Philosophical Speculations

I am starting a new thread on the fourth dimension because I believe its exploration is in general of great help (and somewhat accessible) to developing the new mindset required by the times. In this sense, this thread could collect different lines of four-dimensional inquiry in the future. If nothing else, the fourth dimension seems helpful to at least figure that such a new mindset exists - and that it may stand as a solution to, and an elevation from, the stalemate in which human consciousness seems to be stuck nowadays, at so many levels - scientific, philosophical, societal at large.


At a basic level this exploration can work as metaphor: just as there are explorable conceptual/visual ways to figure the existence of a fourth dimension, so there are unsuspected, developmental ways to awakening to new cognitive perspectives at large - by/through/within which reality can be made one again, inner and outer.


At a more focused level, and beyond its metaphorical value, inquiry about the fourth dimension seems able to strengthen thinking activity in ways that are directly beneficial for the development of sense-free (and memory-free) cognition. This is because it invites the mind to produce and sustain thoughts out of itself (active, present-oriented thinking), rather than out of the comfortable and ready-made templates provided by the perceptions of the 5 senses and memory (passive, past-oriented thinking).


As seen before, Steiner spoke of the fourth dimension multiple times, and there are various approaches to it. One that is usually appealing to the many (thinkers) and not too esoteric in its first appearance, is the mathematical approach. For me personally this is a good exercise, since mathematical thinking is nothing I have particularly developed or used in my experience, other than in basic form or in applied/statistical form. To this end, I have found this recent video intuitive and very well done. Hopefully it can also help others ‘muscle up’ in one's thinking in a simple way, in one of the many possible directions.

Federica wrote: ↑Mon Aug 26, 2024 4:50 pm As seen before, Steiner spoke of the fourth dimension multiple times, and there are various approaches to it. One that is usually appealing to the many (thinkers) and not too esoteric in its first appearance, is the mathematical approach. For me personally this is a good exercise, since mathematical thinking is nothing I have particularly developed or used in my experience, other than in basic form or in applied/statistical form. To this end, I have found this recent video intuitive and very well done. Hopefully it can also help others ‘muscle up’ in one's thinking in a simple way, in one of the many possible directions.

Thanks, Federica. It is a very clear, accessible, and well-illustrated discussion. I have only watched Pt. I so far, but have already noticed how the conceptual discussion can serve as a great recursive metaphor for some core intuitive movements that are also explored in PoF (here I am using 'PoF' to stand in for all similar phenomenological explorations of spiritual activity). Instead of listing the correspondences, maybe it would be better to try a little exercise. I will list a few points made in the video and others can insert what they think is the most relevant passage of PoF that the former is metaphorically pointing to. Others could also add more points from the videos that they feel could be metaphorically mapped onto PoF and then yet others could find corresponding passages for those points.

12:20 - "How do we rotate an object from a space dimension to a time dimension? And wouldn't that process itself take time to occur?"

12:50 - "Where is the 4th dimension? The short answer is that it's perpendicular [or orthogonal] to our 3D Universe."

13:20 - "We might tell Freddie to imagine a 2D planar universe just like the one he lives in but is separate from his own, parallel to his own but slightly offset."

The point of this exercise is simply to get a feel for how diverse conceptual content, which we normally feel to 'belong to' their own separate fields of inquiry, can become recursive symbols for the same imaginative and intuitive movements that structure our knowing capacity. Even if we don't want to share our findings here, I think it is useful to try and notice these analogical correspondences when interacting with the content. We can get a deep sense of how modern imaginative inquiries across the board are all pointing in the same inward direction toward the intentional movements of our Intuitive core, i.e. spiritual science.

AshvinP wrote: ↑Wed Aug 28, 2024 7:20 pm Thanks, Federica. It is a very clear, accessible, and well-illustrated discussion. I have only watched Pt. I so far, but have already noticed how the conceptual discussion can serve as a great recursive metaphor for some core intuitive movements that are also explored in PoF (here I am using 'PoF' to stand in for all similar phenomenological explorations of spiritual activity). Instead of listing the correspondences, maybe it would be better to try a little exercise. I will list a few points made in the video and others can insert what they think is the most relevant passage of PoF that the former is metaphorically pointing to. Others could also add more points from the videos that they feel could be metaphorically mapped onto PoF and then yet others could find corresponding passages for those points.

12:20 - "How do we rotate an object from a space dimension to a time dimension? And wouldn't that process itself take time to occur?"

12:50 - "Where is the 4th dimension? The short answer is that it's perpendicular [or orthogonal] to our 3D Universe."

13:20 - "We might tell Freddie to imagine a 2D planar universe just like the one he lives in but is separate from his own, parallel to his own but slightly offset."

The point of this exercise is simply to get a feel for how diverse conceptual content, which we normally feel to 'belong to' their own separate fields of inquiry, can become recursive symbols for the same imaginative and intuitive movements that structure our knowing capacity. Even if we don't want to share our findings here, I think it is useful to try and notice these analogical correspondences when interacting with the content. We can get a deep sense of how modern imaginative inquiries across the board are all pointing in the same inward direction toward the intentional movements of our Intuitive core, i.e. spiritual science.

Thanks for the exercise, Ashvin (by the way, as I understood it, for now there is only Part 1 in the series, the subsequent parts will be published in the future). I am not sure I am getting the PoF exact passage you are pointing to, but the thinking gestures that try to figure that out are useful in any case. So I can start with the first sentence, and maybe someone else can resonate with the other ones.

"How do we rotate an object from a space dimension to a time dimension? And wouldn't that process itself take time to occur?"

I guess there are a few things to notice in the conceptual laboring expressed here. The point of departure in the video is that fourth dimensional reality exists as a mathematical concept. There exists therefore concepts of four dimensional objects, described, or rather symbolized, by mathematical formulas.

From there, the intellectual effort expressed in the reasoning aims to an experiential understanding of such objects - of the fourth dimensional realm. The attempt is to “visualize” something of this realm, necessarily going beyond our earthly, sense-based visualization capacity, limited to 3D. So the question at stake is: how to “visualize”, how to have a pictorial experience, of a reality that is true (we are sure it exists) and is “larger” than our normal spatial perception?

Now coming specifically to the red sentence, and the question of “time” as a possible candidate for this supersensible, but perceptible, expansion beyond familiar 3D space. To relax the tension to some extent, maybe we can let the label “fourth” fall. As seen in the video, we could just as well consider a flat, 2D object - a square - and ask whether the dimension “time” is a good candidate as an additional dimension to let the object expand and live into, that can support some form of pictorial grasping. (Similarly, we could take a one dimensional line, and explore whether adding the second dimension “time” makes it into an expanded and visualizable new object).

Let’s take a square. We can see that, if we visualize the square, and now let time flow, the experience would be perceptually expanded only if we make the square “move”, only if we animate the square in our imagination - that is, only if we make it evolve in relation to its imagined environment - out of our own decision and will. But if we decide not to, we would remain with the same static square during the time lapse of our observation, without any perception of added dimension. Or, looking closer, what would be added would be the qualitative “dimension” of our thinking applied to the square.

So: based on these considerations, is time a good candidate for a dimension in which mathematical objects, symbolized by a formula, can exist in a way that is visualizable for us? The short answer is yes (let’s not expand on this now), but the red sentence questions that. Since it reasons within the realm of mathematical (quantitative) dimensions, the objection is that an object existing, among other dimensions, in time dimension, doesn’t have an angle at which its time dimension relates to any other of its spatial dimensions. Since time, as a dimension or an axis, is not angled in any way, in relation to any of the 3D axes, it’s not possible to rotate an object out of its current dimensional state (1D, 2D, etcetera) into an additional time dimension. The square can't be rotated into time, to become 3D.
Rotation, as Cleric said somewhere, is a kind of powerful idea that allows expansion. By rotation out of itself, a segment generates a circle, and a circle a sphere. Rotation means leveraging the current state to expand in a new state. Indeed it’s a timely process, it occurs in time. However, time itself is not a state into which an object can be rotated into. Time is the evolving act of rotation itself. As such, it cannot act itself as a geometrical axis standing in some angled relation to other static (visualizable in space) axes. In this sense, the red sentence is correct: the rotation into a new dimension would indeed be a time phenomenon. More: the concept of rotation itself (from a segment to a circle for example) holds the key to break free from sensory, spatial perception of reality. It is movement in space, but of a kind that elevates out of current dimensionality (as opposed to sliding for example). So, rotation, by comprising both stillness and movement, past and future, makes a segment break free from 1D into 2D, for example. But rotation cannot make an object break into rotation. It doesn't make sense.

From here, I guess we can say that, although rotation as a qualitative idea is powerful, the gesture in the red sentence that wants a fourth dimensional axis to be angled in spatially significant relation to the other 3, leans toward a spatialization, or intellectualization, of that dimension. I have no idea how the reasoning will proceed in the upcoming videos, and I have not much explored the topic otherwise. However, in this initial thought of angle measurements for the purpose of visualizing 4D by analogy to sensory 3D space, we can recognize the intellectual effort of building a static picture of a mysterious reality as a composition of spatial building blocks provided by the sense of sight.

Starting from the mathematical concept, there seems to be an attempt to come up with an isolated picture of a standalone object that matches the concept, independent of our activity. In terms of PoF, one passage that comes to mind is the parabola example in Chapter V. There, it is explained how the mathematical concept of parabola is one with the phenomenon of a stone thrown in the air horizontally. It’s only our limited human organization that makes the naive observer understand the experience as complete without the concept of parabola. Similarly, here we can say that the abstract formula of a 4D object is one with its (supersensibly) perceivable picture, and when we stand in between them, trying to grasp the perceptual aspect of that reality, we should remain focused on our activity as it tries to connect the loose ends, rather than searching for standalone visuals.

Federica wrote: ↑Thu Aug 29, 2024 6:16 pm Starting from the mathematical concept, there seems to be an attempt to come up with an isolated picture of a standalone object that matches the concept, independent of our activity. In terms of PoF, one passage that comes to mind is the parabola example in Chapter V. There, it is explained how the mathematical concept of parabola is one with the phenomenon of a stone thrown in the air horizontally. It’s only our limited human organization that makes the naive observer understand the experience as complete without the concept of parabola. Similarly, here we can say that the abstract formula of a 4D object is one with its (supersensibly) perceivable picture, and when we stand in between them, trying to grasp the perceptual aspect of that reality, we should remain focused on our activity as it tries to connect the loose ends, rather than searching for standalone visuals.

Thanks for sharing these thorough thinking movements, Federica. I think you caught the symbolic thread quite precisely.

"How do we rotate an object from a space dimension to a time dimension? And wouldn't that process itself take time to occur?"

Another way to put it is in terms of the Catch-22 - it is the hand drawing a hand drawing a hand, etc... drawing a triangle, trying to catch up to its real-time drawing activity through convoluted perceptual models. The first PoF passage that comes to mind for me is Ch 3 in the discussion of how present activity can never observe itself as perceptual content. As soon as thinking tries to observe itself, the thinking doing the observing changes in the act of observation and the continually morphing real-time activity remains unobserved. It would have to split into two to observe its real-time activity (3rd person perspective) but, of course, such a perspective doesn't exist.

In this mathematical context, we are using the 4th Time dimension as a symbol for our imaginative activity like you said - "the evolving act of rotation itself". The author intuits the problem as well - the very 'dimension' we are trying to visualize through the rotation is being changed as we perform the rotation. By the time we derive a visual model of the 4th Time dimension, the latter has become something different than what is contained in the model. He has yet to understand it all as a symbol for his real-time mathematical activity and seems to be seeking a clever way to capture the 4th dimension, as an external entity, in our imagination (and his techniques are quite clever!). Nevertheless, such efforts are never wasted as long as there are some souls who intuit the only activity such efforts could possibly be pointing to and therefore use the perceptual models as artistic symbols for inner movements.

It's interesting how metaphor and literality coincide in these mathematical examples. If we were speaking of the perceptual content of rivers and plants, for ex., using the dynamics of that content to draw attention to intuitive movements, then we are dealing with more of a pure metaphor. It is still intuitive movements that animate the metamorphoses of plants and rivers, but the perceptual content and the inner movements that structure it are so out-of-phase that the former has become metaphorical. With this pure mathematical exercise, however, the perceptual content is a direct testimony to our real-time imaginative movements. Without those movements, the mathematical content simply wouldn't exist. Exploring that coincidence naturally leads us to the following observation:

The reason why it is impossible to observe thinking in the actual moment of its occurrence, is the very one which makes it possible for us to know it more immediately and more intimately than any other process in the world. Just because it is our own creation do we know the characteristic features of its course, the manner in which the process takes place. What in all other spheres of observation can be found only indirectly, namely, the relevant context and the relationship between the individual objects, is, in the case of thinking, known to us in an absolutely direct way.

And, on that note, I like the way the author framed the whole thing as, first and foremost, an exercise in changing our habitual ways of thinking about these things and trying to stretch our imagination into new inner frontiers. Hopefully, it dawns sometime soon that this sort of exercise is the very process by which reality is constituted and evolves.

by the way, as I understood it, for now there is only Part 1 in the series, the subsequent parts will be published in the future

Right, I figured that out when I was eagerly searching for Part 2 That became a sort of mini-exercise itself, to try and objectively sense the inner movements of 'impatience' and 'frustration' when my habitually expected on-demand YT content was not to be found.

AshvinP wrote: ↑Thu Aug 29, 2024 11:44 pm It's interesting how metaphor and literality coincide in these mathematical examples. If we were speaking of the perceptual content of rivers and plants, for ex., using the dynamics of that content to draw attention to intuitive movements, then we are dealing with more of a pure metaphor. It is still intuitive movements that animate the metamorphoses of plants and rivers, but the perceptual content and the inner movements that structure it are so out-of-phase that the former has become metaphorical. With this pure mathematical exercise, however, the perceptual content is a direct testimony to our real-time imaginative movements. Without those movements, the mathematical content simply wouldn't exist. Exploring that coincidence naturally leads us to the following observation:

The reason why it is impossible to observe thinking in the actual moment of its occurrence, is the very one which makes it possible for us to know it more immediately and more intimately than any other process in the world. Just because it is our own creation do we know the characteristic features of its course, the manner in which the process takes place. What in all other spheres of observation can be found only indirectly, namely, the relevant context and the relationship between the individual objects, is, in the case of thinking, known to us in an absolutely direct way.

Yeah, that big is the impact of sensation on the human organization, or let's say, the impact of the human organization on unitary reality.


"With this pure mathematical exercise, however, the perceptual content is a direct testimony to our real-time imaginative movements. Without those movements, the mathematical content simply wouldn't exist."


Without those movements, the perceptual content we connect to the river, or the plant, wouldn't exist either.
The difference is that the interconnected and holistic objective reality which we begin to know as “river” has a physical ramification (=it grants us existential meaning as dual beings by forcing us to split it in two within us), while the mathematical content doesn’t force us to split anything. In mathematical content, we are able to come into contact with it from the side of thinking alone. We can stay whole in its presence, which means we can pour our undivided thinking into it.
However, this still amounts to brain thinking, as long as we structure and animate our creative, in-principle sense-free, process by analogy to our apprehension of the sensory world - that is, spatially. We do this for example by rotating, sliding, projecting geometrical objects in a way that mimics what our eyes could follow if it were to happen in physicality. So the picturing is literal, as you say, and not metaphorical - because it’s 'sense-free enabled' thinking, if I can call it so - but it remains intellectual, as long as the sense-free potential is not leveraged, but rather collapsed, down into sensory similia.

Federica wrote: ↑Fri Aug 30, 2024 3:19 pm

AshvinP wrote: ↑Thu Aug 29, 2024 11:44 pm It's interesting how metaphor and literality coincide in these mathematical examples. If we were speaking of the perceptual content of rivers and plants, for ex., using the dynamics of that content to draw attention to intuitive movements, then we are dealing with more of a pure metaphor. It is still intuitive movements that animate the metamorphoses of plants and rivers, but the perceptual content and the inner movements that structure it are so out-of-phase that the former has become metaphorical. With this pure mathematical exercise, however, the perceptual content is a direct testimony to our real-time imaginative movements. Without those movements, the mathematical content simply wouldn't exist. Exploring that coincidence naturally leads us to the following observation:

The reason why it is impossible to observe thinking in the actual moment of its occurrence, is the very one which makes it possible for us to know it more immediately and more intimately than any other process in the world. Just because it is our own creation do we know the characteristic features of its course, the manner in which the process takes place. What in all other spheres of observation can be found only indirectly, namely, the relevant context and the relationship between the individual objects, is, in the case of thinking, known to us in an absolutely direct way.

Yeah, that big is the impact of sensation on the human organization, or let's say, the impact of the human organization on unitary reality.


"With this pure mathematical exercise, however, the perceptual content is a direct testimony to our real-time imaginative movements. Without those movements, the mathematical content simply wouldn't exist."


Without those movements, the perceptual content we connect to the river, or the plant, wouldn't exist either.
The difference is that the interconnected and holistic objective reality which we begin to know as “river” has a physical ramification (=it grants us existential meaning as dual beings by forcing us to split it in two within us), while the mathematical content doesn’t force us to split anything. In mathematical content, we are able to come into contact with it from the side of thinking alone. We can stay whole in its presence, which means we can pour our undivided thinking into it.
However, this still amounts to brain thinking, as long as we structure and animate our creative, in-principle sense-free, process by analogy to our apprehension of the sensory world - that is, spatially. We do this for example by rotating, sliding, projecting geometrical objects in a way that mimics what our eyes could follow if it were to happen in physicality. So the picturing is literal, as you say, and not metaphorical - because it’s 'sense-free enabled' thinking, if I can call it so - but it remains intellectual, as long as the sense-free potential is not leveraged, but rather collapsed, down into sensory similia.

Yes, generally agreed.

On the bold, we can experientially differentiate the perceptual content of natural processes from mathematical ones because, even if the particular form the natural processes take is tied to our imaginative activity, they have a sense of objective 'weight' that makes us feel like, even if we weren't there, the processes would still be unfolding. We can't feel the same way about the mathematical content, even if we are hardcore materialists (assuming we pay the least bit of attention to our inner mathematical activity) - it is self-evident that the mathematical symbols wouldn't exist in our consciousness if we weren't inwardly doing something. For the natural sensory content, that is not self-evident and, actually, people find it ludicrous to suggest the content wouldn't be there if we remained passive or simply disappeared.

We shouldn't dismiss that feeling, although we also shouldn't reify it into the thought that the natural world exists independently of our knowing perspective. The feeling points to the weight of intuitive movements that structure our knowing perspective which are much more transpersonal in nature than the imaginative movements by which we generate mathematical content. That is the 'interconnected and holistic objective reality' you mention. That reality was much more unified with the knowing perspective in primordial times at an instinctive level (Barfield's "original participation"), but through the evolutionary process, they became more and more out-of-phase. It is this divergent process that led to the existence of "metaphors". For ex., Barfield points out how all words for psychological processes that we use today can be traced back to words for outer physical appearances and processes.

https://www.rudolfsteinerelib.org/RelAu ... nation.php

Barfield wrote:Now, let us take a look at another group of words, a very much larger group this time, indeed an almost unlimited one. I am referring to all those words which go to make up what the nineteenth century utilitarian philosopher Jeremy Bentham called the “immaterial language.” In other words, I mean all those innumerable words in any modern language which do not refer to anything in the outside world at all, but only to the inner world of human feeling, of human thought — only to states of mind or mental events — hope, fear, enthusiasm, conscious, embarrass, humility, ambition, concept — you can go on reeling them off, any number of them, of course. If you take the trouble to look up the etymologies of these words, you will find that in every case either they or their predecessors in older languages from which we have taken them, at one time referred not only to states of mind or mental events but also to some thing or some event in the outer world; that is of course what one might call elementary etymology. Only this time it is not usually a matter of looking back just a few hundred years into the past. We have to take a much longer survey if we wish to observe the historical process to which I am not seeking to draw your attention.
...
Then you find Jeremy Bentham, hard-headed positivist Jeremy Bentham, in an essay of his also entitled "Language,” [it comes in section four of the essay], writing as follows: “Throughout the whole field of language, parallel to the line of what may be termed the material language, and expressed by the same words, runs a line of what may be termed the immaterial language. Not that to every word that has a material import there belongs also an immaterial one; but that to every word that has an immaterial import there belongs, or at least did belong, a material one.” When, therefore, we approach this immaterial language, these words which refer to the inner world only, we know that we have to do with words that at one time were words of the material language. We know that there has been a transition from the material language into an immaterial one.

Can we go still further and, at least in some cases, observe the transition taking place? The answer is that in some cases we can. You see, if in the case of any word of the immaterial language, we can lay our finger on a period in its history when the older material meaning had not yet evaporated, if I may put it that way, while the later immaterial meaning had already appeared, then we shall have located the transition itself.

But yes, the mathematical content is still metaphorical insofar as we have not inverted our perspective on it and treat it as referring to some apparently external reality akin to the natural world, employing the same mental habits that have developed from our interactions with the latter. That's why I like how the author's aim with these mathematical exercises is specifically to develop new mental habits, although time will tell to what degree that is successful in his case. All too often the old is treated as "new" when, in fact, it is simply the old dressed up in different clothing.

AshvinP wrote: ↑Fri Aug 30, 2024 4:24 pm Yes, generally agreed.

On the bold, we can experientially differentiate the perceptual content of natural processes from mathematical ones because, even if the particular form the natural processes take is tied to our imaginative activity, they have a sense of objective 'weight' that makes us feel like, even if we weren't there, the processes would still be unfolding. We can't feel the same way about the mathematical content, even if we are hardcore materialists (assuming we pay the least bit of attention to our inner mathematical activity) - it is self-evident that the mathematical symbols wouldn't exist in our consciousness if we weren't inwardly doing something. For the natural sensory content, that is not self-evident and, actually, people find it ludicrous to suggest the content wouldn't be there if we remained passive or simply disappeared.

We shouldn't dismiss that feeling, although we also shouldn't reify it into the thought that the natural world exists independently of our knowing perspective. The feeling points to the weight of intuitive movements that structure our knowing perspective which are much more transpersonal in nature than the imaginative movements by which we generate mathematical content. That is the 'interconnected and holistic objective reality' you mention. That reality was much more unified with the knowing perspective in primordial times at an instinctive level (Barfield's "original participation"), but through the evolutionary process, they became more and more out-of-phase. It is this divergent process that led to the existence of "metaphors". For ex., Barfield points out how all words for psychological processes that we use today can be traced back to words for outer physical appearances and processes.

Yes, I see your point, how you use the feeling of weight coming from sensory perception. Surely, various approaches may suit different people differently. For me it’s easier to distinguish mathematical from sensory perception by noticing that there is no difference between a remembered cube and a perceived cube, while remembering a plant and perceiving it are two qualitatively different experiences. Paying attention to the role played by the 5 senses is a more contrasted experience that doesn’t appeal to feeling as much. I prefer that, because the feeling of more substantial weight which we connect to sensory perception is indeed our standard, fully aliased feeling automatically connected to sensory perception in our materialistic times.


For this reason - although I agree we shouldn’t dismiss the feeling but acknowledge it, to start with - I prefer to try and transform it, or educate it, from feeling the weight of sensory perception (which requires no effort and results from the out-of-phase perspective you speak of) to feeling something of the non aliased nature of the reality existing ‘around’ a given punctual perception. For example with a plant, I would try to feel how the seemingly well defined contours of the object-plant start to melt in a larger perceptible environment, when we consider the manifold interactions of the object-plant. We can picture rhythms of soil, water, roots, air, sun, sap, growth, leaves, colors, insects, flowers, seeds, us, and so on, ‘around’ the plant. If we give all that a good ‘spin’ in our mind's eye, while we perceive the plant, we can get some feeling of how the plant we see in the moment is only a shadow trace - or a point of attraction we are bringing forth - of a super interconnected flow of becoming. That trace may feel like a blissful, super-condensed drop extracted from that punctual angle of the world becoming, in which we are reading the encoded harmony and beauty of nature, from one of the infinite possible perspectives.


I believe that cultivating feelings of this kind allows us to take advantage of the supportive, transpersonal, dense character of the reality we make contact with in natural perceptions, while bringing some willed thinking movements into it at the same time. In order words, feelings like these work as sort of ‘equalizers’ for the first person experiential flow. This helps build up the strength for sense-free thinking using a bit of the self-sustained, willed character experienced in mathematical perception, and a bit of the supported, transpersonal character of natural perception. Or at least that’s my belief - that we can do some smart training of thinking muscles in this way.

Federica wrote: ↑Sat Aug 31, 2024 2:55 pm Yes, I see your point, how you use the feeling of weight coming from sensory perception. Surely, various approaches may suit different people differently. For me it’s easier to distinguish mathematical from sensory perception by noticing that there is no difference between a remembered cube and a perceived cube, while remembering a plant and perceiving it are two qualitatively different experiences. Paying attention to the role played by the 5 senses is a more contrasted experience that doesn’t appeal to feeling as much. I prefer that, because the feeling of more substantial weight which we connect to sensory perception is indeed our standard, fully aliased feeling automatically connected to sensory perception in our materialistic times.


For this reason - although I agree we shouldn’t dismiss the feeling but acknowledge it, to start with - I prefer to try and transform it, or educate it, from feeling the weight of sensory perception (which requires no effort and results from the out-of-phase perspective you speak of) to feeling something of the non aliased nature of the reality existing ‘around’ a given punctual perception. For example with a plant, I would try to feel how the seemingly well defined contours of the object-plant start to melt in a larger perceptible environment, when we consider the manifold interactions of the object-plant. We can picture rhythms of soil, water, roots, air, sun, sap, growth, leaves, colors, insects, flowers, seeds, us, and so on, ‘around’ the plant. If we give all that a good ‘spin’ in our mind's eye, while we perceive the plant, we can get some feeling of how the plant we see in the moment is only a shadow trace - or a point of attraction we are bringing forth - of a super interconnected flow of becoming. That trace may feel like a blissful, super-condensed drop extracted from that punctual angle of the world becoming, in which we are reading the encoded harmony and beauty of nature, from one of the infinite possible perspectives.


I believe that cultivating feelings of this kind allows us to take advantage of the supportive, transpersonal, dense character of the reality we make contact with in natural perceptions, while bringing some willed thinking movements into it at the same time. In order words, feelings like these work as sort of ‘equalizers’ for the first person experiential flow. This helps build up the strength for sense-free thinking using a bit of the self-sustained, willed character experienced in mathematical perception, and a bit of the supported, transpersonal character of natural perception. Or at least that’s my belief - that we can do some smart training of thinking muscles in this way.

Right, I take your point that there are many ways to approach the experiential distinction between our intuitive movements in relation to pure thought-perceptions (like mathematical objects) and natural perceptions. The imaginative experiment you describe with the plant also sounds useful for becoming more sensitive to the broader temporal context in which the plant form appears, which we are intimately involved in bringing forth as well.

"Where is the 4th dimension? The short answer is that it's perpendicular [or orthogonal] to our 3D Universe."

I think this one reveals the author is intuiting how we need to seek the processes that explain the perceptual world, not within forms and processes of the perceptual world itself, but from a direction orthogonal to it. Of course, that direction could only be the inner conceptual activity that has reached this very intuition. In other words, the author needs a flash of insight that illuminates how his thoughts about the 4th dimension are also part of the "3D Universe" (perceptual world) and his intuitive activity that coheres these thoughts and reaches the insight that the solution comes from a perpendicular/orthogonal direction is the 4th orthogonal dimension.

The relevant PoF discussion is how our inner organization makes it so that half of the meaningful World content comes through our intuitions/concepts in a 'direction' orthogonal to the other half, the perceptual flow. That is illustrated with the parabola example you mentioned before.

I will make myself clearer by an example. If I throw a stone horizontally through the air, I perceive it in different places one after the other. I connect these places so as to form a line. Mathematics teaches me to know various kinds of lines, one of which is the parabola. I know the parabola to be a line which is produced when a point moves according to a particular law. If I examine the conditions under which the stone thrown by me moves, I find the path traversed is identical with the line I know as a parabola. That the stone moves just in a parabola is a result of the given conditions and follows necessarily from them. The form of the parabola belongs to the whole phenomenon as much as any other feature of it does. The spirit described above who has no need of the detour of thinking would find itself presented not only a sequence of visual percepts at different points but, as part and parcel of these phenomena, also with the parabolic form of the path which we add to the phenomenon only by thinking.

It is not due to the objects that they are given us at first without the corresponding concepts, but to our mental organization. Our whole being functions in such a way that from every real thing the relevant elements come to us from two sides, from perceiving and from thinking.

AshvinP wrote: ↑Sat Aug 31, 2024 9:03 pm "Where is the 4th dimension? The short answer is that it's perpendicular [or orthogonal] to our 3D Universe."

I think this one reveals the author is intuiting how we need to seek the processes that explain the perceptual world, not within forms and processes of the perceptual world itself, but from a direction orthogonal to it. Of course, that direction could only be the inner conceptual activity that has reached this very intuition. In other words, the author needs a flash of insight that illuminates how his thoughts about the 4th dimension are also part of the "3D Universe" (perceptual world) and his intuitive activity that coheres these thoughts and reaches the insight that the solution comes from a perpendicular/orthogonal direction is the 4th orthogonal dimension.

Hopefully it's how you say, but the statement is also an established way to frame the concept of 4D space in mathematics. I believe, simplified, it's the mathematical description of a 4D axis.


13:20 - "We might tell Freddie to imagine a 2D planar universe just like the one he lives in but is separate from his own, parallel to his own but slightly offset."

Here we can perhaps say that understanding "parallel" is half way to, or on the way to, understanding "orthogonal". "Parallel" is the generic opening to something unfamiliar and new. "Orthogonal" requires rotation and creates perspective (angle).

Federica wrote: ↑Sat Aug 31, 2024 9:22 pm

AshvinP wrote: ↑Sat Aug 31, 2024 9:03 pm "Where is the 4th dimension? The short answer is that it's perpendicular [or orthogonal] to our 3D Universe."

I think this one reveals the author is intuiting how we need to seek the processes that explain the perceptual world, not within forms and processes of the perceptual world itself, but from a direction orthogonal to it. Of course, that direction could only be the inner conceptual activity that has reached this very intuition. In other words, the author needs a flash of insight that illuminates how his thoughts about the 4th dimension are also part of the "3D Universe" (perceptual world) and his intuitive activity that coheres these thoughts and reaches the insight that the solution comes from a perpendicular/orthogonal direction is the 4th orthogonal dimension.

Hopefully it's how you say, but the statement is also an established way to frame the concept of 4D space in mathematics. I believe, simplified, it's the mathematical description of a 4D axis.

Yeah, it's unlikely that this approach by itself will awaken those who engage in it to what their thinking is instinctively doing in that process. For that to happen, it is likely that their karmic destiny needs to at least bring them into contact with some esoteric stream.

Mostly it's helpful for us to survey these developments, to try and resonate with how conducting intuitive activity in tight feedback with the concepts that result from its movements will always lead the thinker into the domain of something like PoF. It will always lead thinking gestures to probe the etheric spectrum of more integrated spiritual activity, regardless of what specific field of inquiry is involved. When people take their cues from the conceptual phenomena themselves, letting the latter speak to them and guide their intuitive movements, rather than getting diverted by modern assumptions and prejudices, they will basically develop a phenomenology of spiritual activity without knowing it. I think that is especially the case in the domain of pure mathematics, which is very literally the exploration of present thinking states and their metamorphoses. Others like us can use these symbolic phenomenologies to deepen and enliven our orientation, and in a roundabout way, that will also be for the benefit of those who still remain asleep.

13:20 - "We might tell Freddie to imagine a 2D planar universe just like the one he lives in but is separate from his own, parallel to his own but slightly offset."

Here we can perhaps say that understanding "parallel" is half way to, or on the way to, understanding "orthogonal". "Parallel" is the generic opening to something unfamiliar and new. "Orthogonal" requires rotation and creates perspective (angle).

Right, it's explicitly an imaginative exercise, so that's always good. For me, it resonates with the PoF imagination of the 'relationless aggregate' of sensory impressions. This is not something we will ever find in our first-person thinking experience, just like Freddie would never find a 'parallel' spatial universe, but the imagination serves a very important function. It helps us become more sensitive to how higher dimensional realities, i.e. higher cognitive activity, structure the perceptual flow with its lawful qualities. Again I think this is an example of how pure intuitive thinking movements will always probe the etheric, realizing that imaginative effort is needed to reach into unexplored ideal territory.