Aristo Tacoma [[[ESSAY found at norskesites.org/essay20110915.txt Written talk. Yoga4d.org/cfdl.txt redist license. Consult published works as at yoga6d.org/cgi-bin/news/f3w which are containing key concepts connected to what this writer calls 'neopopperian science' and also 'supermodel theory', which involves also perceptive processes -- concepts effortlessly drawn upon here.]]] THE CONTINUITY, THE INFINITY AND A GRAPHICAL F3 [[[Please also get the picture as found at norskesites.org/essay20110915.jpg mentioned within.]]] I have an ambitious agenda for this session of ours. Since I am not entirely sure if I will succeed, within this session, of showing what I want to show, I will try to conceal this ambition, so the embarassment, in case, will be considerably reduced. If I pull it off, I will declare so afterwards, with great inward satisfaction. Perception -- which involves the art of seeing, it involves recognition, but we can also speak of subliminal perception -- you are noticing things you don't quite notice that you notice -- and hence also intuition -- all this involves, as we have spoken about earlier, such as contrasting similarities and similar contrasts. This is a recurrent theme in what I call supermodel theory. But there is a third element, clearly, -- otherwise we are merely having these two features of similarities and contrasts running after one another. That third element is nearer wholeness as such, which is of course what perception ultimately is about. Am I going too abstract? But I PROMISE it'll get juicier. A keyword is orgasm, but I won't elaborate at it just now. So we have symmetries, for instance, -- the symmetry of a healthy, relaxed smile. The symmetry, or commonness in measure, in metrix, -- sym-metry -- can be playfully broken as in the skewed smile, the girl that tells you she sees right through that snappy line you just reeled off, she KNOWS your intention. So the contrast can be sexy, too: and it is a contrast which plays on the similarities in the smile, in the left-and-right of the lips, all that. But perception has to have this third element, and more. The WHOLE face, the WHOLE body, the WHOLE experience of the beach, the WHOLE music and WHOLE dance and WHOLE sex, -- who are we to try to assemble a whole merely from similarities and contrasts of all sorts? So I have picked a word earlier on, up from the depths of the not overly much used words in the dictionary -- reverberance. A fiction story might use the word, I suppose, in speaking of how the whole room reverberated with the music, or how the whole building reverberated with thunder. Reverberance is as if the vibration, or energy-sense of the whole. I wonder if there is a better word and I have a hunch that a new one, easier one, a more common word yet aspiring towards the same great meaning as reverberance is on the way from the knowledge base within me of English. Certainly also the word "silence" has to be honored, when we look into perception. The silence of being attracted, the silence of being fulfilled, the silence which exists when all worries are gone, and there is a sense of refreshing wholeness. A silence which is whole, not lacking in anything. A silence beyond thought, allowing meditation to come, a beyondness -- an infinity. These themes are not only for science, of course, but exists in religion, as core themes. Silence is in what japanese buddhists call zen, coming through the chinese version of the word ultimately from the indian dhyan, or dhyana more fully, in scholarly sanskrit, that root-language of both English and Norse. Dhyana is the flow of unity within, says a script. In looking at numbers again, dhyana echoes infinity, and infinity the continuum, -- whereas finite numbers are clear marks. I work, you work also perhaps, with computers, where the range of finite numbers is some billion. We can construct a program to make numbers of a type which is having a bunch of more digits -- say one hundred digits. But psychologically, it is pleasantly holistic to keep numbers small and within some nine digits. And numbers must be psychologically meaningful, for if they do not exist clearly in the mind, where do they exist then? In the logic which I find so full of subtle mistakes, where the notion of the limit was discussed as a kind of quasi-solution to big questions on the infinite, in the 20th century and before, we hear talk of allowing a number to be 'as high as we please, but still finite'. And it is discussed whether one can make a formula produce a number which is 'approaching' a result, 'as a limit'. In going 'as far as we want to, can we make the distance as small as we like?' Such themes proliferate when people in logic, or what they so pompously called 'mathematics', sought to avoid looking into the depths of infinity at close range. But as we have perhaps already looked into the other day, and I have written much about it before, and shown this and that rather in the form of a reductio ad absurdum proof, there is no such thing as 'any finite number'. For finite means that we have a clear range -- like plus minus two billion, about the 32-bit limit of a good, meaningful programming approach. Just look at the phrase itself -- 'any finite'. Any finite is as good as saying not finite, nonfinite, infinite. If it is not a definite finite, if it is any, it is other than finite, it is in some sense illimited. A logician of the type of Bertrand Russell might then have objected, if he heard me now, and said: Look, is it not a clear idea to you what a finite number is? We have some examples here, 2, 18, 93, 184, 2049, and can we not generalise from that? But I would say no, it is not obvious how you generalise from that. You think you know, Mr Russell, for you have told yourself and been told and written and read over and over again that we all know what finite numbers are. But seriously, you have no idea -- with all respect, you really have no idea. Either you have a range, like one to a million, or you are doing another business altogether, the business of rangelessness, and that is a land I don't think you have properly wandered into yet, Mr Russell. You have been so cocksure that you have had an overview over what is finite that you also felt pretty sure you could glean a sense of the infinite. But you never got a clean sense of the finite, and so the infinite has been playing foul with you all the time. That is what I would have told Mr Russell, but he is not the judge. It is YOU, your own mind, your own intuition, who has to be the judge. And I submit to you: do you have a clear-cut universal idea or principle to tell you, in sheer abstraction, what a finite number is? I am not asking for examples, for examples always have a range. And a range is indeed what we mean by finite -- it is defined, it is within fences. Take away fences -- that's the not-quite-finite or even the certainly-not-finite -- indeed the infinite. Perhaps, then, when you perceive this and that and the other thing, musically, they blend, -- perhaps you are near a person, or you watch artwork, a drawing, a set of stars, -- or the waves near you, and further away, and still further away --- and they blend and you somehow in mind may feel so holistically attuned that you can naturally say, afterwards -- I forgot myself. I melted, within anyway. And I ask you: is this not what orgasm is? Is not orgasm a certain sublime kind of perception? Whatever there is of bodily participation in it, is it not the entwinement of the finiteness of your mind with something so utterly whole and right and cosmically beautiful to you in that moment that all is well, in an eternal sense? I wonder, at this stage, having said something which sounds dangerously near poetry, we can, without a sense of trampling with big boots in a tender flower-bed, make on the computer a simple model for something not too far away from waves at a beach and gradually further away until they melt in one line of continuity, symbolising infinity? That's fractal, too -- it involves similarities and contrasts, similar shapes at different scales, but it more clearly involves a sense of that wholeness or reverberance since in the distance, it all melts into a unity which is fundamentally unbroken and fundamentally different than the obvious finiteness of the lines near. I have in mind not any attempt to use sine or cosine functions to get rounded stuff indicated at the computer monitor, for I like the nearness to the squarish pixels on the monitor and use of such rounded functions really only give an illusion of roundedness -- it is still pixels, and it somehow feels more pixel-near, if that's the phrase for it, to stick at straight lines when we can. Straight lines which shift direction, back and forth, -- when near. Then less dramatically such shifts a little higher up on the monitor. Gradually so, upwards, towards the straight line of ocean water seen at enough distance that the appearance is that of the straight line. As symbol of infinity, it is very immediate especially when you come to a good beach at just the right time, having had an intense enough time in the city centers that you have forgotten, in a pleasant sense -- forgotten so as to be happily surprised -- what glory one sometimes can bask in, when at a sunny beach, at lucky times. Again the model is so as to ask fresh questions, to explore more, and now we are exploring something of the very process of exploration, namely perception. So let us define something graphical. Shall we try? Let's do it. I imagine that we need to have a loop that goes up on the screen -- that will be in the so-called Y direction, for X is horisontal -- a certain number of times, such as 10. 10 lines, the top line is perfectly straight, and the line which is representing the waves nearest is the most jumpy. It goes a lot up and down, and the degree has to be stored in something -- let's call it ((DATA JUMPINESS 35 JUMPINESS < LINE )) This, by the way, is a line that goes up. The Y goes from 1 to 768, where 1 is the topmost row of pixels. The X goes, then, from 1 to 1024, where 1 is the leftmost row of pixels. The third thing we need to have, in addition to some addition and division or the like, is a bit of Relatively Free Fluctuation Generation, or RFFG. A free number, within the range set by JUMPINESS. Because of games having to have at least two ways of doing RFFG, for the sake of a bit of extra fun, the f3 language has several ways of making such free numbers. One way involves using the word FUNNYRFFG, like this: JUMPINESS >>> => FUNNYRFFG This FUNNYRFFG gives values no less than 1 even when JUMPINESS has reached 0, so we will use a DEC after it, I think, to decrement the value by 1. So we are going to have several such jumps as the computer sketches a very rough type of stone-like line from left to right. It seems we are going to need a bit of repetition, or looping as it is called, within that other loop. Like this: (LET DO-SOME-REVERBERATIONS BE (( )) (( (( 10 (COUNT (( 12 (COUNT COUNTUP) )) COUNTUP) )) )) OK) Of course, in the middle of this we need to put that LINE stuff and the FUNNYRFFG stuff and some clever bit of calculation. I threw in by intuition the number 12, meaning that if we jump something like 50 pixels to the right each time, it will occupy much less than the 1024 we have available in width. So I am going to use a number of anonymous variables, we have N1..N11, they get values by >N10 and such, and they easily tell their value, simply by typing N10. No need with these, as for JUMPINESS, to speak of <>> when retrieving them. The N1 and N3 gives values of the (COUNT .. COUNTUP) stuff, N3 the outermost when referred to from within. We also should put the JUMPINESS to 0 when it has come to line 9 and is going to start on line 10. A check on the value of the outer loop -- to check if N1 has an INTEQUAL, an INTeger EQUALity to 9 -- should do, then we put (MATCHED .. MATCHED) after this, and assert that JUMPINESS should be 0 within that. MUL means multiplication. We are going to multiply with 50 both for X and Y. SUB means substraction. We are going to start bottom of display and work upwards, so some substraction is also called for. JUMPINESS needs to be reduced a little each time, so we put a small value, in the negative, and ADD it to the VARiable by the word ADDVAR. When a line goes up a little, it needs to get back again, so we have a kind of horisontal structure. So I am going to do one LINE and then one more. The first goes 25 pixels to the right, and the second starts exactly where the other finished, and also goes 25 pixels to the right, back to horisontal starting point line. A bit of calculation. It's getting a bit much but stick it out and we get and graphical image -- indeed, a slightly new one each time we perform the program -- afterwards. So it is worth a little bit extra typing. Since we are going to have to start with the most jumpy lines, we must calculate the Y position by some kind of clever arithmetic, some substraction. We could maybe get it all going -- I try now -- rather like this: (LET DO-SOME-REVERBERATIONS BE (( )) (( (( 10 (COUNT (( 12 (COUNT (( 12 ; N3 => SUB ; 50 => MUL => >N10 )) (( JUMPINESS >>> => FUNNYRFFG => DEC => >N8 )) (( N1 ; 50 => MUL => >N6 )) (( N10 ; N8 => SUB => >N9 )) (( N6 ; N10 ; N6 25 ADD ; N9 ; 1 => LINE )) (( N6 25 ADD ; N9 ; N6 50 ADD ; N10 ; 1 => LINE )) COUNTUP) )) (( -3 ; JUMPINESS => ADDVAR )) (( N1 ; 9 => INTEQUAL (MATCHED (( 0 JUMPINESS <