Epistemology, Cognition and Category Theory: An Overview

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★ An Overview ★ A Model for the MindDirective Cognitive Expansion

Lately, I’ve been working on learning skateboarding and some tricking. At the moment, I’m pretty terrible at both. If I had the time to practice more, I would improve very quickly. Especially if I had someone better to practice with who could teach me and push me harder. It’s amazing how the presence of others can stimulate improvement, especially when they are significantly more proficient at what you’re trying to learn.

Of course, after about fifteen minutes of backflips and ollies, my mind is thrust into philosophic overdrive. Typical.

Phenomenology - The Study of Me.

A few ideas have been tumbling around in my head lately and I’m more able to clearly conceptualize certain problems that eluded me before. There seems to be a universal means of modeling ideas, activities and problems that leads me to learn faster. I want to describe how I’ve modeled skateboarding and tricking using category theory as an in depth example – and to exhibit some math ideas I’ve been playing around with. Many people find that the more you learn, the faster you learn new things. I agree, but additionally, I’ve found that conceptualizing the mind both helps me to learn faster and to identify activities to strengthen specific mental faculties.

I love learning new things. I get to experience beginner’s mind again and it gives me a chance to reflect on the process I use to learn. By actively observing beginner’s mind, you can refamiliarize yourself with its nature, so that you might be able to partially apply this state of mind when you need it. By introspecting on this process, I hope to continually improve it. I try to approach new activities and skills from a multitude of perspectives and I like to examine the similarities between everything.

Developing Versatility

Lately, I’ve taken some time off from pondering the finer mysteries of life to examine closer the structure of cognition and knowledge itself in an attempt to discover for myself a more generalized model of cognition. As our world accelerates towards convergence, it’s becoming ever more important for us to consume information and acquire knowledge faster. In a world perilously close to technocracy, where it’s likely that we soon won’t have a need for much of today’s labor force, those who aren’t able to keep up will find themselves disillusioned and searching for meaning. That’s not to say that everyone needs to be a quantum physicist, but we’ll all be dealing with rapid change.

Technological development continues to outdate itself faster and faster. Those who commit themselves today in service of a static vision of the future will find out tomorrow that they’ve oblidged themselves to a future past. New technologies will continue to cannibalize the demand for outmoded tech and apps. Revenue streams which could traditionally be depended on for decades, we can now only count on for the next quarters. Those who are networked and in touch with the right information at the right time will be nimble enough to forward their chips to the next big players. Luckily, risk for technology investments do not systemically affect the entire system in the same way as the housing market.

The rest of us? Plebs. Don’t get me wrong, we’ll have great quality of life, but still we’ll likely be peasants, without much significance in our lives, except that which we create. Those of us who continue to diversify through extensive learning will find their skillsets versatile enough to remain in demand throughout our unpredictable, turbulent journey of convergence.

We’re pretty much living out The Matrix. With Wikipedia, we’re two steps away from downloading the history of Eastern Civilization or Kung Fu. As the nodes in our social network converge toward super-connected, as the speed of communication exponentially increases, so does the rate and amount of information we share. Additionally, the way we share knowledge adapts to this new bandwidth because we also share tools to learn and teach more efficiently. So then, we learn to consume information and acquire knowledge more rapidly. Systems evolve, new tech is created, science is revolutionized and new culture is produced – these all create new things for people to learn.

It’s interesting that, while in the next few decades there will be immensely increased demand for knowledge and versatility, shortly after that, there may be be little to none, as artificial intelligence begins to supplant almost all of our responsibilities and jobs. It’s at this time that we need to push ourselves even harder, if we hope to be capable of taming out-of-control technology.

A Universal System for Conceptualizing Anything

So learning about how to learn seems reasonable. A lot of people have trouble learning new things because they lack multifaceted mental tools to quickly and sufficiently model what they’re trying to learn. So we need a universal system of modeling any problem. Yet, modeling the knowledge and skills to acquire is not enough. We also need to be able to envision a model of the mind which allows us to optimize its capabilities. And a robust process for conceptualizing anything, should also be capable of modeling our mind.

Understanding category theory is fundamental to a universal system of modeling problems because it’s flexible enough to provide the foundation for a universal language of high level math. It sounds complicated, but it’s really not. It’s a shame that most people don’t make it far enough in math to learn about this. And I’m only vaguely familiar with it.

A Brief Journey to the Metaverse

Why could the underlying language of math be used to robustly conceptualize anything? To justify, it’s time for a brief interlude into the nature of the metaphysical. When I refer to information, I mean it as the instances of knowledge that people typically consume, both in life and on the internet, including tweets, news articles, baseball stats, and stories about friends. Bits of information are like real-world manifestations of bits of knowledge that people can directly consume to internalize into their personal knowledge.

Each person has constructed their own internalized system of knowledge representing their understanding of how things work and of all things relationships to all other things. You can begin to group together people along certain dimensions to see how each person’s internalized system of knowledge overlaps with others in their own group, as well as with that of other groups. These dimensions include groupings by geography, culture, family, religion, education, time and many groupings that are more complicated. Someone’s internalized knowledge of the world can be affected by skewed perspective and will include information that is false, inaccurate, oxymoronic, incomplete, undefined or irrationally constructed.

Each person also constructs their understanding of the knowledge of each other person they know, at least to some extent. To greatly complicate the scope of the problem, this knowledge about others’ knowledge is also constructed to form generalizations for the groupings listed above. Not only that, but it’s also recursively reflective – I know that you know that I know that you know … etc. Sometimes considering this reflective information seems incredibly over-analytical, possibly paranoid and just silly. However, there’s many inferences that you couldn’t deduce otherwise, though it’s important not to weight it with much priority.

If you make some important limitations on this extremely complicated system, like cutting off recursive reflection as well as a few others, then you’ll find that the number of nodes and edge’s in this graph is finite – though it quickly approaches astronomical proportions. A googolplex? No, think higher – like Graham’s Number. It’s crucial to note that it is finite. No person or computer could ever model or process all of this information. The computational capcity of the universe is not nearly enough. And we’re just considering the complete graph, including ‘null’ nodes, of one person’s internalized system of knowledge, which includes the dimensional groupings listed above along with a limited number of reflections. It’s important to note that this impossibly large graph is a model that includes nodes accounting for the effect of information that person has not actually stored.

The problem space can be significantly compressed. For example, if you only account for the information stored in that person’s brain, this compresses the size of the graph. However, it doesn’t allow you to construct valid products of the internalized knowledge of multiple people. Other aspects are sacrificed by only considering information stored in hardware. More effectively, you can compress by reducing and generalizing the forms of these pieces of knowledge. You’ll have to forgive me. This is tough to conceptualize and I know that much of what I’m saying is not as coherent as it should be, but I’m visualizing this and while it makes a lot of sense to me, it’s really tough to convey.

Universal Knowledge, the Best Kind

In our future world, we’re going to have to familiarize ourselves with lots of manmade systems of knowledge. For example, Cisco releases a new IOS, network technicians gotta learn about it. Apple releases a new OSX, developers gotta learn it. Google releases new features on Analytics, marketing’s gotta know it. But none of this is really … universal. In fact, as a software developer, I’ve gotta say, it’s pretty fucking annoying.

“That’s just a waste of neurons.” - Bernie Cossell, owner of the eighth email address and my Unix teacher.

On the other hand, mathematics very definitely is universal. Science is a bit flakier. It tries to represent itself as universal knowledge, continually purging itself of any inaccuracies and propagating the updated system to its devotees. This is eerily similar to how a religion operates. So, how does science differ from math in this degree? It’s a system that tries to map as closely as possible to universal knowledge, but can sometimes contain false or irrational elements, whereas math is pure universal truth. It has always existed metaphysically in it’s current and final form since the inception of the universe – by the way, this means it exists outside of time. There are few other fields that can make this claim. Perhaps some of philosophy, particularly logic.

All universally shared metaphysical entities must only be true.

Math is literally universal – fucking space aliens will learn the exact same math we learn. Perhaps their system of math will have a cultural overlay that maps differently. Different notation and extent of knowledge. But it represents the exact same invisible metaphysical structures that must certainly be true. So if we needed tools to robustly model knowledge itself, perhaps we should base it on a completely solid foundation. Yes, every person has their own different and incomplete conception of math, but they all definitely map to the same universal structure, whereas the metaphysical structure of other forms of knowledge is exceedingly fragmented.

The only other universal system of knowledge I know of is GNU and Linux, lulz.

Category theory is [part of] the underlying language of higher level math. If this metaphysical kernel of math can be used to model the rest of such a pure form of information, wouldn’t it be useful in modeling the rest of our knowledge. And interestingly, though math is pure truth, it can be used to model systems that include false & indefinite information.

-1/12 = 1 + 2 + 3 + 4 + 5 + … No, really. It’s true.

Most people’s extent of conceptualizing a problem space ends with tree-like structures, sets and graphs. I mean like graph theory graphs. Most people don’t understand that they mentally model things this way. It’s moreso done subconsciously. And these are fairly powerful, but come up woefully short when trying to intellectually understand things like social interaction, artificial intelligence, learning and cognition, which aren’t usually considered ‘mathematic.’

Modeling Social Interaction

For social interaction, if you try to model this using trees and graphs, your behavior is going to be limited and very repetitive – if your interacting on an intellectual basis. Of course, most people don’t think of it this way. They just interact using subconscious behaviors, which are learned over a long time. But if this stuff doesn’t come naturally to you, then you won’t experiment socially on a cognitive level. So you need a different means of understanding things.

With category theory, you can conceptualize interactions as functions passed from person to person. You can observe specific behaviors, then form ideas about behavior types and patterns. You do this by parameterizing specific behaviors that you observe and imitating them, observing the effects under various conditions and reasoning about cause and effect to optimize your own behaviors.

What do I mean by parameterizing behaviors? For the specific behavior, “John bought a drink for his friend,” you can observe the behavior as a function. Then, you can first parameterize the subject as a variable: “[X] bought a drink for his friend.” So now you can consider the action if performed by yourself or someone else. Then you can parameterize the direct and indirect objects to arrive at an even more meta function: “[X] bought [Y] for [Z].” You can also parameterize the verb: “[X] [V] [Y] for [Z].”

This may sound overanalytical and superfluous, but it’s very powerful because you’ve now arrived at a sort of ‘form’ for a specific ‘kind’ of human behavior. You can build up a vocabulary of these ‘kinds’ of human behavior and recombine them in order to model and emulate nearly any behavior. And because these kinds of behavior are much more generic, there are markedly fewer to know. And the combinations of base forms could be finite, depending on what you consider as a base form.

So you can take the original form with “Even though [A],” to conjoin them into the new behavior “Jerry bought a drink for a homeless guy, even though we told him not to.” This is kind of a high-level overview of how to use category theory to model something, but I didn’t cover monads. In this case, monads are the functions you would use to combine the forms. Additionally, you need to pass in functions that describe how those forms are combined. You can also weave together semantics with the substituted forms, along with optimization, dependency and objectives, for an attempt at autonomous behavior.

It gets a little complicated, but the point is – with category theory, you can recombine bits and pieces of conceptual structure and functionality to arrive at an accurate model of anything. You can get further and further meta with it, to become more adaptive. As you parameterize behaviors you observe and construct behavior-kinds (kind is a concept used in the programming language Haskell btw), then you can partially fixate these behavior-kinds with some of their parameters. At this point, you can begin to compare the similarity of kinds of behavior in various situations. I.E. What would it mean, semantically, if “John bought a drink for [X].” is applied using the various direct objects: his friend, his ex, and a homeless guy. I don’t mean semantically in the sense of the meaning of words. Rather, the meaning of the actions, as perceived by various people. It’s the same type of behavior, and while it has different meaning as applied in different situation, there are also similarities that can be observed and reflected on.

You can even construct these models inside of a kind of cyclic monadic function, so you can acquire behaviors as you observe them, construct the next step’s behavior by recombining existing behaviors and pass acquired information to the next step. I’m sure there’s math terms for most of what I’m describing, but I don’t know what they are. This cyclic function that I’m describing has been particularly interesting to me recently.

Part Two: A Model for the Mind

I’ll briefly overview the various faculties of the brain and the mind and explain how they can be combined. By training various activities and subjects, we can focus on improving specific functions of the mind. I’ll list some examples, briefly explaining how each one coordinates various functions of the mind.