This is mind blowing. I think that it also illustrates what we're talking about and how difficult it is to convey concepts through writing and symbols. The Hilbert's Hotel thought experiment is one way to think about the concept of infinity using mathematics and logic. It delights and surprises when we get it, but having experienced a sense of infinity in the past, I can say that both experiences differ. Now, you can take the idea of infinity and use different arrangement of symbols to convey the idea. In this case poetry:
“To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.””
― William Blake
I enjoyed this poem when I first read it, but I never "experienced it" or "grasped its meaning" until I programmed a psychedelic session with poetry and experienced a sense of infinity in this timeless moment. Only then, I felt that I truly understood that poem. And it blew my mind to the extent that I felt a ecstatic bliss when I read it again while under the influence of psychedelics. But here we have another conundrum, now I'm trying to use words to convey the meaning and experience of that internal psychological experience. Another room in Hilbert's Hotel. That is, I'm trying to use words to convey my understanding of Hilbert's Hotel by using words written centuries ago, so that I can use more words to explain an internal state to try to convey my meaning using more words. I keep moving from room to room, in a manner of speaking. It never ends and hence it's truly infinite (or fractal to use even more words and concepts) 🙃
Great that you read it!
The nature of fractals and how we visualised Mandelbrot gives the impression of infinity, but if you look, it is a constant repetition of the same process and is not transferable to reality, i.e. not to the all-sensory experience, limited to seeing alone. When I was watching it, I always had the impression of being somehow cheated when I was zoomed from the big to the small and suddenly ended up in the big again. I don't know, it was like ... stumbling ... ugh, unable to express myself here.
Because mathematics is something you can transfer from reality to the imagination, you can do such great things with it as fractals and there is no limit to mental flying.
Extasy is very seductive, isn't it. You just have to not let it wear you out. HeHe.
As for poems, the way I see it, they are a high form of contemplation and a very successful short form for what other people write epic long books for. It's truly a high art, yes.
I am in awe with minds who can come up with something like Hilbert's Hotel. I am too uneducated for that kind of logic. But glad that others were and are not. It's fantastic. I am always thrilled when I can find sources like that.
It actually is transferable to reality. The repetition is call iteration and yes, it is self similar at different magnitudes but always slightly different. The fact that this mathematical concept is transferable to reality is the key aspect of it. Now we know that seemingly random processes like clouds, pine trees, forests, coastlines, heartbeats, brain signals, a head of lettuce, seashells, waves, even our conversation, and a multitude of non-linear dynamic processes, perhaps everything in the universe, contain fractal properties. This is the revelation of Chaos theory. It's not about chaos but order. An order that exists in that which we thought was chaos.
... or so I understand
I see what you are getting at.
Thanks for the addition.
This chaos (seemingly random processes), as one may have viewed a brain, cloud formations, etc., I myself did not perceive as chaos, but in fact as a hidden order in the supposed disorder that I so assumed. Even a chaotic conversation and formations of peoples I would also include, yes.
Computer-controlled calculation makes it possible to simulate such processes in fast forward. Since the human being (and all things) but passes through his earthly existence by means of natural ageing, this discovery is a very elegant and beautiful method for spiritual understanding. For example, a nine-month pregnancy or the growth of a broccoli, while generally the same, is slightly different from one individual to another. Sickness then also is order (this is something very hard to accept though). And also death is order.
This is why there's a lot of work being done with quantum computing. This technology works on different principles than linear computation. It will transform society in incredible ways.