We now transition from discussing the Absolute to discussing the Relative. “Relative” means “relationships”. Mathematics is the study of abstract pure relationships. Therefore we take a brief detour and discuss mathematics in the context of the yogic view of consciousness.
Contents for The Yogic View of Consciousness:
|Intro||Ch 1||Ch 2||Ch 3||Ch 4||Ch 5||Ch 6||Ch7||Ch 8|
|Ch 9||Ch 10||Ch 11||Ch 12||Ch 13||Ch 14||Ch 15||Ch 16||Ch 17|
|Ch 18||Ch 19||Ch 20||Ch 21||Ch 22||Ch 23||Ch 24||Ch 25||Ch 26|
|Ch 27||Ch 28||Ch 29||Ch 30||Ch 31||Ch 32||Ch 33|
What Does Math Have To Do With Yoga?
In our discussion of the yogic view of consciousness, Parts 4-7 elaborated on the Absolute. We are now at the turning point between the Absolute and the Relative. In upcoming posts we discuss the bindu, the cave, and the screen of consciousness.
Please recall: The bindu is point of contact between the Absolute and the individual mind. The cave of consciousness is the entirety of an individual mind. The screen, illuminated by the light of consciousness, is the immediate, first-person, subjective consciousness associated with a given mind.
The bindu is the transition point from the Absolute to the Relative. The mind, at all of its layers and levels, is the expression of relationship, where relationship is the essence of that which is relative. Again please recall, the Absolute is the Absolute because it is not related to anything else; it is Kaivalya, alone. The Absolute is indescribable and ineffable precisely because our minds and intellect deal with relative relationships. Thus the Absolute will always be beyond the capacity of the mind. When we are confined to our mind, the Absolute will always only be an ideal limit we may posit, but we will never understand it in any sense whatsoever.
It sounds like a hopeless situation. But it is not. We saw in part 5 that Taimni linked the Absolute to the Western math concepts of zero and infinity. Western math does a pretty fine job of incorporating zero and infinity. In fact, it is safe to say that the vast bulk of Western math would not exist without zero and infinity. Zero and infinity stand as ideal limits approachable by a myriad of different relationships. In this sense then, the intellect makes quite good use of the Absolute without ever knowing exactly what it is.
If the Absolute, the Ever-Darkness, as Taimni called it, is the greatest mystery, it is equally as great a mystery how the Absolute expresses itself as the Relative, how The One becomes The Many. Hinduism in general has a rich set of ideas to express this transition. These ideas are easiest to understand if we approach them as describing increasing degrees of relationship. Starting from the simplest conceivable pattern of relationship, the relationships compound upon one another, producing the inner layers of the cave of consciousness, all the way to the outermost periphery of reality, which is our first-person experience as limited human beings in the physical universe.
The Relative includes the simplest relationship just this side of the bindu all the way to the myriad of relationships making up the physical universe, and everything in-between. The West has developed a very precise language to describe relationships. We call it mathematics. Thus it behooves us to dwell on math for a bit before diving into the Relative.
For those of you who hate math; hate instead your crappy math teachers. Math is one of the most important inventions of Western culture and the serious understanding of anything will intimately involve math. For those of you how know and love mainstream math, its importance goes way beyond mainstream ideas, as we now discuss.
The Best Definition of Math
I’ve read a lot about the history and philosophy of math. I will not try to impress Readers with my reading list. I am by no means an expert, but neither am I ignorant about these important topics. In large measure, my reading of Hermann Weyl is motivated by wanting to get deeper insight into the philosophy of math.
Therefore, it is ironic to me that perhaps the best description I’ve found of what math is comes from an unexpected source. I. K. Taimni in Man, God and The Universe discussed the relevance of math in the contexts of occultism, Hindu philosophy, and yoga. His entire discussion is informative. Here I quote only his main points:
“Fundamental truths of Nature are based on mathematics and are reflected in mathematical relationships…”
“Now, it is not only truths of the physical world which are reflected in mathematical relationships, but also those of the subtler worlds. By this is not meant that they can necessarily be reduced to mathematical formulae but that these truths can be grasped to some extent by the intellect with the help of mathematics without direct realization in one’s consciousness as is done in Yoga.”
“Mathematics deals only with pure abstract relations without taking into consideration the contents of those things which are related to one another. It is obviously, therefore, concerned with the world of the Relative and not with that Ultimate Reality which we refer to as the Absolute. It gives us the foundation principles upon which the manifested universe in all states of subtlety is based, but it cannot touch the Absolute, for, in the Absolute, those different parts or aspects which are related in manifestation become so completely integrated and perfectly harmonized as to appear a void to the intellect.” [Emphasis mine]
(First ed. First reprint, 2005 – pg 229)
It is amazing to me how, by having the yogic view of consciousness as a lens through which to see the world, otherwise confusing and complex issues, such as “what is math?” come clearly into focus.
Math as a Map
Let’s expand on Taimni’s concept of math and then, in the next section, on his notion of the scope of applicability of math.
He says math is the study of pure abstract relations. Taimni’s conception of math is comparable to a map, like a map of a city or country. We do not confuse a map with the country or terrain the map represents. But a map can provide an overview of a place in a way in that direct experience cannot. With a map we see the whole and we see the relationship of the parts in the context of the whole.
But looking at a map is no substitute for going to the places represented by the map. When we travel to the places on a map, we experience all the richness of the various localities; we experience what no map can represent. Nonetheless, it is possible for the man with the map to understanding better the overall structure of a region than someone who goes piece by piece over the land. But if the man with the map never travels the land, his understanding is only abstract and lacks any understanding at all of the vivid reality experienced by the traveler.
Most important in this metaphor: a map is not the place it represents. We do not, in everyday life, confuse a map with the place it represents. My Rand Mcnally Atlas of the United States is not the United States of America. It is a book on my shelf. The book and the landmass are two very different things.
Math is analogous. It provides “maps” of how things can be related, which is why math can be used to describe nature, which is one facet of the Relative. The mind is also a facet of the Relative, and therefore can also be “mapped” by mathematics.
Math describes patterns of relationships. But, as Taimni states, the math itself is devoid of content. The patterns are described only in the abstract. It is how we read meaning into the mathematical relationships that allow us to apply it to understanding the world.
It is precisely for this reason I criticized Max Tegmark for saying the world is a mathematical object in part 9 of What is Science? If Professor Tegmark really believes the actual real world is a mathematical object, then he is confusing a map for the thing it represents. It is just that simple. Maps are not the world; they are things in the world. It is the same with math. I can point to math in the world, and I can also sweep my hand to indicate the World. They are clearly different things. There is nothing deep about Dr. Tegmark’s position. Instead, his view only obfuscates and mystifies otherwise straight-forward issues by confusing maps for the things represented by the maps.
So, to summarize: math is the intellectual endeavor of describing the abstract patterns of relationship that are possible. Recall that Weyl expressed this as “the free construction of the possible”. That too is a perfectly good characterization, but somewhat obscure compared to Taimni’s much more straight-forward description of math.
Over the centuries, a number of languages internal to math have evolved to describe different types of patterns of relationship: algebra, abstract algebra, geometry, topology, analysis, combinatorics, and so on. A professional mathematician is someone who learns these languages, the many patterns already discovered with them (at least in general outline), and who specializes in the knowledge of some specific area of patterns and relationships (number theory, abstract algebra, topology, analysis, etc. etc.), and whose “research” (“contemplations” is probably a better term) consists in finding new patterns of relationship amongst symbols.
Math and Science
Taimni’s quote above offers a seminal idea. To my knowledge, he is the first I have seen to say very clearly that math applies not only to the physical world but also to the nonphysical worlds as well. In terms of precedent, and to give credit where credit is due, van der Leeuw in Conquest of Illusion hinted at this idea when he associated science and occultism with the study of the Relative (Chapter 3 therein). However, Taimni went the extra step and, as quoted above, explicitly said that mathematics “gives us the foundation principles upon which the manifested universe in all states of subtlety is based”.
His logic is, in my opinion, air tight: the inner worlds are of the Relative as much as is the physical world. In fact, the physical world is only the outer-most of the inner worlds according to the yogic view. I elaborated on the relative nature of the physical world in part 5 of Experience, and we will go into it deeper in the next several posts in this series. Therefore, in principle, math can describe the patterns of relationships found in the inner worlds of consciousness as well as using it for describing the physical world.
Of course, few professional mathematicians are experienced with altered states. The closest I have found is Dr. Ralph Abraham [here, here], but I don’t want to tangent discussing such work. The main point to emphasize is that people interested in occult and esoteric topics have good reason to learn about and appreciate math.
However, up to the present, and in general, math has been used with great success only in describing the physical world. Math provides “tools” (intellectual tools) to describe all kinds of possible patterns of relationship. In turn, as we saw considering Hermann Weyl’s ideas, any given pattern can serve as a hypothesis as to how nature is organized. Using math to posit patterns of relationship in nature constitutes making a scientific theory, and in doing so, we are using math as a tool to do science.
Then one does experiments to determine if the math relationships (i.e. theoretical model) conform to nature or not. As Weyl emphasized in his writings, the trick at this stage is to give a suitable interpretation to the math formalism such that we may find points of contact with phenomena that occur in our sensory experience. Once such a suitable interpretation is found, then we may perform what is colloquially called an “experimental test” of the interpretation of the math pattern. As Weyl’s view makes clear, so called “facts” stem from theory, and not vice versa, which is why Popper’s ideas about science got it generally backwards, and Thomas Kuhn, with his “paradigms” was better able to capture the essence of what is going on in science.
If the interpretation of the math pattern and sensory experiences correspond, then someone gets a Nobel Prize (as Plato said: “…they were in the habit of conferring honours among themselves on those who were quickest to observe the passing shadows…”). If not, then it’s back to the drawing board to either: (1) make a new theory, e.g. a new math map of the posited patterns of relationship of some facet of nature, or (2) find a new interpretation of the existing math theory.
Taking our considerations beyond the physical, as was discussed in What Is Science? (again, part 9), since the inner planes are also of a relative nature, they too manifest patterns of relationship. It was discussed there that the inner planes have the general form of going from the specific at the outer fringes of physical existence to the progressively more general the deeper one descends. Math works as a tool of science, I contend, because math is a form of revelation of the more general patterns of relationship found at the deeper levels of consciousness.
This view has much overlap with the Platonic philosophy of mathematics (see WikiP here for an overview of all the different philosophical foundations of math). However, Taimni’s view is informed by the yogic view of consciousness and, in my opinion is simply better because it is grounded in centuries of yogic experience. The “Platonic realm” of math exists, but it is not at all a world of pure math objects envisioned by the mathematicians. Math emerges into waking consciousness as subtle revelations of the patterns of relationship that exist at the avisesa and linga levels of the gunas, that are perceived directly by the yogi in the vicara and ananda states of consciousness. If that last sentence confused you, see part 9 of What is Science? or Part 2 of this essay.
Thus is the intimate link between science and math. In broad outline, there is not much more to the issue. Relative means “being related to”. Math is a language (or set of them), specialized for describing abstract patterns of relationship. Therefore, math can be employed as the basic “language of nature” because nature, manifested existence, is nothing if not ever-changing patterns of relationship (which were generically called “mirages”, “vrittis” and “gunas” in Experience, and what Plato called “shadows”).
To bring this discussion to a close, let me make my main points. As we turn our attention to discussing the Relative, we can turn to ideas in mathematics to provide maps of the inner realities under discussion. In this we follow Taimni, who provides the following warning of approaching things in this fashion (Man, God and the Universe):
“By this it is not meant that they [the realities of the inner worlds – Don] can necessarily be reduced to mathematical formulae but that these truths can be grasped to some extent by the intellect with the help of mathematics without direct realization in one’s consciousness as is done in Yoga. It is true that such a knowledge is bound to be skeletal or like a map. It gives only the relations and not the contents of the realities which it represents. These latter can be known only by direct experiences on the higher planes.”
Thus, we get an idea of the relationships that exist in things that are otherwise inaccessible to people who have not developed the skills to go see these things for themselves in the depths of their consciousness.
A corollary to this view point is the following. Neither the Absolute, nor its manifestation in our experience as our very consciousness itself (drisimatrah) can be understood mathematically.
By our “very consciousness itself” I am referring to what was discussed in the previous post by Weyl as “self-transparent consciousness and real being that I am myself”. Or, to use Fichte again:
“Translucent penetrable space, pervious to sight and thrust, the purest image of my awareness, is not seen but intuited and in it my seeing itself is intuited. The light is not without but within me, and I myself am the light.”
So, in all the following discussions, the light of consciousness is simply given. It is, and its “isness” is our being. It is our rope back to the Absolute (pratyak cetana) if we so choose, or it is the medium of our experiences in the realms of the Relative (paranga cetana).
But all the rest is vrittis, the waves and patterns in consciousness: waves, patterns, relationships, mathematics. These we can discuss with the relative language of mathematics.
People who believe consciousness (specifically, drisimatrah, the light of consciousness) can be mathematically modeled, or captured in some relative terms are just plain wrong. We can capture the relative patterns that appear within consciousness, and that is what science is, what math is, what art is, what philosophy and religion are, in fact what all human knowledge is.
As to our very consciousness, our “self-transparent consciousness and real being that I am myself”, it will forever be a mystery to the intellect. But as van der Leeuw says:
“It is a mystery…the ultimate Mystery, but it is no longer a problem since we ourselves are It.”
Go to Part 9