Abstraction

the concept ouroboros

an old clip, mind your ears if you have perfect “western pitch”

as we’ve been seeing in previous posts, there is a seemingly fractal quality to things. we’ve seen how wholes become more than parts and we’ve slowly crept up the complexity ladder all the way to cells. i’ll go from cells today because they are a key part in understanding all of this.

the first agents that did work were the laws of physics that are responsible for our first structural increase (or gain in information). we went from scattered disorganized particles to big blobs of complex arrangements of particles from forces alone.

and as gravity tug everything together, and as the sun fed enough energy, we managed to get new agents, this time, molecules that themselves can exert effects on other molecules, making them agents.

and as molecules became more and more complex, so did their tasks, such as the ribosome that assembles coded proteins.

but today we focus on a particular kind of cell, the neuron. i will be approaching a simplified model of the neuron. i studied a few models, neural networks and so on, but i am going to provide a different model for the neuron, completely arbitrary an according to whatever i think is correct. pure speculation.

a neuron is a cell that performs a computation described by the following:

$if ~ \{ c_1 \wedge \ c_2 \wedge \dots \wedge c_n \} ~ then ~ fire$

there are many other ways. and in fact, neural networks use a different model that yields a more elegant mathematical formula. the reason i choose this one is that i believe (but can’t really prove) that each $c_i$ above is not a weight, but actually a condition (true or false). i didn’t use thresholds or step functions to model the “firing” either. what i am saying, instead, is that this cell, the neuron, checks if a number of conditions is present, and if so, fires. this is similar to the formulation for neural networks, and i suspect they are almost equivalent. but my focus in choosing a logic formulation instead of a functional mathematical one is to make the following more obvious.

a neuron connects its conditional tendrils to whatever is around it. these can change over time, grow stronger or weaker depending on usage. and then, it has a very long response tail, that spreads this message through thousands of other neurons. i’m not discussing this in depth, and i’m sure there are many inaccuracies here, but for the sake of my point i’m willing to accept some rough edges.

so what the neuron does is to take a group of parts (let’s call them things of layer n) and tests if it is a whole (let’s call them things of layer n+1). so a neuron, being forward only, is an analysis machine, or categorizer. feed it black and white pictures, and a white neuron will fire on the white sections, whereas the black neuron will fire on the black sections. note that “black” and “white” are mere concepts, and since our brain is concept agnostic, meaning, all senses are translated to electrical impulses, these neurons, even though being naturally designed to be sensory processors, might eventually connect to each other, and since they can’t distinguish outside electricity from inside electricity, they would be just as likely to find fictional parts in a brain and in a sensory nerve. as long as there is tingling, there is a possibility of classification. this is why we are bound to find the “brad pitt neuron” (google it, it’s real), the “tangerine dream” neuron, the “smell of mom’s cooking” neuron and so on. that’s what they do.

in my opinion, the very structure of a neuron presents abstraction, since it can categorize correctly different patterns into a single “yes” “no” pulse. let’s call that pulse a word, and use words to go through a computation in a sequence of neurons. let’s say we want to know if something is “checkered”. we will have a layer of neurons that categorize colors into black and white, then we will have a layer of neurons testing if “black” and “white” are alternating in sequence (by using the categories of previous neurons as inputs), and let’s say a neuron that evaluates spatial arrangement and sees if two dimensionally something is checkered (by using the responses of the alternating neurons and aggregating them).

what we have here is a progression in abstraction, from parts to whole. let’s see it in detail in one dimension (look up visual region neurons very interesting and similar stuff).

input (k is black, w is white): kwkwkw
color neurons:

if(k) fire black; if(w) fire white;
turning it into: black white black white black white

transition neurons:

if(black next to white) fire black white; if(white next to black) fire white black;
turning it into: black-white white-black black-white white-black black-white

checkered neuron:

if(black-white next to white-black) fire checkered
turning it into: checkered

what we just saw, and this has been demonstrated scientifically analyzing the visual networks of our brain, is abstraction. abstraction is not something that only big brains do. it’s something that any small neuron does. it is essential to identify the patterns we’ve been describing. neurons are a natural consequence of a “layered” universe. if parts and wholes behave differently (i.e., the wholes have properties unpredictable from the parts alone), then it is only logical that some structure would evolve that demonstrates that hierarchical view.

my model, that things are made of things, is the exact model of what i am saying a neuron is good at categorizing and processing. it takes a series of parts (things), independent of whether they are real (sensory) or fictional (internally generated) and classifies them firing the appropriate concept.

i could say my model is a description of how the brain works and how reality works and how i know the meaning of life the universe and everything. isn’t this suspicious? isn’t it the other way around? isn’t my model a consequence of how the brain works?

let’s look at this wheel. i call it the concept ouroboros. i added only a few topics for clarity.

every human activity starts with a core part, the simplest concept that is recognizable and analyzed, and then abstracts and elaborates on it. since logic is the building block of math, it is taken for granted as an encapsulated thing. physics then uses math as its thing, then chemistry uses physics, then biology uses chemistry and so on. but if we go the other way around, by analyzing what things are made of (seeing what a thing is made of), we would see that math is made of logic, which is made of philosophy, which is made of societies, which is made of humans, which are made of organs and so on.

there is no higher and lower in my perspective. it is an orouboros, eating its own tail. any study or human abstraction claiming to be the “essential” one will be ignoring that its basically just feeding on other things and eating its own tail.

why would this be?

imagine now that this ouroborus is not vertical, but you lay it down on a table. all these points on the circle are instances of the same logic of reasoning: the reasoning of parts and wholes, and laws thereof. which is suspiciously similar to what neurons do. so either this is a coincidence, or we, humans, have mostly become very good at creating an ever expanding ouroborus in the same plane. we can grow our abstraction as deep and wide as we want to. what i see here is a permanent limitation of our own cognition. if we are conscious thanks to our neurons (our parts for thinking), then is it too much to say that the whole might share some properties with the parts? like the charges affecting both atoms and molecules?

what i am saying is that it is that our perspective on reality is more subjective than we like to think. that even accepted concepts such as molecules, atoms and so on, are part of our own categorizing system, and nature is well beyond that.

am i saying all i’ve been writing is nonsense? well, yes and no. i wrote it purposefully to demonstrate its own fragility. i made it generic enough so that it would be acceptable in many fields. and then i showed how this was exactly what our brain was doing, naturally.

so now that i closed a loop and broke the logic of my previous posts, let’s continue. i will continue as if nothing happened, because, unfortunately, i don’t know how we can step out of the ouroborus conceptual world. i do not know what it is to think beyond this plane. but it is a good question that might return in the future. for now, i am going back to our ouroborus plane, and circling around as usual.

as we saw, a neuron is a mapping between parts and whole. since that whole doesn’t seem to exist except in that neuron that fires, i will refer to that firing as a word that is stored in that neural structure. so our brains are a mess of connected words, concepts, connected to each other in hierarchies, and connecting from and to the real (sensory) and the virtual (other neurons).

this means that the brain has physical information. not the information in its genes, not the information in its molecules. the information it its specific sequence of conditions that yield a word. how can we convert a neuron into a word? we have to crack its code. a checkered neuron reads (black-white white-black (…)), so if we only knew the answer (checkered), we would have to find the inverse function that the neuron does. in this case, “checkered” would translate into “black-white white-black (…)”.

contrary to the direct operation, where several conditions yield one result, knowing a word and finding out all conditions that create it is hard, if not impossible. a regular neuron has thousands of conditions for a single word. that means each word can expand into thousands of others. this is going from the whole to the part.

let’s summarize. a neuron takes parts and creates a whole, the word. the inverse, takes a word, a whole, and finds which parts exist, expanding it. this is, respectively, the act of analysis and synthesis.

so the foundation of thinking is actually present in the simplest structures of the brain. in fact, since cortex bearing creatures like us can actually generate words that replace sensory input (i.e., we can feedback words back into the first categorizers, like when we lucid dream a new perception), we are dealing with a universal computer.

i will leave more of this for later, since for now it was a lot to deal with. we are closer than ever to minds, and to demonstrate how the objective creates the subjective, even though we slightly hinted at it.