Steiner and Schrodinger's Equation

[AshvinP]

That's why I used to keep asking you how is that the phenomena that we experience always follow the constraint of the Schrodinger equation? What is the nature of this constraint mechanism, how exactly does is work, where did it originate from? We can ask the same question about any other constraints, for example the one you mentioned about four hands.

I've wrote an essay some months ago but felt that it should be posted in the proper context.

The difficulty is that people expect to understand the Schrodinger equation in itself, they expect some intellectual knowledge that will fit everything and say "Aha, now I get it". But understanding the equation and all of science for that matter, demands that we lift our investigations a level higher.

What have scientist been doing from the time of Galileo onwards? They have been thinking about the canvas of perceptions. They were seeking the thoughts (mostly mathematical) whose thought out dynamics would correlate with the dynamics of perceptions. The Schrodinger equation was the result of seeking this quantification of perceptions further and further. It is similar to painter who tries to replicate the appearances of Nature through more and more precise paint strokes. Scientists art through math. They distill more and more refined math relations, whose dynamics mirror the perceptual content.

In the Schrodinger equation we're doing something akin to Fourier analysis of the perceptual world. Perceptions are thought of as matter waves and the equation basically filters out only that sum of elementary waves, which fit the energy constrains. We do something similar in Fourier analysis where from the infinite possible frequencies, we filter out only those whose sum yields the desired waveform.

So science practically develops a glorified math-painting algorithm. Does this mean that scientific equations have nothing to do with reality, just like a blob of paint has nothing to do with the real and living Mona Lisa? Now this is the tricky part because the question in itself secretly suggest a very specific mode of thinking about reality. Unless we recognize that we need to alter the way we see and think about reality, it will be very difficult to get intuition of what science is doing.

As said, scientists in the last few centuries have been sculpting thoughts about perceptions. Today we are at a very interesting threshold where we should recognize that this thought-sculpting activity is the actual process of reality. So far, the default intuition has been that we're enclosed soul spheres, which arrange puzzles of thoughts about reality-in-itself (that which is beyond the personal sphere). We imagine that the 'real' laws of the Universe work outside consciousness and our thoughts are only their symbolic replicas. The challenge today is to realize that our flow of states, which we can most easily be conscious of when we focus on how through our thinking we meaningfully transition from 'frame to frame' of existence, is the actual first-person perspective law of the Universe. Our first-person willed spiritual activity is in itself a limited aperture of the spiritual force which arts reality and not a side-effect which presents opaque intellectual pictures of reality-in-itself.

When we see things in this way, we begin to realize that through our scientific endeavors so far we've been unknowingly accumulating 'experimental data'. We've been blindly flowing with the activity of the Cosmos, which projected an opaque intellectual picture of itself. Now the Cosmos realizes that that which it has been modelling through intellectual puzzle pieces is the objectified and deadened precipitation of the actual first-person process of reality. So the Cosmos has been precipitating thoughts as nails and hair shed from a living body. Now the "I" of the Cosmos realizes that true reality is the activity which has been secretly weaving behind this shedding process. This process can no longer be modelled but must be lived.

For this reason, the Schrodinger equation and all other equations have so far been secretly informing us about the dynamics of the living spirit which has been thinking them. In certain sense all scientific thinking has been the build up of helping wheels, of a rigid scaffold, which has the potential to awaken us to our living spiritual activity. If we continue to ask questions like "How come the Schrodinger equation describes reality so well?" it simply means that we implicitly support the dualism between the mental picture of reality-in-itself and the first-person experience of that reality, which is its living law.

...

These are the real constraints of existence. It's not an artificial law created by some god, it's the self-evident impossibility to be in any other way. All conceivable states can be considered to be equally possible for our next state but the vast majority would never feel as proceeding from our current, thus the continuity of consciousness would be broken. This can be explored even further through the rhythmic time waves which is connected with the Schrodinger equation and why perceptions seems to be decomposable onto matter waves of different frequencies but that will be a topic for another time. For now it's enough to consider that from the relative perspective of a state, all other states seem to interfere within it either constructively or destructively. In this sense, our current state of being is one where those states which we call our past life, interfere constructively, while all other states (not only 'ours' but any conceivable state of any being) interfere destructively and thus seem non-existent. In this sense, the absolute state is one which sees the whole infinite potential as constructive interference.

I came across a short, seemingly well-reasoned article that argues Steiner actually proposed an equivalent of Schrodinger's equation 6 years in advance of the latter. It would be interesting to hear Cleric and/or Eugene's thoughts.


https://www.yumpu.com/en/document/read/ ... waldorfnet

Schrodinger's equation is nothing but a diffusion equation with an imaginary diffusion constant. The different paths along which diffusion with an imaginary constant occur do not necessarily lead to an additivity of observed effects (as would be the case with a real diffusion constant), but can instead result in destructive interference. This is symptomatic for a new phase in physics, intimately related to the mathematics of complex numbers. The characteristic features of imaginary diffusion have been viewed by many pioneers in the field as the very essence of quantum mechanics.
...
But back to 1920. It was well known that the heat equation can equally well be used to describe the diffusion processes, for example in gases. In fact, the heat equation is mathematically equivalent to the diffusion equation; the concentration of the diffusing substance there plays the role the temperature played in the heat equation. Steiner repeats in the 13th lecture what has been a major theme in the lecture series: “the gaseous realm manifests pictures of the realm of heat”. Indeed, the diffusion is generally pictured as if the gaseous substance were diffusing in space. Diffusion shows the signature of heat.

But then Steiner goes on to propose considering diffusion with an imaginary diffusion constant, saying that this shows the signature of the effects of light. At the time, that was a revolutionary idea of the first order, something totally new.

Thus the 3rd differential equation that Steiner writes down on 12 March in the year 1920 is not only formally equivalent to Schrodinger’s equation. Apart from the fact that the value of the constant is not specified as a number related to Planck's constant, it is Schrodinger’s equation. In particular, Steiner’s physical intuition - considering a diffusion process with an imaginary constant as something intimately related to light and matter - corresponds to the physical intuition of physicists like Feynman.

[Cleric K]

I came across a short, seemingly well-reasoned article that argues Steiner actually proposed an equivalent of Schrodinger's equation 6 years in advance of the latter. It would be interesting to hear Cleric and/or Eugene's thoughts.


https://www.yumpu.com/en/document/read/ ... waldorfnet

That's interesting, thanks! I'll examine the article and the original lecture first.

[Cleric K]

I came across a short, seemingly well-reasoned article that argues Steiner actually proposed an equivalent of Schrodinger's equation 6 years in advance of the latter. It would be interesting to hear Cleric and/or Eugene's thoughts.


https://www.yumpu.com/en/document/read/ ... waldorfnet

That was an interesting exploration. The article author’s line of reasoning is very clear and the parallel between what Steiner has given and the Schrodinger equation can be seen. But it is my personal opinion that Steiner introduced the imaginary term (√-1) in an attempt to express a quite different intuition. Actually, he is very direct about this in the lecture.

In a nutshell, he says that trying to reduce Nature over a single quantifiable axis can never lead to reality. We have spoken about this in different contexts as the fallacy of reductionism. His major goal is to point attention that in the living phenomenological experience we have different qualities.



He places the three ethers on an axis but he also tries to explain that they cannot be conceived simply as three intervals of the same quantitative dimension. He expresses that by way of using mathematics in a quite unorthodox way.

So when we consider W as a positive quantity here (or we might consider it negative) then we have to consider the corresponding chemical effect as:

W=-c*q*du/dx*dt

The foregoing equation corresponds to the chemical effect, and this one:

W=+c*q*du/dx*dt

corresponds to the heat effect.

https://rsarchive.org/Lectures/GA321/En ... 12a01.html

Here the plus and the minus sign are used in a way that would make most mathematicians and physicists angry. To make a comparison, it would be like suddenly putting aside the accepted mathematical notions and assigning some poetic meaning to the plus and minus sign. But this is precisely what Steiner wants to point attention to! We can never advance if our intellect remains in the same flat quantitative plane. He tells us that in our inner experience these intervals are qualitatively different, not simply quantitatively.

Then we come to the middle part – light. His goal is to show that it is also qualitatively different. But now, so to speak, we have run out of metaphors. We have used up the plus and minus metaphors and we have nothing left for the third one. Thus he cleverly introduces a novel third metaphor which basically runs orthogonally to the real axis (minus infinity to plus infinity). This is the imaginary axis, which allows numbers to become two dimensional, so to speak. It allows us to rotate the ordinary numbers into another dimension.



For this reason, as a metaphor it made sense to Steiner to use the imaginary coefficient, which so to say rotates the heat equation from the minus-plus axis, orthogonally into a third direction, which should imaginatively depict a third quality.

The author of the article suggests that in this way Steiner has produced the Schrodinger equation but in my view this is an overstatement. Even though it mathematically resembles what he has given, as explained above, he gave it for quite specific reasons which are nowhere to be found the way the Schrodinger equation works. It still works entirely in the flat quantitative axis (which is the only way a strict intellectual theory can work).

There’s something in the Schrodinger equation which Steiner never intended in this particular lecture. To understand that we should keep in mind that most classical theories work with scalar and vector fields of real (not complex) numbers. An example of a scalar field is, for example, temperature. Temperature can be described as a field T(x, y, z, t). For every point in space x, y, z and every moment of time t, the field has some specific magnitude (the temperature) which is simply a number (a scalar). Vector fields are similar but instead of a single value, for every point we have an 'arrow' with a certain direction and length. This is useful, for example, to quantify the magnetic field. For that we need not only a magnitude. It is not enough to say “The field is so and so Teslas at this point”. We have also to describe its direction. It is as if we can place a 3D compass at every point in space and write down the orientation of the needle in the z, y and z directions.

Schrodinger did something different because his wavefunction was like a field which could take complex magnitudes in each point in space. It is as if at every point we have not only a temperature but that temperature has a ‘phase’. This is crucial for the possibility that these wavefunctions can interfere. It is as if out of phase temperatures interfere destructively (cancel each other), in phase temperatures add up.

I think it is clear that Steiner’s exposition has nothing to do with using the imaginary numbers for such ends. As a matter of fact, as said, this complex wave function still belongs to the flat quantitative space. The fact that we use imaginary numbers doesn't invite any different qualities in the mind of mathematicians. Thus Steiner would say that such a use of the equation fails to address the very essence of what he has been talking about.

Yet, the Schrodinger equation and interference is still a powerful picture, even though it doesn’t yet address the question of different qualities. I readily admit that for me the inner experiences of the different ethers are not in the least clear. In fact, I’m very tempted to project everything on the same quantifiable axis. I think it is an important task to find a way to this differentiation of qualities. Unfortunately, I don’t see a way of that emerging by starting from the flat quantity. That would be like drawing figures on a flat sheet of paper and hoping that at some point the figures will magically protrude from the paper. Thus we can’t help but try to find the qualities directly. Then we’ll be able to understand the minus, plus and √-1 as symbols for these qualities. Yet it is interesting if it would be possible to make the gap between the quantitative plane and the orthogonal qualities as tight as possible. Currently the intellect still feels that it has to abandon too much and take a leap of faith. It would be very exciting if we find a way where the intellect’s thoughts can rise up into qualitatively different imaginations without such a big leap but only through smaller, more comfortable steps.

[AshvinP]

I came across a short, seemingly well-reasoned article that argues Steiner actually proposed an equivalent of Schrodinger's equation 6 years in advance of the latter. It would be interesting to hear Cleric and/or Eugene's thoughts.


https://www.yumpu.com/en/document/read/ ... waldorfnet

That was an interesting exploration. The article author’s line of reasoning is very clear and the parallel between what Steiner has given and the Schrodinger equation can be seen. But it is my personal opinion that Steiner introduced the imaginary term (√-1) in an attempt to express a quite different intuition. Actually, he is very direct about this in the lecture.

In a nutshell, he says that trying to reduce Nature over a single quantifiable axis can never lead to reality. We have spoken about this in different contexts as the fallacy of reductionism. His major goal is to point attention that in the living phenomenological experience we have different qualities.



He places the three ethers on an axis but he also tries to explain that they cannot be conceived simply as three intervals of the same quantitative dimension. He expresses that by way of using mathematics in a quite unorthodox way.

So when we consider W as a positive quantity here (or we might consider it negative) then we have to consider the corresponding chemical effect as:

W=-c*q*du/dx*dt

The foregoing equation corresponds to the chemical effect, and this one:

W=+c*q*du/dx*dt

corresponds to the heat effect.

https://rsarchive.org/Lectures/GA321/En ... 12a01.html

Here the plus and the minus sign are used in a way that would make most mathematicians and physicists angry. To make a comparison, it would be like suddenly putting aside the accepted mathematical notions and assigning some poetic meaning to the plus and minus sign. But this is precisely what Steiner wants to point attention to! We can never advance if our intellect remains in the same flat quantitative plane. He tells us that in our inner experience these intervals are qualitatively different, not simply quantitatively.

Then we come to the middle part – light. His goal is to show that it is also qualitatively different. But now, so to speak, we have run out of metaphors. We have used up the plus and minus metaphors and we have nothing left for the third one. Thus he cleverly introduces a novel third metaphor which basically runs orthogonally to the real axis (minus infinity to plus infinity). This is the imaginary axis, which allows numbers to become two dimensional, so to speak. It allows us to rotate the ordinary numbers into another dimension.



For this reason, as a metaphor it made sense to Steiner to use the imaginary coefficient, which so to say rotates the heat equation from the minus-plus axis, orthogonally into a third direction, which should imaginatively depict a third quality.

The author of the article suggests that in this way Steiner has produced the Schrodinger equation but in my view this is an overstatement. Even though it mathematically resembles what he has given, as explained above, he gave it for quite specific reasons which are nowhere to be found the way the Schrodinger equation works. It still works entirely in the flat quantitative axis (which is the only way a strict intellectual theory can work).

There’s something in the Schrodinger equation which Steiner never intended in this particular lecture. To understand that we should keep in mind that most classical theories work with scalar and vector fields of real (not complex) numbers. An example of a scalar field is, for example, temperature. Temperature can be described as a field T(x, y, z, t). For every point in space x, y, z and every moment of time t, the field has some specific magnitude (the temperature) which is simply a number (a scalar). Vector fields are similar but instead of a single value, for every point we have an 'arrow' with a certain direction and length. This is useful, for example, to quantify the magnetic field. For that we need not only a magnitude. It is not enough to say “The field is so and so Teslas at this point”. We have also to describe its direction. It is as if we can place a 3D compass at every point in space and write down the orientation of the needle in the z, y and z directions.

Schrodinger did something different because his wavefunction was like a field which could take complex magnitudes in each point in space. It is as if at every point we have not only a temperature but that temperature has a ‘phase’. This is crucial for the possibility that these wavefunctions can interfere. It is as if out of phase temperatures interfere destructively (cancel each other), in phase temperatures add up.

I think it is clear that Steiner’s exposition has nothing to do with using the imaginary numbers for such ends. As a matter of fact, as said, this complex wave function still belongs to the flat quantitative space. The fact that we use imaginary numbers doesn't invite any different qualities in the mind of mathematicians. Thus Steiner would say that such a use of the equation fails to address the very essence of what he has been talking about.

Yet, the Schrodinger equation and interference is still a powerful picture, even though it doesn’t yet address the question of different qualities. I readily admit that for me the inner experiences of the different ethers are not in the least clear. In fact, I’m very tempted to project everything on the same quantifiable axis. I think it is an important task to find a way to this differentiation of qualities. Unfortunately, I don’t see a way of that emerging by starting from the flat quantity. That would be like drawing figures on a flat sheet of paper and hoping that at some point the figures will magically protrude from the paper. Thus we can’t help but try to find the qualities directly. Then we’ll be able to understand the minus, plus and √-1 as symbols for these qualities. Yet it is interesting if it would be possible to make the gap between the quantitative plane and the orthogonal qualities as tight as possible. Currently the intellect still feels that it has to abandon too much and take a leap of faith. It would be very exciting if we find a way where the intellect’s thoughts can rise up into qualitatively different imaginations without such a big leap but only through smaller, more comfortable steps.

Thanks, Cleric, for addressing the argument very clearly. Your reasoning here makes sense to me.

The only reason I still feel like Steiner may have been exploring a similar intuition as Schrodinger has to do with the etheric space's quality of 'superposition' or simultaneity of states of being. Particularly with Light, we have discussed before how, from the perspective of the being of Light, all space collapses into a 'point' and it is at all places at once.

From my completely lay perspective, Schrodinger's take on quantum mechanical states was quite similar. For ex. the 'cat in a box' thought experiment where the being of the cat spans the states of both dead and alive until collapsed into one or the other by intellectual observation. Or from the Wiki on his equation:

https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

The Schrödinger equation provides a way to calculate the wave function of a system and how it changes dynamically in time. However, the Schrödinger equation does not directly say what, exactly, the wave function is. The meaning of the Schrödinger equation and how the mathematical entities in it relate to physical reality depends upon the interpretation of quantum mechanics that one adopts.

In the views often grouped together as the Copenhagen interpretation, a system's wave function is a collection of statistical information about that system. The Schrödinger equation relates information about the system at one time to information about it at another. While the time-evolution process represented by the Schrödinger equation is continuous and deterministic, in that knowing the wave function at one instant is in principle sufficient to calculate it for all future times, wave functions can also change discontinuously and stochastically during a measurement. The wave function changes, according to this school of thought, because new information is available. The post-measurement wave function generally cannot be known prior to the measurement, but the probabilities for the different possibilities can be calculated using the Born rule.[23][48][note 4] Other, more recent interpretations of quantum mechanics, such as relational quantum mechanics and QBism also give the Schrödinger equation a status of this sort.[51][52]

Schrödinger himself suggested in 1952 that the different terms of a superposition evolving under the Schrödinger equation are "not alternatives but all really happen simultaneously". This has been interpreted as an early version of Everett's many-worlds interpretation.[53][54][note 5] This interpretation, formulated independently in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a multiverse composed of mostly independent parallel universes.[56] This interpretation removes the axiom of wave function collapse, leaving only continuous evolution under the Schrödinger equation, and so all possible states of the measured system and the measuring apparatus, together with the observer, are present in a real physical quantum superposition. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we do not observe the multiverse as a whole, but only one parallel universe at a time. Exactly how this is supposed to work has been the subject of much debate.

Most physicists probably think of the 'many-worlds' above in a very externalized, physical, quantiative-mechanical way, rather than superimposed states of ideational be-ing that share a common Center with our own ideational activity. 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. Of course, Steiner explores how the etheric space consists of a superposition of states of being, or a 'time-organism', for any given organic 'system' in many different contexts. For ex. the 'death spectrum' that is experienced when the etheric body separates out from the physical sensory body. So that is nothing new.

But that, in this particular lecture, he decided to explore the imaginative qualities of the etheric in terms of unique mathematical equations, seems quite suggestive to me, especially since one equation happened to greatly resemble Schrodinger's. Is any of this reasoning sound or am I just looking for and drawing connections that aren't really to be found?

[Cleric K]

But that, in this particular lecture, he decided to explore the imaginative qualities of the etheric in terms of unique mathematical equations, seems quite suggestive to me, especially since one equation happened to greatly resemble Schrodinger's. Is any of this reasoning sound or am I just looking for and drawing connections that aren't really to be found?

There’s no doubt that these intuitions were very alive in Steiner. Actually, as far as I can tell, he did put more emphasis on the temporal nature of the higher worlds in his later years. For example, in ANTHROPOSOPHY, AN INTRODUCTION he speaks concretely that the astral body can’t be conceived as spatial but he likened it to a comet whose tail spans into the time before conception. Thus, in a sense, the astral body exists simultaneously in the present but also in the time before conception, just like the comet’s tail spans different points in space simultaneously. To grasp the astral body we have no choice but encompass a great interval of time weaved of rhythmic metamorphoses.

To be sure, the physics of the nineteenth and the early twentieth century are most unconductive for expressing higher realities. They deal with quantified sensory frames and portray things in such a way that everything needed for the transition into the next frame is present in the previous – all we need is to apply the rules of transition. But as we know, we can never penetrate the depth of reality without some understanding like that of the Time-Consciousness spectrum, where spiritual ideation extends around the now moment and represents so to speak the curvature within which the frames transition.

There’s no doubt that Steiner has been seeking the concepts through which he could incarnate such intuitions. Alas, at that time the established physics provided very little of these concepts.

I’m quite sure that if he could witness the developments of QM he would make great use of it as a metaphorical language, much like we attempt to do today.

It is simply my feeling that in that particular lecture he didn’t introduce the imaginary coefficient in anticipation that this would lead to something like superposition or as a way to point to that intuition. It seems the focus of the lecture was to emphasize that we can’t grasp reality without the different qualitative domains. There’s no doubt in my mind that he was desperately trying to find the conceptual language for things like superposition and apparently he attempted to do this on various occasions, for example through the introduction of the death spectrum image, it’s just that I don’t think in this lecture he was specifically trying to do that. But of course, I may be wrong.

[AshvinP]

But that, in this particular lecture, he decided to explore the imaginative qualities of the etheric in terms of unique mathematical equations, seems quite suggestive to me, especially since one equation happened to greatly resemble Schrodinger's. Is any of this reasoning sound or am I just looking for and drawing connections that aren't really to be found?

There’s no doubt that these intuitions were very alive in Steiner. Actually, as far as I can tell, he did put more emphasis on the temporal nature of the higher worlds in his later years. For example, in ANTHROPOSOPHY, AN INTRODUCTION he speaks concretely that the astral body can’t be conceived as spatial but he likened it to a comet whose tail spans into the time before conception. Thus, in a sense, the astral body exists simultaneously in the present but also in the time before conception, just like the comet’s tail spans different points in space simultaneously. To grasp the astral body we have no choice but encompass a great interval of time weaved of rhythmic metamorphoses.

To be sure, the physics of the nineteenth and the early twentieth century are most unconductive for expressing higher realities. They deal with quantified sensory frames and portray things in such a way that everything needed for the transition into the next frame is present in the previous – all we need is to apply the rules of transition. But as we know, we can never penetrate the depth of reality without some understanding like that of the Time-Consciousness spectrum, where spiritual ideation extends around the now moment and represents so to speak the curvature within which the frames transition.

There’s no doubt that Steiner has been seeking the concepts through which he could incarnate such intuitions. Alas, at that time the established physics provided very little of these concepts.

I’m quite sure that if he could witness the developments of QM he would make great use of it as a metaphorical language, much like we attempt to do today.

It is simply my feeling that in that particular lecture he didn’t introduce the imaginary coefficient in anticipation that this would lead to something like superposition or as a way to point to that intuition. It seems the focus of the lecture was to emphasize that we can’t grasp reality without the different qualitative domains. There’s no doubt in my mind that he was desperately trying to find the conceptual language for things like superposition and apparently he attempted to do this on various occasions, for example through the introduction of the death spectrum image, it’s just that I don’t think in this lecture he was specifically trying to do that. But of course, I may be wrong.

I am following your line of reasoning here. Do you think it makes a difference how we pose the question? In other words, we could pose it two different ways - (1) did Schrodinger's equation reflect the qualitative superposition that is characteristically experienced in the etheric space, which directs the transition of physical states 'from above'?, or (2) did Steiner's lecture with certain mathematical diffusion equations anticipate the Schrodinger equation IF the latter were to be raised from the flat quantitative space into the vertical qualitative space, i.e. the equation is taken more as a symbolic tool for pointing to qualities of the etheric space?

I think we could safely answer (1) in the negative, for the reasons you have outlined. What I am still wondering about is (2). It seems that any discussion of the etheric space necessarily implicates the quality of superpositioned states of being. Previously you characterized the function of Steiner's use of the imaginary coefficient as follows:

Then we come to the middle part – light. His goal is to show that it is also qualitatively different. But now, so to speak, we have run out of metaphors. We have used up the plus and minus metaphors and we have nothing left for the third one. Thus he cleverly introduces a novel third metaphor which basically runs orthogonally to the real axis (minus infinity to plus infinity). This is the imaginary axis, which allows numbers to become two dimensional, so to speak. It allows us to rotate the ordinary numbers into another dimension
...
For this reason, as a metaphor it made sense to Steiner to use the imaginary coefficient, which so to say rotates the heat equation from the minus-plus axis, orthogonally into a third direction, which should imaginatively depict a third quality.

Based on the context of the lecture, there is no doubt that the above is an accurate characterization of Steiner's intentions with the equations. Are we able to get more specific here on what this 'third quality' of the Light ether might be, in Steiner's thinking, and what, if any, relation there is between that quality and the orthogonal rotation that he uses via the imaginary coefficient? Or are the mathematical metaphors simply unable to serve such a function? Steiner seems to point towards the concrete possibility of gaining that differentiated resolution of the etheric space through qualitative mathematics.

Something real is at the basis of the formula for W. Let us speak of this as heat ether. Likewise something real is involved when we change the positive signs of the heat formula to negative ones, and here we speak of the chemical ether. Where our formulae involve imaginary numbers, we speak of the light ether. You see here an interesting parallelism between thinking in mathematics and thinking within science itself. The parallelism shows how we are really dealing not so much with an objective difficulty but rather with a subjective one. For the purely mathematical difficulty arises of itself, and independently of the science of external things. No one would think that a beautifully built lecture could be delivered on the limits of mathematical thinking, similar to the one du Bois-Reymond delivered on the limits of knowledge of nature. At least the conclusions would be different. Within mathematics, unless the matter slips us because it is too complicated, in this realm of the purely mathematical it must be possible to set up a completely formulated expression. The fact that one cannot do this hangs together with our own relative lack of maturity. It is unthinkable that we have here an absolute shortcoming or limit to human knowledge. It is extremely important that you hold this before your minds as a fundamental. For this shows us how we cannot apply mathematics if we wish to enter reality unless we keep in mind certain relations. We cannot simply say with the energeticists, for instance, “a given quantity of heat changes into a certain quantity of chemical energy and vice versa.” That we cannot do, but we must bring in certain other values when a process of this kind takes place. For the necessity of the case constrains us to see as essential not the quantitative mechanical change from one energy to another but rather the qualitative aspect of the transformation. This is indeed to be found along with the quantitative.

[Federica]

I am following your line of reasoning here. Do you think it makes a difference how we pose the question? In other words, we could pose it two different ways - (1) did Schrodinger's equation reflect the qualitative superposition that is characteristically experienced in the etheric space, which directs the transition of physical states 'from above'?, or (2) did Steiner's lecture with certain mathematical diffusion equations anticipate the Schrodinger equation IF the latter were to be raised from the flat quantitative space into the vertical qualitative space, i.e. the equation is taken more as a symbolic tool for pointing to qualities of the etheric space?

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?

[AshvinP]

I am following your line of reasoning here. Do you think it makes a difference how we pose the question? In other words, we could pose it two different ways - (1) did Schrodinger's equation reflect the qualitative superposition that is characteristically experienced in the etheric space, which directs the transition of physical states 'from above'?, or (2) did Steiner's lecture with certain mathematical diffusion equations anticipate the Schrodinger equation IF the latter were to be raised from the flat quantitative space into the vertical qualitative space, i.e. the equation is taken more as a symbolic tool for pointing to qualities of the etheric space?

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?

By the way, to present something that may or may not be related to this particular question, I came across the following video series on imaginary numbers which I found very helpful and stimulating. If one doesn't want to watch all of them, I would at least watch the last 3 (starting with 11 - "wandering in 4 dimensions"). The whole historical progression of the mathematical inquiries is fascinating and I think these videos can be used as great imaginative tools to contemplate how the intellect strives for a mathematical way to encompass spiritual reality. I think it also helps elucidate what Steiner was doing with imaginary numbers in his lecture.

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.

[Cleric K]

I am following your line of reasoning here. Do you think it makes a difference how we pose the question? In other words, we could pose it two different ways - (1) did Schrodinger's equation reflect the qualitative superposition that is characteristically experienced in the etheric space, which directs the transition of physical states 'from above'?, or (2) did Steiner's lecture with certain mathematical diffusion equations anticipate the Schrodinger equation IF the latter were to be raised from the flat quantitative space into the vertical qualitative space, i.e. the equation is taken more as a symbolic tool for pointing to qualities of the etheric space?

Ashvin, sorry I couldn't reply in time and now I'll have to leave town for few days. Not that I have some well-cut answer to your questions but at least we can try to reflect together on questions like - what we are really doing when we think mathematically? What do we expect to achieve? What is possible in what mode of cognition and so on. I'll write as soon as possible.

[Federica]

I am following your line of reasoning here. Do you think it makes a difference how we pose the question? In other words, we could pose it two different ways - (1) did Schrodinger's equation reflect the qualitative superposition that is characteristically experienced in the etheric space, which directs the transition of physical states 'from above'?, or (2) did Steiner's lecture with certain mathematical diffusion equations anticipate the Schrodinger equation IF the latter were to be raised from the flat quantitative space into the vertical qualitative space, i.e. the equation is taken more as a symbolic tool for pointing to qualities of the etheric space?

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?

"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?”


PS. Thanks, I enjoyed the video on imaginary numbers.