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Cementerio Jardín de Paz, Buenos Aires, Capital Federal, Argentina |
Gradients refer to continuums and shades of gray rather than rigid binaries of black and white. Both hierarchies and holarchies can be described as clearly defined and fuzzy demarcations along a continuum. Size, color, light, temperature, speed, quantity, amounts, elevations, distances, etc. refer to continuums. Most choices for humans and other animals do not manifest as a clear binary, but as a multiplicity along a continuum with no clear “right” or “wrong.”
Gradient of the 2-d function f(x,y) = xe-x2-y2 is plotted as blue arrows over the pseudocolor plot of the function. |
M.C. Escher, Reptiles, 1943 |
M. C. Escher, Drawing Hands, (lithograph, 1948) |
Abstract diagram of M. C. Escher's Drawing Hands. On top, a seeming paradox. Below, its resolution. Douglas Hofstadter |
Twelve self-engulfing TV screens. I would have included one more, had 13 not been prime. Douglas Hofstadter |
Sierpinski triangle |
Alexandre Duret-Lutz, Recursive Blanket Flower |
Igor Morski |
"One of man's important mistakes," he said, "one which must be remembered, is his illusion in regard to his I."
"Man such as we know him, the 'man machine,' the man who cannot 'do,' and with whom and through whom everything 'happens,' cannot have a permanent and single I. His I changes as quickly as his thoughts, feelings, and moods, and he makes a profound mistake in considering himself always one and the same person; in reality he is always a different person, not the one he was a moment ago. "Man has no permanent and unchangeable I. Every thought, every mood, every desire, every sensation, says 'I.' And in each case it seems to be taken for granted that this I belongs o the Whole, to the whole man, and that a thought, a desire, or an aversion is expressed by this Whole. In actual fact there is no foundation whatever for this assumption. Man's every thought and desire appears and lives quite separately and independently of the Whole. And the Whole never expresses itself, for the simple reason that it exists, as such, only physically as a thing, and in the abstract as a concept. Man has no individual I. But there are, instead, hundreds and thousands of separate small I's, very often entirely unknown to one another, never coming into contact, or, on the contrary, hostile to each other, mutually exclusive and incompatible. Each minute, each moment, man is saying or thinking 'I.' And each time his I is different. Just now it was a thought, now it is a desire, now a sensation, now another thought, and so on, endlessly. Man is a plurality. Man's name is legion."
"The alternation of I's, their continual obvious struggle for supremacy, is controlled by accidental external influences. Warmth, sunshine, fine weather, immediately call up a whole group of I's. Cold, fog, rain, call up another group of I's, other associations, other feelings, other actions. There is nothing in man able to control this change of I's, chiefly because man does not notice, or know of it; he lives always in the last I. Some I's, of course, are stronger than others. But it is not their own conscious strength; they have been created by the strength of accidents or mechanical external stimuli. Education, imitation, reading, the hypnotism of religion, caste, and traditions, or the glamour of new slogans, create very strong I's in man's personality, which dominate whole series of other, weaker, I's. But their strength is the strength of the 'rolls' in the centers. "And all I's making up a man's personality have the same origin as these 'rolls'; they are the results of external influences; and both are set in motion and controlled by fresh external influences."
"Man has no individuality. He has no single, big I. Man is divided into a multiplicity of small I's."
"And each separate small I is able to call itself by the name of the Whole, to act in the name of the Whole, to agree or disagree, to give promises, to make decisions, with which another I or the Whole will have to deal. This explains why people so often make decisions and so seldom carry them out. A man decides to get up early beginning from the following day. One I, or a group of I's, decide this. but getting up is the business of another I who entirely disagrees with the decision and may even know absolutely nothing about it. Of course the man will again go on sleeping in the morning and in the evening he will again decide to get up early. In some cases this may assume very unpleasant consequences for a man. A small accidental I may promise something, not to itself, but to someone else at a certain moment simply out of vanity or for amusement. Then it disappears, but the man, that is, the whole combination of other I's who are quite innocent of this, may have to pay for it all his life. It is the tragedy of the human being that any small I has the right to sign checks and promissory notes and the man, that is, the Whole, has to meet them.
People's whole lives often consist in paying off the promissory notes of small accidental I's."
Putney Vale Cemetery and Crematorium, Wimbledon, Greater London, England |
44 Then he saith, I will return into my house from whence I came out; and when he is come, he findeth it empty, swept, and garnished.where a man is cleansed of an unclean spirit who then comes back with seven others more evil than himself and, finding the man’s soul swept and garnished, moves back in with his companions. Sometimes the cure is worse than the disease. I think that the only defense against what I take to be a dangerous and erroneous set of attitudes towards religion is a much more flexible understanding of the possible meanings of faith, as contrasted with belief, in people’s lives, and in the lives of scientists. There is an apparent symmetry of mutual blindness.
45 Then goeth he, and taketh with himself seven other spirits more wicked than himself, and they enter in and dwell there: and the last state of that man is worse than the first. Even so shall it be also unto this wicked generation.
(Matthew xii:44–45)
44 Allora dice: Ritornerò nella mia casa donde sono uscito; e giuntovi, la trova vuota, spazzata e adorna.
45 Allora va e prende seco altri sette spiriti peggiori di lui, i quali, entrati, prendon quivi dimora; e l’ultima condizione di cotest’uomo divien peggiore della prima. Così avverrà anche a questa malvagia generazione.
(Matteo, 12:44-45)
The teaching of the doctrine by the Buddha is based upon two truths: the truth of worldly convention (samvrti) and the ultimate, supreme truth (paramartha).Relative truth (samvrti, which literally means covered or concealed) is the phenomenal world just as it appears-with chairs, people, species, and the coherence of those through time. Ultimate truth (paramartha) is the emptiness of that very same phenomenal world. The Tibetan term for relative truth, kundzop, captures the relation between the two imagistically; kundzop means aU dressed up, outfitted, or costumed-that is, relative truth is sunyata (absolute truth) costumed in the brilliant colors of the phenomenal world.
Those who do not discern the distinction between these two truths, do not understand the profound nature of the Buddha's teaching.
Jos Leys, Kaleido 4D |
Alexandre Arrechea, No Limit |
Rigidity and flexibility can be binaries of space, time, and relationship. Rigidity implies strength and impenetrability, while flexibility implies adaptability and change. In a spatial sense, a tube, sphere, sheet, border, or layer can be rigid or flexible. Boundaries of time can be rigid sequences of steps or stages or can delimit actions and activities. Binary relationships can be rigidly established or provide for flexibility. Both flexibility and rigidity can serve to protect.
Vladimir Kush, Earth Well |
11 | Complex: consider paradoxical observers interacting with self-organizing, unpredictable, paradoxical, non-trivial environments that include the observers, thus eluding trivialization. |
11.01 | Interaction: any limit between the “distinguished” and its “background” vanishes for one or more of these observers interacting with themselves or socially. |
11.1 | Simple: consider logical observers distinguishing non-self-organizing, predictable, logical, trivial environments that exclude the observers, thus embracing trivialization. |
11.11 | Distinction: a clear limit between the “distinguished” and its “background”s in social intercourse. |
11.2 | Observers cannot trivialize organizationally closed unities. |
11.21 | Any attempt to trivialize them will either fail or destroy (loss of organizational closure) the organizationally closed unities (also a failure). |
11.3 | Observers cannot trivialize a complex environment without destruction. |
12 | Mind: consider the activity of the nervous system that encompasses thinking, perceiving, emotions and feelings. |
12.1 | Consider emotions and feelings as the paradoxical activities of closed organizations (that cross and include the sensory and effector surfaces) inside and outside the nervous system of a paradoxical observer. |
12.11 | Therefore, emotions and feelings thoroughly escape the logical observer since the logical observer contemplates only inside or outside the nervous system. |
12.2 | Just as in the network of oscillators discussed in the Introduction, where external stimuli may drastically reduce the possibilities (number of choices available), so may suitable stimuli applied to the nervous system stunt, in different degrees, its potential for emotional, physical and intellectual expressions. |
12.21 | The resulting damage, temporary or permanent, often not obvious and sometimes desirable as in a hierarchical environment, where moderate or no thinking at all constitutes a requisite for membership. |
13 | Language-games: imagine predictable and unpredictable games that observers play, logically, inside or outside and, paradoxically, inside and outside their nervous systems, thus defining their forms of life. |
13.1 | Meaning: consider the uses that observers give to words in language-games. |
13.11 | If the language-games change or vanish, so do the meanings of words used by observers. |
13.2 | Language: consider the language-games trivialized (made predictable) by logical observers, where the meanings of words soon evaporate. |
13.3 | Explanation: consider the attempts to trivialize a language, e.g., using it only to follow rules while striving for a “logically perfect language”. |
13.4 | Communication: consider any attempt to use a trivialized language among observers. |
13.5 | Thinking: consider the activities involving the nervous system of a paradoxical observer, including emotions and feelings, and thus offering new language-games to the observer. |
13.6 | Conversation: consider the activities involving the thinking of one or more paradoxical observers, thus offering new language-games to these and other observers. |