In this essay I will compare the way experience is stored in structures with concepts from mathematical category theory. I will try to show that it is not unlikely that the involution of sensorial experience finds its expression in an observed evolution of biological species and behaves like a mapping process known in mathematical category theory as "Yoneda embedding". I will also argue that there is a primacy of sentience over matter, leading to an idealistic hypothesis of existence.
Warning/disclaimer: This essay is highly speculative and may rest on wrong interpretations. If you are not interested in metaphysics don't bother to read further or to reply.
What is reality? Are the objects, entities and processes we observe with our senses really there? Or is what we observe a mind-fabricated hallucination? It is the ruling paradigm in science that our senses and brains filter the information we receive as an input and then fabricate a kind of simplified representation thereof, which we usually call "reality". But does the information we receive really correspond to anything out there? In the film "The Matrix" (1999), the main character Neo found out that everything he experienced before taking the red pill was not really there in a three dimensional tangible world, but rather a mental illusion fed to his brain by a vast computer system called the matrix to which he was connected in a kind of hibernation vessel. In other words, everything he experienced up till that moment was an illusion produced in the theatre of his brain by interplay of computer and brain information exchange.
This idea has also historical antecedents. Plato's cave with shadows that were taken for real and the notion of Maya in Hinduism and Buddhism. Modern developments in physics -in particular digital physics- invoking the so-called holographic principle have postulated the possibility that we are living in some sort of hologram, possibly projected from the two-dimensional surface of a black hole. Others even go as far as to speculate that we are living in a computer simulation. Perhaps not entirely like in the movie the Matrix, but the analogy is troubling.
Whatever is the higher truth as regards these ideas, at least we can make sense from what we observe. We can distinguish recurrent patterns and use them to our advantage. Technology is a proof, that however limited our understanding might be, at least we can employ this understanding in a predictable manner.
We may never know what reality really is like, but at least we can get an idea of what it is doing. The reproducibility of our knowledge suggests that what we observe is a meaningful and useful representation of the inner workings of reality. Perhaps even an isomorphous representation.
In mathematical category theory, if a category is like another category, there is a mapping between the two categories; a meaningful mapping that preserves the structure of the category when mapping it to another category. Such special structure-preserving mappings are called "functors".
The mappings from A to B can also be considered as the way A relates to B. The relation between A and B could then be considered as the sum of the maps from A to B and the maps from B to A. According to the philosopher Wittgenstein there are no things or objects in reality but only relations. It is the interplay between these relations which create the illusion of localised objects, where there are none. In fact quantum mechanics shows that everything is in fact a giant interference pattern of vibrations and vibrations are essentially non-local. Moreover everything is in a constant state of flux; there is no phenomenon that is exactly identical between two moments. Or as the Greek philosopher Heraclitus said: Panta rhei, ouden menei: Everything flows, nothing remains and "no man ever steps in the same river twice".
How relations build structureRelations at their most fundamental level can then only be a functional process of mutual information exchange, which is continuously updated. The relations are expressed as vibrations, which result in resonance patterns of standing waves: There is a continuous waving and vibrating taking place, but what we observe is a form with a kind of stability.
In other words if we were to consider the forth- and back going vibrations between two points A and B as a mapping activity in progress, this mapping activity results in a physical (re)presentation of another dimension, which we call the standing wave and which we experience as an almost static thing.
In category theory we call mappings morphisms. Mappings show the maps between "objects" (characters, strings, mathematical objects, sets etc.).
A special functor (a mapping between categories) in category theory is the Yoneda functor. Whereas functors normally map objects, the Yoneda functor takes morphisms (mappings) themselves as objects and maps these into a set, which is a new object. (A map of maps so to say).
The analogy struck me. I wondered whether if relations are sets of mappings and such a set can be considered an object, there is at least an artistic similarity with my standing wave idea. I'd perhaps even go so far as to formulate the hypothesis that the structure of an object is a faithful (not in mathematical sense) representation of the functional relations from which it is built.
Perhaps this example is a bit far-fetched, as it is disputable whether vibrations can be considered as relations. But what happens in the brain, may be a better analogy.
Memories in brains are not stored locally as in computers but in distributed ways. Brains store memories in a highly "Wittgensteinian" manner: The patterns that build a concept or an image in the mind are stored functionally in flux patterns of neurotransmitters between neurons and structurally in terms of links between synaptic links between dendrites and axons (the input and output channels) of different neurons. It is the resulting pattern of relations which maps an event or object we have memorised. Whenever we experience something new, the molecular fluxes stimulate synaptic growth to connect neurons. In this way, sensing, which is a functional process forces the formation of structures. It is like a Yoneda mapping taking place in situ in concrete form: the sensorial patterns we observe and categorise according to a certain pattern similarity in our brains are then stored as a new pattern: The morphisms crystallise or fossilise in a set of synaptic links.
But this type of physical direct mapping does not only occur in the brain; at the level of DNA experiences often result in parts of the DNA being post-translationally modified, most often in the form of methylation. The methylation pattern of the DNA can influence whether a gene is switched on or off. It can also be inherited. This is the field of epi-genetics. Environmental influences can strongly influence the way genes can or cannot be expressed as a consequence of environment-induced methylation. This can also render a gene more prone or vulnerable to mutation or influence the way genes are copied or even multiplied upon cell division. In other words certain types of experiences are also stored on the level of the genes or can result in mutations at the DNA level. Again this is an example how sensing the environment and building a relation with the environment is mapped physically in a set of information. Environmental morphisms fossilising in the form of material and informational structure.
In other words, I have drawn an analogy between the abstract way a Yoneda functor maps and embeds morphisms into a set and the concrete way the brain and the epigenome store information resulting from sensorial input. The way the sensorial input is processed corresponds to the morphisms and the concrete stored information in synaptic links or methylation patterns correspond to the embedded set.
Also in this way structure can be considered as a form of fossilised sense.
Yoneda mapping as an analogy for meditationOne of the techniques in Indian meditation is the "Panchadasi" technique. You mentally try to throw your light on a topic of consideration from 15 different perspectives. By doing so, you probe the object functionally and structurally. It is like having an object defined by a few dots and then trying to connect the dots to see what it represents. In fact you are mapping relations between the dots, and the more you progress from these relations you suddenly start to see what the intended object was. From partial links at a certain moment the whole which is more than the sum of parts reveals itself. By performing this technique and considering a topic from as many perspectives as possible, you build as many ontological relations in your mind as possible. At a certain moment, the framework of ontological relations is sufficient to understand the whole. No longer do you experience a broom, a hose and a drum, but suddenly the elephant -of which you had considered the tail, trump and ears separately, without knowing what they were- snaps into your experience. This holistic experience of the phenomenon of contemplation can even result in that you start to feel what it must be "like" to be this phenomenon. Not only do functional relationships reveal a structure, structural relationships can also reveal function.
To speak in category language, not only do the morphisms lead to a representation in a set, but the relations of the objects in the set can by an inverse functor also be back-translated into the morphisms they originated from.
The meditative process thus might be a way to experience "what it is like to be" concerning the object of contemplation. In Latin this is called "quale" from which the word quality derives. Neurosciences often speak of "qualia" as the qualitative aspects of observation, such as the "redness" of a tomato. Meditation is often intended to achieve oneness with the object of contemplation. This is achieved by experiencing the "what it is like-ness" of the object. Perhaps a process which resembles Yoneda embedding or the reverse thereof is involved in this experience.
Funny enough, one of the basic tenets of category theory is that if a category is "like" another category there is a meaningful mapping which preserves the structure of the category (functors).
Pancomputational Panpsychic AkashaIn my book "Transcendental metaphysics" I argue that the ground of existence is "primordial consciousness" (i.e. sentience per se if you prefer). From this formless all-pervading filed, informational units arise, which form a kind of neural computational network in the so-called the quantum vacuum, which has been equated with the Indian concept of the "Akasha". The Akasha even allows for a kind of digital processing in addition thereto. If reality is indeed a computational substrate involving information processing as digital physics suggests, there must be a consciousness to make sense of the information (otherwise it is gibberish). This leads to my hypothesis of pancomputational panpsychism. As this network of reality as a whole is considered sentient in this model, perhaps I can also speculate that the very way in which structures arise in this model is via Yoneda embedding. It is interesting to note that Yoneda embedding requires that the functor which operates the mapping does so from a "locally small category". This is important because I have suggested in earlier posts that sentience is present at the smallest level of reality which can be considered to have a certain individuality and relative locality. If reality indeed creates structure by fossilising sensed experiences, then this is not in contradiction with my panpsychic hypothesis. Moreover the fractal of panpsychic entities, which I have proposed, perfectly fits the idea that functions and structures are each other's transform.
In my model your localised awareness inhabits a vessel which is made out of smaller entities (your cells), which can be considered as a bunch of smaller localised entities. The awareness of a cell inhabits a vessel made by atoms, which in turn can be considered as a bunch of smaller localised entities with a minute form of individual awareness. Thus you get a fractal of entities that on the one hand are sensing entities themselves and on the other hand form structured vessels in cooperation. Each entity is then at one level a functional sensorial living entity and at the same time the structural fossilised building block of a higher aggregation level.
I don't say this is my belief or an absolute truth to me. It's a speculative artistic process of associations, which I explore in the hope that one day I will be able to integrate them into a verifiable hypothesis. Consider these my metaphysical musings and please do not take any speculation for a fact in this essay. Perhaps my analogies are not even valid since I am not a mathematician. But if they are I hope my musings will be read by one of them and inspire them, to help me prove my ideas.
ConsciousnessIn a previous article I have also suggested that primordial consciousness might operate to generate information by self-representation. Again this fits the notion of Yoneda embedding. Self-representation or self-reproduction is a concrete analogy of mapping the functional consciousness process into a fossilised structure that can be experienced , so that the knower generates information as known and by observing its self-generated information comes to know itself as the Ouroboros from alchemy biting its own tail.
ConclusionI hope to have shown that the abstract mapping of morphisms into sets in mathematical category theory may have an equivalent in the way structures arise in physics and biology. The process of Yoneda embedding may not only be involved in such concrete examples but also in meditative processes as well as in the ontogenesis of existence from primordial consciousness.
By Antonin Tuynman a.k.a Technovedanta; inspired by ideas from Eric D.Ryser.
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