Transition to Transcendence: Franklin Merrell-Wolff's Mathematical Yoga

Imants Baruss

King's College, University of Western Ontario

Copyright authors and Journal of Integral Studies.


[Mathematics] is that portion of ultimate truth that descended from the upper hemisphere, to use the terminology of Aurobindo, into the Adhar with minimum distortion, and thus becomes the Ariadne thread by which we may ascend again, most directly, most freely. (Merrell-Wolff, 1995a, p. 27)

Mathematicians--those who develop new mathematics--spend much of their time proposing the existence of mathematical constructions whose existence they then proceed to try to prove from the mathematics that has already been developed. Following that, they often try to prove that those mathematical constructions are unique, that there are no other constructions with the same characteristics. In practice, it is often easier to prove the uniqueness of a mathematical construction than its existence, so a mathematician may proceed by first proving uniqueness, as though the mathematical construction existed, and then using clues from the uniqueness proof to prove existence. I want to follow a similar strategy in this paper, in that I want to talk about transitions to transcendent states of consciousness as though they existed and as though we knew what they were, thereby perhaps uncovering ways in which their existence and characteristics may become apparent.

How are we going to talk about transcendent states of consciousness if we do not even know if they exist? Here, we may be in the situation of the eighteenth century explorers seeking the source of the Nile with only mythology on which to base their expeditions (Bruce, 1790/1972). In that case there were natives who lived at the source of the Nile for whom the river's source was part of their everyday experience. Perhaps similarly, there are those who have realized transcendent states of consciousness that for the rest of us exist only as myths. We shall consider here the account of Franklin Merrell-Wolff who lived from 1887 to 1985 and devoted most of his life to the attainment and exposition of transcendent states.

The information about Merrell-Wolff's ideas has been taken largely from his books (Merrell-Wolff, 1994; 1995b) and from a series of lectures that he gave in 1966 titled "Mathematics, Philosophy and Yoga" (1995a). Additional information has been acquired from his other publications, unpublished papers and audio recordings; from conversations with his granddaughter, Doroethy Leonard, and conversations with Ron Leonard, who lived with Merrell-Wolff for a year and wrote his doctoral dissertation in philosophy about him (Leonard, 1999). I have also written previously about Merrell-Wolff's philosophy (Baruss, 1996). In the following, I have used Merrell-Wolff's language largely to convey his meaning, and have only used quotation marks for identification of specific terms and for directly quoted longer passages.

The Theoretic Continuum

Why choose Merrell-Wolff? Following ideas suggested by F. S. C. Northrop (1946/1966), Merrell-Wolff has maintained that there are continua, specific to the East and the West, along which an aspirant can move from the "determinate" relative domain to an "indeterminate" transcendent domain. Spiritual aspirants in the West have often tended to adopt the methods of the East and tried to move along the continuum belonging to that culture rather than recognizing the possibility of exploiting the capacity for theoretical thinking that has been developed in the West. According to Merrell-Wolff, aspirants in the West could effect a transition to transcendence by moving along a theoretic continuum from its determinate pole, represented by science and mathematics, to an indeterminate, transcendent pole. In other words, realization of transcendent states of consciousness not only does not require setting aside what one does as a scientist, but of using those activities as a basis for further development. It is because of its relevance for scientists that it is particularly instructive to look at Merrell-Wolff's account.

For Merrell-Wolff, the structure of events in transcendent states of consciousness is different from that within its everyday mode. In particular, the subject-object duality that characterizes the manner in which we ordinarily think is superseded by "consciousness-without-an-object." To emphasize this difference, Merrell-Wolff has usually used the term "experience" in a restricted sense for events that occur in the relative domain, and coined the term "imperience" for transcendent events. In our ordinary state of consciousness knowledge is possible through the two processes of sensory perception and rational thinking, whereas in the transcendent domain a new mode of knowledge becomes available, knowledge through identification with that which is known. Merrell-Wolff has coined the term "introception" to designate this transcendent "knowledge through identity," and characterized it as "immediate" and "highly noetic." Furthermore, there is an ontological inversion between everyday and transcendent states. The substance of our everyday consciousness, that we take to be real, turns out to be only apparently real, whereas the ground of being found in transcendent states of consciousness is truly substantial and turns out to be actually real. In fact, for Merrell-Wolff there is an inverse relationship between appearance and reality, so that the more something can be apprehended through ordinary thinking the less it is real, while the less something is ponderable, the more substantial or real it is.

The presence of a theoretic continuum implies that something of introception can be found within the relative domain. Thus, concepts such as objects in the physical world can be perceptually thick but introceptually thin. In other words, for that which is particularly ponderable, there is little of introception present. On the other hand, some concepts, such as mathematical constructions, are perceptually thin but introceptually thick. That is to say, concepts that are so abstract that there is nothing for the senses to grasp are closest to the manner of k nowledge in transc endent states of consciousness. If one can rarefy one's thinking sufficiently, it becomes no longer determinate but "determinate-indeterminate." Such determinate-indeterminate thought, called "transcriptive thought," has both effortful, self-directed, and autonomous, transcendent components, so that it is a blend of transcendent content and relative form.


In my experience, most mathematical constructions cannot be adequately represented visually or, for that matte r, through any of th e other sense modalities. Even less do I think that mathematicians think in formal logical statements though the resultant mathematical proofs are descriptions of logical sequences. That is not to say that mathematicians may not try to represent constructions visually or that they are unconcerned about logic. It is just that most mathematical constructions are too abstract to be entirely captured in these modalities. Thus it is possible that the kind of thought in which mathematicians engage is transcriptive thought.

Perhaps now the rationale for a uniquely Western approach to transcendence becomes apparent. The substance of everyday consciousness turns out to be a matter of appearance. That which is real can be known in transcendent states of consciousness through introception. And there is a continuum between the apparent and the real that can be traversed using our capacity for theoretical thinking. The point is that much of the work necessary for apprehension of the objectless in transcendent states has already been done by a scientist in training herself to work with concepts of such tenuity as those found in mathematics. "This affords an enormous advantage, since the gap between an object of extreme subtlety and true objectlessness is relatively small" (Merrell-Wolff, 1995b, p. 167).

But how is the final gap to be bridged? For Merrell-Wolff, what he has called "mathematical yoga," the mathematical means of realizing transcendent states of consciousness, involves more than just doing mathematics with a high degree of abstraction. There are two other necessary ingredients: philosophy and yoga. Merrell-Wolff has included philosophy because, according to him, philoso phy is that discipline that is conce rned with establishing meanings. In doing mathematics one cannot proceed mindlessly but must consider the meanings inherent in the mathematical constructions. The term "yoga" refers to union of oneself with a transcendent reality. For the mathematical path to be effective in uniting a mathematician with the transcendent, according to Merrell-Wolff, there must be a change of attitude from "self-withholding" to "self-giving." Indeed, according to Merrell-Wolff, through proper practice of mathematics and philosophy one can reach the door to the transcendent but cannot force it to open. In order to hope to succeed, one "must face a complete sacrifice of everything that [one] is and has" (Merrell-Wolff, 1995a, p. 33). Let us look more closely in turn at each of these two additional ingredients.


For Merrell-Wolff, "human consciousness is of such a nature that it may be conceived as flowing or streaming, in part at least, from the subject toward the object" (Merrell-Wolff, 1995b, p. 144) thereby giving rise to the phenomenal world. Thus, that which is real, can never be realized by further movement of consciousness toward the phenomenal. Rather, "[the] Real is attained by a movement of consciousness in the direction opposite from that by which the phenomenon is experienced" (Merrell-Wolff, 1995b, p. 201). This is the point of moving from the perceptually thick concepts of the determinate pole of the theoretic continuum to the perceptually thin concepts toward its indeterminate pole. We move from that which can be readily apprehended toward that which appears in the relative domain as nothingness.

The meanings of concepts that are perceptually thick are given by their references. That is to say, such concepts merely point toward something else. But as we move toward concepts that are introceptually thick, their significance lies less in pointing and more inherently within the concepts themselves in the sense that the concepts enrobe the meanings. If we move far enough, through concepts that cannot be expressed in words and then concepts that cannot even be symbolized in any way, we reach "disembodied Meaning. At this point, the thinness, in the extraverted sense, has become absolute, while the inner thickness has virtually become infinite" (Merrell-Wolff, 1995b, p. 170). To illustrate what is happening, Merrell-Wolff has used the analogy from mathematics of a convergent infinite series whose terms represent related thoughts along the theoretic continuum and whose summation represents the inherent meaning of these thoughts that lies at the indeterminate pole. If we reverse the process, a single introceptive thought can require volumes for its exposition without exhausting its meaning. In particular, as stated in the epigraph for this paper, mathematics is that portion of introceptive knowledge that is available to determinate-indeterminate thought with a minimum of distortion, and hence is the most direct path of return to the transcendent.

If someone pays attention only to the perceptual components of a thought and disregards the introceptual, then she will miss its real significance. For example, I think that this has been true of many of those who have written about consciousness in the academic literature. When consciousness is conceptualized as information in an information processing system, its meaning is established through redirection toward something that is potentially perceptually available and consciousness is thought to be just one more physical event in a physical world. On the other hand, when consciousness is conceptualized as the sense of existence of the subject of mental acts (Baruss, 1987), then focus is redirected back toward an immersion in the experience of what it means to be conscious. Specifically with regard to consciousness, Merrell-Wolff has said AI have not attempted to define consciousness, for the reason that I can no more define it than I can the distinctive quale of any perceptive state" (Merrell-Wolff, 1995b, p. 147). Indeed, he has gone even further to say that "consciousness is itself the substantial substrate" (p. 195) "underlying all experience" (p. 192).

The movement toward apparent nothingness not only allows for increased inherent meaningfulness but is also characterized by increased depth. For Merrell-Wolff, depth cannot be conceptualized or identified as a part of experience but can be felt in genuine religious experiences and directly realized by introception. Depth is the inexpressible element of transcendent states of consciousness that makes them what they are. Any effort to express depth fails to convey its essential characteristics and can always be interpreted in such a way that the very characteristics one aims to convey are omitted, giving the appearance that there is only that which lies on the surface.

I think that this last is an important point. In my own work I have placed emphasis on the development of understanding (Baruss, 1996) which entails Merrell-Wolff's notions of meaning and depth. From the point of view of contemporary computational approaches to the mind, understanding would itself be reified as specific information processing in the same way that consciousness or qualia have been reified as information (e.g., Dennett, 1988). This is not to say that there is no informational component to understanding. That is not the point. The point is that neither meaning nor depth reside in inform ation, but both meaning and depth are possible to someone for whom understanding occurs. On the other hand, for someone who insists on remaining on the surface, this last sentence itself can again be reified in information processing terms, denying any ontological independence to meaning and depth. If Merrell-Wolff is right, as long as one keeps reifying in information processing terms concepts whose purpose is to characterize something deeper, transcendent states of consciousness will necessarily escape her. I think that it is this sense of the development of understanding, as the manner in which mathematics is to be done, that Merrell-Wolff had in mind in saying that philosophy must accompany the practice of mathematics if it is to be effective for bridging the gap to the indeterminate.  


For Merrell-Wolff, consciousness can be conceptualized as flowing from the subject to the object, thereby giving rise to the phenomenal world. Thus, the task of the aspirant is to effect a reversal of at least part of the outward flow. "The function of introception has been defined as the power whereby the Light of consciousness turns upon itself toward its source" (Merrell-Wolff, 1995b, p. 144). In other words, the task can be conceptualized as one of activating introception. But that is not easy to do since we feel compelled to seek satisfaction in life by craving ever more experience, which can never provide the satisfaction that we seek since "it is the thin and insubstantial surface that bounds and hides the Real" (p. 191). So it is that "[the] mystical participation in the object holds humanity in a hypnotic spell that is harder to break than bars of iron" (p. 166). How then, is the reversal of consciousness to be accomplished?

As outlined above, much of the work of liberation has been done by developing the capacity for abstract thinking, such as that required of mathematics, and of doing such thinking with a view to understanding the subject matter. But whereas the intellect may have been loosed from its hold on the objective world, the same may not be true of the will and the feelings. From the point of view of the participant, the required movement toward nothingness amounts to apparent self-annihilation. In other words, one must sacrifice everything that one is in order to loose one's hold on the objective surface of consciousness.

How is this sacrifice to be made? The sacrifice is to be made to "that supernal Other--that which appears as the Numen" (Merrell-Wolff, 1995a, p. 5). Nothing can be held back for whatever reason. Preferred conceptions and meditative techniques, for example, must be given up along with wealth, caree r, family, life, and everything else. The sacrifice is to be a process of complete emptying. There must be "purity, not alone in the more familiar sense in which one eschews obviously lurid ideas, but purity in the far more comprehensive sense of completeness of self-giving--purity that means unmixed motives, unmixed thinking" (p. 5). Then, having made the sacrifice, everything is returned. But, whereas previously one was the owner of private possessions, now one is the steward for their proper handling. "Perhaps not all is returned, but if so, it is better so" (p. 5). "But supposing one has been able to find the key, the key of humility and complete sacrifice . . . and then [one] enters the door, there are certain experiences that transcend far anything within the range of the logic-chopping intellect" (p. 34).  


We have a transition to transcendence that has been proposed by Merrell-Wolff, that of mathematical yoga, consisting of the practice of mathematics, the development of meaning inherent in philosophy and the yoga of self-sacrifice. Merrell-Wolff maintained that mathematical yoga had been the path that he himself had taken and therefore the one that he knew best. After graduating with a bachelor's degree in mathematics from Stanford University in 1911, a year of graduate studies in philosophy at Harvard University, and a subsequent year of teaching mathematics at Stanford University, Merrell-Wolff retired from the world in order to seek a transcendent state of consciousness. His efforts were rewarded in 1936 with two fundamental realizations whose effects persisted until his death.

Not only did Merrell-Wolff verbally attest to a change in his state of being, but those around him would often experience alterations of consciousness while in his presence. When he spoke, Merrell-Wolff would apparently sometimes invoke what he called the "Current," which  Doroethy Leonard, for example,  has said that she would experience as relaxation, unfocused and expanded vision, and "deep peace and profound stillness" (1995, p. v). Others have maintained that reading Merrell-Wolff's books has created alterations of consciousness for them. For example, John Lilly said that "reading awhile alters my state of consciousness into highly regarded and delightful regions" (1973, p. viii). Indeed, such experiences are consistent with Merrell-Wolff's notion of transcriptive thought, which functions not so much to convey meanings in the relative sense but which serves as a vessel for the transcendent.

Does any of the above constitute proof that a transition to transcendence is possible? No. Indeed, given the nature of introception, there can be no proof of transcendence without the necessary self-transformation. Nor do I think that the availability of such proof would necessarily be a good thing. Adopting an attitude of humility and recognizing one's lack of knowledge in order to seriously consider a transcendental philosophy can be a beneficial exercise in and of itself.

We do not have proof, but what we do have is a suggested course of action for seeking the transcendent that may be more appropriate for a scientist than other possible strategies. One can see one's scientific effort as a process of training one's mind to be able to rest in the determinate-indeterminate domain of thought. Coupled with the effort to understand what one knows and to proceed with an attitude of humility, this effort could lead to transcendence. For a good scientist there is a way to find out. Experiment.


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I thank Allan Combs for inviting me to submit a paper to Integralis, Ron Leonard for reading and commenting on the manuscript, and King's College for a paid sabbatical leave and research grants that have allowed me to pursue this research and write this paper.