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The Doctrine of Trialism

The essence of the doctrine of trialism is the metaphysical postulate of One entity (noumenon or thing-in-itself, after Kant), which is being explicated through two complementary presentations (contraria sunt complementa). The doctrine of trialism is suggested to unify two basic ideas, which can be attributed to the Western and Eastern philosophical schools. In the context of mind-matter problem, the case of trialism is explained here.

In the Western or reductionist way of thinking, we are inclined to presuppose the following Weltbild: there are boundaries of our physical world, which can be actually reached, because we use these boundaries as cut-off in our calculations. Example: there is a wall in front of you, which you can reach, but after which there is "nothing". Stated more accurately, the question of what might exist behind the wall is meaningless. If we picture this wall as the Planck scale, we suppose that there exist some fundamental constituents of the world at this scale, which build up our world completely (the so-called Theory of Everything). The doctrine of atomism is a clear example of such metaphysical school of thought. One of its modern versions is spin networks, in which the number of "atoms" are presumed to be denumerable, and have been roughly estimated as 1099 "atoms of volume" in every cubic centimeter of space. Hence in order to build a 3-D space of volume one cubic centimeter, all you have to do is to pack tightly 1099 "atoms of volume". They will build up the 3-D space entirely, without any gaps whatsoever, and you will end up with one cubic centimeter of 3-D space with zero curvature.

Note that the crucial presumption here is about the nature of atoms: denumerable and finite in size. We tacitly assume that something which has finite dimensions, such as one cubic centimeter of 3-D space, can indeed be build of finite number of something that also has finite dimensions, the "atom of volume".

Hence the atom (or infinitesimal, in differential calculus) is viewed as something that is stand still, fixed at the 'final wall' called Planck scale, after which there is "nothing", just as there is "nothing" between the 1099 "atoms of volume" in one cubic centimeter. The atom does not move "further", it inevitably stops at the Planck scale. It can therefore be reached and calculated. There is no room here for some noumenon or thing-in-itself, since the physical world is 'out there', like an island which we gradually study and explore. An island with final, albeit very large, boundaries.

The metaphysics implied here is the following: any object can be fully described by the set of its possible states, and any of these possible states represents the physical reality of the object at a given instant  t . Hence an object 'is' at time  tn , where  n  indexes the states of the object, and is modeled with a continuous variable. If we think of   tn  as the set of instants of a kaleidoscope as rest, then we cannot, even in principle ask (i) what is the state of the kaleidoscope while it is being shaken, "between" the instances in which it will display a fixed configuration of its colored pieces, and (ii) what is the state of 'the kaleidoscope per se'. Also, at each and every point from the continuous variable n  the kaleidoscope exists with probability unit 'here and now', and with zero probability in 'the rest of the universe'. Hence the probability current is conserved along the entire time  tn , and the crucial question of the transition from  tn  to  tn+1  is swept under the carpet. We simply claim that a physical clock can read only the continuous variable  tn , but not the state of 'the kaleidoscope per se', because we cannot squeeze it "between" the instances of the kaleidoscope at rest. And finally, we use this metaphysics as some kind of filter through which we try to understand Quantum Mechanics, since we apply the same metaphysics to the quantum realm. Surely we can switch from phase space (classical mechanics) to Hilbert space, but the latter does not, and cannot, model 'the quantum kaleidoscope per se', nor the very transition of the states of the quantum kaleidoscope: it is non-unitary, and totally mystical, as observed at the scale of our classical watch reading the "collapsed" states of the quantum kaleidoscope. Strangely enough, this way of thinking is considered "scientific", for reason which I was never able to understand.

There is another, complementary metaphysical approach to our physical picture of Nature, which comes from Eastern philosophy. Here the term  noumenon is replaced with Tao. Lao Tze, who lived in the same time with Confucius, explained it as follows: The Tao that can be expressed is not the eternal Tao. The name that can be named is not the permanent name (cf. Guang-jiong Ni, hep-ph/0206103 v2). Surely a person trained in Western traditions will feel very uncomfortable: Tao is defined as something that cannot, even in principle, be comprehended by anything we can say about it.

It's a bit like trying to demonstrate what is 'darkness' with a torch. We cannot comprehend the phrase 'the whole world as One', because our knowledge is relational: we can understand the meaning of  A  only if we can also understand the meaning of  not-A , with respect to which  A  acquires its identity, and vice versa. Hence the only way we can understand Tao is to imagine that we can build finite series of generalized concepts, such that their limit is 'One thing' or Tao. It includes 'absolutely everything' and therefore cannot be directly comprehended with our mechanism of relational knowledge. Psychologically, we can think of Tao as 'pure consciousness', knowing that everything we can say about Tao is some concrete phenomenon, A vs not-A, and is therefore an incomplete explication of Tao, cast in some concrete context. Compared to the example with the kaleidoscope above, we claim that 'the kaleidoscope per se' does exist, and is fused with other, higher-rank 'objects per se', the limit of which is Tao (the Leibnitzian monadology is another example of such paradigm). However, the status of this new kind of reality, and the spacetime of all 'objects per se' is not known: we derive the notion of spacetime only from the Western mysticism.

Physically, Tao is unobservable, too. Every physical quantity, in order to qualify as 'observable', must be invariant under some transformations, related to some symmetry or conservation law. If Tao is invariant under all possible transformations and does not brake any conservation law or symmetry group, then it cannot manifest itself. Instead of playing the role of some 'final wall' that can be actually reached (see the Western mysticism above), Tao can be found in the physical picture of Nature as some 'numerically finite but physically unattainable boundary'. It will be like a wall "fixed" at the Planck scale, but nothing other than Tao can actually reach this wall. The reasons why a physical system cannot actually reach the Tao can only be physical: recall the so-called speed of light, which fixes such 'wall' for all tardyons. Or the absolute zero "temperature". Physically, it will require an infinite amount of energy to reach the wall of Tao. But this wall is 'out there'. It is very real indeed. Here's why.

Lao Tze was wise to say more: Tao generates one, and one generates two, .... . We have discovered the unfolding of Tao in the famous Fibonacci series. They are infinite and are rigorously defined only with irrational numbers. Perhaps everything we observe, measure and expressed with natural numbers is just a crude approximation to some "true" reality which cannot be expressed with any natural number. For example, what is the difference between the length of a table in front of me, which I believe is 2 m, and the circumference of a circle, after Archimedes, that is also 2 m? In the first case I measure the table with my tape, and write down a natural number, hence I feel confident that have learned "the exact" length of my table, while in the second case I calculate it with an irrational number, and know that "the exact" circumference of a circle cannot be found in principle. What matters here is that we apply the same physics to both tables and wheels. The only difference is that we feel far more secure if we can eliminate those irrational numbers, say, by multiplying two infinite series, square root of 3 by square root of 12, after which we obtain a nice clean result, +/- 6, and feel happy. Or we subtract one infinity from another, as in the renorm recipes in Quantum Field Theory, obtain some clean finite value, and again feel happy.

The crux of the puzzle is the nature of continuum, again. Consider the famous Thompson's lamp paradox: Imagine a lamp that is turned 'on' at some instant labeled with 0, and is left 'on' for 1 min, then turned 'off' for 0.5 min, then 'on' for 0.25 min, etc., ad infinitum. Do we have a limit? Obviously yes: 2 min. Even my ten-year old daughter can understand the limit. There are obviously finite things around us, which build up the good old 3-D space, such as a table being 2 m long and a time interval of duration 2 min. Fine, but what is the state of the lamp in the instant labeled with '2 min'? Here some people try to bypass the question, arguing that the final instant does not belong to the on-off series, as if you could fix a wall exactly at the instant '2 min', and claim that the state of the lamp is "beyond" this wall, hence the question of its state at '2 min' is meaningless. Their argument is based on the idea of potential infinity, but other people claim that we are dealing with an actual infinity, and therefore the crucial instant '2 min' can indeed be reached by on-off series, and therefore we should address the issue with great scrutiny. But then, strangely enough, all people stop thinking further, as if there could be no third possibility, namely, an "intermediate" point which is being "inserted" between any two points -- The Gap of Zen. It's juts a new (to physics) kind of reality, which is conditio sine qua non for the good old lamp to exist in some definite state, either 'on' or 'of', at some "point" from the closed interval [0, 2], which should be open as well, (0, 2). Otherwise 'nothing can reach anything', and the state of the lamp an any instant cannot move to the nearest "point" at which it can and will change its state. This "movement" along the continuum of "points" constituting the 3-D space is the direct manifestation of the metaphysical principle of locality. The so-called speed of light is inherently linked to the nature of 3-D space. It is a perfect continuum in which things can exist in some definite state, and we can attach numbers to the "points" of this continuum, as in the old puzzle of Thompson's lamp. Surely the state of the lamp has to "move" from one point to the "nearest" one, or else the lamp will be confined to one of its states only, and will cease to be a lamp. The only solution is the "third" point of the Gap of Zen or Tao. We simply have no other choice but to acknowledge the existence of Tao in that "third" point, and get rid of our Western mysticism.

After Lao Tze, the common efforts of many philosophers, especially Wang Chong (27-100), Zhang Zai (1020-1077), and Wang Fuzhi (1619-1692), produced the theory of Yuan-qi (the primary gas). It suggests a concrete mechanism for the ever-unfolding Tao by two entities of opposite nature, yin and yang. In Quantum Mechanics, the mutual dependence of yin and yang was again shown by Guang-jiong Ni in "Where is the Subtlety of Quantum Mechanics?", quant-ph/9804013: "the complex expression of wave function, its phase transformation and Eq. (2) are nothing but the mathematical description of the theory of "Yuan-qi" (the primary gas, see Ref [2])."

Let me stress that we should not necessarily consider the yin <--> yang interplay as an observable phenomenon. In the example above, yin and yang denote quantum wave amplitudes [cf. Eq. (2) in quant-ph/9804013]. They should perhaps be interpreted as possibility, not probability, as suggested by Nick Herbert (ibid.),

probability = (possibility)2
Hence the interplay of possibilities is completely unobservable with any (inanimate) physical clock. The true subtlety of Quantum Mechanics is in the complex phase of quantum waves. It is inevitably 'swept under the carpet' (along with the Berry phase) by calculating the probability of what we can observe at the scale of tables and chairs under particular experimental context. (Recall that Schrödinger's catalogue of expectation values, which lists all conceivable observables under all conceivable experimental contexts, consists of an undenumerable class of all orthonormal basis of a Hilbert space. Here undenumerable refers to the "number" of points of 1-D Euclidean space, as in the case of the circumference of a circle and the Thompson lamp paradox above.) This is a very important consideration, which can be seen also in John Cramer's Transactional Interpretation: the two yin-yang waves "propagate" in some atemporal, hand-shaking medium. "The process is atemporal and the only observables come from the superposition of all "steps" to form the final transaction" (footnote 14). The next important clarification: "Advanced waves have the characteristic time dependent phase exp(iwt) while retarded waves have phase exp(-iwt). These functions are orthogonal and in principle distinguishable. Reinterpretation is permissible because it is consistent with the observed transfer of energy, momentum, etc., and because the time phases are not observed" (footnote 15).

Time phases? Orthogonal and distinguishable functions of what "time"?

Let me wrap up with the doctrine of trialism. It is a physical paradigm, since the word 'physics' originates from the Greek phusis, which means 'that what comes into existence', which in turns is derived from the Greek verb phuoo which means 'to create or to come into existence'. It is believed that the doctrine of trialism can address the ultimate question in quantum gravity of the emergence of time and space, and can reveal the Leibnitzian pre-established harmony: God casts the die, not the dice (A. Einstein). 

The two schools, Western and Eastern, are not only equally important; they are complementary. They refer to two ontologically different modes of reality, which are subsequently termed 'local mode of reality' and 'global mode of reality'.

In the local (Western) mode, we enjoy a perfect (not coarse-grained) continuum of events, and are in 'short circuit' with the Planck scale. This is also a static world of facts, which we observe only post factum, in line with the basic postulates of relativistic causality and locality.

In the global (Eastern) mode, we enjoy a holistic state of the whole universe as One. This is a discrete and dynamical mode of reality, much like the strips (cf. the Gap of Zen) separating the static frames from a film tape. In this global mode of reality, we always have two yin-yang possibilities. For example, a world made of matter vs. a world made of tachyons. These two possible worlds might "overlap" only at the apex of Minkowski's cone. (See a brilliant presentation of the three kinds of particles in: Ya.P. Terletsky, Paradoxes in the Theory of Relativity, New York: Plenum, 1968; available from DirectTextbooks.) If we wish to compare the intrinsic "time" in the global mode of reality to the one in the local mode, the first one would be 'stand still', if read by a clock in the local mode. This new kind of zero time can be "measured" only by the human brain; it is the intrinsic "time parameter" of the human self.

Then comes the obvious question: why do we observe an asymmetric snapshot from the two cancelled worlds in the local mode of reality, which we call 'material world'? Because of some fundamental time asymmetry caused by the third party -- the 'universe as One'.

Hence we always have three parties to consider, and the doctrine of trialism is both monistic, since the world is One at the state of Tao, and dualistic, since Tao is explicated in the global mode of reality only through two complementary, yin-yang emanations. Then in the local mode of reality, we again have One world, one-at-a-time, along the universal time arrow driven by Tao, presented as the Aristotelian First Cause. Or maybe God [John 1:1-4]. Who knows?

Since this is simply One, we can never tell the difference, if any.

I invite the reader to explore the doctrine of trialism by consulting the following sources.

Regarding the nature of continuum and the mystery of real numbers, see Gregory Chaitin's online book META MATH! The Quest for Omega, New Zealand, March 2004, Ch. 5, The Labyrinth of the Continuum, and his book THE UNKNOWABLE (Springer, Singapore, 1999).

The implications for modern differential geometry are suggested here; outline here.

The existence of global mode of reality can be explained with the famous paper by Ernst P. Specker, "Die Logik nicht gleichzeitig entscheidbarer Aussagen", Dialectica14, 54-55, 239-246 (1960). Here the complete catalogue (wave function) includes counterfactual, and subsequently undecidable, propositions introduced to model "the omniscience (comprehensive knowledge) of God" (Ernst Specker). English translation: "The logic of propositions which are not simultaneously decidable", in C.A. Hooker (ed.), The logico-algebraic approach to quantum mechanics. Volume I: Historical evolution, Reidel, Dordrecht, Holland, 1975, pp. 135-140.

Counterfactual propositions refer to events which would have occurred if something had happened which, in fact, did not happen. More in: The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions. Ed. by M. Davis. Raven Press, NY, 1965. Regarding the 'halting problem' produced by self-referential logical paradoxes, recall that the human brain solves it by referring to its context.

Needless to say, the 'context' lives in the global mode of reality. It can handle undecidable propositions with the simple answer 'Jain'.

See also the application of undecidable propositions from Gödel's theorems (a complete description of a language A cannot be given in the same language A, because the concept of truth of sentences of A cannot be defined in A; cf. Karl Svozil) in quantum morphogenesis and cosmology.

Finally, the global mode of reality suggests a third avenue of research in quantum gravity. More at EPS13 in Bern.


I am very grateful to Mrs. Claudia Nielsen, London Group coordinator in Scientific and Medical Network, for her invitation to present my ever-unfolding speculations, as of May 30, 2002. She also urged me to write some readable philosophical paper, to which I agreed, stupidly. It turned out to be a very difficult task; the first chapter is available from here. My brain still stubbornly fights back my efforts to make it think of itself, but I hope someday to win. Had I not been prompted by Mrs. Claudia Nielsen, I wouldn't have engaged into this incredibly rewarding, and still unfinished, philosophical exercise.


Dimi Chakalov
April 20, 2004
Last update: May 20, 2005
The One is an unbroken Circle (ring) with no circumference, for the circumference is nowhere and the center is everywhere. There's nowhere where God is not.