These are some reflections on what chaos means in the context of mathematics and physics. Chaos must be understood as the absence, or privation, of order, not as the opposite of order in any active sense.
To explore what chaos may mean from the mathematical point of view, we can consider an irrational real number between zero and one in its decimal expansion to try to represent a number representing true lack of order, that is, the ultimate random number. A rational number is not random, since its digits will repeat after a certain point. The ultimate random number will have two properties:
- Not Computable: There is no algorithm to determine the sequence of digits
- Normal: Every digit, and sequence of digits, is evenly represented in the decimal expansion.
Numbers such as √2 and π fail the first condition since there are mathematical formulas to compute the decimal expansion to any desired precision.
In the decimal (or any base) expansion of normal numbers, each digit will appear with the same frequency, i.e., 10%. Furthermore, each sequence of digits will also appear with its corresponding frequency. That is, 10 through 99, 100 through 999, and so on, will also appear 1% and 0.1% of the time respectively. √2 and π are believed to be normal, but there is no proof. The mathematician Gregory Chaitin defined a number Ω, Chaitin’s constant, that has both properties.
Condition 1 is necessary because an algorithm is the hidden order behind a seemingly random sequence of numbers. Condition 2 is necessary because complete chaos would have to include all possibilities.
In our random number, then, each digit is independent in the sense that its value does not depend on the digit, or sequence of digits, that precede it. Investigating this number, we will observe at some point the sequence of numbers from 1 to 1 million. This poses a dilemma. Do we conclude, then, that we have discovered a region of order within that alleged chaos, or are we convinced that it is truly random? This is not merely speculative as it has real world applications.
- In Intelligent Design theory, recognized patterns are presumed to result from a designer rather than random variation.
- In the search for extra-terrestrial intelligence, cosmic radio waves are scanned to look for patterns hidden within the white noise.
- In the multiverse theory of physics, all possible worlds exist and we just “happen” to live in one of them that exhibits the necessary degree of order to support human life.
- Then, there is the Infinite Monkey Theorem that claims that enough monkeys with typewriters, given enough time, will produce the works of Shakespeare.
We have previously asked this question about whether each moment in time is independent of any previous moment or if there is a deep connection between the past and the present. The first is chaos; the second may be either order or chaos deceptively ordered. There is no way, apparently, within a chaotic situation to determine if order is accidental or real.
Two of the conditions of manifestation are form and matter. Chaos can only be associated with prime matter, Prakriti, without property and infinitely receptive to any form. Matter, in this sense, can never “exist”, that is, it can never be a possibility of manifestation. Hence, Chaitin’s constant, is only a thought construction and not a reality. That is why Guenon says that at the heart of the Kali Yuga, where chaos reigns, the state of total disorder can never be reached.
Thus, form is a necessary condition of manifestation; it is transcendent to matter and we know it through our will and intelligence. I design, hence I recognize design; I communicate, hence I recognize a communication; I create, hence I recognize an artistic creation.
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It was a colloquialism, reflecting a feeling I sometimes have, of exasperation and astonishment at the ugliness and, well, chaos of the modern world. When I have the wrong-colored glasses on, I sometimes wonder if literally everything is going to fall apart. Perhaps it’s not a very insightful comment, but even those of us seeking the original Tradition exist in specific bodies with specific tendencies and paths, that result in specific emotional reactions at different stages of those paths.
If one is not seeing things clearly, then learning something that is indeed truthful can come as a great relief — thus heartening. Have you never traveled from error into truth and enjoyed the process? If what Cologero points out in this little article is SO self-evident that it has literally zero power to shed light for any of us, then I suppose it’s time for Cologero to stop writing them. However, at least for me, that is not the case.
Furthermore, I can’t claim that I KNOW the impossible as impossible. I read about Purusha and Prakriti; I meditate on it; but it’s not like I have succeeded in slaying the ego and manifesting the eternal in my moment to moment existence. I don’t suppose I would have much use for reading Gornahoor if I were already totally secure in all my understandings of Tradition.
Bhakti Anand Goswami mentions Meditations on the Tarot in his video:
Tarot & Ancient Symbols of God’s Personal Form – Bhakti Ananda Goswami
http://www.youtube.com/watch?v=-TBUn1Tog20&feature=plcp
He mentions the churning of the milk ocean as the “perturbation of prakiti”.
It’s not really heartening, as Prakriti is constituent to manifestation but requires Purusha to take on any qualities. Knowing the impossible as impossible ought to be emotionally neutral.
Don’t be misled by verbal similarity. I defined precisely what I meant by true chaos, in which there is no possibility of a hidden order, except incidentally. But I agree with you in this sense that a real disorder is not manifestable as “there is an ‘order’ that we simply don’t understand”.
“Chaos must be understood as the absence, or privation, of order, not as the opposite of order in any active sense.” I’m not sure that’s necessarily true. Much of mathematical chaos theory is about observing that there is an ‘order’ that we simply don’t understand (e.g. fractals and ‘strange attractors’). Also, related to your article might be Godel’s “Incompleteness Theorem”–that for any non-trivial formal system there will always be statements that can neither be proven true nor false. In other words, outside the light from the streetlight of, say, geometry, there will always be a geometrical darkness we can’t penetrate. (At least without cognitively stepping outside/above the geometrical system itself.)
“That is why Guenon says that at the heart of the Kali Yuga, where chaos reigns, the state of total disorder can never be reached.”
This is a heartening thing to ponder.