Representation, Algorithmic Complexity, and Quantum Mechanics
How is representation related to the three global paradigms of unity, complexity, and harmony?
A key underlying issue in global paradigms is the standing problem of representation: what is real? Plato addressed this problem in terms of his theory of forms, in which he postulates that all our experiences are shadows of shadows of the true form. In Meno, an early Platonic dialog, he is already formulating this concept by moving the real definition of virtue beyond our grasp. In the Amduat, an Egyptian tomb text, representation is found in terms of numinal quantities, the gods, each one a part of our psyche in manifestations of archetypes, as Kacie grasped immediately and pointed out. In this sense the gods in the Amduat are useful mental representations, not explanations of natural phenomenon, any more than our beloved stories and films serve that purpose. What kinds of representations are we using in science? Humanity spent a long time transitioning from inner, complex representations as we find in the Amduat to unifying representations as begin in Plato and culminate in Grand Unified Field Theories in physics, as we see in the standard model of particles and fields. Likewise, the attempt to use survival of the fittest and Darwinian evolution to explain so much of biology is another example of an attempt at a unifying theory.
In fact, science has been tremendously successful at providing clarity in the paradigm of unity. Recently this paradigm has been challenged by the advent of complexity. Complexity includes features like emergent phenomena, hierarchies of scale, connectivity, and yes, chaos. Measures of complexity include Kolmogorov or algorithmic complexity, which measure complexity by the length of the representation, in particular the computational resources needed. So for example even though pi is an infinite bit string, since it can be calculated from just a few lines of computer code, pi is not very complex. Likewise, many kinds of chaos and fractals are not complex in this sense. On the other hand the internet, DNA, consciousness, and many other phenomena do not appear to be representable in a simple algorithm, or even by iteration over that algorithm. Scientists still hope that such complex phenomena will come down to equations, and it is hard to prove otherwise. But for the moment it appears that complexity is common in the universe, does not appear as any obvious result of fundamental physical law, and cannot be represented by a simple algorithm in most cases. Thus the paradigm of unity (science through the mid to late twentieth century) is giving rise to a new paradigm of complexity now. Perhaps this paradigm is not that of the Amduat. However, we can understand some basic concepts in the Amduat scientifically.
First, unity, a single state, has entropy zero. For the Egyptians and the Sumerians this state is nothingness, uninteresting. Only diversity gives rise to life and interest, to the plethora of gods, representing the complexity of the human mind, found for example in the Amduat. Complexity has continued as a philosophical and religious paradigm in Hinduism and Indian cultures today. Complexity is re-appearing naturally in the sciences and it may be that we need a new paradigm to understand it, one which relies less on grand unified field theories and more on diversity.
Second, we now know that quantum logic is more efficient at solving certain problems, in particular factoring large numbers (Shor's algorithm). So although any problem may be represented by binary logic (yes/no or true/false), in fact some are more efficiently represented by quantum logic, or other forms of probabilistic logic, called modal logic in philosophy. The Amduat prefers to avoid dichotomies like yes/no in favor of multiplicity. It is a system of thought, albeit in a language and format we cannot relate to very well today, which emphasizes modal logic over binary logic. There are several manuscripts of Egyptian mathematical proofs (Reisner papyrus, Rhind mathematical papyrus, Akhmim wooden tablets), and one finds many interesting theorems in them, with correct reasoning: however, the approach to those theorems is different from ours.
Coming back to representation and what is real, quantum mechanics has provided very strong evidence that at some level reality is non-local and probabalistic. Every time we test quantum mechanics, it does even better. As Deborah pointed out, even the many worlds interpretation has now become a mainstream possibility, with serious considerations in physics of the universe as one possibility in an infinite multiverse. A century ago none of us would have imaged a probabilistic non-local representation of reality would be meaningful, let alone accurate and useful enough to build digital computing technology from. What will we find out in another century? What might a new investigation of complexity teach us to see?
I leave the discussion of harmony, a paradigm employed and enjoyed in China, comprising ~1/4 of the world's population, for another post.
What I’ve gathered from this post is that even the paradigm of complexity is becoming quite complex to understand. The modern paradigm of complexity arose from building blocks that were/are being integrated into a single rhizomatic mass of knowledge with many twists and turns. For example, the Grand Unified Field Theories in physics was assembled over time as one scientist understood one force and another scientist found another subatomic particle. Noticeable on the poster are gaps in the Grand Unified Field Theories such as the lack of the existence/observance of the graviton.
ReplyDeleteIn regards to what is real and how representation plays a role, science uses observance to prove existence. Many scientists and researchers must “prove” a new concept or idea with several characterization techniques; it is not enough to have just one IR spectrum or one TEM image. To produce a good paper having a chance at being in a high impact journal, one must have several figures showing the same thing. When three different characterization techniques agree, the hypothesis proposed is supported and believable.
As papers are being published every day with novel ideas, a new understanding of complexity must take place in the form of different paradigms. I propose that these paradigms are moiety and integrality. Our modern paradigm of complexity arose from understanding pieces of the puzzle; this is moiety. Sometimes we cannot grasp the whole picture; and in order to understand any complex thing, we must break it down to its parts and investigate on a local level. These parts may not seem to be related, but as Lincoln stated, “Only diversity gives rise to life and interest”.
When we start to see patterns between the moieties, we can start to bring it all together as the Grand Unified Field Theories has attempted to do. One might view this as backtracking, and in a sense it is. However, by going back to basics, one may find the missing piece to the puzzle bringing the overall picture into focus.
I like your ideas Cat. It is always a pleasure to read and contemplate your posts. Moiety and integrality are excellent words, both in my view far from Western roots, but in line with 21st century thinking and beyond. In Platonic thought we look for the true form of a thing, and approach it in stages. Plato and other thinkers, including many in your own background of Catholicism, look for a Prime Mover or root cause of all things. I think a Grand Unified Field theory is in this vein. In contrast, the standard model of particles and fields actually has many pieces to it, some, like the graviton, still unobserved. The idea that all of physics flows out of one set of equations is Platonic; the idea that we should apply multiple paradigms, such as moiety and integrality, synchronizes with our 21st experience of globalism, multiculturalism, and free exchange of information.
ReplyDeleteYou might consider that integrality is related to wholeness and holistic thinking, existentialism, and other ideas arising mainly in the mid to late 20th century and coming now into fruition. Moiety sounds like reductionism, but without a return to a Platonic form, if I understand you correctly.
In general I think in the 21st century we have the opportunity to apply multiple paradigms: science and humanistic approaches; global paradigms of unity, harmony and complexity; moiety/reductionism and integrality/wholeness; rational and intuitive thought. I feel very fortunate to live in this day and age when I do not, like Spinoza, have to invent Eastern thought from scratch but can take advantage of the high level of development in multiple societies around the globe, and build from there. I think those of who ignore a multiplicity of paradigms are squandering the great intellectual opportunities of this age.