|12 Aug 2010 @ 15:55|
As a child I once got spanked for peeing at the side of David Hilbert's grave in Göttingen. Besides the obvious humiliation, what remained in my traumatized mind were Hilbert's supposedly last words, engraved on his tombstone:
„Wir müssen wissen.
Wir werden wissen.“
("We have to know, we shall know!")
Did his postulate 'stick' with me? Are there 'positive engrams'? Is it that what's driving my relentless mind to dive into the abyss of human thought?
Be it as it may, Hilbert's assertion, and likewise his curve, never ceased to spook around in some remote regions of my brain, and, strangely, just when I thought I could safely forget about it, I'll be reminded immediately that a problem just doesn't walk away if you simply ignore it.
Just like Riemann, Gauss, and Moebius [link] , the ghosts of Göttingen are still haunting me.
Back in LA, Tony Matweecha RIP, the man who proved that Riemann's sphere is NOT a sphere (by the simple laws of homology since there is one point on the top of the sphere for which there is no tangent), Tony had this to say when I told him how and why I got spanked many years ago: "did you notice that your piss went down in a curve, parabolically to be more precise?" Well, right on, that's how a mathematician thinks after all. I already eulogized Tony on this Blog more than once, so here goes another one of his gems, one for which he didn't take credit himself but assigned it to his own math prof at UCLA, a former assistant to Albert Einstein at Princeton:
If Einstein were right and space were curved and Riemann's transformation were applicable, with the help of a super-sharp razor from Occam's stock, being located on Earth, we MUST conclude that the true shape of Earth is in reality a PLANE.
Of course, this didn't win him any friends even though he PROVED IT WRONG, far from it, and so he died alone, after some fruitless NASA years in Pasadena and a decade of visualizing new solutions for approximating 3D splices in a japanese mini-thinktank. Still to these days, the mentioning of the mathematical possibility of Earth being a plane, if Einstein's assumptions were correct, that is, drives anyone ballistic, sure enough, so, for the record, I'll officially refrain from mentioning it and yield to the brute force of Copernicus' counter-Meme.
To the dismay of the managers of the hitech lab, we filled Tony's room with smoke so thick we could study Hilbert's and Beelzebub's curves in the drifting clouds above us, measuring cigarette consumption in octaves rather than packs. Would it not have been for the heroic figure of GZ joining us frequently, nobody other than us would have seen these strange twists of the shape of this Universe, unfolding for us while coughing our lungs out.
To recap, Beelzebub's FIRST law of the Universe is, of course, the law of the triad, "Trimonia". Gurdjieff would not have been the genius he was, if he would have ignored that one. But the second law, Eftologodiksis, is what it's all about, the curvature of the space in which we live, and the resulting birth of the octave and the lambdoma, where Gurdjieff and Pythagoras are joining themselves in the infinity of Meme-space.
It consoles me somehow that Beelzebub pulled out another law, the ‘Accumulation of Similarities’, in order to justify the jump from a curved line joining in itself in infinity to the phenomenon of the Octave. Sometimes I wish that Anton Walter Smetak [link] were still alive as he jungled with the lambdoma like noone else since Pythagoras&friends.
But hope is on the way: I'm working hard on convincing Mark II (what a prodigenous name!!!) to do a retranslation of Gurdjieff's chapter 39 of his 'Beelzebub's Tales to His Grandson'. And, who knows, a congenial mind like his, may very well uncover the mechanics of the ruminations of Gurdjieff&Beelzebub. Let's hope he doesn't twist his brain to pieces while attempting this gigantic task.
Meanwhile, let's sit back and watch the drift... or, perhaps, if I weren't that lazy, I should really start an expedition to find that ONE spot on Earth that cannot be touched by a tangent of REAL Earth, the plane that is, you know what I mean. Which may very well make Hilbert forgiving me for peeing on his grave. After all, it would prove Riemann wrong. What else could a mathematician hope for other than disproving another one of his own kind? More >
|11 Aug 2010 @ 19:13|
Few have realized the full importance of the ability to have the attention on more than one object of the senses at the same time. In fact, other than Gurdjieff and someone whose name I don't remember, was it Osho RIP?, nobody talks about it, if one can believe the Google search engine, do you?, unless it appears as a PROBLEM rather than an ability.
Yes, that's right, a PROBLEM. The mere thought of doing two things at the same time seems frightening to some people and you'd better be prepared to defend yourself, physically if necessary!, if you think of proposing it to your neighbor, friend or foe.
In the attached picture, one of the 'collective' instruments of Anton Walter Smetak (from the book 'Simbologia dos instrumentos', Associaçao dos Amigos do Smetak, Salvador 2001). He called his instruments 'instru-mentos', designed to instruct our minds to see beyond the mono-vision of our prevalent culture, towards a 'supercosmic, supermental, and submental reality' (he quotes Sri Aurobindo).
Music expands our awareness by oscillating between extremes, raising awareness of the polarities in life, the dance of Shiva and Shakti, and the mediating part of communication between the two. Even though his nomenclature of Indian devas and super-devas is drawn from confusing sources (and readers of this Blog are unforgiving in such things!), Smetak's observations of the underlying principles of dualities and triads in music, which for him is LIFE itself, are enlightening and clearly deserves an audience beyond the speakers of the Portuguese language.
Yes, double attention, nothing for the faint-hearted (disclaimer: don't engage in such hideous practices while driving a vehicle or operating heavy machinery!). And it's sorely missed in today's school books.
Such is the case for 'peripheral vision' as well, it seems. Far from being only a 'must' for airplane pilots and not limited to the natural talent of daughters of Oshun in studying male prospects without giving away any sign of her interest, these skills can and SHOULD BE learned by everyone, beginning at the preschool level.
Today's society experiences a state of vertigo. Spaceship Earth is in a spin. Recoverable or not, it's a bad thing, as every pilot knows. Unless you're flying aerobatics. And even then, the last time I did, at Burbank airport, I was vomiting for 2 hours after 5 flat spins in a row (this was in fact the last time and I deep-sixed my planned career as an aerobatic pilot right there and then).
Maybe we should start a war against monovision? Let's beat the foveas out of our lives once and for all! Playing our minds as collective instruments rather than trying to trump each other with intellectual games which are fun but rarely yield what's promised.
Peripheral Visionaries of the World, Unite! More >
|30 Jul 2010 @ 16:30|
Anton Walter Smetak, 1913-1984, wrote in an enigmatic way, mixing contemplations of art with philosophical speculations and humanistic insights of profound depths.
My take on his way of seeing life may not be accurate and I don't know therefore if he himself would have approved it or not.
But he shares a particular direction of viewing, in common, interestingly enough, with fellow Frenchmen Pierre Verger (1902-1996), Claude Lévy-Strauss (1908-2009), and the Englishman David Bohm (1917-1992), to name a few, in that they touched Brazilian ground, especially the magic land of Salvador, Bahia, and reversed their occidental way of seeing Life, Universe, and Everything. Some, like Smetak and Verger, never left, others kept dreaming of being there (Lévy-Strauss: Tristes Tropiques & Saudades do Brasil) or traveled on to other mystic lands, like Bohm teaming up with Krishnamurti.
They all seem to have parted from the nightmarish occidental vision of having fallen from grace, expelled from paradise and they do not endorse the Western lifestyle of consumerism, its ever more obvious decadence, increasingly so in recent decades. Some try to find their way back to nature, Ralph Waldo Emerson-style, and decry the impact of modern technology on human conscience, but they very well know that the wheel cannot be turned back.
Setting foot on Brazilian soil changes perspectives, at least of some of the great thinkers of the past century, and, beyond mere escapism, enables a positive stance, a shimmer of hope, for societies of the future:
Like Jean Baudrillard (1929-2007) puts its [link] : "Perhaps Brazil, Italy and Japan are in this respect more advanced societies than America. Pessimism itself is something that only afflicts Western values and is itself part of Western values."
Below, or behind, these contemplations we can find another paradigm, and Walter Smetak examplified this point clear and concise like no one else:
the question of diversification versus global norms, the former a natural phenomenon in all cultures of the past around the world. the latter now imposed, and even enforced as necessary, equally on all countries on Earth.
It seems that Brazil left the impression on the noted thinkers that it could escape this dictate and preserve at least a portion of its stunning diversity. As time passes on, this too seems an illusion, the tollbooth barring access to once public roads look alike in Brazil and Italy and the United States, and nobody seems to notice that it is a fall-back to medieval practices that were believed to have been overcome. The ever-expanding laws to rule the individuals and their families in every little aspect of their lives walk their grim path forward in unison in every part of the globe.
Smetak proposes, carefully implicitly, that a standardization of cultures is AGAINST the law of Nature, that it may be even blasphemical to curb or squelsh the variety that the human mind produces. That any truly religious man, whatever denomination he may count himself to belong to, should stand up against it and insist that diversification is the 'will of Gxd', whatever name you'd call her or him, if there should exist anything beyond the symbol of itself.
Nature's innocent vanity, its display of beauty on every dimensional level, from the stars at night to the fractal beauty of visualized mathematical formulas, and to the wondrous world under the microscope, indeed would seem to prohibit any 'norm' on any level as an interference with the divine will, the expression of the sacred behind the appearance of the ordinary.
It seems that nothing can slow down the invasion of our last jungles by the global food chains which are implanting their plastic & uniformal trade-marked stamps on everything they touch as they eat they way through our societies.
But it is the people, or better, the manipulated consumers who were made to think that they would have a 'choice', that makes it possible. And who could stop this disastrous march by simply insisting on their own culture. Or by creating other alternatives... More >