The Yogic View of Consciousness 14: Transfinite Madness

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YVC14 coverThe Mahabindu is the point that connects the Absolute to the Relative, connects zero to infinity. While Inside the Looking Glass, we fall down the Rabbit Hole.

 

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

 

Recap
Last time we ended on the completely far-out notion that our minds, both in their conscious and unconscious aspects, are not really “our” mind, but are composite entities, where the vast majority of what constitutes my (or your) mind is put there by other sources. We initially invoked Berkeley, who saw “mind” as a dual composite of “me” and “God”. We then brought in Taimni’s Hindu notion that directly linked the sources of “mind” to the natural structures that make up the Cosmos in which we find ourselves.

This all gets rather awkward to express in words, and so the following pictures were used:

both fig 1

Figure 1: Left, Taimni’s view of minds within minds within minds. Right, my interpretation of Taimni’s mind-fractal.

On the left is Taimni’s conception of the structure of reality. This picture derives from Hindu and yogic thought which, as a variant of Idealism, sees reality as mind. Not just mind, but minds within minds within minds.

The top level, the “biggest” mind, is the Mahabindu. Sub-minds “emit from” or “grow off of” the Mahabindu. These are the innumerable universes flowing out of the Absolute. Because a picture is worth a thousand words, here is another beautiful Hindu image of the Absolute/Mahabindu/Infinite Universes combination:

plate36

Figure 2: Krishna and Radha as the Shiva-Shakti Tattva at the heart of the Mahabindu giving rise to uncountable universes via Virat or Vishnu, who instinctively emanates universes.

Within each universe are innumerable elements. At present, the most basic unit we can identify are the galaxies. Within each galaxy are innumerable stars, and around each star are innumerable objects.

We can recall Alister Crowley from his Book of Lies:

“The Word was uttered: the One exploded into one thousand million worlds.”
“Each world contained a thousand million spheres.”
“Each sphere contained a thousand million planes.”
“Each plane contained a thousand million stars.”
“Each star contained a many thousand million things.”

Crowley’s is a characteristically Western way to describe it, where we are standing as less than infinitesimal specks immersed in the immensity of this inconceivably complex and gigantic structure. In short, an externalized view; what we see when we look out at it, when we are in paranga cetana.

Taimni’s view is the yogic view: what we experience when we go into the depths of our consciousness via samadhi. Here is recognized the real meaning of the deeper layers of the mind, the inner layers of the gunas. These are not just some stage set, or dead environment, in which countless living beings act out there life dramas. No, every level is a being unto itself, composed of innumerable microscopic beings, all consciousness within consciousness within consciousness.

This is called the Bhavachakra, the “Life Wheel”. Here are some graphic examples drawn from the rich Tibetan tradition (click here to see a few more):

bc compAll of these images are different ways to depict how our little lives, our little consciousness are cells inside of greater beings, inside of greater beings, inside of greater beings, and so on.

The West has come to see these as Jungian symbols of myth and archetype, assigning to such imagery intellectual interpretations – sounds, words, sabda. There is value in such approaches, but such understanding barely scratches the surface.

Yoga reveals these images to be the living truth of our being. Taimni, following his own advice about relative relationships, sought to express these truths in a more crisp and logical fashion, for the benefit of the intellect, by his diagram above. That is to say, Taimni is trying to intellectually explain what these other images are trying to depict literally.

Each mind is a composite of myriad microscopic minds, the net effect of which is the mind of a given beholder, an ascending hierarchy: monads, solar logoi, galactic logoi, and so on, up to the universal logoi and beyond into the mists of the Unknown.

My diagram only adds that we may see the various grades of minds as analogous to wave superposition. Waves of mind, nested in waves of mind, nested in waves of mind. I spoke previously about this reality in my book Experience, in Part 5. There I called it “Getting Lost in Infinity”. The Hindus call it Manifestation, also Maya; the Relative.

When we look out at the night sky and see (with our telescopes, that is) planets, stars, galaxies, and our universe, we are seeing the inside of Manifestation from our little simple human viewpoint, just like Mr. Fly sees Times Square in New York City.

flies in times square

Do you believe them?

Pulling Off The Band-Aid
I have stretched this out much more than I anticipated. In part, it is because I did not properly anticipate how difficult it would be to try to explain this vision of reality. But now I have said enough, I feel, and it’s now time to wrap all this up. I want to bring this to its punch line. I’m going to do it abruptly now, like pulling off a Band-Aid in one quick swipe. Here’s the punch line:

According to Taimni, Manifestation – all of this “minds within minds within minds” – occurs within a point.

Space and time are creations of minds. Harking back to van der Leeuw and his “world-images”, space and time are relative, not absolute, realities. Let’s toss some Leibniz in here since he was one of the first in the West to see this clearly (Leibniz Clarke Correspondence, Leibniz’ 3rd paper; as usual, Jonathan Bennett translation):

“For my part, I have said several times that I hold space to be something merely relative, as time is, taking space to be an order of coexistences, as time is an order of successions.”

Under the appearance of the vast, seeming-infinity of Universes within Universes within Universes is a projection occurring within a point: the Mahabindu. It is not real as our minds fool us to believe when we are in the state of paranga cetana. It is but ever changing patterns of relationship. Prakriti: the eternal dance of the gunas.

Existence: The Ghost of Departed Quantities
If we wish to think of Manifestation as a “real thing” we may consider it to be a point that extends for a length, an area, a volume, a hypercube, and so on, where the unit length is delta. And by “delta” I mean the usual definition: the smallest number greater than zero you can imagine.

Manifestation: Maya. It is certainly a surprise “Gottcha!” on George Berkeley who was uncomfortable with Ghosts of Departed Quantities.  All we can tell George is: you win some, you loose some.

Let’s let Taimni speak on this for himself. Be prepared, it’s weird, and we embark now on thinking in terms of math, of relationship:

“If the consciousness of each spiritual entity is centred in a point-and there are obviously an infinite number of such entities in the manifested universe, right from the Cosmic Logos to the youngest Monad-does it mean that these centres of consciousness are scattered throughout the vast space in which the physical universe seems to function? How then can consciousness be considered above space? How can these different units of consciousness have a common basis of underlying Reality? How can the infinite number of solar systems scattered throughout the universe be pervaded by the consciousness of the Cosmic Logos, and energized and controlled by Him?

“….The Occult conception of the relation existing between these different units of consciousness is based upon all these different centres of spiritual consciousness being centred in one Common Centre which we have referred to previously as the Mahabindu or “The Great Point”.

“But the Occult doctrine of all these different centres being rooted in a common centre will mean that an infinite number of points can occupy the same position, or can be contained in the same point. …Let us see how.”

“The following figure represents a number of straight lines meeting at a point 0.”

taimni-1“…Now try to imagine all the points, which by their movement produce the intersecting straight lines, withdrawing towards the point of intersection. What will happen in the ultimate stage when each point reaches its end? Each line is a separate entity and has its own point which traces it. This point cannot disappear into nothing when it reaches its ideal end. It must be present ideally and potentially at its terminus. But we have supposed that an infinite number of lines meet at the point of intersection. So all the points, which have traced these separate lines must be ideally present at the point of intersection. Please note the word “ideally” for in this lies the clue to the mystery. So, theoretically, the point of intersection can contain within itself an infinite number of points which have traced their separate lines in the same plane.”

The Labyrinth of the Continuum
I need to stop and interject here. Taimni is intuitively describing what was formally discovered by Georg Cantor and today is called transfinite numbers, which grew from Cantor’s “naïve” set theory. This is an involved topic, one that is not cut and dry. In fact it is controversial to those aware of it. It involves paradoxes that sit at the heart of mathematics and therefore at the heart of the human intellect.

Cantor discovered what many consider a stroke of genius of a pivotal nature, but what others consider the height of absurdity. He was able to “prove” that there are more real numbers than counting numbers. He did this by a simple math construction called a “diagonal argument”. I will not explain it here. It is absurdly simple and you may follow the links to learn more.

The bottom line is that Cantor appears to have shown that there are different types of infinity.  The basic point is illustrated by comparing the integers to the real numbers. The integers are simply 1, 2, 3…, the familiar counting numbers. The real numbers are the integers plus all rational fractions (fractions with finite decimals), irrational numbers (fractions with infinite repeating decimals), and transcendental numbers (fractions with infinite non-repeating decimals, like the number π). It should seem quite intuitive that by adding in all these other types of numbers on top of the integers that there are more real numbers than integers.

Cantor claimed that the total number of integers is a math object he called Aleph-null, ℵ, which is the “smallest” type of infinity. He then claimed that the total number of real numbers, which traditionally had been called the “continuum” consisted of a “larger” infinity he called c, for “continuum”. He even proved the following math relationship showing c is greater than ℵ: ceqThe above provides background information that will allow us to see where Cantor took these queer notions. Consider the following figure of the simplest geometric objects:

transfine-1We start with a zero-dimensional point. Then, take two points, and draw a one-dimensional line connecting the points. Then, take four lines and hook them in a square to make a two-dimensional plane. Then, stack a bunch of planes to make a 3D cube.

Then we can ask the following questions: (1) How many points make up a line? (2) How many lines make up a plane? (3) How many planes make up a cube?

The answers should be intuitively obvious. It takes an infinity of points to make a line. It takes an infinity of lines stacked side-by-side to make a plane. It takes an infinity of planes stacked on top of each other to make a cube.

Now, let’s take it a step further. If it takes an infinity of points to make a line, but it takes an infinity of lines to make a plane, then how many points does it take to make a plane? Again, the answer should be obvious: an infinity of points for 1 line times an infinity of lines to make the plane, or:

infinity x infinity points in a plane.

Intuitively, it just seems obvious that there are more points in a plane than in a line.

We can also ask: how many points make up a cube? Again: an infinity of points to make 1 line times an infinity of lines to make up a plane times an infinity of planes to make up a cube to give us:

infinity x infinity x infinity = number points in a cube.

Now, here is the weird part. Cantor was able to use his bizarre ideas to mathematically prove that the number points in the line equals the number of points in the plane equals the number of points in the cube. In each case, a line, a plane, and a cube, the number of points making up these objects is c, the transfinite number representing the continuum. That is, there are NOT more points in a cube than in a plane, and there are not more points in a plane than in a line. In fact, the number of points involved is always equal, no matter how long the line, or how big the plane or cube.

The following comment from Wikipedia about this topic states rather dryly what this means:

“Our intuition gained from finite sets breaks down when dealing with infinite sets.”

Back to Taimni
So when we look at what Taimni is saying above about the rays of a circle approaching the center, he is discussing precisely the same type of issues Cantor discussed.

Before proceeding, it is important to emphasize that Cantor’s mathematics described above is not universally accepted. Some find it repugnant.   To again quote Wikipedia:

“Poincaré referred to his (Cantor’s) ideas as a “grave disease” infecting the discipline of mathematics, and Kronecker’s public opposition and personal attacks included describing Cantor as a “scientific charlatan”, a “renegade” and a “corrupter of youth.”…Writing decades after Cantor’s death, Wittgenstein lamented that mathematics is “ridden through and through with the pernicious idioms of set theory,” which he dismissed as “utter nonsense” that is “laughable” and “wrong”.

I present these quotes so that if you feel an aversion towards Taimni’s thinking, then you can see you are in good company with the likes of Poincaré, Kronecker, and Wittgenstein.

On the other hand, if you are favorably disposed towards Cantor’s logic, that kind of boxes you in to accepting Taimni’s basic logic.

Finally, the way Taimni intuitively expresses the problem seems to me to better reveal the heart of the matter. Instead of asking how many points some Euclidean geometric object is composed of, Taimni asks about the very nature of the relationship between something and nothing. For a point is merely a nondescript mark, that “which is without parts”. In short, quantitatively a point is nothing, zero. Taimni is asking about the property whereby nothing, a point, becomes something, a set of rays emanating from the point.

Taimni is asking about nothing less than the age-old problem of The One and The Many.

The One and The Many
Taimni continues…

“One might say that there is only one point at the centre, and the multiplication of points takes place after the central position is left. This will mean that the central point has divided itself into an infinite number of points which trace the different lines, and the same anomaly will thus appear in a different form. We are thus dealing here with a paradox which always appears when a mystery of the spiritual plane is sought to be comprehended by the intellect in terms of the intellect. The mathematical paradox we have dealt with above really represents the mystery of the One and the Many, i.e. the co-existence of oneness and separateness.”

“We have seen above how it is possible for an infinite number of spiritual entities to function in the realm of the mind from a single centre. Each entity, whether He is a Solar Logos or a Monad, projects His own independent mental world and functions in that world although He is rooted in a common centre. The common centre in the case of the Monads is the Centre of the Solar Logos to whom he is attached, and in the case of the Solar Logoi, the Centre is theoretically and mathematically possible and therefore there is nothing absurd in the idea of the centres of consciousness of an infinite number of spiritual entities like the Solar Logoi and Monads being rooted in the Common Centre or the Mahabindu of the Cosmic Logos.”

“The paradox of a number of points occupying the same position in space is seen in the correct perspective when we understand the true nature of ordinary space. Ordinary space from the highest point of view is an illusion. It is not something independent of the mind which conceives it. It is the result of the mental projection in the realm of the mind of a world from a centre of consciousness.”

“The mental worlds which are projected are worlds of different dimensions but not their source, consciousness, which as we have seen contains potentially all dimensions and can therefore be projected only through a point. Dimensions can come into play only when the threshold of the point is passed, and pure consciousness emerges into the realm of the mind on this side of the threshold, just as colors can come into play only when white light passes through a prism and emerges on the other side of the prism.”

Whoa Nellie!!
So once again we are faced with the situation described in Chapter 5: “Taimni simply asserts the most abstract things. It would be the height of absurdity, but for the context.”   I defended him there and so won’t repeat myself. Instead, let’s try to decode what he is saying.

First, he is saying the Mahabindu is a point. By point, he means the classical Euclidean definition of a point as “that which has no parts”.

Then, he says, imagine spokes coming out of the point, but now follow the spokes back to the center and keep getting closer and closer. He is clearly using the math concept of a limit.

A mathematical limit is a strange concept. The easiest way to think about it is to keep moving half way between a starting and ending point. Each step you take cross half the remaining distance. It is obvious you will never get to the end point because you can always cut the distance in half, no matter how small that distance is. This was one of Zeno’s paradoxes.

2499

Cut in half at each step and we never get from one side to the other.

There are a couple ways to interpret what Taimni is trying to do. One is mathematical, and the other is to try to link it to physics. On the physics side, there is the possibility that space and time are not infinitely divisible. However, given that we are talking about the Mahabindu, the limits of the physical visesa gunas simply do not apply. Therefore we will consider it from the abstract side of mathematics where we can indeed play at cutting something in half forever and ever infinity times.

Zero and Infinity Are Joined at the Hip
From this math perspective, Taimni expresses an important intuition in the above quote:

“Dimensions can come into play only when the threshold of the point is passed”

Taimni is expressing a very subtle idea. If something is zero, which is what a point is, then, when does it no longer become zero? When does it become something? Another way to state this is in the form of the question: what is the first number after zero?   For people familiar with this quandary, they know there is no answer to this question. But for people to whom it is new, let’s spend a minute thinking about it.

Normally, we count 0, 1, 2, 3, and so on. But there are numbers between 0 and 1, for example, ½.   We could write it in decimals: 0, 0.1, 0.2, …1, if we count in 1/10ths. But why not count in 1/100ths: 0, 0.01. 0.02, 0.03…1. Why not 1/1000? 1/million, 1/trillion? Do you see the problem? What is the smallest fraction you can imagine?

Trying to imagine the smallest fraction is just like trying to imagine the biggest number. You just can’t do it. For any “biggest” number you can imagine, you can always just add 1 and get a bigger number. Then invert the big number to 1/(big number) and you get a small number.

Cantor side-stepped this whole issue by just asserting the existence of Aleph-null and c. The fact that he just asserted his scheme into existence is why some, like Poincaré or Wittgenstein, were (again to intentionally use understatement) “uncomfortable” with Cantor’s thinking.

Nonetheless, what this illustrates is that the idea of the biggest number is related to the idea of the smallest number. If, theoretically, we had the “biggest number”, we just divide 1 by the “biggest number” to get the smallest number.

Taking this line of thought to its logical extreme, it shows us that zero and infinity are joined at the hip, you might say. We have to repeat Nicholas of Cusa here:

“Since the absolutely Maximum is all that which can be…And just as there cannot be a greater, so for the same reason there cannot be a lesser, since it is all that which can be. But the Minimum is that than which there cannot be a lesser. And since the Maximum is also such, it is evident that the Minimum coincides with the Maximum.”

Nicholas was smart. Unlike Cantor, Cusa removed the problem from numbers altogether and just spoke of the Maximum and the Minimum. They become qualities, instead of quantities. With Cusa, there are not different “sizes” of infinity, there is just a basic paradox that the Maximum is the Minimum, and there is only one instance of it. It is, in fact, the same solution discovered by the Hindus, which they call Brahman, or various other names.

Today there is a working concept in mathematics that corresponds to Nicholas’ idea of the Minimum. I used it above: delta. The smallest quantity you can imagine that is greater than zero. It is not a number. The whole thing doesn’t make sense when you think of it as a number. Yet, in practice it works because one can just make delta equal to some really small number, and people use it all the time to solve real problems in math, physics, and engineering.

For our purposes, however, we don’t substitute a number. We just use Cusa’s idea of a quality that is simultaneously Maximum and Minimum. Call it delta. Imagine it is the first number after zero if you need to. Taimni refers to it above as the “threshold at which the point is passed”.

We can thus interpret Taimni as follows: the unmanifest is the point, zero. The manifest is the threshold past zero, which is delta, or Cusa’s Mimimum, which is also the Maximum. I stated it at the top: the absolute scale of Manifestation is delta, the Minimum, which is also the Maximum. Hopefully now I’ve fleshed in some meaning behind the statement.

This now is my assertion, my reading of Taimni: we can interpret Manifestation as having an absolute scale, and that absolute scale is delta. This, my friends, is the meaning I read into Taimni’s “Mahabindu”.

Absolute Scale? WTF?
Since this has been one of the longest chapters so far, let me wrap up for now.

The idea that there is an absolute scale to anything should send shivers up and down the spines of anyone who knows how stuff is measured in the real world. In fact, I probably sound like a complete nut job to people who know about this stuff when I use the term “absolute scale”.

But my “trick” is quite obvious. The absolute scale is no number at all. It is a quality identified by Cusa as the Maximum/Minimum, and identified by Taimni as the “threshold past zero”.

But if we follow Cusa’s logic just one step further, we can then focus all this on how the Absolute, which is the antithesis of quantitative and Relative, can give rise to the Relative via this Ghost of Departed Quantities I am calling “delta”. Cusa states it as:

“The Maximum is one.”

Not so informative. His quote supporting this is rather twisted, so I will just summarize. Basically, there can only be one Maximum. It is, by definition, the Greatest, the “Top”, the “Big Daddy”, whatever you want to call it. Since it is such by definition, there cannot be another like it. There can only be one instance of it. So, from Cusa, we get a form of logic that was clearly expressed by a Westerner at the dawn of the modern age, but that never caught on in Western math. Instead, you got Cantor floundering in fantasies 400 years later. In the meantime, it has always been the logic of Hinduism. Here is the formula:

Maximum = Minimum = One

The Absolute Greatest is the Absolute Least is the only One of its kind. Brahman.  If one is even slightly sensitive to understanding these ideas, it should give a new meaning to the term “Holy Trinity”.

What this means is our absolute scale of delta = Maximum = Minimum = One

And 1 implies division. 1 can be subdivided. And here is the genesis of all Relativity. Here is the Relative in the Absolute and the Absolute in the Relative. Recall this is where we began way back in Part 4, when we spelled out van der Leeuw’s descriptions of the Absolute and the Relative.

Hinduism has always thought in this fashion. A lone Westerner, Nicholas, thought like a Hindu at the dawn of the modern age. Then everything just went its own crazy way in the West, as Manifested things are wont to do.

Where We Go From Here
Okay, we’ve now ripped the Band-Aid off. We have bottomed out on Taimni’s abstractions of what the bindu really is.  We’ve gone full circle.  Recall my initial definition of the bindu given way back in Part 2:

“…the bindu is that which links the individual to the universal.”

Now we can see in greater depth what this means.  It touches on unresolved issues in philosophy and mathematics.  It touches paradoxes at the center of the human intellect, paradoxes that have existed since Humans have used their minds to try to make sense of the World:  What is the One and the Many? What is zero? What is infinity? What are we in relation to these things?

We have presented the Hindu answer to these questions, as filtered through Taimni’s writings, and pepper throughout with some Western contributions.

The bindu is the nexus between Absolute and Relative. It is the Source of Manifestation. It is the Sphinx.

6702813677_1514e8a07d_b

Next time we close out the discussion of the bindu by discussing how this “One” that projects through the point of the Mahabindu divides itself, seemingly to infinity, generating the vast spectrum of forms of consciousness that make up Manifestation, what I’ll call the Spectrum of Becoming.  This spectrum is like a giant plate of spaghetti, all tangled up and plugged into itself forming a type of network that we can move around in when in the state of samadhi.

See you in Part 15.

4 thoughts on “The Yogic View of Consciousness 14: Transfinite Madness

  1. Andrew

    Wow. Possibly my all-time favorite Plane Talk post. It seems strange that people would have a problem with something as obvious as Cantor’s math or Cusa’s minimum/maximum idea, but one time I tried to talk to my father in law about Achilles and the Tortoise (because I think it’s fun) and he hated it. He tends to be a black-or-white type thinker. I guess, as you say, folks who think in that way do not appreciate this sort of stuff. Oh well. At least I now know that William Blake’s poem wasn’t just pretty sounding, it was literally true:

    To see a World in a Grain of Sand
    And a Heaven in a Wild Flower,
    Hold Infinity in the palm of your hand
    And Eternity in an hour.

    • Hi Andrew

      Great to hear from you! Thank you so much! Your encouragement is really very deeply appreciated! You are really helping to supply the impetus for me to keep going on this series! Thanks so much for that!

      As to the math stuff, it is really truly controversial. The critics of Cantor question whether he did math or philosophy. You find the same criticisms being echoed today in the debates about the multiverse. There is a school of thought in math that says that one should be able to write down and SOLVE concrete problems. Cantor’s work cannot be approached in that fashion. For example, you cannot program a computer to deal with infinity. Critics of Cantor are called “constructivist” mathematicians, and I sympathize very much with them.

      On the other hand, when we bring altered states into the discussion, then Cantor’s way of thinking, especially as it’s reflected in the Hindu ideas I discussed above, does start to become literal. In our normal waking state, we won’t be seeing the World in a Grain of Sand, but one can see this in samadhi.

      Again, Andrew, thanks for commenting and great to hear from you!

      Best wishes,

      Don

    • Hi Kashyap! Great to hear from you! If I can accomplish one thing with this series, it is to illustrate that Hindu philosophy and yogic experience has for millennia dealt with “transfinite” concepts in their own fashion, and that we moderns can learn a lot from the ancient ideas.

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