1 minute ago, OldDog said:
No - there are several human cultures that do not count about the number five - instead just using "several" or as in the case of Daoism - "10,000 things" - and again ALL human cultures use the octave, Perfect Fifth, Perfect Fourth that has infinite resonance as the empirical truth of reality.
So the Western math based on the continuum assumes a materialistic foundation of reality - called "idealistic materialism" in philosophy. So in other words the "infinity" is considered a measuring process directly tied to technology. Math professor Abraham Seidenberg researched the ritual origins of Western math - in the Brahmin and Zoroastrian and Egyptian religious solar calendar rituals. And so at first there was a symmetric logic based on "divide and average" logic.
I corresponded with math professor Luigi Borzacchini who also researched this comparative math issue, and the music origins of Western math. So at first there was a "negative paradox judgment" - which is what is being debated between Brahmins and Buddhists about what Sunyata means as "zero." And Aristotle was also against zero as "negative infinity." So in the West, the zero is tied to the geometric continuum also containing logistics or logarithms - irrational magnitude.
What happened, as Professor Richard McKirahan documents, is that the mathematical term for geometric magnitude was transferred into music theory that uses continued proportions as ratios. So then it could be argued that there is a reduction to absurdity about rational number ratios and therefore an Alogon geometric ratio music exist in the music ratios. So the mathematical term "surd" in Arabic is a direct translation from Alogon. The west normally considers Logos to mean ratio as in logical geometric reasoning but actually Logos is from music theory with Alogon meaning no musical rational ratio.
But to say that there is no geometric rational ratio is NOT the same as to say there is no infinite resonance through pure number as harmonics, that can be logically inferred. Stephen Hawking makes this point about Indian mathematics in his book "God Created the Integers." So in India there was the divide and average math, just as in Babylonia, but the geometry was not reducible to a numerical arithmetic - rather the irrational ratios were considered to be "transcendent" to an immaterial reality, as "sacred" geometry. But with Archytas and Philolaus - the music ratios lended themselves to an emphasis on "logistics" or pure ratios without the need for a visual geometric proof. China adopted the 10-based rod system of counting from India - because try to subtract the lunar calendar from the solar calendar using ideogram language numbers!
Since the musical proof was a "Negative judgement paradox" then that which could not be demonstrated physically through geometry must therefore not be talked about - it can only be logically inferred through silence as meditation. But once this proof was demonstrated in music then it could be transferred into geometry by simply covering up the inherent noncommutative ratios embedded into the irrational continuum. In other words - when we LISTEN to music, our ear does not distinguish between the noncommutative ratios - they are both heard as the Perfect Fifth even though the geometric ratio to the "one" or root tonic is not the same. So the Perfect Fifth is the Single Perfect Yang but it contains within it both yin and yang at the same time - as a nondual or noncommutative phase. So the ratio 2/3 as C to F subharmonic was NOT allowed in Greek music mathematics in order to cover up this noncommutative or complementary opposite yin-yang resonance, as the empirical truth of reality.
OK so for Archytas relying on Philolaus using the "double octave" or "Greater Perfect System" - then what was called the Subcontrary Mean (the Perfect Fourth as Yin) was then changed into the Harmonic Mean with only 4/3 allowed. So for Archtyas, the equation in music theory was then (Arithmetic Mean x Harmonic Mean = Geometric Mean Squared). This was the FIRST logarithmic equation and thereby launched the Greek Miracle as the continuum. This is discussed in math professor Luigi Borzacchini's 2007 publication but he was discussing it on a math forum with mathematicians in 1999. So he notes in his published paper that Plato's dialogs about irrational numbers then refer to 16, 17, 18 from Egyptian math (based on Isis, Osiris and Horus, cited by Plutarch). But, as Borzacchini points out, this is the same ratio attempt to divide 9/8 evenly - although it is obviously not an even ratio. This was the basis for Archytas' proof against the ability to divide the Octave or the 2 into even rational ratios.
So in every human culture around the world - it is just accepted that music is based on intuitive listening as harmonics - and this inherently contains 1:2:3:4 as complementary opposites, the empirical truth of reality. But for Plato he argued that a "unit" is an inherent geometry symmetry that pre-exists BEFORE counting numbers - as a Platonic Ideal. So therefore, Plato argued, that this is obvious if we consider our 2 eyes or our 2 hands or 2 feet - these are all first considered as an "empty set" or geometric ideal of 2 that is not differentiated as a cardinal or ordinal number. Rather it is simply just a "symmetric empty set" as 2.
But anyone who studies Daoist alchemy knows that Plato's claim was a total lie!! We know that the left eye for males is yin qi and yang shen and the right eye is yang qi and yin shen and the left hand for males is yang and the right hand is yin and the left foot for males is yang and the right foot is yin. We know that for males the lower body is yin and upper body is yang and the outside external body is yang and the internal body is yin and the back of the body is yang and the front of the body is yin. In contrast to the Left eye being Yin qi, the Left ear is Yang qi. This is the exception to listening perception - and the secret in Daoist alchemy referred to as seeing with the Ears or listening with the eyes.
So Plato, Archytas and Eudoxus and Philolaus - they contrived a very sophisticated "bait and switch" system - something that math professor Luigi Borzacchini calls a "deep pre-established disharmony." Why? Because inherent to this materialistic idealism geometric continuum is a left-brain cognitive bias that assumes a linear ordering of time. This is why science has proven that humans can hear FASTER than Fourier Uncertainty (the technical and mathematical limit of technological measurement of time as a linear operator). So our human hearing is inherently noncommutative and nondual (and at the subangstrom wavelength - smaller than light waves). And the phase coherence between the right and left ear is inherently noncommutative. I have corresponded with physics professor Manfred Euler about this - who considers the right and left ear to be the analog of a quantum "double slit" experiment, thereby proving the nondual nonlocal and noncommutative foundation of reality through time-frequency harmonics.
So what appears to be very simple intuitive cultures based on music (non-literate and no math) is actually a very precise "quantum biology" resonance culture using quantum relativistic math (modeled by noncommutative phase logic or de Broglie's Law of Phase Harmony). Science can not "unify" relativity and quantum physics because of what is called the "measurement problem" in quantum physics - which is the inherent noncommutative phase of time with frequency. But this is because science assumes a visual measurement of time as a linear operator. And also this visual measurement inherently creates Entropy - whereas the empirical reality of life is from Negentropy - as Schroedinger realized in the 1930s when he published his book, "What is Life?"
So to say that other cultures just have a different type of math, does not acknowledge that Western mathematics has a deep preestablished disharmonic bias - a "cognitive bias" as math prof. Luigi Borzacchini calls it - that is the "guiding evoltive principle" of science as Borzacchini calls is. So Western science tries to argue, as you have done, with your Western bias, that math is "inherent" to reality - but does not realize that Western math has an inherent "externality" due to the Western materialistic idealism bias that has covered up the inherent noncommutative phase or nonlocal nondual foundation of reality. Philosophy of Science professor Oliver L. Reiser called this the "Music logarithmic spiral" - a term from Esther Watson (daughter of famed inventor Thomas Watson). Esther corresponded with Einstein about this "music logarithmic spiral" as Einstein supported their research - on what I dubbed the Actual Matrix Plan. https://www.bibliotecapleyades.net/ciencia/ciencia_matrix43.htm
Science debates which is "first" in reality - mathematics or physics. But now even "biology" has been considered to be first, as physics professor Brian Josephson has realized and he practices qigong regularly - he also is the basis for the origin of the Volt, and for the creation of MRI machines, etc. - he got the Nobel prize for his Josephson Effect. But I have corresponded with Nobel physicist Josephson also - about music theory.
So now Professor emeritus Josephson is studying math professor Louis Kauffman who worked with Eddie Oshins on this noncommutative phase secret of Daoist Neigong alchemy training. Professor Josephson now argues that this acoustic alchemy is the secret of reality as well - through cymatics but again with this secret noncommutative phase foundation. And as I have pointed out - Fields Medal math professor Alain Connes makes this same argument about music theory - that music provides the "formal language" to explain noncommutative phase logic that enables a unification of relativity and quantum physics. The only problem with this new Western science insight (that is just realizing the secret truth of the ancients) is that Western science and its originators in Brahmin-Vedic-Egyptian math - this is created an inherent entropy on Earth as the destruction of ecology.
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Avshalom C. Elitzur, Shahar Dolev
Black-Hole Uncertainty Entails An Intrinsic Time Arrow, Dec. 2000
So this is the "cognitive bias" that math professor Luigi Borzacchini is referring to, whereas in the PreSocratic greek culture, as in nonwestern cultures, the music plays a much stronger cognitive bias. The musical training is considered the foundation of the culture for spiritual healing - and this musical training is a different type of biological time process than the Western bias of "observation" as a left brain measurement using technology. I have also discussed this paradox with math professor Joe Mazur who had asked me to submit my music research for publication in a math journal. He is now finishing a new book on time perception - and he said he was going to include a chapter on music. I asked him to consider Precognition - since I know that precognition is real but almost all of Western science precludes such a possibility.
For examples of the music - go to Dr. Victor Grauer's website, "Sounding the Depths" - his old blog. I have corresponded with him as well. He gives links to audio-visual examples of the original human culture music as it spread around the world (and became the basis for Daoism). http://soundingthedepths.blogspot.com/p/audio-visual-examples.html
But you would have to study the San Bushmen culture to find the secrets of this music. It is similar to mantra meditation.
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