AshvinP wrote: ↑Fri Oct 13, 2023 7:04 pm
By the way, if we are looking for some concrete visual image for how this 4th-dimensional step of 3-dimensional objects 'coinciding' occurs, like we had for the previous steps, I don't think we will really find it. This step can be described by abstract mathematics, since it occurs purely in the stream of (qualitative) time, but I think the only visuals we can get are what Steiner presented in that lecture, or perhaps what was presented in the video series on imaginary numbers.
Thank you! Your illustrations are clear, I can follow the well written connections. I’ve now listened to the lecture again. Steiner also suggest the fourfolded terms: we can’t perceive the fourth dimension because we ourselves are 4d beings. Hence we easily perceive up to 3d, in the same way that a 2d triangle-being, for instance, would only recognize existence of lines, 1d, within its space of perception. Therefore, fourth-dimensional is the nature of our perception-cognition itself, which is why it’s a tough task to wrap our head around it and get a sense of the real nature of the World Content. So the type of effort we make through PoF Part 1 is similar to the attempt to grasp the meaning of 4d. In one case, we work on phenomenological terrain (which is of 3d nature anyway) in the other, we work in symbolic, mathematical terms. In your analogies, we are on yet another possible 'way’, that of the overarching grand architecture of reality that can be initially apprehended indirectly, through clairvoyant accounts, and can illustrate the other two approches. through analogy.
If we epitomize the fundamental unity of reality as: knowing = being = doing, maybe we could associate each of these ‘moods’ with the three approaches. Maybe PoF Part 1 is more like a doing, the symbolic-mathematical approach is knowing, and your illustrations of the higher worlds' organization is like timeless being.
But in the same way that we can strive all the way through the given of experience to touch reality, and that we can develop clairvoyance to directly ascend to the analogies you have traced, I believe the mathematical mode of understanding also can be pursued in itself, with the same intention. That the sphere in the example symbolizes our I-consciousness incorporating itself is insightful, but for me I know an additional step of intuitive mathematical kind is required, otherwise the analogy remains a standalone parallel. I understand that we can't find a visualization in 3d space that would account for the dimensional step up. Still, from my side there is something left to conceptualize-intuit. Clearly that connecting intuition is with you, otherwise you wouldn't have formulated the analogies, and I don’t think there’s more you (or anyone) could say to help. I only feel that I should go further on these mathematical tracks, before switching to the alternative tracks of analogy.
In other words, I want to make sense of the examples in the lecture - why those in particular? Beyond the symbolism of the initial and final states, as you have explained, how are the thought-exercises supposed to symbolize the transformation between states, and what do a point brought within a sphere and a left glove on a right hand have in common? Surely these cues are supposed to elicit recognition of some common feature.
So far, the most insightful visualization for me has been the straight segments of growing lengths, made into bigger and bigger circles, by connecting their edges. The longer the segment, the bigger the circle, and the more imperceptible the curvature applied to the segment, until an infinitely long segment (a line) acquires the 2d quality of circularity, by being locally imagined as portion a circle of infinitely big size. In this way, circularity gives the line a way to ‘come back from its infinity’, and so to encompass ‘direction’, that is, growth, movement. I guess the same applies to a sphere versus a plane. A plane can be locally understood as (a plane is) the surface of an infinitely big sphere. With this knowing, the plane ascends to 3d level, or we could say, it discovers 3d nature within its 2d constitution. This enables the plane, from that higher standpoint, to encompass not only ‘vectors’ of growth/movement, but also self-contained forms and geometrical patterns of any sort - forms with unique character. Similarly, a 3d-shaped being should be able to push its boundaries against its 4d confines and so become fully operational in its 3D environment. For example, a sphere-being could be realized as an infinite sphere volume and its nucleus (potential) at the same time, and so it would become able (from that 4D outlook) to fully apprehend the whole volume of 3D world content and its interconnected dynamics, through the tension between manifestation and potential streaming from within and without the space. And here I should pause for now, before I bring complete chaos to my inner spheres