Martin_ wrote: ↑Tue Nov 30, 2021 10:55 pm
Yes. Totally cognitive crack. I do wonder, since they haven't been around for long in our perceptual world, what kind of effect they have had on our situation since their introduction. Then again; They have been available to discover in Nature for a long time.
I would say at this time fractals work primarily in the aesthetic domain, in the sense Jeffrey speaks of it. They face us as something which rings some mysterious strings deep in us but our intellect simply works in completely different wavelengths at this time, and thus can't grasp this mysterious appeal cognitively.
The purely visual aspect of the fractals and their comparison with natural forms (like broccoli) is only the most superficial side of the story. Yet it is also the side that is grasped by the intellect. That's why at this time it's difficult to use fractals for metaphors of the structure of inner space, because they immediately produce purely spatial conceptions in the intellect. Thinking is in the blind spot and imagines some fractal spatial structures. Ultimately it comes to a point where it has to ask "OK, but what am I within this structure?" And we're once again up against hard problems.
To understand the deep nature of fractals we must understand things not only spatially but also temporally. Yes, the Cosmic Mind has temporal structure. The GR's block universe has something true about it as far as time is concerned, in the sense that from the highest perspective all states of being - past and future - exist as simultaneous potential. Where the GR picture goes astray is that is presents a picture of matter/energy and curved spacetime as the foundation of reality (which is really only abstract mathematical structure in the mind). In the case of reality this must be found as something living, in the way we find the meaningful relations between our own contents of consciousness.
Here's one example how we can use fractals as a metaphor for what we can experience in higher cognition. We know that the copies of the Mandelbrot shape are found everywhere along the filaments.
The bulbs around the main cardioid have specific orbital periods which reflect in the fact that different bulbs have filaments with different number of spikes. Above it's shown two small Mandelbrots, one taken from the filaments with three spikes, the other - with seven spikes.
Even though the Manelbrots look the same, we can see that one is 'made of' three-spikes filaments, the other of seven-spikes. If we zoom even more in the Mandelbrots, they have their own bulbs, their own filements but all of them are 'made of' those three- or seven-spikes respectively.
What does this has to do with consciousness? Let's build a metaphor. We can imagine that a single thought is like a small Mandelbrot. This thought may have some specific meaning, for example "one". Yet this thought never exists in isolation. Could we think this thought if we were not a human being with properly developed cognition? The thought always exists deeply embedded in Cosmic
context. If we think the thought now and then again few seconds later, even though its meaning is generally the same (the shape of the Mandelbrot is almost the same) the
context is different. Different filaments press into the Mandelbrot shape and give it its form.
Many things will become clear if we begin to pay attention that our thinking is always embedded into context. Of course, before we can pay attention to this, we must first pay attention that we at all think, and this is big enough challenge in itself for modern people. But assuming that we're conscious of our thinking metamorphoses, the next step is to become more and more aware of the conscious context. Only in this way we can gradually overcome abstract thinking. The phantom layer of the intellect is produced precisely when thinking hops from Mandelbrot to Mandlebrot but all of this exists as a floating layer of cognition, completely self-contained.
Ashvin spoke in his music essay about the liminal spaces. What we speak of here is practically the same thing. The space between thoughts is not empty, it's full of the contextual filaments. The meaning of the idea "one" is the same every time (in the same way we experience the same idea of the Mandelbrot shape when we see its different instances) but the thought-form (the Mandelbrot shape) is never absolutely the same. For example, if we are sad, we're in one type of context - say, four-spikes. Then if we think "one" it's the same general Mandelbrot shape but its 'made of' four-spikes. If we're happy, the same thought will be made of other number of spikes filaments.
The point is that gradually our consciousness should lift itself from the purely abstract. To live in the purely abstract is to hop from Mandelbrot to Mandelbrot, to arrange them in the most varied configurations and imagine the world-in-itself through these configurations. When we do philosophy, when we choose our ontological primes, it's like we're saying: "I'm taking this and this Mandelbrot shapes, I place them one here, on there. This is for me the world". So unwillingly we have once again drawn a picture of the Kantian divide as it manifests in its spiritual reality. Abstract thinking cares only for the general shapes of the Mandelbrots in which it experiences the general meaning. We move away from abstractness and approach reality when we understand that when we think the Mandelbrots, each on of them, even if having the same general shape (and thus reflecting the same general meaning/idea), the thought-forms exist deeply embedded into a spiritual context. We approach reality when we stop pretending that with our thoughts we exist in completely independent layer of reality, where we try to imitate the world through arrangements of Mandelbrots.
When we meditate in the way that is appropriate for today's developing consciousness, it is precisely the goal to gradually become aware of the liminal context by virtue of which the intellectual shape of the thought can at all exist. We pick the meaningful image for meditation and place it at the center of our consciousness. Initially it looks only like a Mandelbrot shape floating in vacuum, that is - abstract thought/image. But the deeper our concentration goes the more we begin to perceive the meaningful context within which the thought at the center exists. Our life situation, our spatial and temporal state, our feelings, goals and so on, they all form the filament web within which the Mandelbrot thought is embedded.
So that's the moral of the story. First we become aware that every time we think a thought - even if it reflects the same timeless idea - the thought-form is shaped by unique constellation of filaments. Normally we're completely unaware of this spiritual context. That's why thinking becomes abstract. Thoughts race in a phantom layer of cognition which it seems is completely opaque to reality. As long as we think within this layer our "I" feels to be completely disconnected from reality (or simply illusionary). When we grasp a thought and begin to concentrate our activity on it, around it begins to expand the living and unique context which presses into and gives the shape of the small Mandelbrot form. In this way thinking expands and we begin to understand in a panoramic way the invisible landscape through which we normally move. The great difficulty for imagining this, is that the landscape is not spatial but temporal. When we're conscious there, our moment 'now' expands and we understand the living ideas that unite a little more of the past and the future in a meaningful whole. The Imaginative panorama is not something that we build out of mechanically arranged Mandelbrots. It's the opposite - it's the living flow withing which the Mandelbrots are constricted. Interestingly, as the panorama expands we also sense the potential for all other Mandelbrots in the filaments. We experience cognitively the whole panorama but within it there is the potential to reduce it to small Mandelbrots. This is how Imaginative cognition is being translated into concepts that can be communicated - exactly in the way it's being done now. It is also the reason why Imaginations can be perfectly well thought through with normal thinking. When we experience livingly the small Mandelbrots, we're moving along the same filaments from which they have been initially extracted. In this way, through thinking we're touching our way through the invisible landscape and we gradually gain intuition of its 'geometry'. It's a powerful metaphor but not easy to grasp - just as the the filaments are 'made of' small Mandelbrots, so we can say that Imagination is not something that we grasp as a 'thing' but is the infinite variety of thoughts which can describe its inexpressible essence. Here we're touching upon a very fundamental mystery but I'll leave if for another time or the post will have to double in length.
Through this metaphor we can also see why mystical meditation (which dissociates from spiritual activity) remains sterile. It can live in the filaments through feeling but the thoughts (small Mandelbrots) simply dissipate and become no different than any other phenomena. Ultimately we're faced with impenetrable Imaginative wall, which we encompass with powerful religious feelings but the world of thoughts has no place in this state. The world of the filaments becomes not only religiously felt but cognitively known when we rise along the gradient of meaning, which shapes the context giving shape of the individual thought.
The same things can be explained with simpler words. The fractal concepts make great material for metaphors but in general they are too complex. The intellect becomes lost in the details of this complexity and forgets that it's all an image of higher order dynamics. For this reason we should use simpler metaphors at first. But when we break away from the phantom layer and begin to experience that our thoughts are only the tip of a spiritual iceberg, then fractals will find their renaissance.
Although I suspect the above metaphor might have been too abstract to follow by most, I hope that those who succeeded, can appreciate the way in which through transfigured thinking we must grow into the spiritual organism of reality, of which we otherwise experience only floating Mandelbrots against the background of perceptions.