slowed down progress in mathematics and science. That's why it took so long for Europe to go from Euclidian to non-Euclidian geometry, and whatever improvements and contributions the ancient Greeks achieved in mathematics, would have been made in Mesopotamia also, had it not been for the fall of Assyria and subsequently Babylonia, and had they enrolled education to the same extent as the ancient Greeks did.

    Quote Originally Posted by Pendragon1 View Post
    No offense, broseph, but Mathematics is not your strong suit so maybe you should stick to a topic you know more about ?
    I'm offering another perspective on this topic, also I know more than you do about Babylonia and Mesopotamia.
    Last edited by EliasAlucard; 2017-08-25 at 23:36.
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    Not surprising. Finding antecedents of ‘Greek inventions’ elsewhere is expected for several reasons:

    1) The Greek cities that thrived academically and economically were the ones that settled outside of Greece, at first. Especially the Greeks in Anatolia. The fact that these eastern colonists fared better initially than the ones in the Greece, is not a coincidence: they were closer to the Middle East.

    2) The ancient Greeks’ outlook in life was oriented towards the Middle East and the Caucasus, not towards central Europe. Maps reconstructed from ancient Greek geographers are littered with Asian place names and ethnonyms, while western and northern European lands are less defined (reflecting ignorance about/lack of interest in the geography) and only sparsely populated with names. When populations orient themselves towards a particular region, it’s telling. It means that they regard that region as important in terms of their cultural priorities. And we all know that education and borrowing of 'ancient knowledge' was generally valued in Greek culture.

    3) Seeming lack of precursors in Proto-Indo-European heritage. PIE people seem to have been at least somewhat anti-intellectual. They would have been very much like George Martin’s Dothraki in terms of ideological simplicity, nomadism, lifestyle, affinity for horses and solid ground, militarization, constant infighting, etc. Evidence for this can be found in ancient descriptions of IE speakers that seem to have preserved the PIE lifestyle. For instance, interactions between Greeks and Persians during the initial Persian conquests are telling. Persians during this period equated settling down with being soft and feminine and despised aspects of the Greek model of civilization many value today. These cultural differences must have contributed to the fact that the Persians and Greeks had no recollection of kinship between themselves, despite the fact that they were close cousins at the time, with recent divergence times. This makes it seem like many intellectual features epitomized by Ionian Greeks lack antecedents in PIE heritage. Greeks seem to be a cultural mixture of this PIE heritage, the things they adopted from ‘older’ populations in, and en-route to, Greece and their own contributions. The fact that more conservative Greek tribes are more similar to the pre-conquest Persians, supports this. For instance, conservative Spartans resemble pre-conquest Persians more than progressive Ionians did.

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