Aristo Tacoma
[[[ESSAY found at norskesites.org/essay20110913.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.]]]
ON NUMBERS, INFINITY, LOGIC THOUGHT AND THE WORLD
-- And some brief notes on the f3 and golden ratio
Now I happen to know that some of you have given time to
some forms of science, philosophy or logic, but I do not
know exactly what all of you have worked with, or how
well you have succeeded, personally, in bringing it all
together as a meaningful whole. Does all of logic appear
to be nothing but a collection of puzzles to you? Well,
in that case you may have hit the mark perhaps better
than another, who possibly thinks that logic is nothing
but a collection of cut'n'dried simple answers to the
full set of big questions.
In this informal miniseminar, a bit of higher
education in a sense, I will sketch some ideas that to
me represent insights, and bring in some bits of the f3
programming language so as to show that it is coherent
in thought to do so -- it is a fluid transition, from
thinking about these things to sketch this and that and
the other bit in the Lisa GJ2 Fic3 formalism.
First, let us muse over the question: what is the
relationship between language and the world? By language
I mean also anything we do in logic, and as a formalism,
but also anything we say such as in English, in natural
language, and I also mean our togetherness in doing so.
By world I mean the wholeness of existence in the most
ultimate sense, but also the beaches, the flowers, the
long legs and the sex and the food.
So what is the relationship between language and the
world?
First, though it would not be practical, we could
imagine an existence in which people didn't talk, but
wandered about in silence, eating, making love, bathing,
swimming, -- the world still exists. So the world is
simply not dependent on language.
Are we seeing this together? The world is beyond
language. I do not mean that it is easy to say -- that
is the world, and this thing over here is language --
for in each particular case, we may be a bit confused
unless we have given the question great attention.
But as a general statement, the world is the greater,
and language is the smaller. Language is within the
world, not just possibly but certainly, but unless we
are trying to take the point of view of God writing the
universe into existence along the lines of a
story-writer, then, for all practical purposes, for
humanity and for the muses -- you know? -- for all but
God, language occurs within the world but the world
isn't dependent on language.
Naturally, language may engage cause-and-effect and
such within the world, but the world is still the
greater. This is a fact, and the fact can be called a
kind of humility that language must have relative to
what is not language.
Put in other words, actuality doesn't depend on
thought. Thought must have the humility to regard the
infinity beyond itself as essentially beyond it, and as
the carrier also of what there is of thought.
If there is any disagreement about this, let me
propose that it may be that those opposing this humility
are more interested in expressing themselves -- at best
it can be called poetry -- rather than being honest
about the understanding of the general features of
reality. There are those who try to make a kind of
expressive type of language-music in which questions
like the ones we just touched on are brought in, and
negated whismically. I don't think they REALLY agree,
but I do think that they are trying to make themselves
interesting and perhaps, for fake reasons, try to make
others say that they are genius-folks, when they are
simply throwing words around clownishly, without
awareness or attention to what they are doing. I would
not recommend it, in short. If it is a kind of
self-therapy, I would suggest more humble means of
self-therapy than throwing about words clumsily
concerning the greatest questions of what thought is to
the world.
No matter, then, what thought portrays to itself as a
so-called General or Deep insight or a Pure Deduction,
it may be that it has nothing at all to do with the
world. It may be that it is but a piece of false play, a
false note, having nothing to do with anything. The
world is not constructed by thought, but it exists and
it is real and actual, and then thought tries to
construct something and it may call it 'the world', but
what thought constructs may simply be a map which is a
map of nothing at all -- the map of a fantasy-land.
But what we are suggesting, when we look at the words
we just used, is that thought CAN indeed relate to the
world beyond it somehow. Some thoughts match and some
thoughts do not match. In the case of the weather, it
may be simple to work out; in the case of something like
reincarnation, it may involve a large number of
assumptions and a great deal of intuition to be able to
do, as I frankly do -- and claim that reincarnation
indeed is real, for all humans, always. But the
word-sounds themselves may mean one thing in one
religious context and another thing in another religious
context, and so we cannot always speak of how well a
thought matches reality just like that. We must rather
speak of the whole network of thoughts, the net of
assumptions, and we can weigh, intuitively, whether we
have many or few or very few or possibly none illusory
assumptions in a context. Is the network of thought
involving CORRECT assumptions?
So the notion of a CORRECT assumption, and the notion
of an INCORRECT assumption, means that we are allowing
ourselves to pass judgements on thoughts of some types.
Not every thought is claiming anything much about the
world. Those that do claim something about the world, we
attend to; and we also attend to the world; and we
attend as best we can to the degree of matching,
connectedness, -- and from this attention, we pass a
judgement. When this goes deeper than the sensory
organs, we speak of intuition. When we focus on sensory
checking, we may speak of experience, or data, or even
research data, and all of the latter we can also call
'empirics', which is a word meaning experience, but
experience of a kind that has been paid very clever,
analytical, good, honest attention to, whether in a
scientific context or not.
Note that we have not spoken of whether the thoughts
of one person is somehow viewable by another directly or
not. In other words, we have not spoken on the nature of
mind and minds in this world, whether they are all like
petals of a rose or more divided, whether they can be
seen by higher beings -- as I in more religious contexts
suggest that they can -- and all sorts of things like
that.
It is also not easy to very quickly, using experience,
if you have been deeply and intimated related to
particularly mind-sensitive or 'psychic' people, say for
sure just how independent human minds are.
Let me say that I regard human minds as largely
interrelated, but that they are also having more or less
private zones to some extent.
Now, where does logic and formalisms and such come in?
Once one has the essential humility that thought
doesn't for sure say anything about the world, one may
find that the world tends to have, as shown by objective
experience, certain regular features, which may look
very similar to some patterns one may model e.g. on a
computer, or just think about, in more or less formal
terms.
When one then, with humility -- always with humility!
-- plays with something like a little computer program,
in a vague inspiration from experience, also intuitive
experiences, to use that phrase, -- one may find that
the program, in turn, inspires one to look afresh at the
world -- perhaps with a new sense of question.
Is it then science? I would be careful to use the word
science just like that -- see, if you have time, the
list of points that I think one should consider, as a
kind of checklist, before considering whether something
like an article could be considered a contribution to
science.
Let us here more humbly say that at present, we are
exploring.
For instance, have you thought about there being
something about long legs relative to a short torso --
something a child may have, it is not about overall
height -- which relates in turn to what is often called
'the golden ratio'? The longer legs, given some approach
to the measurement, may compare to the torso, the
upper body including the head, by a factor of something
much like 1.6, a number which is not far from 5 divided
at three. It may apply in more ways than one, also
relating to the hips accentuated by a g-string (which
is a general, generic name and we do not need any such
name as "t-string", in the qualified opinion of this
beach meditator).
Why does such a golden ratio speak to the mind?
For the mind, eager to adjust thoughts to fit with
reality, must be aware of similarities of contrasts and
contrasting similarities of all kinds, not just some
kinds, since both thought and the world beyond are so
infinitely complex.
And there is something about the golden ratio which
involves a repetition of similar contrasts within one
another, and also spiralling out: in order words, the
simple shape may be a visual metaphor of a type of
ensnaring infinity; an infinity one may also encounter
by interesting angle-similiarities and shape-likenesses
between such as lips and jaw, lips and eyes, the high
wrist of a girl's foot with the curve of her thigh, and
so on. Each girl of beauty is an equation onto herself,
unlike all others in a marvel that speaks of infinity.
The religious mind is, like the scientific mind,
willing to concede that beauty speaks of the highest
order of the universe, and as such do not deny the
sensual, nor the sexual which is always naturally part
of the sensual. So the love of beauty is part of what
a true understanding of God must be, in the opinion
of this thinker.
Let us for the sake of starting with something formal,
not because it is exactly the most general question or
theme one can touch on, but because it is inspiring for
our artistic aspirations, look at the numbers which,
when divided pairwise on one another, tend to be more
and more accurately the golden ratio -- for numbers
which each are within the typical computer range of
32-bit or about plus minus two billion.
The series of numbers goes back in the history of
number studies to one Fibonacci, and so we speak of
'Fibonacci numbers'.
(LET FIBONACCI-NUMBERS BE (( ))
((
}* .. }*
)) OK)
So we are going to make something formal, give some
flesh to a structure like this. The formal language is a
kind of mantra, it is a set of reminders, or rituals, so
as to bring about a contemplation for the type of
activity that is resonant with doing formalisms. So it
is important to not just look for computational content,
or calculations. We must allow the art of the formal
structure to arise for a sense of beauty and wholeness
in the mind to come about simultaneously. I find
personally that doing even small programs once in a
while make me open ever-afresh to the beauty of girls.
It helps art. It helps paintings. It cleanses the mind.
When we program, therefore, we are going to do things
which are not always as compressed, if that's the word I
want, as it can be. We want to expand a thought by means
of the formalism f3. Later on, it can be compressed
more, if we have reasons to make a quicker or more
compact version of it as part of another program. But it
is typically so that when we watch the world, and
vaguely appreciate some patterns, these have to be
expanded before they are compressed. But in art, in a
way, you start with the compressed sense of it, the
contracted image within as it were, and then expands it
when you are drawing or painting or dancing it. In that
way, it is not an imitation.
Fibonacci noted that adding two numbers, like 1 and 2,
gives a new number which can be put to the right of the
two first, so that the process can be repeated; and that
when it is repeated just some times, the ratio between
the two numbers quickly settle to about 1.618.
So 1 and 2 gives 3. Then 2 and 3 gives 5. Then 3 and 5
gives 8. Already, 8 divided at 5 is much the same as 5
divided at 3. And even 3 divided at 2 is a pretty good
approximation.
((DATA FIBO-NUMBER-A ))
((DATA FIBO-NUMBER-B ))
Just to be very explicit, this time we do not use
anonymous variables inside a function, but spell it out.
The two numbers defined -- higher up in the program than
the function which we have still to give flesh to --
then should have some initial values. Let us say 1 and
2.
(( 1 FIBO-NUMBER-A <N1 in the function header.
To print a number on the screen, with a space after, we
can use the word POPS. This works fine in text mode. In
graphics mode, we would use something like B9-POP. But
here we assume text mode. Finally, the <>>
is what we want to retrieve the value from the
variables, as they get higher and higher. The word
INTGREATER compares two whole numbers, two integers. The
word (MATCHED and the completing word MATCHED) then
leads to an action on condition of the comparison
working out. We would want something like a GOUPn here,
such as GOUP1, where the number 1 refers to a point
higher up in the function to return to, because the
function is not yet finished. This we indicate by
GOLABEL1:. The addition we do by the word ADD.
All right, we are getting something like this --
where I put in the extra blanks, the extra (( and )) and
the extra => in order to make it easy to look at --
using the conventional correct type-setting of the Lisa
GJ2 Fic3 language of mine. Also, I use N10 and not just
N1 to store some temporary values, for each function
has its own set of eleven such, N1..N11.
(LET FIBONACCI-NUMBERS BE (( >N1 ))
((
(( FIBO-NUMBER-A >>> => POPS ))
(( GOLABEL1: ))
(( FIBO-NUMBER-B >>> => >N10 ))
(( N10 => POPS ))
(( FIBO-NUMBER-A >>> ; N10 => ADD
FIBO-NUMBER-B < INTGREATER
(MATCHED
(( GOUP1 ))
MATCHED) ))
)) OK)
This is all well and good but if we want to run several
test-runs of it, we would like the numbers to be reset
to their beginning, and perhaps we want a more snappy
function name also. Let me put those initial statements
giving start values to the variables inside a function
with a quick name, which then calls on the above. The
completing line, CRLN, puts in a lineshift. This is
text mode, so we have to allow the lines to be a
bit unformatted -- a number going too far right
will be chopped and its completing digits will be
all on the left side -- just like political extremists
of the right equals much those on the left ;)
(LET GOLD BE (( >N1 ))
((
(( 1 FIBO-NUMBER-A < FIBONACCI-NUMBERS ))
(( CRLN ))
)) OK)
I put the above in a file called GOLD.TXT, then started
F3 by the command F3, and typed :GOLD IN to load it.
Then I typed
50 GOLD
and the computer displayed
1 2 3 5 8 13 21 34 55
Naturally I couldn't hold myself and put in really large
numbers just for fun. It is a good thing, to lean back
and have the computer do such tasks, stretching it a
little bit, a kind of BDSM whip on it. So is every
programmer a sado at heart?
Let us note that 34 and 55 looks a bit like 3 and 5.
But, clearly, 5:3 and 55:34 are not exactly the same
number. It seems that we can get from 5:3 to 50:30 by
multiplying with ten, multiplying both factors in a
ratio by the same number doesn't change the ratio. But
to go from 50 to 55 we would add exactly one-tenth of
50; whereas to go from 30 to 34 we would add more than
one-tenth of 30. In other words, the number 55:34 ought
to be slightly smaller than 5:3. I go into the F3 again,
and use it as decimal calculator. The function \R
divides using not just large whole numbers, but also
such large numbers with decimals, and R( prints them
directly in the text mode of f3:
$5 $3 \R R(
and get a number like 1.666666 and more digits like that,
completing with a 7, as a rounding up.
Then I type
$55 $34 \R (R
and get cirka 1.618, which confirms the little informal
calculation. (The $ and the 'R' in the above refer then
to such caculations, which in f3 formalism is called
"using the rich stack", so R for Rich.)
It is often so that the mind has a greater joy in going
into something deep, if one does it without too much
exhausting detail in each session. But there is always a
progress. Next time we explore, we can surf through
earlier insights with swiftness and delve right into
something new. Then, coming back to earlier insights in
a new round, one will have learned something of the
overall progress and can see new aspects one didn't pick
up the first time.
I think that reincarnation is just this: the aptitude
for learning is heightened, even if the memories of past
lives may be very far from concrete indeed.
It is not about ego.
But before we complete this little exploration into
some great features of the world, I wanted to touch on
questions of the infinite, for the human mind needs a
little bit of the wilderness of a beach of this type.
Not too much at a time, and certainly not all the time,
but as a contrast to questions of finiteness.
Let us appreciate the truth of a falseness. In other
words, let us dwell a little bit on an illusory way of
relating to infinity, so as to see more of a right way
to relate to, and respect, that awesomeness called
'infinity'. What I have in mind is that some people, on
looking at the numbers such as the Fibonacci numbers
above, and noting that as they go from a range such as
cirka 50 to such as, for instance, cirka a million, they
get steadily more decimals in place of a number which
tend to level out -- namely this golden ratio -- where
the first digits indeed are as noted with 55:34, namely
1.618. You can also switch the ratio, 34:55, and you get
much the same number just one less, namely cirka 0.618.
So they notice, aha, we go from 50 to a million, but
what if we simply let it go 'on and on'? And they try
and calculate around this 'on and on' and a large number
of people, including such as the logicians Abel and
Cantor and Russell, all have had a tendency to regard
this as pretty much an easy thing to do.
But with what right can one assume that any such thing
as addition works once one lets numbers go on and on? It
is not obvious that it can work in a context which no
longer has a well-described boundary on the numbers.
What will an endless, infinite context do to the
addition? What will it do to the comparison? What will
it do to the division? What will it do to the storage of
two numbers? Indeed, what is a number, once the context
has to an utterly extreme degree transcended all
possibility of being part of the manifest universe, and
is a mental fleeting idea of boundlessness?
One must be in a great haste, and rather hypnotised,
to avoid conceeding that on changing from a context of
something such as f3, which has a well-defined range of
numbers essentially between minus two and plus two
billion and a related range for decimal numbers and for
the amount of digits involved in decimals, to a context
of presumed endlessness, it is extremely questionable
whether there is a well-definedness of absolutely every
every other feature of this context.
And, indeed, the more one looks into what happens when
one crosses from having a range of numbers such as
1..1000, to having a kind of 'et cetera' situation
without any upper bounds, the more one will see that
this involves a full change of the senses of all
operators and even of all numbers. I am not claiming
that the infinite is not real, but I am claiming that as
human thought grapples to come to terms with a finite
calculation, it cannot merely paste the letters "et
cetera" or some three dots after a number series with a
clear-cut beginning, and assume that it still grapples
with the situation.
I say the infinite is real, indeed that the infinite
in some sense is the foundation (not basis, which means
zero, but foundation, or ground) of all and everything
else -- including the ground of the finite numbers and
the simple forms of addition, division and comparison we
can do with these finite numbers. The world IN ITSELF is
infinite. Thought, and more generally the mind, may have
something about it which is infinite. But then thought
must be humble enough to regard the infinite as living
and coherent and beyond such simple rules as one may
find to apply, as it were temporarily, when we play
finite games.
Let us round off with a brief reflection on the
relationship between the idea of the golden ratio as
simlarities of contrasts of interest to art, and what we
can rather immediately surmise when we look at the
Fibonacci numbers, that finite series.
When we watch 1 2 3 5 8 we are watching 1 and 2
together as 3, 2 and 3 together as 5, 3 and 5 together
as 8. So there is a sense of containment, one within
another -- and, as we have just calculated on, with
something of the same relationship or ratio being
preserved.
The mind is doing its visual calculations
spontaneously on all that it apperceives. Thought knows,
for instance, how to chop a square out of a rectangle --
subconsciously, we do such things all the time, in order
to weigh and ponder and muse on the order of great
things.
And so, when a shape is about 5 units -- it may be
centimeters -- along one side and 3 along another, then
a square chopped off would mean 3 times 3 chopped off,
leaving a smaller shape about 2 units to 3. But that is
again part of the Fibonacci series. So you see there is
a kind of containment, or spiralling reflection of the
Fibonacci series, in visual shapes having such
proportions.
Let me be clear that I regard Fibonacci numbers as an
EXAMPLE of similar contrasts and contrasting
similarities involved in perception, and that beauty is
not one but several.