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Being a personal garden of epistemological
fancies
bearing on the language, logic, and frailty
of Science, Mysticism & Common Sense
by
Don Berry
An Accidental Publication
v 0.8
© 1994 Don Berry
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PREFACE
CATCHING YOUR MIND IN THE ACT
I've chosen the various examples in this chapbook -- illusions, number games, anecdotes, etc., -- primarily to give you the chance to observe your mind in the act of cognizing. That is, assigning internal meaning to an event in the outside world.
It's usually difficult to observe your mind in action, because your attention is focussed on the object-of-knowing, and the mental action is more or less invisible in the background.
I've tried to find moments when a particular kind of cognizing takes place, which you can observe for yourself, and which is easily repeatable until you get the point.
In my view, the inherent nature of all cognizing is some form of "getting the point." In some cases the joke may be rather trivial, in some cases it may be the Cosmos itself. But in all cases, "getting the point" is a wordless inner explosion of meaning whose principle characteristic is that it leaves you perfectly satisfied.
So, with the examples in this book, watch not only the object in front of you, but observe your own mind at the moment of "getting the point."
PROLOGUE
I am sitting at a small white table. In front of me are three objects: a glass of pure water, a felt tip marker, and a blank sheet of paper.
(...and a ring of keys, a small saw-toothed knife blade, 8 pieces of unopened mail, a broken smoke detector, 4 unpaid bills, a theater program, a cassette of a friend's songs, 10 computer printed lyric sheets for same, a business card from the other side of the continent, a torn piece of cellophane with a price tag of $2.49, a bottle of black pepper, a draft of a four line contract, a bonus coupon from an espresso stand on some other island, a blank computer disk in a #10 envelope, an empty box of Fisherman's Friend cough drops, a short manuscript on the Musical Mathematics of Pythagoras, a yellow legal sheet with scribbled trial lyrics for a song (not mine) called You're the One, a rusted spring from a toe-nail clipper, a rubber band, a twist-tie, a printed booklet of two of my short stories, a recipe from my daughter-in-law for a salsa called Pico de Gallo, a sheaf of receipts for prescription medicine, a photograph of myself, my daughter and granddaughter getting out of a dinghy, and a plastic tumbler base filled with loose salt. These things do not count. Trust me...)
SCENARIO #1
ACT I
I am sitting at a small white table. In front of me are three objects: a glass of pure water, a felt tip marker, and a blank sheet of paper.
I take a sip of water.
This is how I know water. My thirst is quenched.
ACT II
On the sheet of paper I write a large
H20
This is how I know water. There is neither thirst nor the quenching of thirst here.
DIRECT and INDIRECT
Scenario #1 demonstrates modes of knowing we can call Direct and Indirect.
Among the characteristics of Direct Knowing (the sip of water) are these:
It arises entirely from present experience.
It is self-evident.
It is self-contained.
It is inexpressible.
It is not mediated by concepts, words, or symbols.
It carries apodictic certitude; that is, certitude not subject to proof or disproof.
The content of this can be called knowledge OF water.
This is the language and logic of everyday experience and mysticism. It depends on the interaction between Knower and the Known, unmediated by language or symbol.
Among the characteristics of Indirect Knowing (the formula H2O) are these:
It arises from the past experience of others.
It must be learned.
It is contained in concepts, words, or symbols.
It is founded on, and part of, a larger system of knowing, and is not comprehensible without the larger system. (In this case the concept of atomic theory.)
Its proof or disproof is conceptual, involving some form of logical consistency, often a mathematical language.
It depends on an act of faith -- that is, belief that what you have been told by others is true.
The content of this can be called knowledge ABOUT water.
This is the language and logic of science, education and religion. Its basis is in cultural agreement, and the time-binding character of language and symbol.
In the case of science, the necessary prerequisite is MEASUREMENT OF PHYSICAL PROPERTIES OF THE MATERIAL WORLD.
ETC. #1
(1) First, let us dispose of the fallacy that the Direct Knowledge described above is "Subjective" and the Indirect Knowledge is "Objective." No such distinction is possible.
"Objective Knowledge" is an oxymoron. All know-ledge, by definition, involves the interaction between the Knower, (subject,) and the thing Known, (object). The object-of-knowledge occurs in the field of conscious awareness as fish occur in the sea.
(2) It is remarkable how little intercourse is possible between these two realms of knowing. Although the modes appear to refer to the same object-of-knowledge -- ("water") -- this cannot be the case.
I cannot explain my experience to you. Direct experience is ultimately incommunicable and, indeed, my actual experience may or may not correspond to yours. We have no way of cross-checking. This mode of knowing is ultimately and irrevocably private.
Any comparison of experience depends on the definition of words, which, in turn, depend on the definition of other words, a process which almost immediately ends in a tautology. "Water" is defined in terms of "liquidness" and "liquidness" ultimately defined as "water-like." Very few definitions can be carried through more than two or three levels without tautology. It is a miracle in the mind of the child that the infinite complexity of a manifest world can be mapped onto a relatively shallow mental structure like language.
What I can do, however, is give you a glass of water and show you how to drink it. In mystical practice, this is sometimes called "the finger pointing to the moon."
(3) Similarly, my knowledge of the formula H2O does not illuminate my experience of drinking water in any way. It does not add to my understanding of my experience. In fact, it has no bearing whatever on that experience , which remains ultimately private.
I can, however, accurately communicate to you my understanding of the formula and the conceptual basis on which it rests. This knowledge, by reason of its abstraction, has become independent of the space/time limitations of direct experience, and is shareable and public.
In short, the languages (and logics) of Direct and Indirect Knowing (in a pure form) are not directly translatable from one realm to the other. For all practical purposes they are phenomena of different and irreconcilable dimensions. There is an invisible but impenetrable barrier between them.
These modes, owing to their characteristic natures, cannot confirm each other, but it is equally important to observe that they do not necessarily contradict each other.
SCENARIO #2
ACT I
I wake at first light in my tent on the beach. I light the little Bleuet stove and make a cup of coffee. I sit outside the tent to watch the sunrise, luxuriating in the uncanny stillness of earth and sea.
The sky lightens in the east, slowly at first, then quite quickly. The great incandescent disk seems to pop above the Coast Range hills. It rises fast in the sky, but slows as it approiches the zenith. In another twelve hours I will sit in this place and watch the same great light redden in an accelerating plunge through the clouds to meet the distant ocean line and disappear behind it.
This is how I know the sun, at sunrise and sunset.
ACT II
I am sketching the solar system for a child, explaining the cycle of seasons. In my simplified explanation the sun does not move at all.
The little planet Earth, however, spins furiously in quick circles, all the while travemino the long slow orbit about its primary.
This is how I know the sun. There is neither sunrise nor sunset here.
.P O V
Seeing is not believing. Believing is believing.
At first glance, Scenario #2 appears to be much like Scenario #1, in that Direct knowledge is contrasted with Indirect knowledge.
In actuality, Scenario #2, this innocuous little paradigm of the Copernican revolution, represents what may be the most critical moment in the history of Western thought. In this example, the content of Indirect knowledge not only contradicts my Direct knowledge, it turns my living experience into evanescent dream.
What I perceive as still is "really" moving. What I perceive as moving (and which my observation will confirm every day of my life) is "really" still. What I perceive as a change in size is not happening at all. What I perceive as a change of speed is doubly illusory, since that non-moving object clearly has no speed to change. . .
What is most difficult for me is to localize my consciousness. Up until now, I was more or less content with existence as a creature in a World; my Point of View corresponded pretty much with my location.
But now -- where am "I"? Someplace in space, clearly, outside the solar system. Just hangin', apparently, in what I have been led to believe (by the same people) is a vacuum. My POV is noplace real, it is purely imaginary.
From this unreal and non-existent POV, however, I can somehow infer the Real. And that inferred Reality is to be accepted as more Real than my direct experience.
Wow.
(In practice, of course, I infer nothing, because I am not qualified to do so. I simply take somebody else's word for what I would find if I did infer (correctly)). It is an act of faith on my part.
With the adoption of the Copernican theory, Western man completed his divorce from Nature, a long and painful separation that began around the time of Aristotle. No longer was he a part of the World -- he was above it. He took on the mental trappings of omniscience, and adopted the POV of God. No wonder it made the Church nervous.
It makes me a little nervous, too.
Still, having cheerfully accepted this from Western science, how should I doubt the Buddhist if he also tells me the world as I know it is illusion?
SHADOWS, SHADOWS. . .
"Briefly the position is this. We have learnt that the exploration of the external world by the methods of physical science leads not to a concrete reality but to a shadow world of symbols, beneath which those methods are unadapted for penetrating.
A. Eddington: Science and the Unseen World: (1929)
"Please note that the very recent advance (of quantum and relativistic physics) does not lie in the world of physics itself having acquired this shadowy character it had ever since Democritus of Abdera and even before, but we were not aware of it; we thought we were dealing with the world itself."
E Schroedinger: Mind and Matter:(1958)
"The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures. . . They are nothing more than pictures -- fictions if you like, if by fiction you mean that science is not yet in contact with ultimate reality. . . We are still imprisoned in our cave, with our backs to the light, and can only watch the shadows on the wall."
Sir James Jeans: The Mysterious Universe . (1931)
These comments, by 20th century scientists, reflect
on the frailty of the methods of Indirect knowledge. Following is a demonstration
of the frailty of Direct knowledge.
Directions:
(1) Draw a narrow "X" on a sheet of paper.
(William James attributes this figure to Christine Ladd Franklin, first woman President of the American Psychological Association. He reported it in Principles of Psychology, 1908)
(2) Hold the page directly in front of you, pointing your nose at the crossing point of the "X." Tilt the page away from you, holding it almost horizontal.
Focus on the crossing point, (you may have to cross your eyes slightly.) You will see a short "pin" (in the third dimension) sticking straight up from the page. Move your head slightly from side to side.
The point:The essential frailty of Direct knowledge is that it is possible, and in fact very common, to experience directly something that does not actually exist.
The persuasiveness of direct experience, the apodictic certitude it engenders, is the same whether the experience is of something that actually exists or something that is merely an artifact of the observing mechanism -- the sensorium + brain -- of the Knower.
(I separate the Knower and the mechanism-of-knowing here because, despite much diligent research and the stubborn superstition of Western reductionist materialism, there has never been a single shred of evidence that conscious awareness is somehow the by-product of physical brain activity.
We merely wish it to be so because of our passionate
infatuation with matter as the only primary Reality.
YOUR PERSONAL CORNERBOX
Download this pattern by clicking on it, and copy it to heavy paper or card. Cut on outside lines, fold on inside lines, and tape to make a cornerbox.
Cradle the cornerbox in the palm of your hand, with the
corner pointing away from you. Hold it at arm's length and close one eye.
After a moment the corner will suddenly seem to pop out toward you, becoming
the protruding corner of a solid cube. Move your hand slowly from side to
side. Your hand will experience one motion, your eye will know another.
THIS IS FUN. 
THE ART OF EXCLUSION
The first necessary condition of knowing is an act of exclusion. Everything in the universe other than the object-to-be known, is excluded from the mental field.
Examples:
(1) In the Prologue, I described the setting for Scenario #1 as a tabletop with three items. I also 'fessed up as to what the tabletop contained in actuality -- and advised you to ignore the actuality in favor of my abstraction.
This was OK, because the clutter of my table had very little to do with the point I was making. In order to make the situation comprehensible, I had to leave out a lot of the universe, including some of my bad habits.
Am I absolutely certain I didn't exclude something meaningful? Nope. And I'll never know. It's an approximation for the sake of getting on with it. Just common sense.
(2) In Scenario #2, I intentionally falsified again, by drawing a Copernican picture of the solar system in which Sol is unmoving. But Sol and the other four members of the Local Group are shuffling along in loose formation, led by Vega, slightly crosswise to the arm of the galaxy in which we find ourselves, and which is, in turn, orbiting the center of said galaxy, which is, in turn orbiting together with a larger group of galaxies.around. . . etc., etc.,
This time I unquestionably omitted relevant, meaningful stuff, since the object-to-be-known was precisely the motion of astronomical bodies. I narrowed the field of view for the sake`of clarity. Clarity is a desirable quality, and I intentionally lied to achieve it. Common sense told me the "whole" truth was irrelevant.
(3) In the Experimental Method of Western Science, the object-to-be-known is defined in advance, the quantities to be measured are defined in advance, the instruments of measurement are designed in advance to measure those quantities and those alone, and a hypothesis is formed to provide a yardstick of progress. Thus, a measuring machine is constructed, and the crank is turned. This turns out to be an instrument of staggering power.
(4) The traditional Yogic mode-of-knowing known as Samyama is described by the classic Yoga Sutras of Patanjali as consisting of three stages, dharana, dhyana, and samadhi. (See page 48.)
Book III, verse 1 of the Yoga Sutras says of the first stage:
III, 1: Desa-bandhas cittasya dharana
Desa = the place, or exact location
bandhas = confining; or restriction, or binding
cittasya = of the mind
dharana = is concentration
"Dharana, or concentration, is restricting the mind to a precisely limited area."
In this, the methods of Science, Mysticism and Common Sense are in perfect accord.
THE ART OF INCLUSION
Alfred Korzybski set out to develop a non-Aristotelian epistemological system called General Semantics. He created a cluster of semantic structures designed to compensate for weaknesses in the Aristotelian, Newtonian and Euclidean epistemologies as they had developed in European thought.
AK was concerned by the distortions that result from over-abstracting Still, he recognized that it is impossible to use an "actuality-complete" list of terms (such as the description of my cluttered table-top) in reasonable discourse. This was his structural solution:
"A null-A (non-Aristotelian) system, being extensional, requires the enumeration of long lists of names, which, in principle, cannot be exhausted. Under such conditions, I have to list a few representatives followed by an 'etc.', or its equivalents. As the extensional method is characteristic of a null-A treatment, the expression 'etc.' occurs so often as to necessitate a special null-A extensional punctuation whenever the period does not indicate another abbreviation, as follows:
Abbrev: |
Means |
Abbrev: |
Means: |
., |
etc., |
.: |
etc.: |
,. |
,etc. |
.? |
etc.? |
.; |
etc.; |
.! |
etc.! |
A. Korzybski, Science and Sanity (1933 )
Somehow or other, Korzybski's passion for detail precision never really caught on, even with other general semanticists.(However, the journal of the Institute of General Semantics is called "Etc." to this day.)
ON PRECONCEPTIONS
I - An Oft-ToldTale:
Eratosthenes of Alexandria was a philosopher / mathematician of the third century B.C. He was director of research and chief librarian of the Museum of Alexandria, the most complete repository of the world's knowledge in ancient times.
Eratosthenes knew that in the city of Syene (now called Aswan) there was a vertical well which, on the summer solstice, exactly reflected the sun. That is, the sun was directly overhead in Syene. On that same day, however, the sun was not directly overhead in Alexandria, as demonstrated by the fact that a vertical pole cast a short shadow.
It was easy to measure that shadow, and calculate the angle by which the sun missed being directly overhead. The base leg of the triangle thus formed was the distance from Alexandria to Syene, a distance of some 480 miles, which had been accurately paced off by Egyptian mappers.
Knowing that angle, Eratosthenes calculated that the distance between Alexandria and Syene was approximately one-fiftieth of the entire circumference of the earth. His calculation of that circumference was approximately 24,000 miles, (which is very close to the figure we still accept today, 23 centuries later.)
II - A Less-oft Told Tale
The data used by Eratosthenes was common knowledge among Greek and Egyptian mathematicians. In fact, some two hundred years earlier, the brilliant Greek mathematician Anaxagoras had performed the same experiment and the same basic triangular calculation.
However, using exatly the same data and the same arithmetic, Anaxagoras determined that the sun was approximately 30 miles in diameter and was located at a distance of 4000 miles from the earth.
Same accurate observation, same accurate calculation. How on earth could such a thing happen? What's the difference?
Easy. Preconceptions.
Eratosthenes, in the Pythagorean tradition, believed to begin with that the Earth was a sphere and that he was calculating its size.
Anaxagoras, on the other hand, believed to begin with that the Earth was flat and that he was calculating the distance of the sun.
THE POINT: No matter how good your data, and how good your calculation, the meaning you assign to your result will largely be determined by your preconceptions and the intellectual climate of your time.
THE ULTIMATE DEFENSE against knowing is the belief you already know. |
GETTING THE POINT
One of the most noted figures in the history of Zen Buddhism was the Sixth Patriarch, Hui Neng, who revitalized Chinese Zen after it had been brought from India by Bodhidharma. Hui Neng was an illiterate woodseller with no particular knowledge of Buddhism.
One day he was delivering a load of wood when he passed the open door of a Buddhist temple, and overheard a single verse from the Diamond Sutra. He was immediately enlightened. This is the verse:
"Awaken the mind without fixing it in any specific place."
This rather annoying little anecdote, (which through research I believe to be historically factual,) is probably my favorite Zen story. It beautifully raises two quite answerable (and quite Zen) questions:
(1) If you, the reader, were not immediately enlightened by reading that verse -- why not?
(2) If you, the reader, were immediately enlightened by
reading that verse -- how would you know it?( Knowing you were enlightened
would surely fix your mind in a specific place; i.e., your own enlightenment.)
SELF-REFERENCE
"THE MAP IS NOT THE TERRITORY"--A. Korzybski: Science and Sanity (1933) |
" ...nevertheless, Alfred, it is the only thing we know how to read..." --db: Lost in a dream (1994) |
SELF-REFERENTIAL LIMERICKERY
(1) A very sad poet was Jenny --
Her limericks weren't worth a penny.
In technique they were sound,
Yet somehow she found
Whenever she tried to write any
That she always wrote one line too many.
--T. McDonald, quoted in Metamagical Themas (1985)
(2) There was a fair rhymer named Hines
Whose limericks had only two lines.
--db
(3) And what of the poet named Donne?
--db
SELF-REFERENTIAL COUNTING
Fill in the blanks:
"In this sentence the number of occurrences of 0 is __, of 1 is __, of 2 is__, of 3 is __, of 4 is __, of 5 is __, of 6 is __, of 7 is __, of 8 is __, of 9 is __."
Each blank is to be filled with a numeral of one or more digits, written in decimal notation.
--Raphael Robinson, quoted in Metamagical Themas (1985)
(Mr Robinson states there are exactly two solutions to this self-referential problem. It is a particular favorite of mine because it involves both self-reference and paradox. It tickles my mind and makes me feel good all over. I wish the same for you.)
THE MYSTERY PAGE
THE ANTEPENULTIMATE MYSTERIES:
(1) Why does mathematics seem to describe the world so well?
(2) Why does music make us weep?
(3) What is laughing?
THE PENULTIMATE MYSTERY:
Who knows?
THE ULTIMATE MYSTERY:
Cannot be signified.
THE LIMITS OF REASON
The Simulations
Linear, analytic reasoning is a wonderful tool of knowing. What I like best about reason is that it contains a built-in alarm system that goes off when it has reached its limit of usefulness. It is like a little software sub-routine that pops up and says "OK, pal, this is as far as I can take you. You'd better change methods." Most reasoners are unaware of, or simply don't recognize this warning.
As I am one who has frequently overstepped the limits of my own reasoning, I am happy to pass on to you the warning signals as I have come to know and love them. Beyond reason lies a garden of delights.
In my experience, the most fruitful places to explore for the limits of reason are in the fields of:
(1) Logical paradox.
(2)Psychedelic experience
(3) Mathematics (particularly number theory and non- Cantorian concepts of infinity (endlessness)).
(4) Traditional mystical (e.g. ,Yoga, Zen, Sufi,) modes of knowing.
(5) Sensory illusions.
(6) Jokes.
In the next few pages, I will demonstrate simple mental exercises that simulate arriving at the edge of reason. This is not the real thing, but a reasonable model of the process.
OSCILLATION
One of the signs of reaching the limits of reason is when your mind seems to oscillate between two mutually exclusive alternatives, and cannot resolve in favor of either.
THE SIMULATION:
A:
(1) Take a small card, like a blank business card. On one side write "The statement on the other side is False."
(2) On the reverse, write "The statement on the other side is True."
(3) Read until satisfied.
(This calling card was printed in 1913 by the French mathematician P E B Jourdain. This is my favorite version of the classic Greek Liar paradox, the most profound and long lasting of the ancient paradoxes.)
B:
(1) Take a small card, like a blank business card. On one side write "The statement on the other side is False."
(2) On the reverse, write "The statement on the other side is False."
(3) Read until satisfied.
(Is there a difference between A and B?)
LOOPING
Another limiting signal is when an apparently productive analytical procedure unexpectedly enters an endless logical loop. (This is the state of reasoning that tends to wake you up at 3:00 A.M.)
THE SIMULATION:
(1) Take any two digit number (where the digits are not identical.) For example, 56
(2) Reverse the digits. (65)
(3) Subtract the smaller from the larger: 65 - 56) = 09
(4) Repeat steps 1 and 2 with the new number: (90 - 09) = 81
(5) Repeat until satisfied.
GLASS WALL # 495
Another end of reason is where an apparently productive analysis simply stops dead, and ceases to generate new information. (And, no matter where you start, the ultimate answer is always the same: 495)
THE SIMULATION:
(1) Take any three-digit number where the digits are not all identical. For example, (343)
(2) Rearrange digits to make the largest possible number. (433)
(3) Rearrange digits to make the smallest possible number (334)
(4) Subtract the smaller from the larger: (433 - 334 = 099)
(5) Repeat steps 2-4 with the new number: (990 - 099 = 891) => (981 - 189 = 792), etc.
(6) Repeat until satisfied.
THE MIRROR
I include this simulation only because it is a form of knowing of which I am exceptionally fond, for these reasons:
(1) I find it beautiful.
(2) It is True.
(3) I have absolutely no idea why it is True.
(4) To the best of my knowledge, it is entirely useless, and probably meaningless to boot.
THE SIMULATION:
(1) Take any two-digit number (where the digits are not identical. ) For example, 93.
(2) Reverse the digits, and add: (93 + 39) = 132
(3) Repeat steps 1 and 2 with the new number.(132 + 231) = 363
Note that 363 is a palindrome, a number that reads the same backwards and forwards. Any two digit number will eventually yield a palindrome by this process.
(The original number "89" requires the most steps (24) to yield, at last, the palindrome 8,813,200,023,188.)
(These arithmetical simulations come from number theory: For other delightful examples of oddball behavior in the family of numbers, see S. Richards, A Number for Your Thoughts.)
INTERPRETING DIRECT KNOWLEDGE
We have an insatiable appetite for meaning. So insatiable that we will create meaning where none exists, and swear to its truth. We cannot help trying to make "sense" of what we experience. This is obviously necessary, but it also frequently replaces the world-as-it-is with the world-as-I-choose-to-understand-it.
The well-known illusion above (called the Necker cube) is usually used to illustrate our understanding of perspective -- are we looking up at the cube or down? Sometimes it is one, sometimes the other. Never do we see them simultaneously. Our cognitive mechanism demands an either/or interpretation.
However, I use the Necker cube here to demonstrate our "meaning appetite", because of course there is no cube at all. We impose that reading on a flat surface, because of our visual training.
We know that, but it is extremely difficult to perceive it as-it-really-is; a flat pattern of angular lines with no three-dimensional existence at all. Artists know all this very well.
(W. Hill,My wife and my mother-in-law. Puck, 1915
We also have an extremely low tolerance for ambiguity; we resist the perception that an object may simultaneously be one thing and another. We have a distinct need to know which it is.
In the above classic figure, you may see the young woman facing away, or the big-nosed old woman in left profile You cannot see both at the same time. The instant the image switches is the moment of cognition.
Your best chance to see the image as-it-really-is is to strip it of meaning entiirely! Turn the page upside down, so it can be perceived as an abstract pattern of light and dark..
(Incidentally, you will draw this figure much more accurately upside down. Rightside up, your pre-knowledge that "This is a nose. This is an ear." seriously interferes with your perception of the figure as-it-really-is
Try drawing it both ways. Another old artist's trick. Old artists are very tricky.
THE SCIENTIFIC KNOWLEDGE-SYSTEM
N. Herbert, Quantum Reality (1985) |
Bertrand Russell |
THE QUANTUM GUYS
Twentieth-century physics began in 1900 with the idea, conceived by Max Planck, that some phenomena could be more easily described mathematically if energy came in discrete 'packets,' or quanta.
A rough analogy would be heating a pan of water and discovering that the thermometer did not rise continuously, but jumped up in five degree steps.
This was originally a purely mathematical device to make calculation easier. Within five years, however, a patent clerk named Albert Einstein wrote that Planck's mathematical notion of a 'constant of action' accurately described certain observable physical phenomena (the photoelectric effect.)
Thus was launched Quantum Theory, the revolution in scientific thought that has largely dominated the century. Some twenty years later a 24 year old student named Werner Heisenberg took a vacation from Gottingen University to recover from a hay-fever attack. In "one fevered day and night, he invented what was to be known as matrix quantum mechanics." Almost simultaneously Erwin Shroedinger, approaching the mathematics from a different slant, created the 'Schroedinger wave equation,' which is the most commonly used mathematical tool of modern Quantum Theory.
An enormous body of nonsense, some of it very interesting and intriguing, has been written about the philosophical and epistemological implications of these events.
The pages that follow are samples of the quantum physicists' own comments`on the quantum knowledge-system, and, by extension, the knowledge-system of science itself.
HEISENBERG
ON THE ROOTS OF SCIENTIFIC KNOWING
"...But if such a unitary principle of all things exists, then -- and this was the next step along this line of thought -- one is straightway brought up against the question how it can serve to account for the fact of change. The difficulty is particularly apparent in the celebrated paradox of Parmenides. Only being is; non-being is not. But if only being is, there cannot be anything outside this being that articulates it or could bring about changes. Hence being will have to be conceived as eternal, uniform, and unlimited in space and time. The changes we experience can thus be only an illusion.
Greek thought could not stay with this paradox for long. The eternal flux of appearances was immediately given, and the problem was to explain it. In attempting to overcome the difficulty, various philosophers struck out in different directions. One road led to the atomic theory of Democritus. In addition to being, non-being can still exist as a possibility, namely as the possibility for movement and form, or, in other words, as empty space. Being is repeatable, and thus we arrive at the picture of atoms in the void -- the picture that has since become infinitely fruitful as a foundation for natural science. But of this road we shall say no more just now. Our purpose, rather, is to present in more detail the other road, which led to Plato's Ideas, and which carried us directly into the problem of beauty.
This road begins in the school of Pythagoras. It is there that the notion is said to have originated that mathematics, the mathematical order, was the basic principle whereby the multiplicity of phenomena could be accounted for.
. . . . Pythagoras is said to have made the famous discovery that vibrating strings under equal tension sound together in harmony if their lengths are in a simple numerical ratio. The mathematical structure, namely the numerical ratio as a source of harmony, was certainly one of the most momentous discoveries in the history of mankind. . .
But let us come back once more to understanding, and thus, to natural science. The colorful multiplicity of phenomena can be understood, according to Pythagoras and Plato, because and insofar as it is underlain by unitary principles of form susceptible of mathematical representation. This postulate already constitutes an anticipation of the entire program of contemporary exact science. It could not, however, be carried through in antiquity, since an empirical knowledge of the details of natural processes was largely lacking.
The first attempt to penetrate into these details was undertaken, as we know, in the philosophy of Aristotle. But in view of the infinite wealth initially presented here to the observing student of nature and the total lack of any sort of viewpoint from which an order might have been discernible, the unitary principles of form sought by Pythagoras and Plato were obliged to give place to the description of details. Thus there arose the conflict that has continued to this day in the debates, for example, between experimental and theoretical physics; the conflict between the empiricist, who by careful and scrupulous detailed investigation first furnishes the presuppositions for an understanding of nature, and the theoretician, who creates mathematical pictures whereby he seeks to order and so to understand nature -- mathematical pictures that prove themselves, not only by their correct depiction of experience, but also and more especially by their simplicity and beauty, to be the true Ideas underlying the course of nature.
--------------------------
It is certainly no accident that the beginnings of modern science were associated with a turning away from Aristotle and a reversion to Plato.
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. . . the inherent difficulties of the materialist theory of the atom . . . have also appeared very clearly in the development of physics of the present century.
This difficulty relates to the question whether the smallest units are ordinary physical objects, whether they exist in the same way as stones or flowers. Here the development of quantum theory . . . has created a complete change in the situation. The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive cocncepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them of elementary particles. . . .
(It) is important to realize that, while the behavior of the smallest particles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate for a clear-cut account of what is going on."
SCHROEDINGER
ON THE LIMITS OF SCIENTIFIC KNOWING
"The scientific picture of the real world around me is very deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously.
So, in brief, we do not belong to this material world that science constructs for us. We are not in it; we are outside. We are only spectators. The reason why we believe that we are in it, that we belong to the picture, is that our bodies are in the picture. Our bodies belong to it.
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Science cannot tell us a word about why music delights us, of why and how an old song can move us to tears.
For the observing mind is not a physical system, it cannot interact with any physical system. And it might be better to reserve the term "subject" for the observing mind. . . For the subject, if anything, is the thing that senses and thinks. Sensations and thoughts do not belong to the "world of energy."
Student: "Master, give me the first rate answer." Master: "I cannot. The moment I open my mouth it becomes the second rate answer." -- Zen saying |
THE COMMON-SENSE
KNOWLEDGE SYSTEM
--Aunt Minnie |
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MYSTICAL KNOWLEDGE-SYSTEMS
--K. Wilber, Quantum Questions (1985) |
OR?
"The cause of that which is to be avoided
--Patanjali, Yoga Sutras II, 17 |
ELEMENTS/SENSES
In several Indian traditions, notably the Samkhya philosophy, the elements of nature are categorized not in terms of an inferred physical structure, but by the sense organs they affect and the sensations thus produced. This view emphasizes the necessary interdependence of the mechanism-of-knowing and the object known.
In this model of cognition, the senses and the sensation are classed as elements of the Seen, the object side of experience, which is eventually witnessed by the Seer. (Cf. Schroedinger, above)
It's a bit like Dem Bones: The element's connected to the sense organ, the sense organ generates a sensation, the sensation is projected onto Mind (Citta.) The result is Buddhi, or perception, which is ultimately witnessed by Atma, the Self.
ELEMENTS |
SENSE ORGANS |
SENSATIONS (Tanmatras) |
EARTH (Prithvi) |
Nose |
Smell |
WATER (Jala) |
Tongue |
Taste |
LIGHT (Tejas) |
Eye |
Sight |
AIR (Vayu) |
Skin |
Touch |
Ear |
Hearing |
Note that these "elements" are not material substances like Western "elements", but something more like a "medium" of propagation of specific sensory experience. More process than thing.
CAVEAT
All translations from Sanskrit to English, regardless of source, must be regarded with acute suspicion.
Sanskrit is a different system of expressing thought from conventionally evolved languages like English. Sanskrit is a technical language, specifically designed to deal with the domain of spirit and consciousness. As a consequence, many crucial words in Sanskrit have no exact equivalent in English. (There are, for example, somewhere around 30 words in the technical vocabulary of Sanskrit which can only be grossly translated into English as "mind" or "mental".) I guess we name the things that interest us.
The relation of Sanskrit to the domain of consciousness is like the relation of mathematics to physics.
In an attempt to give the reader some direct experience of this quandary, I've followed a common tradition and included word-notes for the verses from the Yoga Sutras.
The following excerpts are millenia apart. The Yoga Sutras are very ancient and the Darsana Mala was composed early this century.
THE YOGIC METHOD
In the West we are familiar with the word Yoga as meaning`the system of physical postures known as Hatha Yoga. The Raja (or Royal) Yoga expounded in the Yoga Sutras of Patanjali is not that practice.
Raja Yoga is a mental and spiritual discipline. Its stated goal is Kaivalya, the Liberation of Consciousness. It is also called the Eight-limbed Yoga, as it has eight stages of practice. The first five stages are considered to be external practices, and the last three stages are considered to be internal to consciousness, and deal with the yogic mode-of-knowing called Samyama.
The Yoga Sutras consists of 196 verses, divided into 4 books. The third book, Vibhuti Pada, (The Book of Accomplishments) begins by defining the nature of Samyama:
III, 1: Desa-bandhas cittasya dharana
Desa = the place, or exact
location
bandhas = confining; or restriction, or binding
cittasya = of the mind
dharana = is concentration
"Dharana, or concentration, is restricting
the mind to a precisely limited area."
III, 2: Tatra pratyayaikatanata dhyanam
Tatra = there; in that place
pratyaya = content of consciousness
ikatanata = flowing; streaming unbrokenly as one
dhyanam = is meditation
"Dhyana, or meditation, is the uninterrupted
flow of attention to the 'object' meditated.
III, 3: Tad evarthamatra-nirbhasam
svarupa-sunyam iva samadhih
Tad = the same
evarthamatra = the 'object' only; the thing meditated alone
nirbhasam = 'shining'; appearing self-luminously therein
svarupa = its own true form
sunyam = empty; void
iva = as if
samadhih = Samadhi
"Samadhi is accomplished when the
object of meditation
shines self-luminously in its own true form, as if
empty of all other characteristics (of mind.)"
III, 4: Trayam ekatra samyamah
Trayam = the three (dharana,
dhyana and samadhi)
ekatra = in one place; continuous; jointly
samyama = is Samyama
"The three taken together constitute Samyama."
III, 5: Taj-jayat prajnalokah
Taj-jayat = by mastering it
prajna = the higher consciousness
lokah = the light
"By mastering it (Samyama), the light of higher consciousness."
III, 6: Tasya bhumisu viniyogah
Tasya = its
bhumisu = in stages
viniyogah = application; use
"Its use is in stages."
THE DARSANA MALA
The Darsana Mala, or Garland of Visions, is a poem of 100 stanzas, dictated by Narayana Guru in 1916.
Narayana Guru was a mystical visionary who appeared in Kerala State in Southern India. He had teachers whom he acknowledged, but none who were recognized in the tradition of the Guru.
Narayana sent his eventual successor, Nataraja Guru, to the Sorbonne for study, wishing to integrate the vibrancy of Western scientific thought with his own ancient tradition. There Nataraja studied under Henri Bergson, and was deeply involved in the hotbed of quantum theory and relativity that was roiling European thought in the 1920s.
Many years later, Nataraja Guru wrote his magnum opus, a three-volume work called Brahmavidya, The Integrated Science of the Absolute. Its premise was the examination and reconciliation of quantum theory with the Darsana Mala.
Since my Western quotes have been mostly from quantum scientists, I felt obliged to quote the Darsana Mala to express the mystical epistemology. I rendered the verses into English because I couldn't read the Sanskrit.
CHAPTER FIVE
Bhana Darsana / Categories of Consciousness
1
Equally present within and without,
in constant bee-like agitation,
object-consciousness is of two kinds,
the generic and the specific.
2
The basis of object-consciousness is four-fold,
consisting of: The material, the non-material,
the causal, and the fourth kind. These names are
also applicable to the appropriate states of consciousness.
3
"I am the body. This is the pot."
What arises in awareness based on material objects
is known as STHULA, or concrete.
4
Here, the consciousness of "body" and "pot"
is the specific.
The consciousness of "I" and "This" is the generic.
5
What arises in awareness based on
the senses, mind, intellect, sense-objects
and the five vital processes,
is known as SUKSMA, or subtle,
because of dependence on non-material objects.
6
"I am ignorant." This consciousness
is called KARANA, or causal (pertaining to itself.)
"I am" is the generic, "ignorant" is the specific.
7
"I am the Absolute." This is praised as TURIYA,
or consciousness of the fourth kind.
"I am" is the generic, "Absolute" the specific attribute.
8
Where there is this awareness, there is an object-of-consciousness.
Where there is no such awareness, there is no object-of-consciousness. Thus,
by agreement and difference, certitude arises.
9
As the eye cannot see itself, the Self cannot perceive
itself.
The Self is not an object-of-consciousness.
What the Self perceives is an object-of-consciousness.
10
Whatever is an object-of-consciousness is conditional.
Whatever is not conditional is not an object-of-consciousness.
What is conditional is un-Real.
But what is utterly unconditional, that is the Real.
AUM TAT SAT
CHAPTER SEVEN
Jnana Darsana / On Awareness
1
Awareness, though essentially one,
is known as conditioned or unconditioned.
That awareness which is free of the ego-sense
of "I am," etc., is the unconditioned.
2
That awareness which arises as "I"- consciousness
inside,
and "this"-ness outside (accompanied by the
corresponding mental modulations,)
is known as the conditioned.
3
That awareness by which one experiences, as pure witness,
the non-Self (such as the ego "I"-consciousness, etc.,)
is true Self-awareness.
The witness alone is the immortal one.
4
That awareness which is identified
with effects belonging to the non-Self
(such as the ego-"I" consciousness, etc.,)
is non-Self-awareness.
5
When things are known as they are,
(as in perceiving the truth of the rope beneath the snike appearance,)
that awareness is meaningful. What is otherwise is meaningless.
6
When, by mere presence alone, everything is illuminated
by itself,
that is characterized as "awareness-by-direct-perception,"
or immediate knowledge. It is also called "inner" knowledge.
7
That form of awareness which arises
by performing mental action on the possibilities
of co-dependent phenomena,
and thus inferring their common source,
is known as inductive knowledge.
8
On going near and recognizing according to the pattern
:
"This animal conforms to the description I have heard of a cow,"
such is called awareness-by-inference, (or analogical knowledge.)
9
Awareness characterized as "I-Mine" is called personalized knowledge. Awareness characterized as "This-That" is called sensory knowledge.
10
That awareness which is verbally expressed as
AUM TAT SAT (Aum, That is the Real)
and experienced as the union of the Absolute and the Self,
empty of functions like willing --
that is known as the ultimate knowledge.
ETC. #2
(1) A knowledge-system is any self-consistent method of mapping experience onto mind. The poles of method are measurement and meditation.
(2) All knowledge-systems are self-complete as to language, logic, method and aim. All are subject to Gödel's theorem of incompleteness and imply a meta-statement from outside the system itself.
(3) All knowledge-systems are self-referential, in that any description of World will resemble the structure of the knowledge-system used for the description. The map and the territory are inseparable.
(4) A knowledge-system will answer only questions posed in its own language. A question posed in the language of qualitative experience cannot be answered in the language of quantitative measurement.
(5) The power and the frailty of any knowledge-system arise from the same source: the limitation of field.
Limitation of field is voluntary and involuntary. What is voluntary is the choice of method. What is involuntary is the distorting effect of the system's preconceptions, and its mechanisms of observation; i.e, the senses, measuring instruments, etc.
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* JUMP OUT OF THE SYSTEM
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(end)