Steiner and Schrodinger's Equation

[AshvinP]

Ashvin, at this point of your exchange with Cleric, the following metaphor comes to mind.

Let’s suppose for a second that I am one incarnation of the Mona Lisa. And let’s imagine that I go to the Louvre Museum to see Leonardo’s masterpiece known by the same name. In that room, a student of fine arts is skillfully reproducing the painting. Let's also imagine that I unexpectedly meet a friend there, who has never heard of the Mona Lisa before. My friend looks at me, then looks at the student’s drawing, and asks: "The resemblance is so great, could it be that you are an earlier version of this drawing?”. "Well, no" - I reply - "I am a being, and that is a drawing." Now, if the friend insists: “But if we remember that the drawing pictures a being's appearance, could we now say that you are a prefiguration of the drawing, given that your face is so resemblant?”, how should I reply then?

Federica,

In the spirit of (2), I think the metaphor would work better if you had done something similar to what the student was doing, but you did it more imaginatively and therefore it presented quite differently. Because, in the context of that lecture, Steiner is trying to think along the lines of modern mathematicians who study and try to model the phenomenal world, but to do it in a way more aligned with the qualitative dimension of reality, i.e. more artistically/imaginatively. Now the question is whether Schrodinger can be considered the 'student', with his intuition of interfering phases captured in his complex wave function, or whether the 'student' is just the average mathematical scientist trying to model the phenomenal dynamics of heat, chemicals, and light. Is there some overlap between these two students?

...

That is to say, if you wish to deal with the relation of heat, chemical action and light working in the same phenomenological field at the same time, you have to use imaginary numbers — your calculation has to involve the mathematical relations expressed in imaginary numbers.

Ashvin,

In your objection in purple above, you are not considering that doing is the same as being and knowing, for someone who pierced the veil, like Steiner did. So, in the metaphor, I didn’t need to be drawing anything, because, in the metaphor, I am. I am living reality, experienced from within, through the depth of various members of being. In contrast, the drawing, no matter how skilfully executed, was the description of a third-person perspective on the portrait. And, in the metaphor as in truth, Schrödinger is indeed a student, he is a student of reality - as you admitted in (1) - just as other scientists are. In their drawings, some are more talented, some are less talented students. What they develop is, as Cleric called it, "a glorified math-painting algorithm". In contrast, Steiner IS, among other things, the timeless reality of the understanding of the three ethers referred to in the lecture. The students, even the most gifted ones, only model the precipitation of that reality into the physical perceptual spectrum.

So, that Steiner anticipated Schrödinger’s equation does not make sense to me, as a statement, or as a question. How can Steiner’s timeless consciousness of those etheric relations - even incarnated in intellectually intelligible formulas (metaphorically intended by Steiner as stimuli for the scientists' intuitive potential) - be said to anticipate a third-person drawing describing the transformation in time of systems on the physical-perceptual plane? That consciousness cannot anticipate anything, since it’s timeless, since it’s one with the flow of transformation itself in all its depth structure, and since it originally and intrinsically contains all possible mathematical descriptions of physical precipitations of phenomena?

Federica,

There is a tendency to mystical reduction here that we need to be careful of, especially if it leads us to feel that even asking the questions and thinking through their implications, as Cleric also suggested in his last post, is irrelevant or meaningless. That is actually the most important component for the strengthening and expanding of our inner soul forces, as Steiner makes clear in many places as well.

I will use a simple metaphor here. Let's say you stumbled across an unknown person's diary and started reading the entries.

"Today, on February 7, I intend to scale a very high mountain peak."

"Today, on March 14, I intend to visit my best friend John."

"Today, on April 1, I intend to go sailing with my friend Peter."

In our metaphor, we are now resonating with the archetypal intentions that structured the author's days, partly establishing the curvature through which his states of being unfolded. But does that in and of itself also communicate to us the details of his living experience when flowing through those curvatures of intent? Do we know exactly how his states of being will transform to accomplish those intents?

When Steiner or any esotericist, even a master, penetrates to the etheric and higher spaces of soul-spirit, there is still much groundwork that needs to be laid for the higher experiences to map onto transformations of the phenomenal (physical) world and for those results to be transduced into lucid conceptual frameworks. Do we imagine that such an esoteric master could, after exploring across the threshold in meditation, walk into a lab dedicated to quantum computing, for ex., and immediately make himself of utmost value to whatever projects they are trying to complete? In fact, Steiner may be one of the very few masters who could adapt his thinking-perception in such a fluid manner because of his early efforts to become intimately familiar with the progression and modes of thinking in natural science and mathematics.

The bold question above reminds me of a similar discussion we had, where you asked:

Because the outer physiognomy constitutes a detour, an indirect course to the spiritual forces. The Will that plays out in limited space-time/in the perceptual world is more indirect than Thinking. So detours can be helpful in certain cases, for certain people, but how could they be helpful for those who have the ability to access the ideal landscape directly, intuitively? What could the perceptual experience teach them of the spiritual worlds that they don't already have direct access to, and knowledge of?

And to which Cleric responded here.

It's misleading if we imagine that we can gain access to the archetypal worlds and from there derive spiritually everything in the sensory spectrum. We should remember that there's a spectrum of reality and no part is fully reducible to the others. It is true that the archetypal beings have a much more encompassing effects (non-local) but it's not the case that from their perspective everything that happens on more local scales is fully determined. For this reason, higher cognition always develops as harmonization between the levels of being.

In that sense, without perceptual experience, it's like living in a completely theoretical ideal world, which could be anything. But the sensory, life and soul gradients are the actual structure that has to be transformed and musically attuned to higher order rhythms.

That is why this anticipation question has relevance and meaning. Steiner is probably one of the few spiritual thinkers who it could even be asked of, and most likely, Cleric is correct that, in this lecture, he was not exploring the same intuition in mathematics that Schrodinger would have 6 years later. Although clearly, I am still undecided on that question and think it is worth exploring. Most importantly, the value for our spiritual development doesn’t come from finding a simple affirmative or negative to the question, but energetically and thoroughly exploring all the various thought-avenues that open up from asking the question. In no case do we want to convince ourselves that it isn't even worth the effort.

"Most physicists probably think of the 'many-worlds' above in a very externalized, physical, quantitative-mechanical way… But it seems to me they are still probing the etheric reality in their intuition, grasping at its qualities, except they don't realize what they are exploring is the true life of their very own thinking."

…”except”? That “except” is everything! I think they are probing physical precipitations, they are not probing etheric reality. You are basically asking: “if we forget for a moment that they don’t understand reality, can we say that they understand reality?”

That is really not the question. Human thinking has so far been in a constant process of expanding its conceptual activity into higher spaces, probing them in useful ways. The very concept of physical states existing in a 'superposition' before collapsing into observable dimensions is something unimaginable from the Newtonian, completely physical mode of thinking, where everything is 'side by side' and linear. The developments in GR and QM reflect to us concrete thought-movements into the more etheric life of thinking, just like certain developments in psychoanalysis reflect to us movements into the more astral life of feeling. Of course, these explorations remain flat, abstract, and dry until the proper first-person experiential thinking perspective is adopted.

[Federica]

Federica,

There is a tendency to mystical reduction here that we need to be careful of, especially if it leads us to feel that even asking the questions and thinking through their implications, as Cleric also suggested in his last post, is irrelevant or meaningless. That is actually the most important component for the strengthening and expanding of our inner soul forces, as Steiner makes clear in many places as well.

I will use a simple metaphor here. Let's say you stumbled across an unknown person's diary and started reading the entries.

"Today, on February 7, I intend to scale a very high mountain peak."

"Today, on March 14, I intend to visit my best friend John."

"Today, on April 1, I intend to go sailing with my friend Peter."

In our metaphor, we are now resonating with the archetypal intentions that structured the author's days, partly establishing the curvature through which his states of being unfolded. But does that in and of itself also communicate to us the details of his living experience when flowing through those curvatures of intent? Do we know exactly how his states of being will transform to accomplish those intents?

When Steiner or any esotericist, even a master, penetrates to the etheric and higher spaces of soul-spirit, there is still much groundwork that needs to be laid for the higher experiences to map onto transformations of the phenomenal (physical) world and for those results to be transduced into lucid conceptual frameworks. Do we imagine that such an esoteric master could, after exploring across the threshold in meditation, walk into a lab dedicated to quantum computing, for ex., and immediately make himself of utmost value to whatever projects they are trying to complete? In fact, Steiner may be one of the very few masters who could adapt his thinking-perception in such a fluid manner because of his early efforts to become intimately familiar with the progression and modes of thinking in natural science and mathematics.

...

That is why this anticipation question has relevance and meaning. Steiner is probably one of the few spiritual thinkers who it could even be asked of, and most likely, Cleric is correct that, in this lecture, he was not exploring the same intuition in mathematics that Schrodinger would have 6 years later. Although clearly, I am still undecided on that question and think it is worth exploring. Most importantly, the value for our spiritual development doesn’t come from finding a simple affirmative or negative to the question, but energetically and thoroughly exploring all the various thought-avenues that open up from asking the question. In no case do we want to convince ourselves that it isn't even worth the effort.

Ashvin,

It [that I deem irrelevant to even only ask the question] is not what I wrote. It’s not that the act of asking the question is irrelevant or meaningless. Rather, it’s the viewpoint presented in the question that doesn't make sense to me, as I wrote. That’s very different. In other words, your idea that I am reasoning under mystical overwhelm is entirely unwarranted. There's no ground it can rely upon. As a consequence, this extensive aside you have made, based on a misunderstanding, allows you once again - after you did the same in your previous post - not to take my argument seriously. It allows you to altogether avoid replying to it in matter-of-factly way. Would you please do it?

Most importantly, the value for our spiritual development doesn’t come from finding a simple affirmative or negative to the question, but energetically and thoroughly exploring all the various thought-avenues that open up from asking the question.

Right. For my part, I have articulated one of those avenues in my post above. It has led to the idea that Steiner’s lecture and the work of Schrödinger operate on clearly distinct planes, which means it doesn’t make sense to speak of Steiner "anticipating" Schrödinger, as illustrated above. Would you please address this objectively?









POST SCRIPTUM

When Steiner or any esotericist, even a master, penetrates to the etheric and higher spaces of soul-spirit, there is still much groundwork that needs to be laid for the higher experiences to map onto transformations of the phenomenal (physical) world and for those results to be transduced into lucid conceptual frameworks.

Right.

Do we imagine that such an esoteric master could, after exploring across the threshold in meditation, walk into a lab dedicated to quantum computing, for ex., and immediately make himself of utmost value to whatever projects they are trying to complete?

No we don’t.

In fact, Steiner may be one of the very few masters who could adapt his thinking-perception in such a fluid manner because of his early efforts to become intimately familiar with the progression and modes of thinking in natural science and mathematics.

Yes. And please notice: it’s indeed Steiner specifically whom we are discussing - whether or not he “anticipated” equations. We were not discussing “any esotericist”. So your whole argument about my supposed mysticism sounds flawed to me, not only in its being grounded in a misunderstanding, but also in its being arbitrarily developed, for example with the introduction of “any esotericist”.

The bold question above reminds me of a similar discussion we had.

That discussion dates back to many months ago.
My viewpoint on the integration of the physical, soul and spiritual worlds has evolved since then.
:

[AshvinP]

Federica,

There is a tendency to mystical reduction here that we need to be careful of, especially if it leads us to feel that even asking the questions and thinking through their implications, as Cleric also suggested in his last post, is irrelevant or meaningless. That is actually the most important component for the strengthening and expanding of our inner soul forces, as Steiner makes clear in many places as well.

I will use a simple metaphor here. Let's say you stumbled across an unknown person's diary and started reading the entries.

"Today, on February 7, I intend to scale a very high mountain peak."

"Today, on March 14, I intend to visit my best friend John."

"Today, on April 1, I intend to go sailing with my friend Peter."

In our metaphor, we are now resonating with the archetypal intentions that structured the author's days, partly establishing the curvature through which his states of being unfolded. But does that in and of itself also communicate to us the details of his living experience when flowing through those curvatures of intent? Do we know exactly how his states of being will transform to accomplish those intents?

When Steiner or any esotericist, even a master, penetrates to the etheric and higher spaces of soul-spirit, there is still much groundwork that needs to be laid for the higher experiences to map onto transformations of the phenomenal (physical) world and for those results to be transduced into lucid conceptual frameworks. Do we imagine that such an esoteric master could, after exploring across the threshold in meditation, walk into a lab dedicated to quantum computing, for ex., and immediately make himself of utmost value to whatever projects they are trying to complete? In fact, Steiner may be one of the very few masters who could adapt his thinking-perception in such a fluid manner because of his early efforts to become intimately familiar with the progression and modes of thinking in natural science and mathematics.

...

That is why this anticipation question has relevance and meaning. Steiner is probably one of the few spiritual thinkers who it could even be asked of, and most likely, Cleric is correct that, in this lecture, he was not exploring the same intuition in mathematics that Schrodinger would have 6 years later. Although clearly, I am still undecided on that question and think it is worth exploring. Most importantly, the value for our spiritual development doesn’t come from finding a simple affirmative or negative to the question, but energetically and thoroughly exploring all the various thought-avenues that open up from asking the question. In no case do we want to convince ourselves that it isn't even worth the effort.

Ashvin,

It [that I deem irrelevant to even only ask the question] is not what I wrote. It’s not that the act of asking the question is irrelevant or meaningless. Rather, it’s the viewpoint presented in the question that doesn't make sense to me, as I wrote. That’s very different. In other words, your idea that I am reasoning under mystical overwhelm is entirely unwarranted. There's no ground it can rely upon. As a consequence, this extensive aside you have made, based on a misunderstanding, allows you once again - after you did the same in your previous post - not to take my argument seriously. It allows you to altogether avoid replying to it in matter-of-factly way. Would you please do it?

Most importantly, the value for our spiritual development doesn’t come from finding a simple affirmative or negative to the question, but energetically and thoroughly exploring all the various thought-avenues that open up from asking the question.

Right. For my part, I have articulated one of those avenues in my post above. It has led to the idea that Steiner’s lecture and the work of Schrödinger operate on clearly distinct planes, which means it doesn’t make sense to speak of Steiner "anticipating" Schrödinger, as illustrated above. Would you please address this objectively?









POST SCRIPTUM

When Steiner or any esotericist, even a master, penetrates to the etheric and higher spaces of soul-spirit, there is still much groundwork that needs to be laid for the higher experiences to map onto transformations of the phenomenal (physical) world and for those results to be transduced into lucid conceptual frameworks.

Right.

Do we imagine that such an esoteric master could, after exploring across the threshold in meditation, walk into a lab dedicated to quantum computing, for ex., and immediately make himself of utmost value to whatever projects they are trying to complete?

No we don’t.

In fact, Steiner may be one of the very few masters who could adapt his thinking-perception in such a fluid manner because of his early efforts to become intimately familiar with the progression and modes of thinking in natural science and mathematics.

Yes. And please notice: it’s indeed Steiner specifically whom we are discussing - whether or not he “anticipated” equations. We were not discussing “any esotericist”. So your whole argument about my supposed mysticism sounds flawed to me, not only in its being grounded in a misunderstanding, but also in its being arbitrarily developed, for example with the introduction of “any esotericist”.

The bold question above reminds me of a similar discussion we had.

That discussion dates back to many months ago.
My viewpoint on the integration of the physical, soul and spiritual worlds has evolved since then.
:

The only line of reasoning you presented so far for why the viewpoint presented in the anticipation question doesn't make sense to you, and why the planes of research between Steiner and Schrodinger are entirely distinct, is as follows.

So, that Steiner anticipated Schrödinger’s equation does not make sense to me, as a statement, or as a question. How can Steiner’s timeless consciousness of those etheric relations - even incarnated in intellectually intelligible formulas (metaphorically intended by Steiner as stimuli for the scientists' intuitive potential) - be said to anticipate a third-person drawing describing the transformation in time of systems on the physical-perceptual plane? That consciousness cannot anticipate anything, since it’s timeless, since it’s one with the flow of transformation itself in all its depth structure, and since it originally and intrinsically contains all possible mathematical descriptions of physical precipitations of phenomena?

This line of reasoning is clearly a means of mystical reduction - "consciousness cannot anticipate anything... it originally contains all possible mathematical descriptions..." - very similar to the line of reasoning in the post I quoted from a few months ago. The questions are nearly identical, except the latest question has become almost rhetorical. It simply isn't an accurate understanding of higher investigation of soul-spirit realities and its relation to phenomenal dynamics of the physical spectrum.

The practical effect of following this line of reasoning is to foreclose on further questioning and comparison on the topic. It makes us feel like there is nothing important to be gained from the effort, that such efforts are practically meaningless. That much is obvious. It couldn't possibly lead anywhere else but that feeling.

I think we need to be open to the possibility that others can notice objective patterns in our reasoning that we fail to notice, because we have not distanced ourselves enough from its usual flow. There is no problem in steering our thinking through such patterns, because they are very common and almost required to move into new spiritual ways of thinking, but the problem arises when we refuse to confront their objective and recurring manifestations in our thought.

[Federica]

...

Ashvin,

Your comments leave yourself wide open and it’s really tempting to smash them and redeem my thoughts from the unfair prejudices. But that seems to be a pattern in our discussions. I want to try to resist it. Instead, would you discuss the topic suggested by Cleric, i.e. the meaning of mathematical thought? I had the intention to reflect in that direction anyway, for example with the video you posted on imaginary numbers as a starting point. Assuming that you would agree - unless you deem me too mystical for such discussion - and with the animation of the "imaginary parabola" in mind, may I submit to your attention the following question, to start with:

Space : Intellectualized Time = Geometry : x

x = ?

[AshvinP]

...

Ashvin,

Your comments leave yourself wide open and it’s really tempting to smash them and redeem my thoughts from the unfair prejudices. But that seems to be a pattern in our discussions. I want to try to resist it. Instead, would you discuss the topic suggested by Cleric, i.e. the meaning of mathematical thought? I had the intention to reflect in that direction anyway, for example with the video you posted on imaginary numbers as a starting point. Assuming that you would agree - unless you deem me too mystical for such discussion - and with the animation of the "imaginary parabola" in mind, may I submit to your attention the following question, to start with:

Space : Intellectualized Time = Geometry : x

x = ?

Since Cleric has written on the nature of mathematical thought (from a spiritual perspective) previously and may be writing again on it in a few days, and since he clearly has a better grasp on such topics than I do, I would rather wait for his post. In the meantime, I asked him about this once and he gave the following response (I am only excerpting the first portion for now), which I'm sure he doesn't mind me sharing, perhaps as an introduction to what he will write later. Particularly the bold part indicates there is a great mysteriousness here, as there is with all space-free and time-free spiritual processes that project into our normal perceptual-conceptual spacetime, so we should be careful not to only seek explanations in chains of concepts. Ultimately everything comes back to the continual metamorphosis of cognitive states of being, which is something to be experienced and lived through with imaginative thinking rather than merely defined/described in concepts.

*** (Cleric wrote)

As we have spoken many times, we discover mathematical concepts within perceptions, which we have called foldnesses. There's soemething in common between a pair of apples, pair of stones, pair of hands. Now things become more mysterious when we consider these foldnesses in their relations. Imagine we take two baskets of apples and third empty one. Then we begin transferring apples from the first basket into the empty one while we keep track of the way foldness there changes - we're basically counting. When we're finished with the first basket, we go on taking apples from the second while continuing to keep the track of the foldness in the third. What we have performed with our will is practically an operation which we can call addition. Now the interesting thing is that we can repeat that operation with stones, pears and so on and as long as we begin with the same foldnesses in the baskets we always get the same foldness in the third. The even stranger thing is that we can lift that operation in our imagination and add imaginary apples. We say that we reach the mathematical concept when we intuit these meaningful qualities that are always the same no matter if we imagine apples, stones, fingers, etc.

Now why there are such lawful relations within the perceptual world and why our concepts can grasp these foldnesses is very mysterious question and we can easily go mad if we try to answer it. The reason would be that we try to find satisfactory answer within the relations of the concepts themselves.

For this reason, it's best if we can clearly differentiate the kind of planar thinking that simply moves through the inner relations of concepts, without trying to see deeper meaning. I would suggest that you try this approach first.

Basically it's all very simple. It's all about taking the time and really live through it. It all boils down to one simple thing - we're looking for thinking experiences that has within itself the rules for its transformation. This is really connected with the topic about 'creation out of nothing'. To grasp pure mathematical thinking you need to embrace the exact opposite - to move in thinking that is entirely determined by the laws through which it operates.

As a very simple example, imagine the following (I have given this example before). At any point you have three possible rules for action 1/ turn left 90 degrees, 2/ turn right 90 degrees, 3/ take a step forward. Now you can live through this in full body imagination or even try it out for real. Very soon you find out that these rules are not particularly exciting. Through them you can experience states that lie on a rectangular grid and that's all.

To get an idea of abstract mathematics, you have to imagine something similar. The natural numbers are like such states that can be traversed. In fact, There's such a function called the successor which is like the step forward. It basically transforms the present foldness state n into n+1.

Abstract mathematics is really the study of patterns in thinking space. For compactness, the rules above can be shortened (symbolized), for example, by <, >, -. Then we can type strings like <--->>--<->. Take something like ->->->->. Can you guess what it does? If you try to walk it you find out that it really leads you to the same starting state.

So in this way we lay down a symbolic cookbook recipe for moving through our imagined states. But take a note that the nature of thinking space has been implicit. We started with spatial imagination. The fact that the string above leads you to the same starting state comes from the implicit constraints of our imagination that we have accepted (we imagine the state as our spatial bodily state). But we can imagine completely different constraints and rules. Remember the example with non-Euclidian geometry where turning at right angles leads you not through four but through five rooms.

The secret to this is to decouple our thinking state from our ordinary intuitions. To make it a little clearer, let's devise a way of describing our state on the grid. We can do it thus: (x,y,d). Here x and y are our grid coordinates (think of the chess board letter/number coordinates) and d is the facing direction one of {n,e,s,w} (north, east, etc.). Let's say that our current state is (1,2,e). If we apply the ->->->-> operation we get the same state! If we apply >, we get (1,2,s) and so on. We have developed an elementary algebra We can call ->->->-> an identity operator because it doesn't change the state (in our algebra there are infinitely many such operators because there are infinitely many ways to walk around and get to the same state). Most algebras have identity operators. For example n + 0 or n * 1 all preserve the n state.

As simple as it is, it really underlies everything there is to abstract mathematics. It all boils down to identifying some attributes of the state (like our x,y,d) and then investigate how the state can be transformed by the possible operators. In the end it is really a thinking state.

[Cleric K]

Not directly an answer to any of the questions here but it might be valuable to contemplate the following phenomenon for those unfamiliar with it:

[AshvinP]

I came across an essay written by Schrodinger called, 'What is Life?' It was written in 1944, so it clearly represents his more mature thoughts and not necessarily something he was contemplating when developing his wave function equation much earlier in 1926. I think it shows, however, that he was striving to develop a nuanced understanding of the etheric forces that act in polar opposition to mere physical forces and thereby sustain life. Of course, he didn't know them as 'etheric forces' or have any understanding of the spiritual nature of these forces, and such a suggestion would be entirely outside the scope of a secular scientific work. He does discuss, however, that quantum mechanical wave functions give a better understanding of what is observed in the dynamics of a living organism, but even that extension to physical laws is not adequate for a full understanding of the phenomena of life, which according to him is directed by hitherto unknown laws. We can clearly sense that he is probing the etheric forces - the "order-from-order principle" - that work in from the Cosmic periphery and taking a rather bold position for a Nobel prize winner writing a secular scientific treatise on biological organisms.

To be perfectly clear, none of this means Schrodinger had a genuine understanding of the etheric forces, which are actually Cosmic formative forces that intelligently shape, grow, maintain, and reproduce the forms of the phenomenal world, including our life of concepts, according to supremely aesthetic and moral impulses. If we are looking for a genuine understanding of these forces that animate our concepts, we can look nowhere better than Steiner's many lectures discussing them and, of course, to also engage in the exercises discussed. For ex. here. Particularly when we weave our thinking in its pure sense-free element, such as mathematical thinking, and strive to become conscious of what we are thereby doing in our thinking, like we may have strove when reading Cleric's illustration quoted above, or also in philosophical or theological thinking, we are already in the process of developing living thinking that weaves consciously in the etheric.

This physical body is permeated by what may be called the etheric body or the body of formative forces a finer organisation of the human being, a Second Man within man, so to speak. How can one have actual perception of this Second Man? It must again and again be emphasised that it is by no means so very difficult to gain a true perception of this Second Man, a perception as clear and authentic as anything perceived by the senses or conceived by the reasoning intellect. One thing however, is necessary, because in our own time man does not live with such intensity in the element of thought itself as he did in earlier epochs of evolution, but adopts a more passive attitude to thought and is content to let impressions simply come to him from the world of the senses. For this reason it is necessary to strengthen thinking by means of exercises. Of course man has thoughts today, but he can hardly have real insight into the nature and activity of thinking because by force of habit he allows the external sense-impressions to stream into his thoughts the moment he wakes from sleep, because he sets store only by these external sense-impressions. True, this fills his thoughts with a content derived from external sense-perceptions but he does not actually feel or experience his own activity of thinking. Modern man can achieve this, however, with the help of such exercises as I have indicated, for instance, in my book, “Knowledge of Higher Worlds and its Attainment.”

Such exercises require man as it were to throw himself with the whole of his being into the activity of thinking, to give himself up to this thinking with all inner intensity and, with complete indifference to what the outer senses present to him, to live consciously and exclusively in this activity of thinking.

It can be of great assistance in these meditative exercises if one has had some practice in mathematics, especially in geometry. As regards the activity of thinking that has to be applied in geometry, one need only take a resolute plunge, as it were, into one's own inmost being, to experience the nature of this thinking in its independence, in its plasticity, in its inner weaving life, and one has an experience of the activity of thinking when drawing, say, a triangle.

*** (Schrodinger)

Let me refer to the phrase on p. 62, in which I tided to explain that the molecular picture of the gene made it at least conceivable that the miniature code should be in one-to-one correspondence with a highly complicated and specified plan of development and should somehow contain the means of putting it into operation. Very well then, but how does it do this? How are we going to turn ‘conceivability’ into true understanding? Delbruck's molecular model, in its complete generality, seems to contain no hint as to how the hereditary substance works, Indeed, I do not expect that any detailed information on this question is likely to come from physics in the near may future. The advance is proceeding and will, I am sure, continue to do so, from biochemistry under the guidance of physiology and genetics. No detailed information about the functioning of the genetical mechanism can emerge from a description of its structure so general as has been given above. That is obvious. But, strangely enough, there is just one general conclusion to be obtained from it, and that, I confess, was my only motive for writing this book. From Delbruck's general picture of the hereditary substance it emerges that living matter, while not eluding the 'laws of physics' as established up to date, is likely to involve 'other laws of physics' hitherto unknown, which, however, once they have been revealed, will form just as integral a part of this science as the former
....
What I wish to make clear in this last chapter is, in short, that from all we have learnt about the structure of living matter, we must be prepared to find it working in a manner that cannot be reduced to the ordinary laws of physics. And that not on the ground that there is any 'new force' or what not, directing the behaviour of the single atoms within a living organism, but because the construction is different from a anything we have yet tested in the physical laboratory. To put it crudely, an engineer, familiar with heat engines only, will, after inspecting the construction of an electric motor, be prepared to find it working along principles which he does not yet understand. He finds the copper familiar to him in kettles used here in the form of long, wires wound in coils; the iron familiar to him in levers and bars and steam cylinders here filling the interior of those coils of copper wire. He will be convinced that it is the same copper and the same iron, subject to the same laws of Nature, and he is right in that. The difference in construction is enough to prepare him for an entirely different way of functioning. He will not suspect that an electric motor is driven by a ghost because it is set spinning by the turn of a switch, without boiler and steam. If a man never contradicts himself, the reason must be that he virtually never says anything at all.
...
In biology we are faced with an entirely different situation. A single group of atoms existing only in one copy produces orderly events, marvellously tuned in with each other and us number of with the environment according to most subtle laws. I said existing only in one copy, for after all we have the example of the egg and of the unicellular organism. In the following stages of a higher organism the copies are multiplied, that is true. But to what extent? Something like 10^14 in a grown mammal, I understand. What is that! Only a millionth of the number of molecules in one cubic inch of air. Though comparatively bulky, by coalescing they would form but a tiny drop of liquid. And look at the way they are actually distributed. Every cell harbours just one of them (or two, if we bear in mind diploidy). Since we know the power this tiny central office has in the isolated cell, do they not resemble stations of local government dispersed through the body, communicating with each other with great ease, thanks to the code that is common to all of them? Well, this is a fantastic description, perhaps less becoming a scientist than a poet. However, it needs no poetical imagination but only clear and sober scientific reflection to recognize that we are here obviously faced with events whose regular and lawful unfolding is guided by a 'mechanism' entirely different from the 'probability mechanism' of physics. For it is simply a fact of observation that the guiding principle in every cell is embodied in a single atomic association existing only one copy (or sometimes two) -and a fact of observation that it may results in producing events which are a paragon of orderliness. Whether we find it astonishing or whether we find it quite plausible that a small but highly organized group of atoms be capable of acting in this manner, the situation is unprecedented, it is unknown anywhere else except in living matter. The physicist and the chemist, investigating inanimate matter, have never witnessed phenomena which they had to interpret in this way. The case did not arise and so our theory does not cover it -our beautiful statistical theory of which we were so justly proud because it allowed us to look behind the curtain, to watch the magnificent order of exact physical law coming forth from atomic and molecular disorder; because it revealed that the most important, the most general, the all-embracing law of entropy could be understood without a special assumption ad hoc, for it is nothing but molecular disorder itself.

The orderliness encountered in the unfolding of life springs from a different source. It appears that there are two different 'mechanisms' by which orderly events can be produced: the 'statistical mechanism' which produces order from disorder and the new one, producing order from order. To the unprejudiced mind the second principle appears to be much simpler, much more plausible. No a doubt it is. That is why physicists were so proud to have fallen in with the other one, the 'order-from-disorder' principle, which is actually followed in Nature and which alone conveys an understanding of the great line of natural events, in the first place of their irreversibility. But we cannot expect that the 'laws of physics' derived from it suffice straightaway to explain the behaviour of living matter, whose most striking features are visibly based to a large extent on the 'order-from-order' principle. You would not expect two entirely different mechanisms to bring about the same type of law -you would not expect your latch-key, to open your neighbour's door as well. We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics. For that is just what is to be expected from the knowledge we have gained of the structure of living matter. We must be prepared to find a new type of physical law prevailing in it. Or are we to term it a non-physical, not to say a super-physical, law?

[Federica]

Not directly an answer to any of the questions here but it might be valuable to contemplate the following phenomenon for those unfamiliar with it:

Thanks Cleric! A few notes, in case there are other neophytes like me who couldn’t properly understand the experiment as described in the video. I believe that for Youtube some basics had to be left out. Maybe obvious things for many, but not for me. I found the missing pieces here.


In particular, I was missing what a superposition is - the basic functioning of the bomb tester, before the bomb is introduced. It’s only one photon at a time, but in a sense it takes both paths. From the linked summary:

The behavior of elementary particles is very different from what we experience in our macroscopic world. Their observed behavior can be that of a wave or of a particle (see wave–particle duality), their wave-like behavior implies what is called "superposition". In this state, some properties of the particle, for example, its location, are not definite. In a superposition, any and all possibilities are equally real. So, if the particle could feasibly exist in more than one location, in certain senses that are experimentally useful, it exists in all of them simultaneously. The particle's wave can later be "collapsed" by observing it, at which time its location (or other measured property) at the moment of observation is definite.

Also this seems especially important:

To understand how this experiment works, it is important to know that unlike a dud, a live bomb is a kind of observer and that an encounter between the photon and a live bomb is a kind of observation.

Finally, the word “beam splitter” was confusing to me as a complete layperson. It doesn’t split anything, it only sends the photon either straight or at 90 degrees angle (but these either/or events are superposed probabilities simultaneously covered by the photon, in its undisturbed nature).



My initial thoughts on the experiment:

I think, in the end we can say that there is nothing weird with this experiment, if there is nothing weird with non-locality, so I would disagree with Sabine. I guess one can see it in two specular ways.


One way is, a live bomb (not a dead one) is an observer that creates the collapse of the photon’s wave-like behavior, full stop. It doesn’t create the collapse only in that 50% of cases when the photon happens to hit it. Once the live bomb becomes part of the world (part of the experimental box), bomb observes, no matter what. Its ability to react makes it into an observer. And the world has been constrained in such a way that maneuvering space, will and freedom are excluded from that reality: if/when the photon is not on the lower path, it must be on the upper path.

When we detect the photon in A, we know for sure the photon went the upper path. It means, it was forced to materialize there (somewhere) by a reactive observer (the live bomb) through its non-observation/non-explosion. Because non-observation, in such a constrained world, equals observation on the only alternative path. So, if the photon is detected in A, the photon was observed on the upper path, it was forced to collapse. And only an actionable bomb can have forced the collapse, simply by monitoring the only alternative possible. So it’s not weird. An active bomb has the quality of an observer no matter what, and observation creates wave collapse.


The other way to see it would be in terms of the live bomb/the observer being sucked up into the non-local reality of the photon. In this sense, it doesn’t matter where the bomb is positioned. Exploded and non-exploded bomb, are both equally real superpositions. Indeed, the authors of the experiment did say that the bomb is both exploded and not exploded:

...the photon, paradoxically does and does not interact with the bomb. According to the authors, the bomb both explodes and does not explode.[5] This is only in the case of a live bomb, however.

So they say it, and they even say that such state only pertains to an alive bomb. I believe a deeper explanation of this idea is precisely that: we can think of the experiment in terms of the live bomb/observer being sucked up into non-locality, so that the positioning of the bomb becomes irrelevant. What is crucial is only that the bomb is part of the world, and that it is alive. Because a live bomb has a reactivity that gives it a semblance of interactivity with the photon. Explosion is a symbol for life, ether. In the non-local world of the photon, an alive bomb is simply alive/explodable and one with the photon, connected with it. Therefore, this second take would be the atemporal and aspatial take on the experiment. Another way to put these two takes would be:


--> The second take (non-local environment, the live bomb is sucked up in the photon’s non-local nature) is the thought experiment level.

--> The first take (collapsed environment, the live bomb drags down the photon in space-time determinacy) is the lab experiment level.

[Federica]

Since Cleric has written on the nature of mathematical thought (from a spiritual perspective) previously and may be writing again on it in a few days, and since he clearly has a better grasp on such topics than I do, I would rather wait for his post. In the meantime, I asked him about this once and he gave the following response (I am only excerpting the first portion for now), which I'm sure he doesn't mind me sharing, perhaps as an introduction to what he will write later. Particularly the bold part indicates there is a great mysteriousness here, as there is with all space-free and time-free spiritual processes that project into our normal perceptual-conceptual spacetime, so we should be careful not to only seek explanations in chains of concepts. Ultimately everything comes back to the continual metamorphosis of cognitive states of being, which is something to be experienced and lived through with imaginative thinking rather than merely defined/described in concepts.

*** (Cleric wrote)

As we have spoken many times, we discover mathematical concepts within perceptions, which we have called foldnesses. There's soemething in common between a pair of apples, pair of stones, pair of hands. Now things become more mysterious when we consider these foldnesses in their relations. Imagine we take two baskets of apples and third empty one. Then we begin transferring apples from the first basket into the empty one while we keep track of the way foldness there changes - we're basically counting. When we're finished with the first basket, we go on taking apples from the second while continuing to keep the track of the foldness in the third. What we have performed with our will is practically an operation which we can call addition. Now the interesting thing is that we can repeat that operation with stones, pears and so on and as long as we begin with the same foldnesses in the baskets we always get the same foldness in the third. The even stranger thing is that we can lift that operation in our imagination and add imaginary apples. We say that we reach the mathematical concept when we intuit these meaningful qualities that are always the same no matter if we imagine apples, stones, fingers, etc.

Now why there are such lawful relations within the perceptual world and why our concepts can grasp these foldnesses is very mysterious question and we can easily go mad if we try to answer it. The reason would be that we try to find satisfactory answer within the relations of the concepts themselves.

For this reason, it's best if we can clearly differentiate the kind of planar thinking that simply moves through the inner relations of concepts, without trying to see deeper meaning. I would suggest that you try this approach first.

Basically it's all very simple. It's all about taking the time and really live through it. It all boils down to one simple thing - we're looking for thinking experiences that has within itself the rules for its transformation. This is really connected with the topic about 'creation out of nothing'. To grasp pure mathematical thinking you need to embrace the exact opposite - to move in thinking that is entirely determined by the laws through which it operates.

As a very simple example, imagine the following (I have given this example before). At any point you have three possible rules for action 1/ turn left 90 degrees, 2/ turn right 90 degrees, 3/ take a step forward. Now you can live through this in full body imagination or even try it out for real. Very soon you find out that these rules are not particularly exciting. Through them you can experience states that lie on a rectangular grid and that's all.

To get an idea of abstract mathematics, you have to imagine something similar. The natural numbers are like such states that can be traversed. In fact, There's such a function called the successor which is like the step forward. It basically transforms the present foldness state n into n+1.

Abstract mathematics is really the study of patterns in thinking space. For compactness, the rules above can be shortened (symbolized), for example, by <, >, -. Then we can type strings like <--->>--<->. Take something like ->->->->. Can you guess what it does? If you try to walk it you find out that it really leads you to the same starting state.

So in this way we lay down a symbolic cookbook recipe for moving through our imagined states. But take a note that the nature of thinking space has been implicit. We started with spatial imagination. The fact that the string above leads you to the same starting state comes from the implicit constraints of our imagination that we have accepted (we imagine the state as our spatial bodily state). But we can imagine completely different constraints and rules. Remember the example with non-Euclidian geometry where turning at right angles leads you not through four but through five rooms.

The secret to this is to decouple our thinking state from our ordinary intuitions. To make it a little clearer, let's devise a way of describing our state on the grid. We can do it thus: (x,y,d). Here x and y are our grid coordinates (think of the chess board letter/number coordinates) and d is the facing direction one of {n,e,s,w} (north, east, etc.). Let's say that our current state is (1,2,e). If we apply the ->->->-> operation we get the same state! If we apply >, we get (1,2,s) and so on. We have developed an elementary algebra We can call ->->->-> an identity operator because it doesn't change the state (in our algebra there are infinitely many such operators because there are infinitely many ways to walk around and get to the same state). Most algebras have identity operators. For example n + 0 or n * 1 all preserve the n state.

As simple as it is, it really underlies everything there is to abstract mathematics. It all boils down to identifying some attributes of the state (like our x,y,d) and then investigate how the state can be transformed by the possible operators. In the end it is really a thinking state.

Ok, thanks for posting it Ashvin. Not that I can see any direct connection between the quote and the question, but it’s certainly a useful introduction. Regarding any previously posted writings on this topic, I have read this one for now, found through the keyword “foldness”. Are there other important go-to posts on the forum?

Following the quote, my first thought is, we discover mathematical thoughts in perceptions, in particular as sort of supra-concepts. It feels like the mysteriousness of numbers can be ‘reduced’ to the mysteriousness of unit, of separation. And ‘normal’ concepts - in fact the concept of concept itself - comprise this quality of separation.

In more decohered, spatio-temporal terms, another concept that comes to mind is reproduction. Reproduction could be an important mathematical idea, since it’s the function that transforms one into two on the physical-etheric plane, generating separation from unity, while counting/adding is a more extended, more general function of ideal transformation.

In other words, the essence of mathematical thinking at the spiritual level seems to be connected with articulation of reality through unity of being in relation to the existence of separate units, while mathematical declination in the decohered world manifests as counting, adding, and other forms of interaction among units, in multiplicity and in worldly transformation in time. Maybe mathematical thinking can be seen as a scaffolding that conveys spiritual hierarchical organization to the level of intellectual thinking and thought-images and mediates between the two?

I know I am not following the advice to start by reflecting on the nature of mathematical relations without searching for deeper meaning, but I don’t really understand how to keep these steps separate. I do follow the example of planar, abstract math thinking. I remember it from the cell intelligence initial post:

But where do we go from there?

[AshvinP]

In other words, the essence of mathematical thinking at the spiritual level seems to be connected with articulation of reality through unity of being in relation to the existence of separate units, while mathematical declination in the decohered world manifests as counting, adding, and other forms of interaction among units, in multiplicity and in worldly transformation in time. Maybe mathematical thinking can be seen as a scaffolding that conveys spiritual hierarchical organization to the level of intellectual thinking and thought-images and mediates between the two?

Federica,

It is probably useful to first start with the question, what is thinking in general? As you know, thinking activity contains both a separating and an integrating function - it is the portal through which unified spiritual processes separate into distinct concepts-percepts for isolated analysis and also the portal through which those distinct concept-percepts are reintegrated into laws, archetypes, and principles, with the benefit of the new relationships discerned from the unique decohered perspective.

Mathematical thinking is a subset of this general thinking in which, as Cleric says, the rules or logic by which thinking transforms is explored. In that sense, it only becomes possible in its abstract modern form when thinking is able to observe itself (consciousness soul) and thereby formalize and predict its own activity. So here we are already lifting out from thinking governed only by the transformation of sense-perceptions to a more sense-free thinking, where concepts arrive from supersensible realms. But if we start with certain intuitive spatialized assumptions about the rules through which states of being can transform, then our mathematical thinking will be constrained to that spatial domain. If our intuitions can loosen from such rigid constraints, however, our mathematical thinking can become more imaginative and explore the transformation of states of being in time, independent of space (or in 'hyper-dimensional' space).

But, to be clear, this can only go so far as long we remain trying to model our thinking states using those same thinking states. Eventually, we need to surrender to the experience of the thinking activity itself, to intuitively sense the qualitative depth structure that animates our current states. Then our quantitative mathematical thinking is brought to a higher level from which it can really awaken to what it was always doing.

I know I am not following the advice to start by reflecting on the nature of mathematical relations without searching for deeper meaning, but I don’t really understand how to keep these steps separate.

I think the first step is to simply get a living feel for what is being discussed. So when Cleric says - "Imagine we take two baskets of apples and third empty one... What we have performed with our will is practically an operation which we can call addition." - we should actually live through this experience in our imagination. We usually take for granted that simply interpreting the meaning of the words is sufficient to understand the essence of what is being referred to, and then we start deriving conclusions from that surface meaning. Especially when it seems like such a simple set of observations and mathematical things we learned in grade school. But instead, we can assume the opposite - we have little idea what these words are pointing to and therefore we need to carefully live through each step, like we are curious school children learning about these things for the first time. We should trust that the lived through experiences themselves will become our teacher when the time is right, which could be the next minute, the next day, or the next week. Their deeper meaning will shine through when we are able to release our need to grasp at that deeper meaning.

I do follow the example of planar, abstract math thinking. I remember it from the cell intelligence initial post:

But where do we go from there?

From here we go to Part 2

*** (Cleric)

As simple as it is, it really underlies everything there is to abstract mathematics. It all boils down to identifying some attributes of the state (like our x,y,d) and then investigate how the state can be transformed by the possible operators. In the end it is really a thinking state. Basically we try to constrain the degrees of freedom of our imagination. For example, someone may decide to describe our state of being as (x,y,z,t,e) where we have three spatial coordinates, one time coordinate and 'e' for emotional state. It could take discrete values but more likely it would be a varying scale between sad and happy for example. Then one can think of different operators that transform that state in different ways.

All our foundational sciences have transformed into such abstract mathematics. QM for example, defines abstract space of states , where we have attributes like spin, magnetic moment and so on.





It is actually all very clear as soon as we give up trying to imagine what these numbers mean in reality When we look at the math itself it is in principle no different than our algebra, even if much more convoluted. In our algebra you can think of any combination (x,y,d) and that would be a valid state. From the above table you can also write down all (infinte) possible combinations (n,l,ml,ms). Then it is all about defining an additional attribute - the amplitude. Think of it as a clock arrow with length and direction. When you take all the infinite amplitudes for all possible states, you have the so called wavefunction. These arrows are determined through the Schrodinger equation, which is in principle not that different from the Fourier transform through which we find the needed arrows for drawing any curve we want. And now we come to point which no longer has any place in mathematics. The (squared) length of the arrows for each state is interpreted as the probability to find that system in that state upon measurement. The collapse itself is not part of the mathematics.

The peculiar thing about mathematical thinking is that even though we explore it in time by moving through our thinking states, the relations themselves are timeless. If you apply our identity operator today, the result will be the same also tomorrow. This allows us to think about the whole thinking space as something already present. For example, for our system we can ask questions like "Is there any pattern in strings of rules, which always return to the same state?" For instance, can we reach the same state if we have odd number of total turns <> in our string (no matter how many of each as long as the total is odd)? Now that's an example of pattern. Just by looking at a string, we may not be sure if it is identity operator but if we see odd number of turns we can be certain that it is not. This can usually be proved in some way by investigating what would happen if there's really an identity operator with odd turns. In most cases this leads to some contradiction which is taken as the proof that our assumption couldn't have been correct (thus its opposite must be true).

It is really this thinking in a more encompassing ways about the whole mathematical space that is more interesting. That's where it is also spoken about mathematical intuition. For example, in this case I just made up this odd rule. I'm not 100% sure that it's like that but on first glance, based on my overall feel for it, seems that it should be the case. So intuition in that sense shouldn't be taken as some magical faculty that is always right. It's really a sense of orientation in the thinking space of the rules. And by thinking space we shouldn't imagine metaphysical Platonic realms either. It's enough to focus on the concrete states and simply seek orientation for their transformations. My current understanding is that a vast majority of these abstract patterns, such as the Mandelbrot set, are something unique that can only be reached through following such abstract rules. It is of course a map of our thinking, but this particular kind of thinking is only possible when the spirit decoheres into intellect. In that sense, it's beautiful that we can explore such unique patterns of thinking. (if you're interested I can mention few words about how the Mandelbrot set is generated)

Now one important thing that very much interested mathematicians at the turn of the 20th century was to find such a mathematical system of states (mathematical objects) and rules which is so encompassing that it can capture consistently all known mathematics. Something like a unifying mathematical language from which all branches of mathematics are only more specific forms. I think the logic of this is much easier to grasp through Turing Machines.



The reason is because it's more easy to identify our thinking with the actions of the Turing machine. Then once again we can think more broadly about the patterns that these ideas exhibit. One such broad idea is that of the halting problem but maybe we can leave that for next time.

The important thing is that in the first half of the 20th century, through the work of Gödel, Church, Turing and others, we have practically reached the limits of thinking that seeks to grasp its state through some attributes and then explore how that state can transform through certain rules. The notion of universal Turing machine has been reached, which is such a machine capable of simulating any other conceivable Turing machine.





You may have heard of Conway's game of life (CGL). It is probably the most famous example of cellular automata. You have a rectangular grid (think pixels) where each pixels is either alive or dead (represented by the color). Every cell has 8 surrounding neighbors. At every frame of the simulation we go through every cell and its 8 neighbors and apply the following rules:

If a state is alive and has exactly 2 or 3 live neighbors, it stays alive.
If it is alive and has less than 2 or more than 3, then it dies (as if by loneliness or overcrowding )
If a dead cell has exactly 3 live neighbors it spontaneously comes to life.

You can experiment here:
https://conwaylife.com/

Hit the 'play' button and use the pencil tool to draw alive cells and see them transform by the rules.

Now the interesting thing is that these simple rules actually allow for a Universal Turing machine. For example, the following is a system that simulates CGL inside CGL



There are example where actual Turing machines are created. So the whole point is that as long as we have sufficient basic rules (Turing complete) we can mimic through them the behavior of any possible system and its operation as long as we find a way to encode it in our system.

The same thing holds also for the foundations of mathematics. In a way, we have reached understanding of what is possible with the kind of thinking that in one way or another seeks to describe its state as a combination of some attributes and then explores how the state transforms according to certain rules. Really, thinking is trying to model itself as a cellular automata. The interesting things happen when thinking begins not only to model some general thinking but when it tries to model its real time thinking. Then we come to the impossibility, where we feel as a dog chasing its tail. And here is of course the pinhole leading to higher order spiritual activity. But this requires that we let go of our desire to feel our thinking as the end result of computation. Actually, the problem is not that we see our thinking as an end result of something but that we insist on only representing that something within our thinking. As an analogy, if we take the CGL inside CGL and we imagine that the intellect is the simulated CGL, it feels it is impossible to be conscious within the foundational CGL. Instead, it tries to model a third level CGL that serves as the model of reality.