voidisyinyang Posted July 25, 2015 Let's move this discussion along - the Dude - what's his tag name Zhongdong? Can't even read my article? haha. He cites ONE source of Borzacchini that I quote. Man he's slow - I cite several sources of Borzacchini. There's two sources alone just for that "preestablished deep disharmony" phrase that Borzacchini uses. And again it's not like Borzacchini is my only source. The claim is I am quoting out of context. And so I give a full quote - no "half sentences" - like some people I've debated. If you google the full quote - you get the pdf link for the whole book. I posted another quote from that link. The book clearly states that Plato was closest to Archytas and ARchytas was the basis for Plato's philosophy of the World Soul. So the question what was ARchytas promoting? So now we have Borzacchini. He is focused on Archytas? Yes - and the question is the origin of incommensurability as irrational magnitude from music theory - that is the square root of two. So that's 2 sources. Carl Huffman's book on ARchytas is a third. Ernest McClain is a fourth. Peter Kingsley is a fifth. John Curtis Franklin is a sixth. Then there's the Pythagorean structural analysis of Plato - that's a 7th source. What did I say? A dozen sources? Well math professor Joe Mazur read my research. Btw Borzacchini said I had good math. Mazur said I had done impressive research. He's not really a source per se - but he did encourage me to follow up on David Fowler which I did. So Fowler is an 8th source. Mazur actually had me submit my research for publication. O.K. so I got an Orthodox Pythagorean analysis that I quote - that's a 9th source. then's another musciology analysis in there - a 10th source. Oh yeah I referenced the music analysis of Archytas - 11th source. Economist Michael Hudson is a 12th source. He cites Burkert - but Burkert is an old school Pythagorean analysis. everyone cites him. Oh yeah - Jamie James - a 13 th source. I referenced another source in my masters thesis that I posted here - a 14th source. Oh yeah then the "irrational magnitude" as Plato's basis of Apeiron - that's a 15th source. I sent that to Borzacchini and he was interested - he said he couldn't access the link I gave him and so I sent him another link which he could access and he thanked me for it. That was just a few weeks ago. Oh wait - then there's Hugly and Sayward's analysis of the Power Set Axiom - the square root of 2 - that's a 16th source. There's math teacher J.J. Asher's article, "The Myth of Irrational Numbers" - a 17th source. there's Bertrand Russell's quote - "the real numbers are a convenient fiction." - 18th source. Share this post Link to post Share on other sites

voidisyinyang Posted July 25, 2015 O.K. so instead of just relying on that "one" quote of Borzacchini and claiming it's out of context - let's look at Borzacchini more closely - was he referring to the square root of two? This displacement of the problem from music to geometry, to be ascribed inmy opinion probably to Archytas himself, was even the rationale of the nameof the 'geometrical' mean, because it could produce no musical consonances,whereas had precise and easy geometrical instances. http://mathforum.org/kb/message.jspa?messageID=1177277 keep in mind this math forum is before he actually published his research on the topic. I think that probably it is wrong to look for the 'first' proof of theincommensurability, even because the numerical 'fact' of someincommensurable results (for example side and diagonal of the square) wasalready known to the Babylonians, whereas a rigorous proof required insteadthe introduction of the "absurd" proof in an earlier visual and constructivemathematics, so that the theorem had to be proved together with theestablishment of its method of proof.However it is of great relevance the hypothesis of a 'musical' backgroundfor the discovery. And actually a 'negative' proposition, asserting theincommensurability in musical and arithmetic terms, can be found in theprop.3 of the "Sectio Canonis", ascribed to Euclid (Appendix).The same proposition can be found in Boethius' "De Institutione Musica"iii,11 (DK 47 A19), ascribed to Archytas: "No mean proportional number canever be found between two numbers in a ratio superparticularis". 'Ratiosuperparticularis' is the 'epimorion diasteema (logos)', i.e. the ration+1:n or mn+m:nm, for n,m integers (Appendix). Bingo - diagonal of a square as the geometric mean is the square root of two. Share this post Link to post Share on other sites

voidisyinyang Posted July 25, 2015 I would like instead to stress the 'musical-arithmetical' origin of the problem of incommensurability even in its theoretical establishment. More precisely, I believe that at least in Archytas the core of mathematics was in "logistic", which was not simply a "practical art of computation", but the "science of the relationships between numbers", the "theory of the logoi", including even a pre-Eudoxian theory of proportions about numbers, theoretically solid enough to deal with the theoretical aspects of incommensurability and give us at least the negative result. o.k. so he's talking about the music origin of the transition from arithmetic to irrational geometry. He's saying it's from Archytas and Plato relied on Archytas. Music was instead the core of the Pythagorean philosophy until Plato. We can find even in the Respublica (424c) the echo of Damon's learning: "never musical modes can be changed without changing the most important laws of the polis". Music was the ground of the Platonic theory of education, and appeared both in elementary (with gymnastic) and superior (part of the Quadrivium) education. In Philolaus the same structure of kosmos' harmony reflected musical consonances (DK 44,B 6). Moreover, cutting the musical intervals by the geometric mean of the superparticular ratios meant to find the way to connect those seven modes of greek music (dorian, phrigian, lydian, etc) which were considered by the Pythagoreans (and even by Plato) basic for the harmonic behaviour of the citizen and the city as well. Plutarchus (de an. procr. in Tim. c17, 1020E) reminds that the crucial problem was the division of the tone (9/8, i.e.the interval between the fourth and the fifth) in teo 'equal', i.e. 'proportional', parts, and that the Pythagoreans discovered it to be impossible because 9/8 is epimoric. Equivalently the octave could be divided in 6 tones (according to Aristoxenus) or 5 tones and 2 not joinable semitones (according to the Pythagoreans). We can even remember the words of Plato in Respublica 531 a-c against the musicians who try to find the "least interval" by ear, "placing the ear before the mind", and, at the opposite of the Pythagoreans, Aristoxenus' defence of the musical practice to reveal the real consonances, and his research of something like our "equal temperament" (without the relative mathematics) to allow the connection in one framework of the different modes: "there is no least interval" (Elem. Harm. II,46). O.K. Borzacchini - from my understanding, translates the Greek himself. But again we are talking about music theory and math here - this isn't based on a secondary translation. It's quite clear - Plato changed the Pythagorean harmonics (orthodox Taoist) to be an Archytas analysis of Pythagorean harmonics (an irrational magnitude for Apeiron) and this ushered in the Greek Miracle - the basis of incommensurability. this music origin was LOST - and by being lost more importantly what was lost was the complementary opposites logic of Taoist-Pythagorean harmonics. Something I reveal in my analysis - and I use quantum physics to corroborate my analysis. so now the 2nd source of Borzacchini's phrase "preestablished deep disharmony" - his pdf description of his book in Italian, "Plato's Computer" This idea of syntactic representation was the basis of the parallel genesis of Greek philosophy and mathematics, but ever since this beginning it was clear that, inside this relationship between those two worlds, there was a deep ‘preestablished disharmony’: words and things were not alike, neither in their being nor in their becoming, some words (being, not, true, equality) did not represent any ‘thing’, a part of a word did not represent a part of the represented thing, language represented diachronically a synchronical reality. This disharmony grounded many formal paradoxes that endure up to the present time, first and foremost ‘the liar’ [3rd and 4th chapters]. now notice the choice or words - philosophy, math and disharmony (music)..... Beyond language, music also played a role in the development of Greek mathematics (even the discovery of incommensurability probably had its beginning in the musical problem of the tone dichotomy), an involvement that lasted until the 17th century: afterward, mathematically there will only be ‘sound’, and musical harmony will become something belonging only to the irrational realm of ‘beauty’ [11th chapter]. so is incommensurability one of the formal paradoxes that continue to this present time? https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0CC4QFjACahUKEwjUo9SwnvXGAhUJHR4KHSNaC-Y&url=http%3A%2F%2Finfolet.it%2Ffiles%2F2014%2F12%2Fsummaries-borzacchini-2014.pdf&ei=r_SyVZSQB4m6eKO0rbAO&usg=AFQjCNFlqHJQr2pWwQTAo_5giD3d79ZioA&bvm=bv.98717601,d.dmo&cad=rja that's the pdf link btw (iii) after Dedekind, Cantor, Hilbert, Zermelo, Goedel, Cohen we know that the Aristotelean and Euclidean continuum admits numerable models, that we can not give to its modern versions a first order categorical axiomatization, that the geometrical continuum can not be proved coincident with the numerical one, that it can not be empirically verified, that the place of the numerical continuum in the transfinite hierarchy is one of the greatest so far open questions, that it is linked to the most disputed axiom of set theory, etc. If the continuum has never got empirical nor logical evidence, derives from complex processes of cognitive development and does not appear outside our civilization, we can suppose that its evolution in Greek mathematics was quite complex. So as a mathematician Borzacchini is admitting, like Bertrand Russell - the real numbers are a "convenient fiction." Sure math works - science uses it - but logically it remains elusive. And for whom does math work? that was the point I raised with Joe Mazur regarding his book Euclid in the Rainforest - he has a quaint story of how trignometry solved a problem for him down there in Costa Rica. I said well I spent a college semester there studying conservation biology and as far as I can tell it's Western math that is destroying the rainforest not saving it. So yeah math "works" if you support global genocide and ecological destruction, etc. That is also the point that Michael Hudson makes about Archytas and his fake Pythagorean harmonics. Well that's enough for now - I have more quotes of Borzacchini from his published article and more quotes from the sources I list above. Share this post Link to post Share on other sites

voidisyinyang Posted July 25, 2015 The math is wrong becuz of disharmony. No personal issues needed. Share this post Link to post Share on other sites

voidisyinyang Posted July 25, 2015 Apeiron wS wrongly defined by plato as irrational magnitude. Wong math as the tracteory of western civilization. He got it from archytas. If u disagree then present the math that is correct. The music theory of natural harmonics is empirically correct as real infinity. What is covered up is the complementary opposites harmonics of the geometry. My anaylsis exposes that logical error by showing it got rediscovered in quantum time frequency analysis. All the social injustice and ecligical destruction is built into the math as a wrong definition of infinity. A proper definition means the harmonics create a mind body transformation training that has been lost in the west since the orthodox pythagoreans. Share this post Link to post Share on other sites

voidisyinyang Posted July 25, 2015 I don't agree about the symbols of western math being played around. They are inherently applied. Thats the big lie that there's pure math. Share this post Link to post Share on other sites

Zhongyongdaoist Posted July 26, 2015 My concern is not with the quantity of Innersound's quotes, which are plentiful, indeed, often a tangled overgrowth, but with the quality. Whether or not they are faithful to the context from which they are taken is another matter. That they are a fair representation of the author's thought and not a distortion is the duty of the person making the citation.I am going to go back to one of the original quotations to show why I originally dismayed by Innersound's use of it: Hence Arithmetic is the source of that preestablished harmony between realityand language (Emphasis mine, ZYD) that we can not not believe after almost four centuries of astonishingachievements, but we must even say that, neither tendentially, syntacticrepresentation can thoroughly mirror reality, become someway iconic. And thisbecause it is marked in its basic principles with a preestablished disharmony, thatis even its hidden evolutive principle. (Emphasis in the original, ZYD)It plays the role of source of never ending paradoxes well recognizable ever sincethe beginning of formal thinking. Negation, truth and being ground anantinomical argument, from the “negative judgement paradox” (impossibility ofasserting falsity), through the “liar paradox” (contradictory nature of self-assertingfalsity), to set-theoretical paradoxes and to Gödel's and Tarski's limitativetheorems (Emphasis mine, ZYD). Luigi Borzacchini, THE SOPHIST. GENESIS OF FORMAL THINKING IN GREEK PHILOSOPHY ANDMATHEMATICS. (Dipartimento di Matematica, Università di Bari). Reading this for the first time I focused on the other passages that I have emphasized, as well as the one Innersound had emphasized and interpreted it in the light of my experience with Gödel in my own high school "advanced" math class in number theory, as I recounted here: Gödel's Way; Exploits in an undecidable world, Gregory Chaitin, Newton da Costa and Francisco Antonio Doria, CRC Press, 2012Kurt Gödel (I finally figured out how to put umlauts in these posts!) is one of the single most influential people in my life. Among other things Gödel contributed to my accepting the Dao De Jing as a fundamental text (though S. I. Hayakawa's work on General Semantics and my high school physics teacher's oft repeated statement that physics was just 'modeling' contributed). So it is only appropriate that I post on a book called Gödel's Way on the Tao Bums.I don't remember exactly when I first became familiar with it, but I think it was about the time I turned seventeen and was taking an advanced math class in number theory my senior year in high school. Gödel's notion of incompleteness seemed to be a rough equivalence to the first chapter of the, at that time, Tao Te Ching (D. C. Lau translation, Penguin Books, 1963), about how the way that could be spoken is not the eternal way, in other words no account that could be put into words was ever going to be a complete account. That combined with the fundamental theory of General Semantics, that the map is not the territory and some of my own musings about the relationship between mathematics and physics, lead me to see Laozi as having possessed a profound insight into the nature of reality and so I decided to make the Dao De Jing my fundamental mystical text.Gödel opened the doorway to infinity for me, since the implication that I drew at the time was that there was a world that could be endlessly, explored, endlessly formalized and never be exhausted. As I decided at the time, 'We will never be bored', because we will never have all the answers.All that was forty-six years ago and my life since then has been a strange Dao indeed. Seeing Borzacchini comments in light of Gödel's Incompleteness Theorem, which as part of the actual quote, I saw nothing which merited taking “preestablished disharmony” and pasting it all over the place, because it is paired with “preesablished harmony”, which is not pasted all over the place. The disharmony is identified as a “hidden evolutive primciple”, and the matter is also identified with “formal thinking” without any mention square root of two, all of which was compatible with my own original understanding.Later when I read the whole paper, in which the square root of two is not mentioned at all, but “preestablished harmony” is mentioned two other times and which ends with this: There is no 'ignorabimus', but an essential and changing 'incompleteness', never-ending and changing 'breakdown' in our capacity of 'saying' the world, that makes our scientific work not the patient reconstruction of an image of reality, but a wonderful adventure not only 'outside', but even 'inside' us. (Emphasis mine, ZYD) Following directly after the aforementioned quote, I was really staggered by the disconnect from context which characterized Innersound's use of “preestablished disharmony”, from any faithful interpretation of Borzacchini's quote. The essential and changing 'incompleteness', reinforced my own initial reaction and the conclusion that this incompleteness was "a wonderful adventure not only 'outside', but even 'inside' us”, showed and emphasized Borracchini's positive evaluation of this interplay of “preestablished harmony" and "preestablished disharmony", just as I had positively interpreted Gödel's Incompleteness Theorem, in late 1967. There seemed at that point no way to justify Innersound's use of the quote and as I pursued other sources I found more examples of this type of noncontextual use of citations. I have posted this here as my last post dealing with Innersound's attacks on Platonism in this thread, I have started my own thread Plato and Platonism 101, where I will continue this type of analysis of Innersounds use of citations. At this time he has already started spamming that thread, but I have a "fun" way that I will deal with that. I will post a little more on Confucianism, at least some of which should be very interesting to everyone and I hope that the OP will find them interesting enough to have made this derail worthwhile. Share this post Link to post Share on other sites

voidisyinyang Posted July 26, 2015 (edited) My concern is not with the quantity of Innersound's quotes, which are plentiful, indeed, often a tangled overgrowth, but with the quality. Whether or not they are faithful to the context from which they are taken is another matter. That they are a fair representation of the author's thought and not a distortion is the duty of the person making the citation. I am going to go back to one of the original quotations to show why I originally dismayed by Innersound's use of it: Reading this for the first time I focused on the other passages that I have emphasized, as well as the one Innersound had emphasized and interpreted it in the light of my experience with Gödel in my own high school "advanced" math class in number theory, as I recounted here: Seeing Borzacchini comments in light of Gödel's Incompleteness Theorem, which as part of the actual quote, I saw nothing which merited taking “preestablished disharmony” and pasting it all over the place, because it is paired with “preesablished harmony”, which is not pasted all over the place. The disharmony is identified as a “hidden evolutive primciple”, and the matter is also identified with “formal thinking” without any mention square root of two, all of which was compatible with my own original understanding. Later when I read the whole paper, in which the square root of two is not mentioned at all, but “preestablished harmony” is mentioned two other times and which ends with this: Following directly after the aforementioned quote, I was really staggered by the disconnect from context which characterized Innersound's use of “preestablished disharmony”, from any faithful interpretation of Borzacchini's quote. The essential and changing 'incompleteness', reinforced my own initial reaction and the conclusion that this incompleteness was "a wonderful adventure not only 'outside', but even 'inside' us”, showed and emphasized Borracchini's positive evaluation of this interplay of “preestablished harmony" and "preestablished disharmony", just as I had positively interpreted Gödel's Incompleteness Theorem, in late 1967. There seemed at that point no way to justify Innersound's use of the quote and as I pursued other sources I found more examples of this type of noncontextual use of citations. I have posted this here as my last post dealing with Innersound's attacks on Platonism in this thread, I have started my own thread Plato and Platonism 101, where I will continue this type of analysis of Innersounds use of citations. At this time he has already started spamming that thread, but I have a "fun" way that I will deal with that. I will post a little more on Confucianism, at least some of which should be very interesting to everyone and I hope that the OP will find them interesting enough to have made this derail worthwhile. Zhongdong - you see some connection between Godel and Taoism? that's hilarious! In short, either there are theorems that our mathematics is simply not capable of dealing with, or our mathematics is itself inconsistent, neither prospect having much appeal for the career mathematician. A.K. Dewdney, Beyond reason: eight great problems that reveal the limits of science (Wiley, 2004), p. 139. Math Professor A.K. Dewdney states in his book Beyond Reason that one interpretation of Godel’s incompleteness theorem based on Cantor is that math is “inconsistent.” Godel, as mathematician A.K. Dewdney points out, shows math - symmetrical logic (not Taoism) - is either incomplete or "inherently inconsistent." That's not a judgement against math - it's a logical truth! http://www.iep.utm.edu/math-inc/ In 1931, Kurt Gödel's theorems showed that consistency is incompatible with completeness, that any complete foundation for mathematics will be inconsistent....In light of Gödel's result, an inconsistent foundation for mathematics is the only remaining candidate for completeness. Godel is based on Western math - nothing to do with Taoism. As for the "pre-established harmony" of arithmetic - that is NOT the pre-established disharmony from syntactic representation (geometry) that Borzacchini is focused on - his music analysis. You keep claiming he's not talking about the square root of two - but I've already detailed that he is - incommensurability is about the square root of two. Incommensurability is based on syntactic representation - that is the disharmonic foundation he is talking about. It's also the inherent inconsistency that Godel proved. Or as Bertrand Russell stated the "real numbers are a convenient fiction." You can say Godel was more like a Jainist since Godel starved himself to death like the Jains did. From this general result, for n=1, we get the irrationality of the square root of 2. For more information about this topic we address the reader to a forthcoming paper (Borzacchini, 2001). Most authors (Burkert, 1972, Knorr, 1975, Szabo, 1978) more or less agree with this hypothesis, ascribing to it however only a (more or less) minor role, “just a start”. Nevertheless, from an anthropological point of view, even a “start” seems very important if we consider that incommensurability seems almost the beginning of European mathematics. In other words it seems to us anthropologically very relevant to claim that European Mathematics did not stem as a by-effect of purely technical geometrical enquiries, but as the result of a socially and politically crucial musical problem. Luigi Borzacchini. LIke I said - I've corresponded with him several times - he said my math was good. O.K. so there's three references to Borzacchini using the term "pre-established disharmony" - all deal with irrational geometric magnitude as the combination of arithmetic with syntactic representation. Not JUST arithmetic. The syntactic paradigm [pre-established deep disharmony] was the result of the Platonic and Aristotelian foundation, and developed its 'strong' form at the beginning of the XX century science. In this framework modern science achieved its greatest breakthroughs: quantum mechanics, formal logic and computer science. All of them, however, can not avoid the occurrences of the never ending paradox connected to the syntactic paradigm. Below the surface of the antinomical form, we can maybe reveal the deep 'preestablished disharmony' of the link between human knowledge and reality. O.K. so nothing about arithmetic here - clearly modern science is based on the syntactic paradigm. http://www.dm.uniba.it/~psiche/ Edited July 27, 2015 by Innersoundqigong Share this post Link to post Share on other sites

Apech Posted July 27, 2015 This is getting tiresome. 2 Share this post Link to post Share on other sites

SirPalomides Posted May 15 On 7/17/2015 at 4:48 PM, Zhongyongdaoist said: Historically there are two main schools of Confucian thought, those that follow Mencius and those that follow Xunzi. Dong Zongshu, or more exactly Dong Zhongshu, is a Han dynasty figure who is "innocently" described on Wikipedia as: What this leaves out, is that he favored Xunzi and Xunzi's program of social control, and marginalized and suppressed the study of Mencius, who favored a program of self-cultivation that has many common points with the Neiye, and is better described as a program of self-realizaton, I quote Mencius' informal outline description here: What I'm finding out, reading about Dong Zhongshu, is that he is a bit harder to pin down. A lot of what is written about him in general overviews seems quite unfair. He has a somewhat quirky view of human nature that seems to share its basic premise with Mencius, but its conclusion with Xunzi, but more developed than either; he also has a very paternalistic view of the role of rulers in training people to be virtuous. In the realm of cosmology and spiritual cultivation, he is quite in league with Mencius with additional influence from the Yin-Yang, Five phases thought. While he voiced disagreements with some of Mencius I don't think he actually suppressed his texts- he assumed his readers were familiar with them, and owed a lot to Mencius anyway. He did have a program for the institutionalizing of Confucianism that was realized, though perhaps not the way he envisioned. Much like Zhu Xi gets unfairly blamed for a lot of later Neo-Confucian developments, foot-binding, etc., I think perhaps Dong Zhongshu is tarred with some developments that were really out of his hands. Share this post Link to post Share on other sites