"; #Find the current month while (@sd0[1] ne @mnt[$j] && $j <= 11) #If @sd0[1] == @mnt[$j] Then @rd[2]/4 must be == $j { $j++; } if ($j == @edt[1]) { #CGI expires Same month. Then the current date must be le recorded date if (@sd0[2] <= @edt[0]) { $cv = 1; } } else # Different month. If it is $j + 1 { if ($j == 11) {$j = 0;} else { $j++; } if ($j == @edt[1]) { #CGI expires Next month. Then the current date must be gt recorded date if (@sd0[2] >= @edt[0]) { $cv = 1; } } } } # Main body of the script sub do_main { $guestbookPage = $ENV{'HTTP_REFERER'}; $cl = $ENV{'CONTENT_LENGTH'}; print "Content-type: text/html\n\n"; &vcv; if ($cl > 0) { read(STDIN, $_, $cl); $_ .= "&"; # Append an & char so that the last item is not ignored $pquery = &reformat($_); while ($pquery =~ /city=([^&]*)&/) { if (!$city) { $city = $1; } else { $city = $city."\n ".$1; } $pquery =~ s/city=([^&]*)//; } $city = &reformat($city); while ($pquery =~ /state=([^&]*)&/) { if (!$state) { $state = $1; } else { $state = $state."\n ".$1; } $pquery =~ s/state=([^&]*)//; } $state = &reformat($state); while ($pquery =~ /country=([^&]*)&/) { if (!$country) { $country = $1; } else { $country = $country."\n ".$1; } $pquery =~ s/country=([^&]*)//; } $country = &reformat($country); while ($pquery =~ /comments=([^&]*)&/) { if (!$comments) { $comments = $1; } else { $comments = $comments."\n ".$1; } $pquery =~ s/comments=([^&]*)//; } $comments = &reformat($comments); # <<<<< Do not alter anything in the above section <<<<< # >>>>> Start of User configurable section 2 of 2 >>>>> print "
\n"; print "\n"; print "
Form accessed at $ProcessTime from $ENV{'REMOTE_HOST'}\n"; # Although the next line can be removed without causing an error, we request you to kindly retain it. print "
\n";
print "\n";
}
}
# <<<<< End of User configurable section 2 of 2 <<<<<
$misterwolf = `/bin/date`; $misterwolf =~ s/\n//g ;
$ProcessTime = `/bin/date`; $ProcessTime =~ s/\n//g ;
$mailreceiver = "arch\543p@pratt.edu";
$|=1;
eval '&do_main';
sleep(1);
# ***** End of the Perl Script file. *****
{
print " Please set it manually as follows:The Italian Passport
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".... Is a science like geometry possible? How as a systematic, endlessly growing stratified structure of idealities, can it maintain its original meaningfulness through living reactivability, if its cognitive thinking is supposed to produce something new without being able to reactivate the previous levels of knowledge back to the first?"
What Husserl is asking is where does one begin, where does one start in the challenge of understanding geometry? How far back do you have to go to make geometry self evident? Husserl suggests to go to the origin of geometry, to find out how and for what purpose geometry developed, but in doing so, Husserl cautions us from the historicism that doesn't go beyond the usual facts. The reactivating of geometry must include in it a personal vision, because it "involves a lively productively advancing formation of meaning." Geometry, Husserl says, "is not a handed down ready made in the form of documented sentences." To be meaningful, geometry must have I think that this means that there is room in geometry for interpretation. Serres does what Husserl suggests, by realizing that "beneath the theorem of Thales (involving the pyramids) a corps was hurried." Serres connects two parallel lines by bringing ritual back in to the history of geometry. Husserl brings ritual back to the act of trying to understand geometry, in the present. He writes, "it is something special...to have the intention to explicate, to engage in the activity which articulates what has been read, extracting one by one, in separation from what has been vaguely, passively received as a unity, the elements of meaning, thus bringing the total validity to active performance in a new way on the basis of the individual validities. What was a passive meaning - pattern has now become one constructed through active production. This activity is a peculiar sort of self evidence; the structure arising out of it is in the mode of having been originally produced." (Later in this paper, this will become the definition for drawing, it also sound to me like a definition of abstracting (?)). So in order to reactivate geometry, one must go to the absolute origin of it but still somehow "originify" the past by a kind of invention. Geometry, I think, exists only if we are conscious of it, and for one to be wakefully conscious of geometry, geometry must touch on more levels of our lives than just logic. How does geometry mean more? Could the deaths of Hippasus of Metapontum, Parmenides, and Theaetetus (which Serres suggests were related to the crisis of irrational numbers) mean more to the development, and present existence of geometry than we are ready to admit? If so, should we document more closely the deaths of those flirting with the fifth postulate?
Lets go to Euclid's five postulates written in about 300 B.C.
Let the following be postulated:
In other words, through a point outside a given line it is possible to draw only one line that is parallel to the given line. Euclid wasn't satisfied with the fifth postulate because straight lines were infinite. Many struggled to prove the fifth postulate (the new crisis). The elder Bolyai, in a letter written in 1820, warned his son against any obsessive interest in postulate five. "You should detest it as much as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life." But young Bolyai did work on the fifth postulate and he wrote his father, "I was astounded...out of nothing I have created a strange new world." What led him to this strange new world was assuming that the fifth postulate was wrong. The way that I understand it is that Bolyai and those who followed him were reading geometry three dimensionally, and so those two lines that are on the side on which the angles are less than two right angles, don't have to meet (one can be above the other).
What does it take to visualize non-Euclidean geometry? We must try to visualize non-Euclidean geometry within the three dimensional domain (the two dimensional diagram doesn't allow for point of view (we are not talking about perspective), in the three dimensional, choosing a point of view is necessary). Reichenbach says that we need to adjust our conception of congruence because "congruence is a matter of definition." "The adjustment necessary for visualization of a curved space consists in projecting congruence differently into three dimensional space." Basically the process that I see that the Euclidean mind should go through to see non - Euclidean is as follows: say something "wrong" about a "fact" and now find a way to project three dimensionally in such a way that makes the "wrong" possible, with out having to change the original "fact", or diagram. Euclidean geometry assumes a certain definition of congruence - don't, and you're in the non-Euclidean.
Three Models:
1. Bolyai Lobachevsky |
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| 2. Lines: Length | ||
| 3. Torus: inbetweeness |
The postulate that now replaces Euclids fifth postulate is, that through any point not on a given straight line, an infinite number of parallels, to the given line can be drawn. That is, that these lines will never have to meet (later the mathematician Riemann showed these lines will always meet because there are no parallels).
It is possible to visualize non - Euclidean geometry, so the question that I have now is how can one draw, or can one draw non - Euclidean geometry? If Poincare write that non - Euclidean geometry is about "the movement of variable solids", and the putting together of different perspectives of the same body, seeing several points of view so that "the object and the sensory being considered ... form a single body", can this geometry be frozen, can/should it be drawn? In the true sense of the word to draw (as in water from a well, or as in Husserl's reactivation), yes, because to draw means to reactivate. So, it is possible to draw this geometry if the viewer reactivates the drawing. But, this drawing as an end in itself is completely meaningless. The drawing must be drawn.
I think that Cubism was an attempt at abandoning Euclidean geometry, but by reassembling fragments according to classical geometric principles. Still, in my opinion, the cubist painting assists us in acting non-Euclideanly.
What does it mean to act non-Euclideanly? Vertov wrote: " I am the cinema eye, I am a mechanical eye. I, a machine, I can show you the world as only I can see it ... I ascend with aeroplanes, I fall and rise together with falling bodies." This, to me is a description of non-Euclidean action - the "I" plays a crucial role. Engaging in non-Euclidean geometry, or in a drawing - activating these, requires a point of view, an "I". Point of view can't be completely objective. Euclidean geometry, as I understand it, doesn't require more than one "flat" point of view, there is only one way to read it. Lines that look like they meet, do meet. Non -Euclidean geometry, because it moves, demands of us to be "I"s, to be narcissistic. Merleau - Ponty says, "since the seer is caught up in what he sees: there is a fundamental narcissism of all vision. I am not sure that all vision is narcissistic, (or equally narcissistic) but, Drawing and reactivating has to be, with out "I", non - Euclidean geometry wouldn't exist.
1996 Neta Katz
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Extended Bodies in Space
by Lawrence McDonald |
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A single shower of glittering spray, all that remains of the angels great fall. Down deep, a frozen descent, a realm of ice, a white void waiting to be conquered, waiting to be ruled. She ran her fingers along the black laces, smoothing them out perfectly,. Each end precisely twined through the holes, no hesitation. Like the most beautiful Lucifer, his image vanishing beneath a cascade of scales and coils that became his flesh, she too descended into new form. No sparkles, no vibrant hues, no medal winning smile with gleaming white inside. Black leather, bare legs. She set out to conquer the ice, to make it more than just a canvas, to make it her slave, a landscape that would absorb the slices, the grooves, the digs of her blades and would yield with each swift turn and spin. She would not offer it the devotion of grace, only that passion that erupts from some dark place in each of us...
"Chaos does not exist" asserts Deleuze; it is an abstraction, it is inseparable from a scene which makes something - something rather than nothing - emerge from it. Chaos would be a pure many, a purely disjunctive diversity, while the something is a net a pre-given unity, but instead the indefinite article that designates a certain singularity. a or an, that does not fix the identity of the noun modified. How can the many become the one? A screen has to be placed in-between them.
...She breathed in deep at the gate. The cool air rushing down into her lungs and she felt it course through her body. She launched out onto the ice, a flawless, seamless beauty; so pure. It welcomed her to the challenge. Her blades cut sweetly and smoothly through the first slick layer, was flying to the center. In the heart of the rink, she dug her heel lightly into the ice; a hold that fixed her entire body still. First waming. She in turn was given her own. The buckles and straps that held the leather fragment against her breasts and groin were icy against her skin. But anticipation began to thaw her. The crowd waited silently, oddly. They watched a mistress, hair teased wildly, eyes rimmed again and again in thick black lines, her lips, thick and vicious red. A leather teddy wrapped tight, almost cruelly around the perfect, leanest body. DeRant! Almost dating the crowd to watch. A woman with black skates, more a raven than any preffy peacock that had previously skirted so daintily along the ice.
Leibniz has been able to ascribe several approximations to chaos. A cosmological approximation, chaos is the sum of all possibilities, all individual essences in so far as each tends to exist on its own account; but the screen only allows for the best combination of possibilities, or compossibles.
She sensed the beat, heard it calling somewhere in her mind, instigating the power in her limbs and the madness in her imagination. She breathed in, knowing at the moment of exhale the beat would come and urge her on and on until the ice was a tatter of dust and shards and cuts and grooves. The bass was deep, she felt it kicking in her heart and began her trial. She gained momentum slicing around the corners in sharp and angry swift movements. Leaping up into the air, she spun and twisted wildly, tightly like some maniac left crazed in his straitjacket.
Chaos is composed of elements, each of which is extended over the following ones. This notion of extension is the first component of both Leibniz and Whitehead's definition of the event. "Extension exists when one element is stretched over the following ones such that it is a whole and the following elements are its parts."(Deleuze, p.77) This extension of parts to whole forms an infinite series that does not contain a final term nor a limit.
"Time and Space are not limits but abstract coordinates of all series, that are themselves in extension, the minute the second the tenth of a second."(Deleuze, p77) This now leads us to the properties of extensive series in the event, these too are in extension. But, extensive series, when saturated to there limits offer relations and conjunctions. These are no longer extensions! It has become something rather than nothing, but also this rather than that: no longer the indefinite article but the demonstrative pronoun. A demonstrative pronoun specifies or singles out the person or thing referred to: the demonstrative pronouns these and that. The images below can be seen in this light as temporal sections of an event which contain intrinsic properties and characteristics unique to that particular moment -yet born in fluvia.
The crowd's whoops and whoas came and then descended into applause as she deliberately crashed her blades back into the ice. And then up again, thrashing and rigid, she beat her arms against the cold air. She caught a glimpse of a spectator's face, awe, surprise; in fact, confusion. She was attacking the ice, she was beating it down in front of their wondering faces, breaking their expectations of some pink lady with the grace of elegance and stance. She was raw energy, it surged through her muscles making them tight as she raced along. She leapt up, her legs kicking out. All of the power reaching out and out from the blades which she brought down and across on the ice. And there she looped and spun, bringing her body low approaching the challenger face to face and then brought herself back up. She brought her arms from above, flexed with fists clenched and sent them crashing down as she raced again...
The individual is creativity according to Whitehead. It is the formation of the new. It is no longer the indefinite article nor the demonstrative pronoun but a "personal mood." The individual is a concrescence of elements. Further it is a prehensions: "An element is the given, the datum of another element that prehends it by degrees. Prehension is individual unity. The vector of prehension moves from the world to the subject, from the prehended datum to the prehending one. Thus, the data of prehension are public elements, while the subject is the intimate or private that expresses intimacy & individuality. But, the datum, is itself a preexisting or coexisting prehension, such that all prehensions are prehension of prehension (See attached video stills). The event thus becomes a nexus of prehension. I.e. the entire sequence played as one continuous movement. Each new prehension becomes a datum. It becomes public." (Deleuze, p.78) We can see now that the event is the objectification of one prehension and the subjectification of another (the subjective intent/contemplation/planning of the next move, however slight) it is at once public and private -THE SKATER THINKS, THE AUDIENCE GASPS.
. . . The bass and the beats pounded so loudly now, they bled into her ears, so profusely, she could hear nothing else. So loud, it became all she saw and felt and she no longer controlled her body. It was all bass and fury that moved her. She was blind beyond thought Only movement, simply spins and leaps and blades, she was the device of something higher, used to etch a bit of fire and insanity into the ice. She was numb, almost out of body, carried away by the passion. . .
Beyond the video still there is another element to the event, the Record. The record hear is a direct mapping of the skaters movements. It is the impressions and scratches left on the ice. It is an example of a physical prehension come eternal object. The scratch is a trace of what has been born in fluvia, a pure virtuality actualized in prehensions/datum's and recorded as eternal artifact and record. Figures, temporal sections and mapped traces on ice..
"determine extension and are inseparable from the process of actualization or realization into which they enter and gain a limited permanence, within the limits of the flux which creates them, or the prehensions which actualize them. They are eternal objects that have ceased becoming incarnate, just as a new thing, it has found its condition."(Deleuze, p.). The scratches represent a measurement. They are the intentional transmission of information onto the ice, albeit, a byproduct of the event, nevertheless these vectors of prehension are teleological, that is, they had a purpose and where brought about not simply by a causal relationship, but as man made artifact. Each skater, the identifiable source, will know his own record, the variance of different records is infinite.
. . . Then, agony. In full leap, in mid air, the light flooded into her eyes, hundreds of waiting eyes melted into her own. The beat had left her body, and floated somewhere above her. Her limbs felt almost sectioned off, parts amputated and sewn back in new places. Her blades, as if her claws, somehow detached from herself. The impending white god rushed faster and faster at her, its face absorbing all sense; devouring her as it gleamed its revenge for the blasphemy. Her body broke against it The crowd gasped, their voices drowning out the last of the beat The dark maiden acknowledged her defeat in front of this court's curiosity and concern. The thought of another day came in the instance before black out as peacocks and pink ladies alike glided mellifluous to lift her dark carcass from the ice.
1996 Lawrence McDonald
es such that it is a whole and the following elements are its parts."(Deleuze, p.77) This extension of parts to whole forms an infinite series that does not contain a final term nor a limit.