Let the mystery be
Iris Dement
Still low with the flu, but my spirit is lighter than it was last post and I wanted something up here to reflect that.
New content next week. Have a safe and encouraging holiday.
posted by Jeff Wells at 12/24/2007 06:42:00 PM
35 Comments:
Happy Holidays, Jeff. Get healthy for Pete's sake.
Love,
yer old pal Jerky
www.dirtfiles.com
Blessings, Peace and Love to all
For you all
Patty Griffin - Mary
I heard this first at the end of the film 'The Ground Truth' which is well worth seeing.
Joy for all
May the New Year see you well!
Good to hear it, Jeff. Best wishes to you and the family.
Happiness to all :).
Very cool song sung by that lady.
Love and light and happiness all around, Jeff.
Peace,
PP
I really liked that video. The lady radiates love for her husband, the guy to her right.
'Tis the Season:
http://welcome-to-pottersville.blogspot.com/2007/12/dubya-bush-superstar.html
Hey Jeff,
Here's something for you for Christmas, along the lines of Ms. Dement's tune, and because I feel bad for calling you a schill in re to WTC 7... (I know you'll come around on that one, eventually ;-)
"At first, this Earth, a stage so gloomed with woe
You all but sicken at the shifting scenes.
And yet be patient. Our Playwright may show
In some fifth Act what this Wild Drama means."
-Tennyson
ps I've decided butch pederasts run the world.. check out The Pink Swastika, homophobia and all, for a well researched foray into Nazi homo-occultism...
Happy Holidays!
Anonymous One,hey why don't we all meet up for a drink at "Himler's Castle",you know where he planned for the "Center Of The World".Some how this always points back in the Nazi camp,by the way I just love the photo with the little baby uberchild,later.
Merry Crimbo to all, get well soon...
Equal-tempered tuned instrument? watch-out! I just sent the below to math professor Joe Mazur from the http://mind-energy.net link:
Against Archytas: How the West Lost Alchemy or Paranormal Complimentary Opposite Harmonics
by drew hempel, MA
(anti-copyright, free distribution)
The early Greek mathematics used the 60-based number system of Babylon from which Archytas, a collaborator with Plato, received the harmonic tetrachord or the continued proportion 6:8::9:12. This tetrachord creates a geometric mean between the octave, perfect fourth and perfect fifth music intervals, or 1:2:3:4, through “divide and average” logarithmic-based mathematics. So 6:8 and 9:12 are in the continued proportion 3:4, the perfect fourth music interval, while 6:9 and 8:12 are 2:3, the perfect fifth music interval, and 6:12 is 1:2, the octave. The geometric mean is A:B::B:C or B squared = AC or the square root of AC = B. What Archytas added to this Babylon “divide and average” harmonic mathematics was the concept of the Greek “incommensurable” – the algebraic axiomatic proof of “alogon” or a precise irrational number, the square root of two. This process ushered in what’s called “The Greek Miracle” that continues to be the structure of science: symmetry-based mathematics.
Instead of the above system, the alchemical Pythagorean Tetrad relies on complimentary opposite harmonics so that an equilateral triangle of geometric points equals the continued proportion 1:2:3:4 as the octave, perfect fifth and perfect fourth music intervals. In “orthodox” Pythagorean harmonics this was known as the “subcontrary mean” whereby the complimentary opposites of the Tetrad were maintained in violation of “divide and average” mathematics. So for the Tetrad A:B is 2:3 and B:A is 3:4 against the commutative property, A x B = B x A. In music theory this complimentary opposite inversion of the perfect fifth and perfect fourth is taught as 2:3 is C to G while 3:4 is G to C. This process of complimentary opposites is listened to, as the perfect fifth, perfect fourth harmonics, which create all the notes. Most importantly the complimentary opposite harmonics transduces sound throughout the whole energy spectrum, as I’ve described in previous articles..
Philolaus, one of the early Pythagorean writers, detailed that this “subcontrary mean” or complimentary opposite harmonic caused any attempt at subdividing the scale into symmetry as a failure. In contrast Archytas changed the “subcontrary” complimentary opposite mean into the “harmonic mean” using “divide and average” mathematics. The outcome has precisely opposite the meaning of “harmony” which for Pythagoreans referred to the paranormal source of sound as the Goddess Harmonia or what I call female formless awareness. For Philolaus the perfect fifth as 2:3 could be inverted to 3:2 and then extended another fifth to 9:4 and then divided back into the octave, below 2, for the major second interval of 9:8 or C to D. Yet 9:8 cubed or three major second music intervals equaled the 3:2 perfect fifth music interval, plus a tiny ratio called “the comma of Pythagoras.”
This “comma of Pythagoras” is the difference between the “divide and average” octave system adopted by Archytas and the complimentary opposite fifths inverting into fourths, used by the orthodox Pythagoreans. The “comma of Pythagoras” is the key to harmonic alchemy whereby 2:3, the perfect fifth, is yang in Taoism and 3:4, the perfect fourth, is yin. As Gurdjieff desribes the “shock” of the diatonic scale, whereby the “inverse ratios” do not line up with the octaves, is intensified as the octaves expand. In contrast Archytas argued that 9/8 cubed or three major second intervals equals the square root of two as the Greek Miracle, the axiomatic algebra of the precise incommensurable irrational number. What Archtyas essentially did, as I’ll describe, is equate the perfect 5th or 2:3 with the perfect 4th or 3:4 as equally-divided or symmetric ratios through a “divide and average” mathematics.
Archytas took the Babylonian geometric mean of 6:8::9:12 used for harmonics and then applied the Pythagorean Tetrad 1:2:3:4 so that the 2:3 ratio of complimetary opposite frequency was converted to 3:2 as a materialistic vibrating string length. This became known as the Law of Pythagoras even though it goes against the true meaning of the complimentary opposites when this “inverse ratio” is combined with the “divide and average” commutative property. Gurdjieff, for example, still relies on the “inverse ratio” of density or string length versus frequency or consciousness. But Gurdjieff does not use Archytas’ “divide and average” symmetric-based mathematics, instead Gurdjieff relies on the Law of Three aka the Tetrad, or octave-fifth-fourth, to resonate through the comma of Pythagoras as the “shocks” of alchemy. In Taoism this system of alchemical shocks is taught as the 12 harmonic nodes along the outside of the body, enabling healing and paranormal energy, an exercise called “the small universe.”
The equation used by Archtyas, from Babylon, was arthimetic mean times harmonic mean = geometric mean squared. For the Pythagorean Tetrad this means if A = 1 and C = 2, the octave, then B = 3/2 for the arithmetic mean (A + C divided by 2) and B = 4/3 for the harmonic mean or 2(AC) divided by A + C. Meanwhile B = the square root of two for the geometric mean or the arithmetic mean times the harmonic mean equals the geometric mean squared (3/2×4/3 = 2).
The error that Archytas makes is ignoring the “comma of Pythagoras” arising from complimentary opposites harmonics so that the square root of two is equated with 3/2 through the “divide and average” converging sequence. The square root of two is greater then one and less than two which can be solved through the “divide and average” geometric-based continued fraction series of (1 + a)squared = 1 + 2a + a squared. 2a + a squared = 1. Or a(2 + a)=1. Therefore a = 1 divided by 2 + a. Then just keep replacing “a” with “1 divided by 2 + a” for an infinite series that converges as the square root of two. The first iteration is 1 + 1/2 or the approximate series solution, 3/2 = the square root of two.
It needs to be emphasized that the square root of two is actually a “transcendental” number although this is only acknowledged in number theory and not in standard math. There is no positive proof demonstrating that the hypotenuse of the 1-1 triangle equals the algebraic symbol the square root of two since there’s no algebric equation demonstrating the square root of two, only an infinite algebraic series that is not a closed set. Most people just learn the geometric proof for the square root of two, demonstrating a “proof by contradiction,” which simply states that the ratios are not rational, but it does not consider other options for the ratios, especially the case of diverging complimentary opposite harmonics.
In contrast music theory, based on logical inference, uses listening to complimentary opposites, 1:2:3:4, as proof that the foundation of reality is female consciousness with the male number 1 as an infinite resonance creating an octave, 1/2, that expands in frequency through the perfect fifth or 2:3 or yang, inverting to the perfect fourth or 3:4 as yin. In western music theory this is taught as the “circle of fifths” so that the perfect fifth or 2:3 starts with C to G then continues to finish the octave C through the 12 notes of the scale. C-G-D-A-E-B-F#-C#-G#-D#-A#-F-C. This return back to “C” again ignores the empirical fact that the perfect fifth overtone inverts into the perfect fourth interval – through complimentary opposites, a dynamic that can be heard in music. So if you have a string marked into 1/2, 1, 3/2 and 2, a node at 3/2 actually is 3/4 of the string. Or you could start the string with zero, and again a node at 2/3 is 3/4 of the string. Similarly a node at 3/4 is 2/3 of the string. What’s important is the yin-yang dynamic of this complimentary opposite harmonic thereby creating alchemy.
In other words there’s a complimentary opposite between the nodes and the numbers which can be heard as harmonious. For this reason that musical “inverse induction” extension of the perfect fifths does not line up with the the extension of the octaves and this difference is called the “comma of Pythagoras.” In Nature there is no “circle of fifths,” but rather an infinite spiral of energy transduction that starts and ends with the male number one resonating as a complimentary opposite into female formless awareness and then resonating out as the perfect fifth harmonic which inverts as the perfect fourth to pull back to one and then, through its complimentary opposite – female formless awareness. This process continues as resonance overtones, just as Dennis Gabor’s Quantum Time-Frequency Uncertainty Principle describes: As the time gets less the frequency spreads across the whole energy spectrum. It’s no accident that in quantum mechanics the commutative property is also violated with momentum times position not equaling position times momentum – only in science this is converted back into symmetric-based math using logarithms. Quantum physicist Henry P. Stapp makes this paradox of Number and Order central to the mystery of consciousness in quantum mechanics.
The Golden Ratio also does not converge geometrically, unless, like the perfect fifth music interval, 2:3, the order of the Fibonacci number series is reversed so that there is symmetry between zero and one, using the “divide and average” commutative property. In the converging series expansion the continued proportion A:B::B:A + B of the Fibonacci series, 1, 2, 3, 5, 8, 13 is reversed to A:B::B:A-B so that A(A – B) gives a positive solution for geometric convergence. What this means, again, in terms of music is that the frequency ratios of 4:5, the major third, and 5:8, the minor sixth have to be reversed to materialistic string length as 5:4, the cube root of two, and 8:5, an approximation for the golden ratio and also the cube root of four. Kepler used this Golden Ratio as the 3:5 music harmonic to combine it with 5:4, the major third, in order to justify his elliptical orbit analysis. Similarly Newton’s inverse square law of gravity was derived from his application of Archytas’ symmetry-based logic so that it takes four times the weight on the end of a string to increase the tension to twice the string’s frequency. Not until the 1960s did the Philosophical Transactions of the Royal Society of London publish this newly discovered Pythagorean-based source for Newton’s gravity.
I discovered that Archytas’ proof for precisely doubling the cube, his most famous equation, relies on this secret harmonic conversion of ratios into irrationals. Up until now, only a geometric magnitude proof is given for doubling the cube so that A:X::Y:2A refers to X being the side length of the cube that needs to be doubled while the volume as 2A needs to be cubed with the geometric mean equation as 1:2::4:8. The original side length equation is 1:cube root of two::cube root of four:2. In fact these geometric mean ratios are from music harmonics as the major third and its inverse, the minor sixth or Golden Ratio, giving 1:5/4::8/5:2. None of the mathematicians have been able to make this connection to Archytas’ conversion of the 2:3, perfect fifth music interval, for this “doubling the cube” proof that creates the Greek Miracle – an axiom for an irrational number. David Fowler’s Mathematics of Plato’s Academy book certainly acknowledges the mystery of the music ratios origin for Archtyas’ doubling the cube proof. Other mathematicians, like Professor Luigi Borzacchini, with whom I’ve corresponded, have certainly pondered the math-music incommensurability issue.
And so again the continued proportion proof for the square root of two in its first iteration gives the value 1 + 1/2 or 3/2 = the square root of two which is what Archytas relied on. This same proof is tested by squaring both sides so that 9/4 = 2 (a first iteration in the series) or algebraically y squared + or – 1 divided by x squared = 2. In the geometric mean proof, also used for the Golden Ratio, AC = B squared or N = x(x-1). This also converts back to the Babylonian geometric mean equation so that 6:8::9:12. Because 9/4 = 2, as the first iteration of the square root of two series, this is actually based on the Tetrad harmonics of 3/2 squared which must be divided back into the octave, less than two, as 9/8, the major second interval. Or again Archytas combined the complimentary opposite harmonics of 1:2:3:4 into the geometric mean 6:8::9:12 for an algebraic solution to the square root of two with the iteration of 3:2. So the geometric mean became paradoxically 1:8::9:2 or 1:2 cubed::3 squared:2 but the order is reversed to 9/8 since it’s a materialist string length, and not just frequency ratios. In terms of the geometric mean for doubling the cube we can see that 5/4 is just 9/8 as two major second intervals or 10/8 reduced to 5/4, now justified as the cube root of two as the major third while the minor sixth, as 8:5, is just the half and then inverted.
Again Archytas’ use of “just tuning” diatonic ratios, also used by Gurdjieff, such as 9:8, 3:5, and 5:4 were solely due to Archtyas’ conversion of 2:3:4 as complimentary opposites into the “divide and average” symmetry or the arithmetic mean. So 2:3 became 3:2 from A + C divided by 2 = B with A = 1 and C = 2 as the octave. This conversion of the complimentary opposite Tetrad perfect fifth of 2:3 into 3:2, as an arithmetic mean, then could be doubled, 9/4, and inverted back into the octave as 9/8, the major second interval and then converted to the geometric mean as three major second intervals or the square root of two also known as the “Devil’s Interval,” the tritone – C to F#.
An easier way to understand this is described on this physics website: http://hypertextbook.com/physics/waves/music/
“Solution …
The ratio of the diagonal of a square to a side is √2:1. (Galileo stated the order of the ratio the other way around, but this is a minor detail.) Each half step (a semitone) up the equal tempered scale multiplies the previous note by the twelfth root of two, two half steps (a whole tone) multiplies the note by the twelfth root of two squared, three half steps by the twelfth root of two cubed, and so on …
1 semitone minor second 12√2 12√2
2 semitones = 1 tone (whole tone) major second 12√2 12√2 6√2
3 semitones minor third 12√2 12√2 12√2 4√2
4 semitones = 2 tones (ditone) major third 12√2 12√2 12√2 12√2 3√2
5 semitones perfect fourth 12√2 12√2 12√2 12√2 12√2 2.4√2
6 semitones = 3 tones (tritone) augmented fourth 12√2 12√2 12√2 12√2 12√2 12√2 2√2
Six semitones is equal to the twelfth root of two to the sixth power, which is equal to the square root of two. This interval is called a tritone, an augmented fourth, or a diminished fifth; for example, C and F♯ (G♭) or F and B. Had I given you a more complete quote from Galileo you would have already known this.”
In orthodox Pythagoreanism this use of an attempt to equal-temper the scale into 12 fifths, using the 9/8 ratio as the geometric mean, would not have been allowed since it enables setting up a quadratic equation based on the commutative property and the Pythagorean Theorem. A square x B squared = C squared was always averaged in other mathematic systems but now it could be combined with zero to create a geometric convergence as an irrational number – the Greek Miracle based on a deep disharmony. The complimentary opposite harmonics which naturally resonate as yin-yang dynamics have now been destroyed. Even supersymmetry is just an extension of what Professor Oliver Reiser called “the music logarithmic spiral” so that mass squared is inversely proportional to energy frequency distance, as detailed by physics professor Gordon Kane.
There is no pure science. Archytas’ “doubling the of cube” miracle was used for catapult technololgy while Newton’s “inverse square law” from Archytas’ geometric mean analysis has been the key for all projectile military technology just as Galileo’s Pythaogorean math was used for cannons.
What enabled Archytas to ignore the “comma of Pythagoras” which in alchemy creates an infinite resonance of energy through complimentary opposites was the vast difference of error between the Golden Ratio, the slowest converging irrational number and the square root of two series. So that the inversion of 5:8 into 8:5 for both string length use (instead of frequency) and for use of the quadratic zero, geometric convergence, does not greatly affect the harmonic series accuracy. It’s inverse is the conversion of 5/4 or 10/8 into the cube root of two. This is the true secret of the Greek Miracle – combining the Brahmin cipher system of the commutative property, using zero, with Babylon’s equation of the arithmetic mean times harmonic mean equaling the geometric mean squared. Eudoxus simply extended Archtyas’ use of the harmonic mean so that it could be applied as the Golden Ratio mean. As the book Excursions into Number Theory notes: “For instance, 99/70, the sixth convergent of square root of two, differs from square root of two by .000072; but 13/8, the sixth convergence of the Golden Ratio, differs from the Golden Ratio by .0070, showing an error nearly 100 times as large.” (p. 134)
In conclusion – mathematicians have never been able to figure out why the ratio 2/3 was sacred in Egypt. Now you know the secret – or at least to what extent complimentary opposite alchemical harmonics have been covered up.
Happy holidays!
Looking forward to your next post Jeff, but don't feel stressed about getting stuff done. Your blog was my favorite from the start, and always will be, and everyone here would agree :)
Love and Light!
Hey Jeff I ate 3 BULBS of garlic in 12 hours -- it completely destroyed the flu! I also did the below following research as a follow up to the article you posted. Thanks and happy holidays.
"How Birds Sing" by Crawford H. Greenewalt, Scientific American, Nov., 1969 has the secret of "positive coupling" so that an increase in membrane tension increases frequency but also retracts the membrane from the air tube thereby increasing amplitude.
A normal resonant chamber has an exponential decrease in amplitude as harmonics increase exponentially with increase in tension or string length inverse to frequency.
The secret again is waveform with it being a pyramid, tetrahedron, spirochete, vortex or full-lotus body position, that must be measured from logical inference complimentary opposites.
For Descartes a body thrown up vertically with twice the velocity takes twice the time to descend. This is force(t) = momentum x velocity. To convert this back to Archtyas -- mass = the square
root of momentum x velocity just as string length or geometric mean equals the square root of arithmetic mean times harmonic mean.
Leibniz used work as Fs = mv(squared) divided by two -- which is equating arithmetic mean with harmonic mean as an average.
So, like the secret of bird song, this also is a
"positive coupling" because normally the Law of Pythagoras
states that twice the string length = 1/2 the
frequency. So the longer the string the lower the
frequency, as an inverse ratio.
The secret of Archytas was that geometric mean changes
the harmonic mean to arithmetic by using WEIGHT for
geometric mean and in classical physics this means
momentum and velocity HIDE the complimentary opposites
because weight is the average of the extremes. So
twice the velocity is Archytas' "twice the string
length" or 3/2 (Arithmetic Mean) x 4/3 (Harmonic Mean)
= 2 which also means 1/2 the frequency.
But since it's also geometric mean squared the same
new "positive coupling" creates an increase in
string length as momentum or amplitude and an
increase in frequency NOW AS TENSION from weight.
This is where Newton got his "inverse square law"
with 4 times the weight (or pressure) stretching
the string length to twice the frequency, again
in contrast to the law of Pythagoras stating that
twice the string length would be half the frequency.
What Einstein did was just consider that at the speed of light the change in velocity (c) now just converges
at its own maximum (so it's c squared) while the
weight or momentum changes as mass.
Again Einstein is relying on mass which was originally weight
as frequency turned into amplitude as string length --
the concepts combined as geometric mean to create mass
while the concept of complimentary opposites was lost.
But the "positive coupling" of natural resonance whereby
subharmonics of frequency create a significant increase
in amplitude, as biology professor Brian Goodwin
details in his "Temporal Order of Cells" book, indicates
not the use of weight as mass, with geometric mean,
but instead the change of wave-form with nonlinear
feedback that actually diverges to consciousness
or what some biologists call "sound-pictures." This
positive coupling, instead of being based on weight,
is simply using the complimentary opposite harmonics
and is modeled in science as the Time-Frequency
Uncertainty Principle.
Great Galactic Gasshole, you really are a colossal
................
crashing................
bore. Go Away. DIE!!!
GGG: if you're going to make brash claims you should at least be more careful about your wording.
Sqrt(2) is not transcendental. Transcendental means that it is not algebraic which means that it is not the root of any polynomial with algebraic (integer, rational) coefficients.
If you are asserting that sqrt(2) fails that test could you solve
x^2=2
for me?
If you mean it doesn't have a closed form you could just say that. But thats not very glamorous considering NO irrational numbers do
to G.G.G. ...
but ... can you hum it ...? does it groove ...? "Shruti Mata, laya Pita" as they say in India !!
Jeff, good luck & get well ... garlic's a plus but so is warm brandy & aspirin, MOSTLY; rest!
Happy New Year to all ...
AD
A Short Quote from Satan to his Legions: "Don't worry, folks, it's all downhill from here."
The Book of Tobacco, Chapter 13, Verse 39
Jeff,
Never posted here before, but Happy Holidays/Merry Christmas/Happy New Year, and I hope you feel better.
Thank you for this- I've heard of this lady but never heard her before and this song is what I needed to lift me out the slump I've been in these last few weeks; thanks for the Christmas present- you did this for me last year too, with "A Fairy Tale of New York". She looks down-to-earth kissable and cuddly; keep you warm on these long nights, eh?
Also, if you run short of verbiage in the comments I have a 200-odd-page PDF on fiber LAN networking from Corning I've been wading through with lots and lots of paragraphs and things, just what's needed to fluff everything out on a slow day and keep everyone's scrolling fingers exercised. Lemme know if you need any of it ;-).
Peace
Happy yule and a benevolent solar year, Jeff
Hey Jeff,
I have not visited in a while because of work but will always come back for more. Although I question some of your positions I fully appreciate the way you write them, truly a given talent.
I wish you and your family the best for 2008, as well as other bloggers on the boards.
Yep my hips as LOOSE and I listen to Anuradha Paudwal all night long.
Here's the paper you'd need to read on the square root of two:
Philosophy (1999), 74: 169-176 Cambridge University Press
Copyright © The Royal Institute of Philosophy 1999
Published online by Cambridge University Press 04Apr2001
Did the Greeks Discover the Irrationals?
Philip Hugly and Charles Sayward
Abstract
A popular view is that the great discovery of Pythagoras was that there are irrational numbers, e.g., the positive square root of two. Against this it is argued that mathematics and geometry, together with their applications, do not show that there are irrational numbers or compel assent to that proposition.
Late breaking news:
http://www.washingtonpost.com/wp-dyn/content/article/2007/12/29/AR2007122901476.html
Excerpt:
New York Mayor Michael R. Bloomberg, a potential independent candidate for president, has scheduled a meeting next week with a dozen leading Democrats and Republicans, who will join him in challenging the major-party contenders to spell out their plans for forming a "government of national unity" to end the gridlock in Washington.
Those who will be at the Jan. 7 session at the University of Oklahoma say that if the likely nominees of the two parties do not pledge to "go beyond tokenism" in building an administration that seeks national consensus, they will be prepared to back Bloomberg or someone else in a third-party campaign for president.
Conveners of the meeting include such prominent Democrats as former senators Sam Nunn (Ga.), Charles S. Robb (Va.) and David L. Boren (Okla.), and former presidential candidate Gary Hart. Republican organizers include Sen. Chuck Hagel (Neb.), former party chairman Bill Brock, former senator John Danforth (Mo.) and former New Jersey governor Christine Todd Whitman.
Boren, who will host the meeting at the university, where he is president, said: "It is not a gathering to urge any one person to run for president or to say there necessarily ought to be an independent option. But if we don't see a refocusing of the campaign on a bipartisan approach, I would feel I would want to encourage an independent candidacy."
The list of acceptances suggests that the group could muster the financial and political firepower to make the threat of such a candidacy real. Others who have indicated that they plan to attend the one-day session include William S. Cohen, a former Republican senator from Maine and defense secretary in the Clinton administration; Alan Dixon, a former Democratic senator from Illinois; Bob Graham, a former Democratic senator from Florida; Jim Leach, a former Republican congressman from Iowa; Susan Eisenhower, a political consultant and granddaughter of former president Dwight D. Eisenhower; David Abshire, president of the Center for the Study of the Presidency; and Edward Perkins, a former U.S. ambassador to the United Nations.
My word verification was "wawewjba" (looks kinda Jewish, don't it? or rather, a "goyish" way to say "jewish", or something)
IC
A thought for you - how's the shoulder, man? Rest up and all best wishes for the next stretch.
Looking forward to reading you again soon.
Here's to your health!
Jeff, after all these years I never had a chance to say thanks for the link that STILL points to my old writings.
You date to enter where others fear to treat. Even if many of us readers rarely "decloak" to express our support, it IS there.
Pax
can someone verify for me whether that is standard kentucky bluegrass?
It seems to me to epitomize the highest virtues for which mankind is designed and may aspire to.
However, due to hearing impairment, while I can hear the music, I cannot understand any of the words.
GGG
could you possibly summarize the article on the sqrt(2)? I can only find page one available without paying some crazy amount for the 8 page article
thanks, very interested
A transcendental number is a number that can not be solved in an algebraic equation. The essay "Did the Greeks Discover the Irrational?" (1999) by Professors Hugly and Sayward argues that the square root of two is NOT solved as an algebraic equation -- specifically that while it's proven there's no rational number, this is not an algebraic proof for a positive number called "the square root of two." In other words the answer to their title "Did the Greeks Discover the Irrational?" is NO and no one else has as well. This is why Bertrand Russell called the square root of two a "convenient fiction." Or to put it another way it's proven, by contradiction, that there's no ratio of phonetic letters, based on the commutative principle, for the hypotenuse of a 1-1 triangle. That is also the definition of a transcendental number -- that there is no algebraic equation demonstrating the existence of the square root of two. I already gave an earlier source discussing the transcendental value of the square root of two -- the book "Enquiries In Number Theory."
The real clincher for this complimentary opposites argument is Simon Stevin's 17th C. conversion of Archytas' diatonic scale into equal-tempered tuning. Stevin relied on the octave defined as a starting value of 5000 with it's "double" as 10,000. Stevin then argues that half of the octave is the square root, or the tritone and so a third of the octave, or two major second intervals, the major third, is therefore a cube root of two.
This fully accepted modern basis for equal-tempered tuning -- that which is considered to be the truth -- is directly from Archytas' proof for doubling the cube, namely that if a cube has a side one then to double the volume to two, the side must be cube root of two with the proportion 1:5/4::8/5:2. That's the exact equation Simon Stevin used -- only converted to logarithmics.
As I discussed in my article above and in my previous blogbook chapter, the subject of several emails from math professor Joe Mazur, Archytas' source for the cube root of two is from Babylon's use of the equation, arithmetic mean x harmonic mean = geometric mean squared.
So again Stevin ASSUMES the value of the cube root of two without discussing the ORIGINS of the square root of two and all this time no one has questioned that fact that the arithmetic mean x harmonic mean equation Archytas relied on to create geometric mean is based on the octave, not as a doubled value, but as a SQUARED valued.
Again having arithmetic mean 3/2 x harmonic mean 4/3 = 2 with 2 as geometric mean squared so that 3/2 x 3/2 = 9/4, the major second above the octave or the 11th interval (with 4 as the octave "squared" not doubled) and then halved to the sixth root of two as 9/8, the major second, cubed as the tritone or the square root of two is the source for Simon Stevin's equal-tempered tuning. The cube root is then just double the sixth root -- or 10/8 as 5/4, the major third music interval.
So Simon Stevin used the geometric mean equation A/B = C/X with X=BC/A just as Archytas used the arithmetic mean equations with A = 1 and X = 2. Only with Archytas it's not said what "X" is -- so the Babylonian geometric mean is 6:8::9:12, ostensibly the same as Simon Stevin's A:B::C:X but this time reduced to either 2:3::2:3 or 3:4::3:4. Archytas, in solving for the square root of two excludes the START of the octave -- which again is now no longer doubled, as is the case in the harmonic series, but is squared. SIMON STEVIN CONVENIENTALLY IGNORES THIS HARMONIC SOURCE FOR THE SQUARE ROOT OF TWO. So Archytas converts this process that starts with 1:2 as 6:12 so that 6 would be A and X would be 12. Instead Archytas reduces this to a 3 term equation with no "X" so that A = 1 and C = 2 and then what had been 2:3 as 6:9 is now the RESULT of the octave as arithmetic mean (A + C divided by 2) equals 3/2. What had been 3:4 as 6:8 is now the RESULT of the octave as harmonic mean (2 x AC divided by A + C), thereby HIDING the complimentary opposite harmonics of 1:2:3:4 and replacing a doubling of the octaves with a squaring of the octaves (2 is now geometric mean squared with "half" of the octave now the square root of two as the tritone).
The "Greek Miracle" was to take that "divide and average" algebraic series for the square root of two and then apply it to geometry as the PRECISE SYMBOL, "the square root of two," -- no longer an approximation. It was called "alogon" but was similar to the apeiron or "negative infinity" used by Plato to introduce zero. The article I refer to argues, as is obvious, that the algebraic solution is a proof by contradiction, when applied to geometry, and as an algebraic series, the solution is infinite and not geometric. The algebraic equation does not converge to the square root of two as a positive solution and even Cantor could not prove that the real numbers converge to a set, but only exist as a series. Therefore the PRECISE symbol for infinity, the square root of two, is logically flawed and, again, "a convenient fiction" (Betrand Russell).
This logical issue is contemplated in math (for example in Carl Boyer's book "A History of Calculus") and ignored because math "works" -- but the question is for whom does math work? It's based on a rotten root and so as the math expands, as mass squared inversely proportional to energy frequency distance, so too does the ecological crisis expand.
My point is to reveal the secret complimentary opposites foundation of where the square root of two originates -- in music harmonic ratios. So just as the Golden Ratio requires REVERSING the order of the Fibonacci Series to enable a geometric quadratic solution, using zero, so too does the square root of two algebraic solution ignore the REVERSAL of the harmonic series ratios as frequency, into time as geometric distance.
WTF what happened to RI?
Something suss is happening here!
What's with all the BS cut and paste comments about irrelevant crap.
Also I was sure Jeff would have commented however briefly about the current intrigues developing on the subcontinent.
This was once an awesome blog and discussion place but seems to be heading down the toilet
Mystery solved AND dig that funky background sound, @ YouTube
http://www.youtube.com/watch?v=Z7iQRFP_e90
there will always be a new RI so why bother trying to stop it?
pity the fools
Nice video, Jeff. It's good to escape a little now and then, if not just for the sake of sanity.
I'm a little worried that when I order Spore when it ships in March, and I'm also worried my computer isn't up the challenge. I mean, have you heard anything about Spore system requirements? It's got to be a process hog...
The home of the infamous european toxic clan, psycho urban fraggers that pawn the virtual return to castle wolfenstein enemy territory battlefields.
Just Pub, a dumb return to castle wolfenstein enemy territory comic strip by feuersturm.
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