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.
Background
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 structure
Relations 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 meditation
One 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 Akasha
In 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.
Consciousness
In 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.
Conclusion
I 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.
You can find my book
here.
Image from
http://eresaw.deviantart.com/art/Soap-Bubble-Ballet-293874327