More details on that Plato-Aristotle number debate:
It
was when the Attic alphabet arose that Number aligned with a Form as
the phonic symbol enabled Number to no longer be inherently Cardinal but
instead be just a "heap" of "substance" , as both integers and
geometric units combined. see John J. Cleary, "Aristotle's Criticism of Plato's Theory of Form Numbers," in Platon und Aristoteles, sub ratione veritatis: Festschrift für Wolfgang Wieland zum 70. Geburtstag
Plato holds the number Two is generated by Twoness.
The Platonic Form of Twoness is Two.
page 14:
"Aristotle
argues....if the units in the first Two come into being simultaneously,
then they can not be ordered as prior and posterior, as the hypothesis
of non-comparability [of Platonic Forms] implies."
https://www.youtube.com/watch?v=FlDnPHqv0cs
I'll explain this song in a second. haha.
(3 plus 4 = 4 plus 3) for commutativity but a lot of nonwestern tribal cultures might not even use that level of addition!! Usually it is even claimed that addition might be conceived in terms of geometric proportions instead by non western tribal cultures!
Is 1/4 Cup More Than 1/3 Cup?
So this person asks a seemingly simple error in math logic
because they are actually confusing "number" with "proportion" as
geometry! So it turns out this is a kind of basic error in logic that three is a "smaller" number yet a "bigger" proportion
...So even simple arithmetic
when thought of in proportion might not be so straightforward or vice versa. It even
seems too simplistic to point out this error - and yet there it is!!
LO!! haha. People really do "think" in this way sometimes since our
brains are kind of separated sometimes (the left side from the right
side)...
That link "explains" that proportions in Western modern math actually need to have a common invariant as a unit.
When the above link says an invariant common unit they mean a
materialistic standard for math but in fact "unit" originated as simply
"pure" geometry supposedly aligned with "pure" arithmetic.
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls).
So this means a "proportion" is secretly assuming a common materialistic "unit" whereas a ratio does not need to make that common assumption but still assumes a symmetry. How? This was the secret error of the Pythagorean Theorem (that I cited in that 2012 book) - exposed by Professors of philosophy Charles Sayward and Philip Hugly, "Did the Greeks Discover the Irrational?" (1999) They say NO because the Pythagorean "proof by contradiction" taught in school is a confusion of the "common unit" of geometric length with arithmetical distance. Godel's Incompleteness Theorem is also based on this same proof - that calculation is not "understanding as consciousness." And so there had to be a previous "assumption" of a common unit of "twoness" for the modern "irrational number" proof by contradiction argument called the Power Axiom Set.
Plato's argument was this is obvious when we look at our bodies - our "set" of hands or our "set" of arms, or our "set" of eyes are all symmetrical. Actually Daoism and even Egyptian alchemy is not based on this symmetry nor is Indian yoga, etc. Traditional nonwestern cultures are based on complementary opposites, not symmetry. And so Plato was just using a rhetorical sophistry argument! Aristotle argued that two numbers can exist at the same time and yet be different values (one and two) and thus "twoness" as arithmetic addiction does not mean symmetry...seems kind of obvious but Plato needed a common variant unit foundation for this "ratio of ratios" concept as proportions.
So Fields Medal Math Professor Alain Connes is arguing that mathematics as a discrete arithmetic number exists on its own terms as noncommutative frequency and time (but not as Platonic geometry). Usually Western mathematics is taught in terms of the Platonic Realm as the irrational number (from the symmetric twoness unit as an irrational magnitude) - as this is what Plato argued as the realm of Platonic Forms or whatever he called it. But this secretly came from an error in music theory!
Connes is arguing that in fact the discrete numbers being noncommutative are MORE DENSE than the geometric continuum of irrational numbers.
So in music theory there is "pitch" as a third term. This is also conceived or was conceived by Plato as a kind of "platonic realm" (really from Archytas and Philolaus again as "ratio of ratio").
George Musser kind of captures why "Pitch" is strange in music theory.
Suppose you play two piano keys, middle C and the adjoining D key.
The C key creates a sound wave with a wavelength of 1 meter 32
centimeters, and D produces one with a wavelength 14 centimeters
shorter. These waves overlap in the three dimensions of space through
which they propagate, yet they’re independent of each other, as if they
were located in different places. In a sense, you can think of the sound
waves as residing 14 centimeters apart within a fourth spatial
dimension.
The farther apart the keys are on a piano keyboard, the
farther apart they are within this imaginary dimension; a given
distance along the keyboard translates into a given distance within the
dimension. You don’t see this dimension as such; to you, it’s an
abstraction that captures the acoustical independence of sound waves.
But it’s a remarkably fitting abstraction. Musicians call the difference
between pitches a musical “interval,” which has connotations of
distance, as if our brains really do think of the differences between
pitches as spatial separation.
OK that's my "old" blogpost that has the above music pitch quote from George Musser.
So now consider what Basil J. Hiley tells George Musser on what is the secret truth of reality.
George Musser: How does this enter into quantum mechanics?
Basil j. Hiley: In noncommutativity. Every day in our life, we
always have to be careful of the order. You’ve got a cup in the
cupboard. You’ve got to open the cupboard door before you can the cup
out. All our experience is doing things in the right order, so our
activity is noncommutative. It comes into quantum mechanics because
Heisenberg sought to explain atomic energy levels and what he found was
he had to make his objects into things that didn’t commute with each
other. The order was vital. There was a difference between first
measuring the momentum and then measuring the position, from measuring
the position and then measuring the momentum. That became the basis of
his Uncertainty Principle.
It seemed to me that he was actually discussing a process. He was
talking about how something goes from one to the other, and he called
that a momentum transition, and a position from one position to another.
In other words, it wasn’t x and p, p and x. It was rather x0, x1, p1, p2, and so on.
So that is funny since George Musser - even though he wrote a whole book about quantum entanglement - he still does not understand noncommutativity!! It's hiding out in the open!! It's essentially this logical error between proportion and number.
So Alain Connes explains that frequency and time exist BEFORE "spacetime as proportion" (with the assumed common materialistic denominator as units of symmetry as the geometric continuum).
If you read those links I gave above for my "old" blog and my academia article - they go into the noncommutative music-math stuff a bit more - as does the "final chapter" of my "Strange Vibrations" book, etc.
That song link I sent - is the Minneapolis Wallets Band who were taking the same music theory class I took when I was 16 years old - a year after that music video was made!! My piano teacher "bragged" to me that they were in the same class as me also. hahaha. So my piano teacher (from when I was five years old) - she was teaching the class to adults (I was the only child in the class or teenager)...
One of the tricks she taught us was "4 against 3" polyrhythm. So what's fascinating about learning this "4 against 3" is that the left hand is used for a basic "three" as syncopation since, just as with a Waltz, the three has a "ONE" emphasis - like in funk music - the "one" is key. So this "three" would be the "measure" as similar to a "scale" as the "octave" in music theory. Western music assumes the basic unit of time is a "symmetric" octave. But in fact the time is more like 4 against 3 based on the 3 as the measure as a syncopation time polyrhythm. You can also do this with "two against three" by keeping a steady two beat in the left hand and a syncopated three beat in the right hand (much easier to do)....
As Professor Michael Corballis points out the left hand is used to keep a steady rhythm as time when you tap out time with your hands. Why? The timing is left brain dominant while frequency is right brain dominant but this is due to the connection to our cerebellum used to process emotion via the vagus nerve!! In other words, for the cerebellum the left hand is "wired" to the left side of the brain while the right hand is wired to the right side of the brain. Notice this is the OPPOSITE as for vision. Taoist Alchemy also relies on this paradox - as does Tibetan meditation, etc.
So what is fascinating is that the right side vagus nerve connects to the left side of the brain but the left side vagus nerve does NOT connect to the right side of the brain. So left brain dominance cuts off people from processing the subconscious emotions via frequency of music as right brain dominance.
As she taught us basic music theory, suddenly I noticed this logical error of "noncommutativity" in basic music theory. I won't go into the music theory details again - as I mentioned above. haha. You can read the links and my other "books" for details. haha.
Of course I had no idea it was called that at all. hahaha.
George Musser was explaining "Pitch" above by making this same "error" of symmetry or commutativity. What he called "pitch" as the 4th spatial dimension is actually space from frequency as symmetry!! I call this the "Liar of the Lyre" since it originated from Philolaus flipping his lyre around...
In quantum mechanics the particle "IS" the wave whereas in classical physics the "wave" (as time and frequency or amplitude) exists in a "medium" - even for light the "medium" is spacetime. In music it is assumed the medium is air but we LISTEN to music first as an internal perception!!
But for a "quantum photon" the medium is actually "spin" as a quantum force. The same is true of a quantum "phonon." For Einstein's Nobel Prize he relied on the "quanta" as a conversion of phonon into photon!! Both being based on energy as frequency in discrete units of number.
So in western "symmetric" science the time and frequency are a linear operator that supposedly are symmetric and thus "uncertain" inherently but in fact they are ASYMMETRIC and thus inherently nonlocal!! hahaha. Alain Connes emphasizes that instead of a geometric distance between two points there is a nonlocal noncommutative frequency of the future and past overlapping!!
In other words "time-frequency uncertainty" originates from nonlocal noncommutativity!!
This "spin" is inherently noncommutative or asymmetric time-frequency and it's not a wave or a particle but it's actually the "inner cross products" of the matrices as discrete numbers of time and frequency. It's also nonlocal - so that at each "zero point" of spacetime there already is the future and past overlapping.
What's fascinating about precognitive visions is that they are "more real" - i.e. more lucid - than being awake! All our perceptions originate from this nonlocal "ether"-information that we inherently can't see since it is superluminal - from the future. Our brains can then absorb these negative frequencies "back into light" as a vision more real (since it's from a coherent laser source that is holographic) than being awake!! We can also "smell" through the nonlocal ether, etc.
I had my first precognitive vision in 1995 soon after I was initiated by qigong master Effie P. Chow.
At the time I never made the connection to qigong. I was keeping a journal and I woke up at 2:30 a.m. to write down this dream that was "more real" than being awake! I wrote that I thought "would come true." It came true in detail three years later - long after I had forgotten the dream. haha.
Of course when I saw the photo that was the same image as my dream - of my environmental activist friends with native indigenous activists all standing together on the roof of a house to protect a sacred forest - (as I wrote down in my journal in 1995) I saw the newspaper photo as a photocopy in 1998 and instantly I got this uncanny sensation since I remembered my 1995 dream. I drove to my parents (where my journal was stored) to verify that the dream was indeed the same as the photo - and I had the dream in my journal from 1995. hahaha.
Anyway a good book on those types of precognitive dreams is the book "Transcendent Dreaming" by Dr. Christina Donnell. She relates her own experiences with those precognitive dreams. The irony again being that the precognitive dream is "more real" than being awake!!
OK I'll go back to the music theory as noncommutative number ratio. So if 1/3 is a proportion and thus "greater" than 1/3 as a ratio of frequency number (as the fourth dimension of space) then why is 1/3 the "pitch" of C/F (as undertone) while 3/1 is the "pitch" of G/C a number...!! This violates the commutative property of a "one to one" correspondence between number and geometry. So when we say 3 plus 4 = 4 plus 3 that is assuming number but as a ratio of number (3/1 plus 4/1) then the 3=G while the 4=C since the 2 as "twoness" is the symmetric scale octave or unit of the C=1.
Yet if we reverse the order so that 4/1 (C) plus 3/1 (G) is added we get a Perfect Fourth overtone to the G (since C is a higher frequency as number and so it's a Perfect Fourth ratio as time number). This means the reversal of the "addition" of the frequency number as a ratio of the one CREATES a new "spacetime octave" of C to G or 2/1 to 3/1 but C to G is not a Perfect Fourth, rather it is a Perfect Fifth!! So the reversal of the number as a proportional ratio creates a noncommutative resonance in terms of the perception of pitch. This is clearly explained in traditional Indian (East Indian, South Asian) drone music tuning - that the Perfect Fourth is never an overtone of the root tonic "one."
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