The Yogic View of Consciousness 7: The Absolute According to Hermann Weyl

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We close out discussing the Absolute considering the ideas of Hermann Wyle, who made important contributions to 20th century math and science. Wyle’s views provide a natural fit with the yogic view of consciousness and illustrate the integration of science, philosophy, and religion. The example he sets should shame those modern-day scientists and philosophers who see only antagonism where Wyle saw harmony.


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

 

[Housekeeping remark: As well as being part 7 of The Yogic View of Consciousness essay, this post can also be taken as Part 2 of my Hermann Weyl post.]


Introduction

I cannot do full justice to Weyl’s thinking or contributions in one blog post.  This is a long post as it is, given the few major points of his that I expound.  When discussing Weyl—what influenced him, and the influences he exerted in math and science—we are entering ground that is well-trodden by Western intellectuals. There is a rich literature analyzing Weyl’s many contributions to 20th century math and science. I acknowledge this literature but don’t draw on it here. Instead, I allow Weyl to speak for himself, and interpret his comments in terms of the yogic view of consciousness.

Weyl was neo-Kantian, meaning he accepted the basic premises of Kant’s transcendental idealism, but also expanded and extended Kant’s ideas to take into account the developments in science, math, and philosophy that occurred after Kant.

My intent is to show that Weyl’s neo-Kantianism is not only consistent with the yogic view, but that the yogic view provides the natural framework in which to fit Weyl’s ideas. All great Western philosophy ends where yogic understanding begins. Weyl stood at this threshold.

Misunderstanding the “Orient”
Before getting into specifics I want to discuss how Wyle misconstrued Eastern thought. Consider this comment from his Open World essay (1932):

“It is the great achievement of the Greeks to have made the contrast between the finite and infinite fruitful for the cognition of reality. The intuitive feeling for, the quiet unquestioning acceptance of the infinite, is peculiar to the Orient; but it remains merely an abstract consciousness, which is indifferent to the concrete manifold of reality and leaves it unformed, unpenetrated.”

I have not yet found if Weyl elaborates this point in other writings. If he does, please let me know. For the moment, it is all I have of his perception of Eastern thought, so it is difficult to know what he really meant. I can only assume he lumps together all the great Eastern traditions such as Hinduism, Buddhism, Taoism, and so on under the heading “the Orient”. Lacking evidence to the contrary, it will be my working assumption that he does. If Hinduism and yoga are included in his “Orient”, then Weyl could not be more wrong in his assessment.

First, Hinduism has actively pursued the contrast between the infinite and the finite as we have repeatedly seen. The previous post discussed three different views of infinity from the Hindu perspective. One may argue that Weyl meant fruitful for the development of mathematics. But the ancient Indians had math like the Greeks, so this interpretation doesn’t work. The ancient Greeks and Indians took math in different directions.  But if Greeks gave us proof, the Indians gave us zero.  Arguably, the Indian contribution has been more important to the development, and certainly the application of modern math.

Second, his statement that “Oriental” thinking leaves the “concrete manifold of reality” “unpenetrated” is incorrect. Weyl apparently had no idea that Patanjali’s raja yoga has as its main aim to “penetrate” the bindu (dharma mega samadhi) and thereby discover the very basis of “the concrete manifold of reality”.

Third, the idea of the “quiet unquestioning acceptance of the infinite” suggests Wyle had no knowledge of yoga. Although Patanjali’s yoga is the stilling of the mind, in this stillness power of unbelievable magnitude is released. Yoga is hardly “quiet” when the gods stop and take notice of the advanced yogi (Yoga Sutras 3.52 see [1], [2]).

Finally there is no “unquestioning acceptance” of anything. Yoga methods derive from the deepest possible questioning into the nature of the mind, the Self, and the objects of perception. Yoga, in a sense, is philosophical skepticism taken to its logical extreme.

On the basis of the above quote, coupled with the fact that I have found no Hindu influence in Weyl’s writing (again, I am open to correction), we can safely conclude that Weyl knew nothing whatsoever of Hindu philosophy, let alone Patanjali’s raja yoga.

Therefore, I can assert that Weyl came to conclusions almost identical to yogic ideas, independent of any influence of Indian teachings.

With this said, we can move on to his specific ideas.

[SIDE BAR: I would be remiss if I failed to mention that Weyl’s lack of Hindu influence stands in contrast to people like Schopenhauer and Erwin Schrödinger, who openly acknowledged Hindu influence. Schrödinger was Wyle’s friend and Wyle had an affair with Erwin’s wife Amy for many years. So, while Erwin and Hermann had similar tastes in women, they apparent did not have similar tastes for Indian philosophy.]

Weyl As A Kantian Dualist
Let’s first review how Kant was effectively a dualist. Kant posited the dualism of phenomena verses noumena. Phenomena are the appearances of the world as presented to our immediate awareness. It is how the world appears to our consciousness, what van der Leeuw called the world-image. The noumena are the world as it is outside of our minds, the objective truth of the things-in-themselves. According to Kant, there is an unbreachable gulf between phenomena and noumena, and we are forever trapped in our minds. For Kant there was no other way to know than through the mind, and therefore we can never know the thing-in-itself.

As I have stated repeatedly, yoga allows us to escape the Kantian dilemma. By mastering yoga, one can exit the mind through the bindu and thereby enter the Absolute. The experience of the Absolute is the solution to Kant’s dilemma, precisely as described by van der Leeuw.

How does Wyle fit into this picture? Wyle accepted Kant’s terms of phenomena vs noumena. But he had a more sophisticated and modern understanding because of the 100 plus years between him and Kant. Weyl, of all the philosophers I have ever read, actually devised a workable scheme to circumvent Kant’s dilemma.

This scheme is Weyl’s very definition of science. Thus, Wyle could explain how it is that science can work even though Kant’s dilemma is in place. Below we will call Wyle’s method the “scattered buckshot” approach, an irreverent moniker that nonetheless expresses a serious idea.

That Wyle was able to overcome Kant’s dilemma and simultaneously provide an effective working definition of science is a STOP THE PRESSES moment which appears to have escaped the notice of the Western intellectual world. Therefore either I am completely wrong in my assertions here, or people just didn’t get what Wyle was saying. I will press on, and you Readers can judge for yourselves.

Because Wyle was able to find a means to circumvent Kant’s dilemma, he naturally had thoughts about the nature of the noumena, the real world outside our minds. We will see that he equated the noumena with the ideas of God and infinity. This brings him in consonance with the yogic view of consciousness.

Weyl, like Kant, did not know yoga and so Weyl had no idea that one can escape from the cave of consciousness. Thus, he inevitably left some issues unresolved and was unable to infer the whole picture of the yogic view of consciousness. Nonetheless, this hardly detracts from the greatness of his insights, which are indeed great because of the depth of insight he was able to extract from contemplating only the shadows on the cave wall.

Weyl and Dualistic Consciousness
Paralleling the dualism of phenomena and noumena, Weyl saw consciousness as taking on two very different forms and thus had a dualistic view of consciousness. This is not the standard mind-body dualism, but is a dualism in the very nature of consciousness. This is described in the following quote from his essay The Unity of Knowledge (1954):

“…it is now time to point out the limits of science. The riddle posed by the double nature of the ego certainly lies beyond those limits. On the one hand, I am a real individual man; born by a mother and destined to die, carrying out real physical and psychical acts, one among many (far too many, I may think, if boarding a subway during rush hour). On the other hand, I am “vision” open to reason, a self-penetrating light, immanent sense-giving consciousness, or however you may call it, and as such unique. Therefore I can say to myself both: “I think, I am real and conditioned” as well as “I think, and in my thinking I am free.”…”

“And yet, nothing is more familiar and disclosed to me than this mysterious “marriage of light and darkness,” of self-transparent consciousness and real being that I am myself. The access is my knowledge of myself from within, by which I am aware of my own acts of perception, thought, volition, feeling, and doing, in a manner entirely different from the theoretical knowledge that represents the “parallel” cerebral processes in symbols….”

“I will not succumb to the temptation of foisting Professor Bohr’s idea of complementarity upon the two opposite modes of approach we are discussing here….”

His idea of the “double nature of the ego” is easily understood in yogic terms. Using his own terminology, Wyle identified the fundamental distinction between consciousness per se (“a self-penetrating light”) and the vrittis within consciousness (“a real individual man; born by a mother and destined to die”).   He calls this the “marriage of light and darkness”: the light of consciousness per se, burdened by the darkness of our mundane, everyday life in the world with all our problems, ups and downs, uncertainties and frustrations, in short, the vrittis.

It is noteworthy that he uses the same analogy to light that yoga does to describe consciousness. He repeatedly sources this idea to the German neo-Kantian philosopher Johann Gottlieb Fichte and cites the following from Fichte (this is cited in the essay Mind and Nature, 1934):

“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.”

Thus also did Fichte bequeath to Weyl the notion that consciousness = being. This is precisely the yogic understanding: consciousness is akin to a light that gives not illumination, but being.

A couple other things deserve quick mention. First, Weyl’s sense of humor: too many people on the subway at rush hour. Cute.

Second, and quite importantly, Weyl refuses to invoke Bohr’s principle of complementarity. Recall, the essay was titled “The Unity of Knowledge”. Positing eternal opposites is not conducive to unity. How then does he propose to unify this “double nature” of our being?

Scattered Buckshot Will Hit the Broad Side of a Barn
He unifies consciousness by recognizing that, embedded in the mind of the “man born by a mother and destined to die” is the “’parallel’ cerebral processes in symbols” whereby man can take a stab at, basically, guessing the nature of the noumena. Let’s see how this works.

Associated with the double nature of consciousness is the double nature of knowing. On one hand there is first person introspection, which is the intuition, the direct experience of Kant’s phenomena in consciousness (“my own acts of perception, thought…” etc.). Then there is our attempt to understand the noumena, which happens via “theoretical knowledge” expressed “in symbols”.

In my previous post on Weyl, I dwelt on his idea of the “free construction of the possible” using math and symbols. I repeat his quote from the previous post:

“In physics we do not a posteriori describe what actually occurs in analogy to the classification of the plants that actually exist on earth, but instead we apply an a priori construction of the possible, into which the actual is embedded on the basis of the values and attributes indirectly determined by reactions…But construction a priori must be joined with experience and analysis of experience by experiments. “

In the first Wyle post, I did not link this idea to Kant. But here I assert that this quote reveals Weyl’s solution to Kant’s dilemma. We are trapped in our mind and have no direct perception of the noumena. In his essay Mind and Nature in particular, Wyle spends a great deal of words discussing that our immediate, first-person perceptions of the world cannot serve as a basis to understand the noumena.

For example, color we directly perceive, mass we do not. Color is useless for telling us about the noumena. But when embedded in a suitable mathematical framework, the symbol representing mass tells us something of this mysterious, unperceivable thing in its relationship to other such symbols in the construction, and thereby provides a perspective on the noumena.

Therefore, if our first-person “intuitions” cannot tell us about what is outside of our minds, then what are we to do? Here now is Wyle’s genius: We make a guess. If we guess enough times, the odds are that we will eventually get something right.

Wyle is too sophisticated to say “make a guess” so he says it like this (Mind and Nature):

“…it is left to the tact and genius of the inquirer to find the weakest point of theory which can most suitably be altered to fit the new facts. Scarcely any general rules can be set up in this respect, as little as for the weight to be given to the several facts (which we know or think to know), for the purpose of their theoretical interpretation.”

It is, I am sorry to say, a fancy way to say “guess”. Certainly it does not exclude educated and informed guesses, but guesses nonetheless. The previous two quotes are a long-winded and flowery way to say that physicists get around Kant’s dilemma by guessing at mathematical models of how the world works.

[SIDEBAR: I note in passing his dissing of the philosophers of science, and I would ascertain Popper specifically, when Wyle said: “Scarcely any general rules can be set up in this respect…” ]

To get what he is saying, first, we need to understand what a scientific “law” is. It is simply some pattern of relationship expressed by the mathematical symbols. This is what math does: it describes patterns of relationships amongst symbols. So, a scientific “law” is just some pattern of relationship amongst the objects in the math symbolism. So, step 1 of Wyle’s “guessing algorithm” is: guess at the overall math pattern.

There is a second level involved too. Once we have an overall math pattern, that pattern gives rise to infinite solutions. For example, how many lines do you get out of the math pattern y = mx + b? You get all of them. The statement “y = mx + b” contains all possible lines. You specify which line by giving values to m and b. The whole set of possible lines is what Weyl means by “a priori construction of the possible”. The specific line you get by specifying m and b is “the actual is embedded on the basis of the values and attributes”.

The second level isn’t really guessing per se, because the overall math pattern implies the infinity of solution. Nonetheless, when searching parameter space for fitting data, guessing certainly has its role in the process.

Then, given some interpretation of the symbols of the theory, the symbols can be linked to some aspect or another of our sensory experience, and thereby be subject to experimental test. As Weyl says above: “on the basis of the values and attributes indirectly determined by reactions”. The way he is using the word “reaction” simply means “experimental setup”, as one can see if they read the whole essay.

Thus, although Weyl addresses this in fancy, flowery, sophisticated language, what he is really saying is that we can get around Kant’s limitation by using math, and making guesses at what we think the noumena is, until something finally sticks. It really seems appropriate to call it a “scattered buckshot” approach to science.

Analysis of Weyl’s Scattered Buckshot Approach
The thing is, it works. This method allows us to get some kind of handle on what occurs outside of our mind.  As to the relative value of this methodology, I discussed that in What is Science? and so won’t repeat myself here.  People call this method “theoretical” physics, but it is really just making guesses in the form of mathematics. Again, they may be highly educated and well-informed guesses, but in the end, one guesses.

Don’t just take my word for it. Feynman understood this and you can see him say it out loud (see his talk here). Whether he got this notion from Weyl or not, I cannot say. He probably did not because it’s just the way these folks do their business.

A point I make in passing is that there is much more to this “shut up and calculate” thing than people suspect, as the present context indicates. It is by no means as mindless as some people would like to think. It is pragmatic, and at a certain level, it is humble because it accepts that progress occurs slowly and only in little chunks at a time.  The method does not lend itself to grand philosophical generalizations, which Weyl notes thus (The Open World):

“One of the great differences between the scientist and the impatient philosopher is that the scientist bides his time.  We must await the further development of science, perhaps for centuries, perhaps for thousands of years, before we can design a true and detailed picture of the interwoven texture of Matter, Life and Soul.”

So, the bottom line here is that: (1) Weyl acknowledged the limits of reason determined by Kant and in doing so he was able to (2) craft an “algorithm” (of sorts) that allows the “double nature” of our mind to find concrete means to link the phenomena of the intuitive mind to the world of noumena, of things in themselves.

It’s hardly a programmable or computable algorithm however, given that its main ingredient is guessing.  I suppose it kind of resembles radioactive decay.

The link and the key to the whole enterprise is mathematics. Math, as a form of symbolic language, expresses patterns of relationship in the most pure form we here in the West can imagine.

It is interesting to note that Weyl’s ideas have had little impact on the philosophy of science in the 20th century. Weyl’s ideas seemed to have escaped the notice of the Poppers, Kuhns, and Feyerabends of the world. It’s kind of funny then that Weyl’s notions should garner serious acknowledgment here, in a discussion linking his ideas to yoga, of all things.

Thus, Weyl has confidence that we can make links between the two worlds that Kant thought were forever separated. However, Weyl was hardly naïve on this front. He realized that, at best, we can make links here and there, but we can never wholesale transport the noumena into the phenomena. In this he is in complete agreement with the yogic view of consciousness, which leads us to Wyle’s idea of the Absolute.

Whatever the Absolute Is, Science is Its Best Reflection Yet
This longish quote from his Open World essay expresses very clearly Wyle’s concept of the Absolute, of Kant’s noumena. Read it, and we’ll discuss it afterwards.

“The beginning of all philosophical thought is the realization that the perceptual world is but an image, a vision, a phenomenon of our consciousness; our consciousness does not directly grasp a transcendental real world which is as it appears. The tension between subject and object is no doubt reflected in our conscious acts, for example, in sense perceptions…The postulation of the real ego, of the thou and of the world, is a metaphysical matter, no judgment, but an act of acknowledgement and belief. But this belief is after all the soul of all knowledge. It was an error of idealism to assume that the phenomena of consciousness guarantee the reality of the ego in an essentially different and somehow more certain manner than the reality of the external world; in the transition from consciousness to reality the ego, the thou and the world rise into existence indissolubly connected and, as it were, at one stroke.”

“But the one-sided metaphysical standpoint of realism is equally wrong….”

“Knowledge is unable to harmonize the luminous ego (the highest, indeed the only forum of all cognition, truth and responsibility) which here asks in despair for an answer, with the dark, erring human being that is cast out into an individual fate. Furthermore, postulating an external world does not guarantee that it shall constitute itself out of the phenomena according to the cognitive work of reason as it establishes consistency. For this to take place it is necessary that the world be governed throughout by simple elementary laws. Thus the mere postulation of the external world does not really explain what it was supposed to explain, namely, the fact that I, as a perceiving and acting being, find myself placed in such a world; the question of its reality is inseparably connected with the question of the reason for its lawful mathematical harmony. But this ultimate foundation for the ratio governing the world, we can find only in God; it is one side of the Divine Being. Thus the ultimate answer lies beyond all knowledge, in God alone; flowing down from him, consciousness, ignorant of its own origin, seizes upon itself in analytic self-penetration, suspended between subject and object, between meaning and being. The real world is not a thing founded in itself, that can in a significant manner be established as an independent existence. Recognition of the world as it comes from God cannot, as metaphysics and theology have repeatedly attempted, be achieved by cognitions crystallizing into separate judgments that have an independent meaning and assert definite facts. It can be gained only by symbolical construction.”

“Many people think that modern science is far removed from God. I find, on the contrary, that it is much more difficult today for the knowing person to approach God from history, from the spiritual side of the world, and from morals; for there we encounter the suffering and evil in the world which it is difficult to bring into harmony with an all-merciful and all-might God. In this domain we have evidently not yet succeeded in raising the veil with which our human nature covers the essence of things. But in our knowledge of physical nature we have penetrated so far that we can obtain a vision of the flawless harmony which is in conformity with the sublime reason. Here is neither suffering nor evil nor deficiency, but perfection only.”

And there you go. I suspect that the content of this quote explains why Weyl never caught on in philosophy of science, nor even as a philosophical position amongst real practicing scientists, in spite of the wholesale adoption of Weyl’s contributions in both math and physics.

He uses the “G” word. Oh my!

[Sidebar again: One of my favorite mean things to do is compare some modern person with a contrary view to the person under consideration.  So, Dawkins thinks God is stupid.  But what has Dawkins done scientifically compared to Weyl? Whose scientific contributions have been more important for the forward progress of science? Why then, pray tell, would one take Dawkins seriously about these types of philosophical issues compared to Weyl?]

Note also how Wyle takes both idealism and materialism to task. They both suck. To Wyle, our very consciousness, the self-penetrating light, is of the essence of God, and the flawless harmony of the laws of nature are his proof of God’s existence.

Stare at that a few times: Weyl uses science as, effectively, proof of God. It’s one thing when some uneducated kook says something like this. It’s a totally different matter coming from somebody of the intellectual stature of Weyl. For any pygmies out there reading this: just think about it.

What else can explain the fact that the noumena, the transcendental, the world is a cosmos and not a chaos? As he says: “the ultimate answer lies beyond all knowledge, in God alone…”

Umm…anybody? Does that sound like the Absolute to anyone else out there? Hello! Hello!

Really, what he says has the same impact on me as van der Leeuw’s words. It leaves me speechless, silent. All I can do is resonate with the truth contained in the words.

I Can Talk Again
Is what Wyle says science? Is it religion? Is it philosophy? It is a compound, a harmonious blending of all these perspectives. I have only presented the few choice quotes given above. The full impact of his thought needs to be felt by reading his essays in their entirety (book here).

I want to now wrap this up by bringing it back to the yogic view of consciousness. Recall our diagram of the projector, light, cave, and various screens:

f5
Weyl clearly expressed the distinction between the screen (the “intuitive”; “a real individual man; born by a mother and destined to die”) and the light of consciousness (“I am ‘vision’ open to reason, a self-penetrating light”). The screen is the darkness and consciousness the light in his “marriage of light and darkness”.

He understood that there was an Absolute supporting the whole panorama of experience (“…this ultimate foundation for the ratio governing the world, we can find only in God”).   And he understood that this foundation was the very source of our consciousness (“…flowing down from him, consciousness, ignorant of its own origin…suspended between subject and object”).

What in this picture did he not understand? He didn’t know about the various strata under the surface of consciousness. Weyl only knew of the world of visesa gunas and vitarka consciousness. He did not suspect that the light of consciousness, with its self-penetrating property, can turn around and flow back to its source. He never could have guessed at the property of pratyak cetana. Without the ability to descend into the cave of consciousness, neither could he in his wildest imagination know the literal realities of vicara, ananda, and asmita gunas.

Since he didn’t know about the depths of the cave of consciousness, the thought that one could penetrate the bindu and experience the Absolute was beyond his reach.

In a way this is ironic because, in the history of the 20th century intellect, Weyl was a shining example of a mind open to the subtle vibrations from the depths of consciousness. He expressed them deeply and elegantly as math, science, and yes, philosophy. In doing so, he contributed in a most significant way to the world, to mathematics, and to the science that is our legacy today.

He obviously cannot be blamed for these omissions. He was a busy fellow doing the things he was supposed to do. It is amazing that he discerned as much of the yogic view as he did.

The Moral of the Story is…
Wyle serves as an example of the best that Western thought has to offer. He sought to discern the interrelationships of math, science, philosophy, and religion.

Wyle, and the fruits of his efforts, stand in stark contrast to the nonsense that passes for science and philosophy today.  Today there is too much abundance of disgusting ideas that see only division and conflict between math and science on one hand, and philosophy and religion on the other hand. Compared to the sublime ideas of Wyle, such ideas appear as but the childish psycho-babble of kooks. Such thinking is an affront to the memories of the great people like Weyl who bequeathed to us the intellectual legacy we hold now in our hands, minds, and actions.

When we see the depth of Wyle’s thinking, it becomes clear that the current crop of philosophical pygmies has turned into the very thing they proclaim to despise. The two-bit pygmy philosophies being expounded today are exactly the kind of postmodern blather they declare to hate. It is the classic case of being so consumed with hatred for another that one becomes the object of hatred.   That’s the punchline.

On these thoughts we leave the Absolute. In part 8, we segue into going deeper into the bindu (deadpan drumbeat, audience groans) via a preliminary discussion of the place of mathematics in the yogic view of consciousness.

4 thoughts on “The Yogic View of Consciousness 7: The Absolute According to Hermann Weyl

  1. kashyap vasavada

    Hi Don:
    Yes. Hermann Weyl was a great mathematician, theoretical physicist and philosopher. He can be called father of very successful gauge theory. Unfortunately he was not familiar with eastern religious concepts like many western scientists. Recent tirades against religion and metaphysics by western scientists may be due to this ignorance.
    Your idea of outward projections reminds me of few things. In one Vedic philosophy talk, the speaker said that just as sensation of rays of light from an object enter brain through our eyes, there is something which goes from brain to the eyes . The reason is that sometimes even when eyes are open, you do not see the object!
    The other intriguing ideas are from physics. Maxwell’s equations for electromagnetic waves have two solutions. One is the usual solution called retarded i.e. after emission it gets to the observer after a while because velocity of light is finite. The other solution, the so called advanced solution, is thrown away as unphysical because literally it will get to the observer before the emission process. This would cause causality violation. So in classical physics it is thrown away. That is ok for classical physics. Your TV certainly does not send any wave back to the TV tower.
    But in quantum theory something interesting happens. You might know that Feynman was Wheeler’s Ph. D. student. They worked out a theory which contains both advanced and retarded solutions. The advanced solution can be interpreted as something going from observer to the object in a time reversed fashion! Feynman later worked out the quantum field theory by means of the so called Feynman diagrams. As an example, suppose you are studying electron A scattered by electron B. In one diagram, A emits a photon which reaches and is absorbed by B after some time. In another diagram B emits a photon which is absorbed by A after some time. The second diagram can be interpreted as advanced solution from the point of view of A. In relativistic theory both the diagrams are combined and both are needed. The Feynman propagator contains both advanced and retarded propagators. There is no violation of causality.
    Recently someone has also given a so called transactional interpretation of quantum mechanics using the advanced solution as something going backward in time!
    If you are interested, you might google for “advanced and retarded waves” and then we can discuss it further.
    Honestly I do not know if these ideas have anything to do with the idea of “something going back “from observer to source or some image of a source” but it is intriguing parallel to the projection idea!
    Best.
    Kashyap

    • Dear Kashyap
      It’s very nice to hear from you. Thank you for sharing all these ideas. I did not know about the advanced and retarded solutions for the electromagnetic (EM) waves. I have spent a good part of today trying to learn more about them. One small advance for me is I now have seen some of the formalism from which the virtual particles arise, or vacuum polarization as Feynman called it, via his “propagators”. However, overall the ideas are quite beyond my training and background. It strains my (small) math understanding. It is good to exercise those skills. But I fear my understanding will be very superficial compared to yours and any comments I make must be taken keeping this in mind.

      On a quick side note, I found a Lubos post on Physics stack exchange where he dismissed the transactional interpretation. You of course can judge his criticism better than I, but, as usual, Lubos maintains his Copenhagen “purist” view and did not feel this was a useful addition to quantum mechanics. It is quite beyond me to judge the issue at all.

      As to your main points, I can’t express my thanks and enthusiasm enough that you would seek to further the idea of the “projection” of consciousness through the bindu. That is very kind of you to take the ideas seriously and seek to add to them. I am certainly using the idea in a metaphorical sense at this point. As I mentioned near the end of Part 2, there are three math-related ideas that seem pertinent: (1) virtual images, (2) the idea of “non-orientable” surface as exemplified by a Möbius strip, and (3) the 720 degree rotation required to return a spinor (e.g. like a fermion) to its initial state. I was just looking on the web, and it turns out properties 2 and 3 are somewhat related (see here), as intuitively it seems they should be since it takes 2 rotations to return to one’s starting point on a Möbius strip.

      The intuition behind using a Möbius strip is to explain pratyak cetana as analogous to a 360 rotation around a Möbius strip (recall pratyak cetana is the transition from one state of consciousness to another). So, for example, when you fall asleep at night, this would be like rotating 360 degrees around the Möbius strip, so now you are pointed in the “opposite” direction, e.g. pointed towards the world of dreams. Then, another 360 degree rotation “points” you back to the world of waking awareness, when you wake up after sleep. This is, concretely, an example of the processes I am trying to model.

      That said, I wonder if the two solutions of the EM equations can somehow be related to the virtual image aspect? Feynman uses the idea to get virtual particles due to the opposing nature of the solutions. Perhaps some analogous logic can apply here too. Please allow me to think out-loud:

      The virtual image idea applies to paranga cetana, or the outward directed nature of our consciousness. If, in the Möbius strip example, we imagine a vector pointing perpendicular to the surface, then this outward directed-ness would be the state of paranga cetana (pointed towards visesa gunas). If we looped 360 degrees around the Möbius strip we would then be “pointed outward” towards the dream world (or the world of avisesa gunas). In either case, the images perceived would the the “outward directed” images, the virtual images.

      Now, my very next post is going to talk more about the bindu and the possible relationship between point-like events in the Absolute and events that appear to be in space-time when projected onto the “screen” of consciousness. It may well be that your suggestion could apply here. It seems like the result with the Maxwell equations is some type of mirror symmetry in the solutions. It might be an analogous type of mirror symmetry between “events” in the Absolute and events as we perceive them on the screen of consciousness as a projection. That is, perhaps the outward (paranga cetana) projection of consciousness is the retarded solution, and the events in the Absolute are the advanced solution? This would be an attempt to directly apply the ideas, as opposed to find an analogy or to use them in a metaphorical fashion.

      A weird constraint we get from van der Leeuw’s description is that, in some sense, the Absolute is a “block universe” where all time is simultaneous and time does not flow. When our consciousness is paranga cetana, the main feature is the flow of time. Patanjali also effectively describes this same situation: The final stage of yoga is dharma mega samadhi, the “jumping out” of time and into timelessness. But it sounds like the advanced wave goes backwards in time, in some sense, so it is not clear if this is compatible with a “block universe” type idea.

      Anyway, those are just some very rough thoughts in reply to your suggestion. In some sense a mirror symmetry is in play, otherwise, how could we speak of a “virtual image”? The advanced and retarded waves certainly sound like a type of mirror symmetry. Please feel free to correct me if I am completely wrong on this.

      Ok, I will close here. These are just very rough ideas thrown out there for the sake of “blue skying” it and to toss ideas out for consideration. Again, Kashyap, thank you so much for explaining these ideas and for taking these rather obtuse topics seriously. I am extremely grateful and appreciative that you would do so!!

      All my best,

      Don

      • kashyap vasavada

        Dear Don; Let me think some more whether there could be any connection between your idea of projection and advanced solution. Lubos is of course pragmatist, shut up and calculate person! But amusing stuff that has been happening in modern physics is this. Most of the interpretations of what one is doing by means of equations are metaphysical! I personally do not mind. I like metaphysics! But a typical physicist may be worried about associating with metaphysics! So the tendency is just to shut up and calculate and sweep the interpretations under the rug!!

      • Hi Kashyap!

        I will look forward to any further thoughts you have to offer. I updated the above post with a quote from Weyl which justifies the “shut up and calculate” mentality. Wely considered philosophers to be impatient because each philosopher on his own wishes to achieve the grand synthesis of understanding. As Weyl says, scientists “bide their time” knowing we cannot grasp everything in one fell swoop. Sometimes I see Lubos as like an antibody of the immune system who acts to keep quantum mechanics pure and free of the “disease” of impatient philosophy! This is where I feel the yogic and Hindu ideas can contribute: they provide a wealth of new ideas by which to contemplate our sciences and they help us see the fronts where progress is possible right now. Of course, the many branches of Hinduism and yoga offer so much more, but they offer this too.

        Best wishes!
        Don

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