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On the last congress of cinema-makers  the secretary of the Goskino, famous for his sharp wits, suggested that they adopt the honorable title of «the Invalid of Brain Work». I suppose many of us could claim this title, and at the same time I suggest that we address each other appropriately: «Cripple Matizen», «Cripple Roshal», «Cripple Kosakovsky», etc.

When a seminar lasts for a long time, a lot of remarks accumulate «a parte», so I’ll start with them. 

Particularly, I would like to say that the Geizenberg-Bohr criteria (CGB) can also be applied to the language: the more precisely you speak on one aspect, the more another one becomes obscure. The closer to the object, the further from the subject, and vice versa. Say, Cripple Gutin  very expressively described himself, but the subject he spoke on was as obscure as the Universe.

After Cripple Aristov’s  lecture the question about the eternity arose. In St. John the Theologian’s Revelation an angel says that «there will be no Time anymore». There is no time anyway, but from the moment the solemn sitting of the Doomsday’s assizes starts, it won’t exist as such.   In the cinema, by the way, there is the model of stopped or eternal time - it is Stalin’s cinematography, which incarnated not the changing historical reality but its stable image in the way it appears to the mind’s eye of every believing communist, sorry for this tautology. That’s why, by the way, all the efforts to expose this cinema are useless.

And again my remark to Cripple Gutin: not any kind of cinema is performative, that is ordered or normative. It was not for nothing that the Chief used to say that the cinema is the illusion that imposes its own laws on life. Although if it occurred to some fool to really follow the models imposed by the cinema, he would right away find himself in the less remote from Perm parts, where we so lovely spend the lacking time.

Cripple Prozhiko asked Cripple Shemyakin how many interpretations can be extracted from Cripple Kosakurov’s creative work. The deeply scientific answer to this fundamental question sounds like this: «It depends.» On what? - you’ll ask. On where you extract these interpretations from - frames or the emptiness between them. The emptiness is fraught not only with  quarks for Mr. Clark but also with senses. From frames  the necessary senses are extracted, from the emptiness between them -  the admissible.  The former can be withdrawn from the film, the latter can not, but they do not contradict it. The necessary senses belong to the film, the admissible - to the interpreter. Sucking the senses out of the Emptiness is equivalent to blowing them into it and can be illustrated by a popular gag: a doctor shows a patient squares, one by one, with one, two and three rectangles inside of them and suggests that the patient describes the images appearing in his mind. «A room, a bed, a naked woman. A room, two beds, two naked women...A room, a bed...My God, doctor, you are a sexual maniac!» By the way, men more tend to interpret frames, women - what lies between them.

The famous «Kuleshov’s experiment» just illustrated blowing sense into a frame gap. The face of Moszhukhin in the first frame and a bowl of soup in the second have formed the idea in spectators’ minds that the man is hungry. In the film «The Bliss» by Cripple Mansky, who is absent today, they slaughter a pig. There are given  the sequences where women seem to watch it. Cripple Gutin has come to the conclusion that the reflected sacrifice of the pig Vaska is more artistic that its direct demonstration. But the women had been filmed the day before in an absolutely different environment. I am saying it as a man who was standing off screen during the shootings. By the by, Cripple Voronov, who splendidly shot this film, for some reason missed out  the most expressive moment in that scene: after Ampley  first time stabbed Vaska with a knife, it gave a frenzied shriek as if being slaughtered, fell down, got up, scarcely able to stand, and feverishly started eating the grass, erupting blood and urine at the same time. I want to say that if the naturalistic shooting was continued, the fixation of the fact could create an artistic quality.

By the way, it’s not true that when Pilatus in St. John’s Gospel asked Christ: «What is the truth?» - Jesus gave no answer. It was the author who gave no answer, and into this famous biblical Silence between the lines, so expressively described by Charles Auerbach in «Mimesis», we are blowing our senses.

The lecture of  your Cripple Matizen perhaps may be called «An empty stretch as the basic model of the film’s interpretation». For starters, I will show how two models of the subjective time, which were mentioned in our first «Kama-s-utra»,              are inscribed into the stretch. They are both connected with Xenon’s first aporia. It sounds as follows: to walk a stretch of a way, one must  walk its first part; to walk its first part, one must walk its quarter, etc., but this process never ends. One can also formulate it in a different way: to walk a stretch, one must walk its first part, then another quarter, then one-eighth, etc. Indeed, the paradox is that one can walk this stretch, but can not enumerate all the indicated stages of passing. The refutation of Xenon’s law is not that one wise man  started walking in front of another but that he started walking without a word: if it occurred to him to describe at the same time his steps, he wouldn’t finish till the end of times.  Xenon’s aporia in some sense is connected with the subjective time. So, our first «Kamasutra» stated that human life in a subjective experience  is accelerated from the beginning to the end. It may be described in the way that its second part lasts for a man as long as the second quarter which lasts as long as the second one-eighth, etc.

The second model is the model of suspense. Thus passes time in train, in sauna, when outstaying someone under water, when one needs badly to use the WC which is very far, and also during a seminar when an audience can’t wait for a lecturer to finish. Here the first part of the lecture lasts as long as the third quarter which lasts as long as the seventh one-eighth, etc. 

Now let’s depict on the stretch the model of real time which passes in the documentary which is shot - to make it simpler - without rapids, with one camera. Let’s divide the stretch at our own choosing into parts and paint them consecutively red and black. The beginning of the first red stretch is the physical time of the beginning of the first shot and included into the film frame, let’s say, the 19th of January, 1998 at 3.45pm, the end of this stretch is the physical time of its end, let’s say, five minutes later. The first black stretch is the physical period of time between the end of the first frame and the beginning of the second, and so on. The last stretch is the last frame and, naturally, it must be red.  

This, I am saying that again, is the real shooting time of the film which consists of red frame intervals and black  hiatuses between the frames.

There are three possible variants of the correlation between the general length of frames and the general length of hiatuses. The total length of frames is the length of a film which varies between several minutes and an hour and a half. I am not considering series here.

In the first case the sum of hiatuses equals zero. This corresponds a one-frame film (without montage gluing) - like «Ten Minutes Older» by Hertz Frank of its Pechonkin’s remake «The Game».

In the second case the sum of hiatuses is of the same length with the film. On the whole, this is the case of almost continuos, uninterrupted  time, although it may be proved otherwise with clock hands, changing clothes, etc.

In the third case a much longer period of time passes between  frames than inside of them. This is the case of continuos cine-observation about which Cripple Muratov spoke. Here frames, considering their relatively brief duration, can be denoted as dots on a time stretch.

Now let’s see how the interior time  of the film passes when frames are edited not in a temporal but in an artistic sequence. In other words, I am going to draw the transformation of the plot into the story. Let’s choose a frame that will be the first one in the film, and from its end we’ll draw a curved arrow to the beginning of the second frame, from the end of the second frame - to the beginning of the third, and so and so forth. At the same time on top we’ll draw arrows that go in the direction from left to right, that is ‘real time-wise’,  and on bottom - those that go ‘counter-real time-wise’. What we a have is a curve that consists of arcs. I would only like to mention that the idea of this curve occurred to me while I was reading the classical work  on  Ivan Bunin’s «Light Breath» by Lev Semyonovich Vygotsky; Bunin has already been mentioned today by Cripple Shemyakin. Vygotsky’s discovery was, as you remember,  that  the artistic form cancels (not in the photographic but in Hegel’s sense) the impression of the material. The material makes a heavy and obscure impression (which in the story remains canceled), whereas the story frees of affect or creates catharsis. Vygotsky was the first one to draw the line between the plot and the story, but he used two stretches - the plot stretch and the story stretch which he placed as parallels above each other, and draw arrows from the first to the second.

Mind you that in the film hiatuses often are of no less importance than frames - not only because the sense reads there but because the aesthetic effect is produced by the time leap itself. Besides, as Cripple Aristov fairly pointed out, this leap of time can only be noticed by space changes inside of a frame. The greater is the space differential, the greater is the aesthetic shock - all known rules of frame montage and movements inside of frames are based on that.

Now I will quote Eisenstein’s thought. He takes as an example Pushkin’s quatrain: «That one is knocked over with a mace, another one is hit by a light arrow, and this one, held down by a shield, is trampled by a furious steed.» The piece doesn’t seem very significant. And only such pathologically thoughtful man as Sergey Mikhailovich could wonder why the weapons were placed in the poem in this particular order. He found the following explanation: he assumed the light arrow as weight 1, the heavier mace as weight 2, and the heaviest steed - as weight 3, and declared that the aesthetic affect of the whole scene equals the sum of «leaps» from  the weight of one weapon to the weight of another. If we place them so that the weight gradually increases, that is arrow-mace-steed, the total effect will be 1+1=2, but the way Pushkin put it the effect equals 1+2=3. One can not obtain a greater result. Eisenstein also compared this optimal artistic effect with the way a man, to hit a ball harder, first swings back his leg and only then hits the ball.

            The situation can easily be generalized; we get any number of «weapons» or «frames» if we attribute an artistic effect of certain value to every montage gluing and set the task to find the sequence of gluings which gives the greatest total effect.  Mathematically this task does not differ from laying the longest route through the cities, marked on the map, because to every pair of cities corresponds a certain distance between them. In our case the frames-«cities» are placed on one line, and the aesthetic effect from gluing two remote in real time frames can be compared to the length of the time interval between them.   Our task is to draw the longest route of arcs passing through the marked points.

            Not immersing into all the computations, I’ll tell you the result: the optimal route has a spiral-like form, starting from the middle point and then jumping back and forth.  Among the curves there are parables and pissoids, i.e. the curves that people make when they pee. I modestly suggest we call this highly artistic spiral the matizoid.

            This is the model of non-stretchable, inconvertible inside of a frame, one camera time. With a  greater number of  cameras it is necessary to take a few time stretches, mark frames that were shot with one camera on each one, and connect the frames with montage arrows. Accelerating, decelerating and reverse motion of time should be marked specially. An interesting paradox: it seems that if you show the film «Ten Minutes Older» backwards, from the end to the beginning, what you get is the anti-film «Ten Minutes Younger». But in fact, what you get is the same film - especially if you don’t pay attention to the music. By the way, the actual number which is reverse to itself is one. Frank’s film is the unit of measurement of the documentary cinema.

            It is of no less interest that this film is the only one that equals its «mirror» reflection: imagine the same kind of ten-minute film about the same boy who’s watching «Ten Minutes Older» - it would be actually the same film «Ten Minutes Older». It is possible to make a whole sequence of films-reflections: 1) the one who’s watching something (even his own reflection in the mirror) 2) the one who’s watching the one who’s watching something 3) the one who’s watching the one who’s watching the one who’s watching something, and so forth.

            Concerning this, I think there is a point in showing one more axis - the axis of subjective time of the one who’s watching the film, i.e. the time of the spectator. We all know from experience that in fact a short frame sometimes may seem eternally long, while a long film seems to last an instant which is also no good since everything converges at one point, like in a music video. A perfect cinema is the cinema whose inner time is isometric to the time of the spectator.

            Principally non-linear time I’ve noticed here only in one film, «Lyoshka’s meadow» by Cripple Pogrebnoy. It is the scene where they show a close-up (three quarters of screen) of a TV set  where is played an amateur video film made by one of the characters. If they showed that video film on full screen, we could mark it on the synchronic parallel axis and show montage with arrows. But the whole point is that here is given «the past in the present». The same situation would occur if the characters watched one of the earlier parts of the same video film, and in this TV set could be seen one more TV set, and so on.

            With this silly but absolutely real infinity I’d like to finish my lecture because otherwise I couldn’t finish it - just like Xenon’s traveler can never end his journey with its synchronic description. But I won’t finish it because there’s still something I’d like to say.

P. S. Digressing from the cinema for the sake of the no less pleasant topic of the mentioned joke about who is actually the sexual maniac, mind you that the interpretation of the scheme of the stretch with the arcs depends on the degree of the rapporteur’s depravity. I mean, let us suppose that the beginning of the stretch represents the birthday of a representative of the fair sex, and the end - her dying day. The first point is the moment of the beginning of her love life, the last point is the moment of the end of it, and the interval between them is called amorous. The first arc is the time of her first love affair, the second arc represents the time of her second love affair, and so on. Now a few definitions: a lady is called non-idling, if at least one arc passes over every point of the love stretch.  The lovers are called partners, if their arcs  pass over at least one common point. One lover dominates over another, if his arc totally covers the arc of another. A lover is called dominant, if he dominates over all the partners. A lover is called global or super-dominant, if his arc stretches over the whole love interval.  A lady who has a global lover is called relatively faithful. A lady whose love arcs do not have any common points under them is called locally one-loving. Any amount of one lady’s dominants is called her intimate circle. The total amount of the lengths of all the stretches under the arcs is called love time. The ratio of love time to the length of the love interval is called the intensity of love life. The average number of lovers throughout all the interval is called the average density of love life. What would you call a lady whose love time is longer that her life time? Let it be your home task. Cripple Shemyakin’s favorite toast: «Let’s drink to my health because if I am healthy, all women of our town will be healthy. If all women of our town are healthy, all men of our town will be healthy. If all men of our town are healthy, my wife will be healthy. And if my wife is healthy, it means I will be healthy, too!» draws a classic love noose. 

Let this brief introduction to my mathematical «Theory of Love Liaisons» be a brief conclusion of today’s «Kamasutra».