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Originally posted by DenyObfuscation
reply to post by fulllotusqigong
If you're doubling the cube then the volume is three times as much not twice as much so if the volume was 2 then it is 8.
Well first I'll say I don't care much either way it's just that doubling the volume seems to be the trick where doubling the length of an edge or doubling the volume of a square shouldn't qualify as any great achievement. If I'm wrong about this I'm not the only one.
Three such problems stimulated so much interest among later geometers that they have come to be known as the "classical problems": doubling the cube, i.e., constructing a cube whose volume is twice that of a given cube;
Source
Also I can see 1 is to 5/4 as 8/5 is to 2 but I don't see how 5/4:8/5 fits the sequence, at least not mathematically. I know 1*5/4*8/5=2 but that seems to work with any "doubled and inverted" fraction such as 3/2 4/3, 11/7 14/11 etc.
And when I asked about F-C being a P5 I meant in standard theory.
My personal opinion is that reductio ad absurdum 'emerged' slowly together with the idea that incommensurability was not just a numerical difficulty (as it was already in Babylonian mathematics, similar for example to the absence of the inverse of 7), but was a theoretical confirmation of the ontological opposition between discrete and continuous. If this interpretation is not completely unfounded we could say that reductio ad absurdum was a 'work in progress' since the end of the 5-th century, that was completed most of all between Aristotle and Euclid. By the way, I wrote something more on this topic in a paper "Music, incommensurability and continuum: a cognitive approach" on Archive for the history of exact sciences, 61, 273-302 (2007). Best wishes Luigi Borzacchini
Several super-conducting space-time sheets are probably involved with the control and complex super-conducting circuits are certainly involved. The structure of the cell interior suggests a highly organized ohmic circuitry. In particular, cytoskeleton could be important carrier of currents and atomic space-times sheets of the microtubules could be in crucial role as carriers of the ohmic currents: there is indeed electric eld along microtubule. The collagenous liquid crystalline networks [9, 10] are excellent candidates for the carriers of weak ohmic currents in the inter-cellular tissue. Fractality suggests that also structures like proteins, DNA and microtubules are in a similar ow equilibrium controlled by super-conducting ion densities at protein/DNA/microtubule space-time sheets and probably also larger space-time sheets. Bioelectromagnetic research provides a lot of empirical evidence for the existence of the direct current ohmic circuits, mention only the pioneering work of Becker and the work of Nordenstrom [7, 17] . For instance, these direct currents are proposed to be crucial for the understanding of the eects of the acupuncture. The ancient acupuncture, which even now is not taken seriously by many skeptics, could indeed aect directly the densities and supercurrents of ions at super-conducting space-time sheets and, rather ironically, be an example of genuine quantum medicine.
As physicist and Nobel laureate Brian Josephson outlines: “Music is like atoms in terms of quantum theory.” He proposes parallels between DNA and music ideas, and also theorises that music stimulates a primary level of consciousness. Not only that. Josephson likens balance-imbalance conditions in bio-systems to the tension and release patterns found in music -- and, suggests that music "models" can help maintain balance in the human organism.
To sum up, one could see super-conducting space-time sheets as controllers of the evolution of the cellular and other biological structures and the model of organism could be specied to some degree in terms of the densities and currents of the super-conducting particles at various space-time sheets besides the values quantized magnetic uxes associated with various many-sheeted loops. Setting up the goal at controlling space-time sheets would force the atomic space-time sheets to self-organize so that the goal is achieved. This clearly provides a quantum mechanism of of volition. A fascinating challenge is to apply this vision systematically to understand morphogenesis and homeostasis.
The deviation of the external magnetic ux from a quantized value is coded to a small supercurrent. This mechanism combined with stochastic resonance possible for SQUID type circuits [4] makes it possible to 'measure' extremely weak magnetic elds of MEs by amplifying them to biological eects. MEs can also form junctions (possibly Josephson-) between two super-conducting circuits. In this case a constant electric eld associated by ME denes the frequency of the induced Josephson current: the weaker the potential dierence, the slower the oscillation period. This mechanism might explain why the eects of ELF em elds in living matter occur in intensity windows.
Frequency entrainment for both ELF and high frequency branches can be understood if both the thickness and length of the magnetic ux tubes are subject to a homeostatic control. The assumption that the total magnetic energy of the ux tube remains constant during the frequency entrainment together with the magnetic ux quantization implies that the ratio S=L of the area S of the magnetic ux tube to its length L remains constant during entrainment. Thus the ratios fh=fELF of the magnetic transition frequencies to characteristic frequencies of MEs would be homeostatic invariants in agreement with the empirical ndings. The value of the ratio is in good approximation fh=fELF = 2 1011.
Matti Pitkanen
One of the mysteries related to Hearing is the ability to hear frequencies much higher than the maximum rate of nerve pulses which is below kHz. The coding by Josephson frequencies and representation of them as quale of the magnetic body resolves this mystery.
Thus the phenomenon of octaves could relate to the p-adic length scale hypothesis, which implies that physically preferred p-adic primes correspond to primes near prime power powers of two. For instance, this implies that the massless extremals (MEs) associated with physically important padic primes have fundamental frequencies which are octaves of each other. Therefore a classical resonance via the formation of join along boundaries bonds becomes possible and real space-time sheets corresponding to preferred p-adic primes can form larger resonant structures. This universal resonance could explain why octaves are experienced similarly. The problem of this argument was that primary p-adic time scales would come as half octaves instead of octaves. Octaves seem to have much deeper signicance than I thought originally and seem to emerge at the level of fundamental formulation of quantum TGD rather than characterizing only a very special kind of sensory experience. In the recent formulation of quantum TGD using zero energy ontology [21, 22] one uses zero energy states which have their positive and negative energy parts at the light-like boundaries of causal diamonds consisting of future and past directed light-cones....This assumption allows to deduce
p-adic length scale hypothesis (p ' 2k, k integer), and to identify T as a secondary p-adic time
scale. For electron this time scale is .1 seconds and corresponds to the fundamental 10 Hz biorhythm.
For non-standard values of Planck constant T is scaled by a factor ~=~0. Thus octaves become a
key element of fundamental physics. One can say that causal diamonds as space-time correlates of
self appear naturally as octaves. Also rational multiples of fundamental frequency emerge via the
hierarchy of Planck constants: in principle all rational scalings of the basic hierarchy are allowed.
Perhaps music experience actually involves in a very essential manner also magnetic body. That "eastern" music favors additive instead of divisive rhythm could be understood as higher right brain dominance. The extremely mechanical rhytms characterizing the popular music today, the lack of melodic aspects, and the use of the volume of music as the basic means to induce emotional eect, could in turn interpreted in terms of extreme left brain dominance.
For instance, the ability of good music to generate vibrations in spine could relate to this negentropic aspects. Music as purely intellectual experience could induce essentially an analysis of what was heard based on the use of holistic-reductionistic dichotomy. Chopin's music has especially strong healing eect. Tempo rubato might re ect the profound integration of rhytmic aspects, melodic, and harmonic to single organic whole both at the level of representation and music experience.
The ability of the 'note selves' of the chord to have stable
ux tube bonds between
themselves should depend crucially on the fact that the frequencies of the notes of the basic chords
have simple rational ratios so that the oscillations involved are commensurate and match together.
Hence a resonance phenomenon ins spirit of classical physics involving rational ratios of frequencies
would be in question. During listening the chord self continually decomposes into sub-selves when
listener consciously concentrates attention to some notes in the chord....The ability of the music to occasionally create thrills in spine could correspond to whole-body consciousness in unusually large length scale. Note the this scale could correspond also to the secondary time length scale assignable to CD. It presumably involves a resonant fusion of also other than note sub-selves to larger negentropic sub-selves by the formation of stable join along boundaries bonds identiable as magnetic flux tubes. The ability of certain sounds ('Om') to promote the emergence of whole-body consciousness could be due to the ability to very eectively generate negentropic entanglement direction.
The original continued proportion is from my book -- as I have quoted the mathematicians -- it's an unsolved mystery how the continued proportion was given actual number ratios for doubling the cube.
In my opinion we can instead explain this as revealing a sharp passage
from the musical to the geometrical framework on the line from Archytas to
Eudoxus, with the vanishing of the earlier approach. The translation was easy because geometric similarity was well known, and the connection between duplication of the square and the mean proportional between 1 and 2 was known as well, if Hippocrates of Chios could reduce the duplication of the cube to two mean proportionals and Archytas accomplished it geometrically.195
To clarify this tricky business of compounding ratios, here's how Wilber Richard
Knorr's The Ancient Tradition of Geometric Problems (1986) describes the equation: If for any two given lines, A and B, we can insert the two mean proportionals, X and Y, then A:X = X:Y=Y:B. Thus, by compounding the ratios, one has (A:X)cubed = (A:X)(X:Y)(Y:B), that is, A cubed:X cubed = A:B. Thus, X will be the side of a cube in the given ratio (B:A) to the given cube (A cubed).
Professor Ken Saito in his essay “Doubling the cube: a new interpretation of its significance for early Greek geometry,” Historia Math. 22 (2) (1995), 119-137 notes that “Strangely enough, in contrast to the abundance of solutions for inserting two mean proportionals, we have little testimony on how Hippocrates' reduction was proved in antiquity.”
The secret of the sect music equation for the compounding proportions of the side lengths is this: A:X::X:Y::Y:2A = 1:5/4::5/4:8/5::8/5:2. That's the secret of the Greek Miracle -- converting Pythagorean harmonics into the irrational geometric continuum. In contrast the Kaplans just give the geometric phonetic values for this equation: X = the cube root of two multiplied by A.
Earlier in David Fowler’s definitive book on the subject, The Mathematics of Plato's Academy, he wrangles with this music issue, stating: ...the manipulations of music theory seem to depend fundamentally on the operation of compounding, an operation which seems to pose some serious problems for mathematicians. My purely speculative suggestion...is that music theory might plausibly give some help with this problem.196
Originally posted by DenyObfuscation
reply to post by fulllotusqigong
C4-G4 is 2:3 freq ratio with C=2 G=3. G4-C4=3:2. That much is commutative. What difference does it make what G4-C5 is? If that can be explained then I can stop asking.
4/3 divided by (9/8 x 9/8) (the difference between the fourth and the third made from 2 whole tone notes) = 256/243. (256/243) squared (the two semitones) does not equal 9/8 (the whole tone) and therein lies the problem for creating polyphonic harmonics using chords, key changes, etc.
1+1/4 of 1 =5/4. 5/4+1/4 of 5/4 =25/16, not 8/5. 8/5+1/4 of 8/5 =2. So my question is in what way is 1-5/4-8/5-2 proportional? Same deal, explain it and I can stop talking about it.
(8 / 5) cubed = 4.09600
In order to double a cube, 1-2 is not the issue. Anyone can multiply 27*2 to get 54. If I'm to be as anal as the Greeks were about precisely doubling a cube I need to know how to use music to determine by what proportion to increase the sides of my cube which currently measure 3 units. I'm just trying to apply the theory.
J.G. Landel’s writing on torsion-spring catapults “classified in terms of the missile they were
designed to shoot” informs us on the particulars....The third method, described by Hero and Philo, is much more accurate. It starts from the known spring-diameter of a successful catapult. For this purpose, let us take a ten-mina machine, where M’ x 100 = 1000, and D = 11 dactyls.” (mina is just under 1 lb and dactyl is about 3/4 inch). Suppose M” = 40, we then require two numbers, x and y, such that 10 : x = x : y = y : 40. The simplest way of finding these is by a geometrical construction, which would be within the scope of all but the very dimmest artificer. Measure with a ruler…. We draw two lines AB and BC at right-angles, their lengths proportionate to M’ and M’‘ (i.e. the ratio 10:40). Complete the rectangle ABCD, and draw its diagonals AC, BD, intersecting at E. Produce DC and DA for some distance. Then place a straight-edge, pivoting on B and cutting the extensions of DA and DC. Rock the straight-edge about B until each of these points of intersection is the same distance from E, measured with a ruler, and call these points F and G (i.e. FE=EG). It will then be found that AF and CG are the mean proportionals between AB and BC — that is, AB:AF = AF:CG= CG:BC. It also follows that the ratio AF/AB is the cube root of the ratio BC/AB, and that the spring diameter suitable for M’ (11 dactyls) multiplied by this ratio (AF/AB) will give the correct spring-diameter for M”. Once this basic dimension D has been calculated, the rest becomes easy. Both Philo and Vitruvius give a long list of other dimensions, all expressed in terms of this diameter.
as the Perfect Fifth as F to C -- not as C to G
Originally posted by DenyObfuscation
reply to post by fulllotusqigong
as the Perfect Fifth as F to C -- not as C to G
So F to C is A P5 like C to G is A P5. Remember your response when I asked if F to C was a P5? Think I'm gonna take a break from this mess.
In contrast the Kaplans just give the geometric phonetic values for this equation: X = the cube root of two multiplied by A.
So for your question the length of the side is 3 multiplied by 5/4 as the cube root of two is 3.75 and as the side length 3.75 cubed is 52.73. So it's again proto-algebra -- it's not 54 but it gives the formula from the music ratio.
posted on 11-2-2012 @ 08:34 PM this post reply to post by fulllotusqigong Do you believe 5/4 is the cube root of 2? Also,
I can't see why you expect it to be commutative as presented. What similarity is there between Perfect Fifth and Perfect Fourth? In this example doesn't C ascend to G and then G to C an octave above the original C? For Western symmetric logic C to G is 2:3 and G to C is 3:2. If they're the same C and G wouldn't that be true?
So the Perfect Fifth is 3:2 as C to G and the Perfect Fourth is G to C as 3:4 but this is noncommutative mathematics!
The example is noncommutative because it's from F to C as 2:3x and then C to G as 3:2x but it's never stated what "x" is -- that's the "bait and switch" tactic. So then F to C is squared as 4:3x but since it's within the same octave it is actually 3:4 as G to C and C to G as 2:3. Archytas had to use only 3:2 and 4:3 based on the double octave whereas the frequency harmonics use the octave as 1:2 and the perfect fifth as 2:3 and the perfect fourth as 3:4. This is the natural resonance harmonics instead of trying to extend a scale using logarithmics.
Why is F in the response which is in no way an answer to my question? C to G, interval. Same G to higher C, different interval. C to G and back to same C is analogous to A x B = B x A.
Should A to C interval = C to A interval? Maybe this question will give insight as to the source of my confusion.
I don't know the ratios for A to C or C to A but I would not expect them to be commutative. Do you?
You do repeat many things but never explain anything. You continually ignore the discrepancies in your logic. You condemn western everything while stating tai chi and the yin and yang are literally the P4 and P5 you rail against. Can you demonstrate the complementary opposites with their ratios? Can you explain how anyone can arbitrarily assign invalid values to sounds when the sounds are what they are? Does anyone get what I'm asking?
reply to post by fulllotusqigong west bad. western 4th 5th bad. 4th 5th yin yang good. HOW?
reply to post by fulllotusqigong how is the 3:2 4:3 problem different in nonwest tuning
F to C as the Perfect Fourth is created from the subharmonic of G to C as 3/2. So F to C is 2/3.
Originally posted by DenyObfuscation
reply to post by fulllotusqigong
But it's not -- it's F to C as the Perfect Fourth.
There's one.
3:2 and 4:3 are alchemically transmuted to mystical indefinite values upon departure from the west. How in the name of dragonball z is nonwestern string division by the same ratios an explanation of the question? The answer is not in a vid, it is not in me and apparently it can't be found in you.
All I'm asking is why anything you say about western tuning is not then applicable to your yin and yang. The noncommutative bait and switch on the 4th and 5th seems to be a basic premise of the theory. It's a very simple and obvious question.
What is the signifigance of "noncommutative" as applied to your theory?
What is the SIGNIFIGANCE of noncommutative as applied to your theory? Yin and Yang are noncommutative but that doesn't appear to be any problem. You know very well that A x B = B x A IF A = A and B = B. In C to G and then G to C, C does not = C, as they're separated by an octave..The symbol is the same but the value is different. A 4th and 5th are different intervals so why would they ever be expected to be commutative?
The commutative property in math has nothing to do with intervals in a musical scale. To call the relationship between two different intervals noncommutative is as relevant as pointing out the fact that neither interval possesses even a single flavor of the skittles rainbow. Why would you do this?
Never once did I say the scale is commutative. I'm trying to understand why that seems to be so important to you.
I'm just trying to point out why it "doesn't work". Noncommutative seems an illogical description TO ME which is why I keep trying to find out the signifigance of that label. In light of the fact that you call yin and yang noncommutative and I assume yin and yang are important to your beliefs I'm completely confused by what appears to be a criticism when it's western but somehow a positive thing for eastern.
Did you mean to say this? Isn't 1/2 divided by 2/3 equal to 3/4? Does this matter? Did I miscalculate?
Why is F to C 2/3? Isn't it a 5th also? Do different 5ths have different ratios?
This motion takes place at a characteristic, or resonant, frequency of six gigahertz, or six billion cycles per second. (Tuning forks also have a resonant frequency—in the order of kilohertz—but the mode of resonant vibration in that case is to oscillate sideways rather than to expand and contract.) The team's first result was to show that at such chilly temperatures the width, or amplitude, of the resonator's vibration becomes quantized—in other words, there is a small amount of vibrational energy, called a phonon, below which the resonator is essentially still. The existence of discrete packets of energy is a hallmark of quantum behavior, and phonons are the mechanical equivalent of light's photons—they are the ultimate, indivisible quanta of vibration, whether thermal or acoustic. Next, the team put the superconducting circuit into a superposition of two states, one with a current and the other one without. Correspondingly, the resonator was in a superposition of vibrating and not vibrating. These quantum states continued for about six nanoseconds—about as long as the team expected—before fading away.