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 <