Monday, December 5, 2016
It is now time to admit that Gödel's problem can be solved by High Schoolers. #Gödelsproblem
Let me show you how. #Gödelsproblem
First let us admit That most proofs are mechanical. #Gödelsproblem
so for any given proof we may solve it by mathematical means. #Gödelsproblem
but we first must ask if the problem is mathematically oriented. #Godelsproblem
we can do this by a mathematical statement saying "Is X provable by mathematical means" #Gödelsproblem
so the query is " is X provable" or 17 Gen(r) #Gödelsproblem
then we ask: if this can be proven, then the opposite can also be proven. #Gödelsproblem
which means that it is statement is: " X cannot be proven." #Gödelproblem
but if this is true, then any proposition that comes from it must be false. #Godelsproblem
this has been known for quite some time in popular literature. #Gödelsproblem
but, says Gödel, if a problem is mathematical, then it can be arranged as a sum of primes. #Gödelsproblem
because each prime will represent one truthful mathematical statement. #Gödelproblem
So that means one has to use recursion. which is by now in the language of mathematics. #Gödelsproblem
thus we can set a counter, say g++ #Gödelsproblem
and incremented for each time we pass through the problem. #Gödelsproblem
this means that the problem is incremented by 1, and is thus different. #Gödelsproblem
but says Gödel, this to is a mathematical principle #Gödelsproblem
so each time is a recursion which is different #Gödelsproblem
which means that each time through is a unique problem #Gödelsproblem
and since the problem is unique in terms of primes, but solvable and finite #Gödelsproblem
Thus a unique collection of primes is also a proof. #Gödelsproblem
so the mathematicians stated that cannot use " this statement cannot be proven" #Godelsproblem
which seems to head Gödel off at the pass #Gödelsproblem
but, says Cohen, their is more than one place to introduce a proof like Gödel's. #Gödelsproblem
Thus one cannot simply say that in one place a prohibition will work #Gödelsproblem
so what we can tell high schoolers, is that Gödel's problem is a problem for Boolean logic, on which it is based, and a simple provision will not get rid of it #Gödelsproblem
references: On Formally undecidable propositions of PM and related systems (Gödel) and Set Theory and the Continuum Hypothesis (Cohen) #Gödelsproblem
And the extension is based on Cohen, I am just copying it down #Gödelsproblem
In a Hall Half His Age
The Museum of Fine Arts
“Now and then it's good to pause in our pursuit of happiness, and just be happy.” Guillaume Apollinaire
The stillness in the air is a confusion of prisons and sorrow, he lifts his eyes from the page and stayers into a heady distance. The watcher who stands looking at the pen and ink drawing realizes that he is watching not a figurine dressed in ordinary clothes, but a picture of the inner garments of the man, conjoining each manifold in a geometric structure. The old world of romantic poetry is overthrown, and the inner triumphs over the outer. 30 years before, he would assume and Impressionist form of life, for example, by Monet, or perhaps one of the other workers in that same vein. 50 years ago, he might catch the eye of romantic attachment, only vaguely whispering the insincerities of just a hint that says that this painting is not real enough, but has the hint of something beyond real. But not too much, people would not understand this.
A heady moment comes over him, because he was just outside a few minutes ago, where it was not very warm, but he had been exerting himself, because of all of the throngs of people visiting the Museum of Fine Arts, he was perhaps, the only person who was specifically going to see a few drawings on the wall which were marked within 50 years of the beginning of the last century. It was entitled something grand, something extraordinary, which no one else but Museum curators would barely notice, and would be forgotten by the masses of people, most of them looking for their favorite piece, or pieces, of art.
This being the MFA, their was a large selection, some people were here for the Egyptian, some people here for the Greek and Roman, still others would be staring at the Renaissance, and a few more for the Chinese, and of course there were the people who flogged their favorite era which only they knew the meaning of. Then there were the people who want something new, and would be enthusiastic about whatever they were told to be enthusiastic about.
But the young man was virtually the only person to really look at the pieces, and to begin to form in his mind a fast detail which he only glimpsed the barest fraction of. The didn't know which pieces he would assemble, but he would gravitate to some which spoke his internal language. One which had stopped him was the angular detail of a poet, by the name of Apollinaire. What he knew about him was only from one book of his poems, and some detail from an obscure commentator, whose prose gravitated towards the abstruse, not to say clouded in his language; because that was just barely not the case. But there was far more in the single detail of a brushed stroke, then in the myriads of prose dumped on the page by the would be author between poems of Apollinaire.
“When men want to make a machine that would walk he created the wheel, which does not assemble a leg.” Apollinaire
Between the seething text of the scholar, in its propped up scale of detail, there was a glimmer - the original being far superior to the translated text – that showed a man of the 20th century gliding his way after what then was called The Great War. In it he cast away many of the old lessons, though he kept a few, and looked in to the common eyes of man; there he found meaning, not in the concepts there described, because he did not think much of the common man, in sich, but in the mass of their humanity. He was struggling to put on paper that detail that was inescapable. In other words, he was trying to tell the intelligentsia, who was poor but noble, what they were trying to get the common man to believe.
“Without poets, without artists, men would soon weary of nature's monotony.
The plastic virtues: purity, unity, and truth, keep major in subjection.” Apollinaire
He had not been much of a fan, except for a few poems, which he felt were fresh and new and different than the other poems that he wrote. But then, he understood that what had happened was that Apollinaire had not been given the primary necessitated of genius: that being a follower who could explain what is he was trying to say, and point out which works were important, and which works could be dispensed with, or at least, left for later.
If after this discussion you do not realize that the author was not the person who would act as intercessor for his subject, I don't know what will draw out the line. I am trying to say, delicately, that the scholar was shit. And even this expression is part of the problem, because in the interwar years, people want to express most things in deep enamored tones, and then draw out in scatological device the excrement which surrounds and encompasses them. This is because the hallways were clean, but the entry ways, and more so, the outside, was covered in what the French call “merde”.
Between the heightened and exquisite prose, and the device that contrasted them with more baser impulses was the height of expression of this new style. The older style did not recognize the baser, it divorced all aspects from its vocabulary. No hint or trace of the vocabulary of retching, shitting, or any such vestiges would remain in adult conversation. The entrance of such words, while contrasted with such fullsome interpretation that remains true to its higher purpose. Thus, it maintains a link backwards to the purest of the old, while linking forwards to an unknown world, where the raw stuff of the world at large rests, and that includes the baser reflexes. And that means shit, not excrement. Now Apollinaire was only the beginning of this process, and he did not even mention shit, but it was the expectation of engaging in a distant present which made it inevitable. There is simply no way to talk about the present, with out talking about to talk about the differences between excrement and fornication, and shiting and fucking which lies at the end point of this process.
It began with forming a picture out of words; The young man remembered one such picture as a face with a broad brimmed hat and some kind of shirt, but in fact the lines on this face were etched out of words. “Recamais-toi” piqued out of the hat, and other words draped out of the shirt. He remembered it very well as he looked at the painting in the foreground. Know and of what was to happen in 20 years would ever usher forth, and yet there was indeed something queasy about it.
“Come to the edge, he said. They said: We are afraid. Come to the edge, he said. They came, and pushed them, and they flew.”
Words and pictures, the two are as oil and acrylic, never the twain shall meet.
While he might look as if he were standing there, in reality his minds eye had captured his brain, and loosed it images which were both word and picture both. The minds eye kaleidoscope over a tundra of images, each one called for his attention, each one different from the last. But what made the most impression was of la tour Eiffel, made up with words he could not quite grasp.
Remember at the time that the image was raised on canvas, it was only 25 years since the tower was raised, and that meant that not only was words and pictures a new thing, but the tower itself was a modern image, not something old, and established. The young man could see the Eiffel Tower from across the river, where he viewed it on the days when he lived there, going down to Avenue de New York and stared over the wall separating what he thought as North from South. He remembered all of the details, though he was sure he had filled them in, rather than remembered them. But still the same, he could picture himself staring up at the Tower, and then it faded into a melange that was of words and pictures he had seen some 10 years ago, on a magazine cover. He thought it was Pari Match, but he was not sure, except that it was French in content.
Even at the time he read several languages, that being one of the gifts from an uncle, the gift of speaking. Which was greater than every gift he could realize.“I love men, not for what unites them, but for what divides them, and I want most of all what gnaws at their hearts.” Apollinaire
But now he stares at an assemblage that is meant to represent what the drawer perceives as the core, not internally, nor externally, but hidden beneath all windows and expression getting to the deep core of the Inner Man. Thus it in no way resembles a drawing which depicts, nor does it depend only on expression has defined by the Germanic school, but instead carries with it A certain Latin clarity, Reverbertion ou lumiere of the Roman empire that France, rather obviously to them, should be the inheritor of.
Which is why there is not one respective, but several, interlining and overlapping with a collage that resembles a series of stained glass, from the Romanesque period. This is as it was as it began, the medieval guidelines with the modern, especially in the eyes, glaring out in two space, as opposed to a picture one could actually believe took place. Of course it couldn't, because there was no respect that actually represents the figure, everything being to sharp and clear. It was that way in this picture, but it was garish in the details of it, and took such flare in repeating the tawdry little details that come with a prospective wholly out of line with anything natural. In short it was a prism, capturing the inner essence without a single trace of beauty.
“One can't carry one's father's corpse about everywhere.” Apollinaire
Thus it stared out at the viewers, as much as they stared back at it. And if really looked, that distortion of prospective grinds into your eyes, until you don't know whether you are staring at the canvas, or whether the candidates is staring back at you. And as people tried to mill away from it, by either turning away very suddenly, or by backing away with their face still upon the picture, it created a zone around it where the magical eyes held sway over all that truly looked at it. Of course a number of people did not look at all, only glance at it while talking of other things, either towards the Contemporary Wing, which this was temporarily a part of, or coming back and discussing which room they were going to visit, absorbing the French Baroque, or other manner of old rooms that were ahead.
But the people who had here eyes establish in the early part of the 20th century, could not look away with a straight face. Some were enamored and beguiled by a person who sat on canvas as if still alive; others were disturbed by numerous perspectives all competing for allegions with their eyes. But the man stared in two the page, letting all of the people whisk by him, trying to fathom what was he was thinking about. The man seemed very calm, indeed calmer then most of the people looking at him, he also had something on his mind. But what remained the question. It was absorbing to the man; though no trace of what it was beguiled the whisper on his face.
“Joy always came after pain.” Apollinaire
Try as he might, the young man could not imagine what it was; and so slipped in to dreaming about it, fashioning himself as a spectator on the canvas, talking about what it was was on Apolloniare's mind. This though he did not know exactly what it was, but he imagined it was something intellectual and brilliant, as the poems were underling. Then he slid back out in to the vantage point of the museum, and looked down at a poem.
I realize this is the right moment to talk about the Jean Metzinger, which though in the same style, is wholly different in its partaking of the same subject. The drawing in the museum does not depict the human side that Metzinger wanted to capture under need the cold exterior, but want to capture the pure cerebral intellect. Normally the painting would have hung in Harvard, so it was a short hop to displaying it across the river in the Museum, but it was far in terms of the number of visitors which it captured. Their were more people in an hour, then in whole weeks in its permanent home.
“A structure becomes architectural, and not sculptural, when it's elements no longer have there justification in nature.” Apollinaire
The problem, you see, is that when nothing is happening, just the eyes of a person communing with a painting or a print, that is the time when there is true affection, or hatred, or anything else that wants to name. When there is action, it might seem like that is what is truly important, but that is never the case. It is in that repose of quiet that the real activity is happening. Because in that arc second there is a true connection, even though nothing is happening, because it is interior forces, such as the main character in Max, a quite little film with Hitler played by not a Hitler, but someone else who has different aspects then the real one. Max, of course, is the main character – and his of sessions become ours if we want them to be.
That is also what is happening in the Museum of Fine Arts, for every moment that slips away, every second rejected and gone, is another second which everything is turning and the entire exhibit is turning into a minor key. But this is a rich minor key indeed, and no usual sounds can come out of this. It drips and wafts, and then stands upright like the Dragon in Wagner. Who is creepily in tune with the young man who is thinking about the relationship of eras which have revolution on their mind.
The main difference between German and French forms of revolution, was that the German form when you looked at it became messy and there were the kind of lumps, the kind that made everything foreboding and forbidding. Where as the Frankish form became lighter and could dance on the head of a pin. It performed as dancing music, where as the German form portrayed people who were dressed up like Vikings, and sang a great deal.
But what truly wrenched him in to the present, having wafted in an of his minds eye, was a group of people who were gaping and gawing over the whole set of works, not a very much attention to any of them. Then a little girl pointed at Apollinaire, and said very loudly, having not yet realized their was the etiquette of speaking softly in a museum, “Mama, what is that?” The adults rushed to muffle her speech, but the young man sent down on his haunches, and looked in to her blue blue eyes. Then he said:
“That is a great man, of which you have not heard. Go home, and look up Apollinaire, and begin reading about him.”
The battle for Mosul stalls: 'we are fighting the devil himself' | World news | The Guardian
The premature announcements of victory were mistaken.
The premature announcements of victory were mistaken.