reality = chaos + order, and Plato's allegory of the possibly infinite lightshow

Here I want to record this feeling that I've been having. I guess I've always had it every now and then but I'm noticing it more now. It's the kind of feeling that there's probably some obscure German word for, but for lack of better words and lack of effort in searching for them, I seem to have written now a whole article to describe it.  

A while back, I read about the "weak Pinsker conjecture". I'm no mathematician, but what it seems to  say is that any dynamical system of a certain class can be seen as a product of some chaos and some order. 

My whole life I have believed in the orderliness of life. I was convinced that everything had structure. For instance, as a child I believed that by studying hard, I could get into a good school (for some reason, it had to be Princeton), and by getting into a good school, I could have a good job, a good life, whatever. 

But as I grew, I realized that these rules, these laws, institutions, apparently fundamental, immutable properties of society were not quite what I had imagined. As one grows in mind, they learn through experience that the things they were taught were only projections of deeper structures. Honesty is the best policy... except for when it isn't. As it turns out, honesty is rather an emergent sub-goal of a larger objective -- perhaps harmony? And when we realize this we feel some kind of temporary euphoria: Ah -- it's not about doing X, X is just an element of this deeper Y! And understanding Y empowers us to make better decisions /be better people / perform better at __ / etc. 

But even in the throes of such euphoria we are perhaps living in a delusion. To use Plato's analogy, we are perhaps only seeing the fire inside the cave projecting the shadows on the wall. But we have not seen the sunlight yet.  

Examples

Music is not about music theory, it's about the pitches played in combinatorial sequence. But as it turns out even that's not very general: music is about something deeper. Rhythm, timbre, pitch -- all sort of projections on the wall of what makes music, music. Outside of the Western study of music, music is much more innately connected to dance, perhaps even inseparable. And expanding our minds the tiniest bit, we might be able to grasp how this could be. Music is not about vibrations per se, but it is that vibrations are manifestations of physical movement, which is something innate to the human mind. Perhaps it even begins in the womb, as we listen to our mothers' heartbeats. 

But back to the thing about getting into Princeton. As it turns out, life isn't as simple as I had imagined. But that whole school -> job -> life logic? It's not totally wrong, either. That's because there's this aspect of determinism in the system -- the rule works, kind of -- but with some (a lot?) of added chaos. Which... makes the rule not quite a rule, but a heuristic... if even that. 

So, what is this "added chaos"? Well, it's exactly this "deeper structure" that people tend to discover as they build their set of experiences across time. It's not about getting into school, but maybe more about finding a good job, which typically requires skills, which presumably you can get lots of at a good school (like Princeton). But wait, do you even want to get a good job? Jobs are actually a medium of trade, a way to trade labor, time for other goods and services. So I suppose the goal here is to attain goods and services, at least as much as we need to continue our existence? But then, is that really what it's all about? As it turns out, to many, life is about more than surviving. Surviving happens to be a part of it, ceratinly, but there's something more, some deep, personal goal. Clearly, this topic is deep enough that entire books of philosophy are written about it.  

No proofs, no guarantees

When we run into roadblocks with our current understanding of the world, most of the times we can reach out for external inspiration, perhaps to mentors, teachers, books. There we might pick up on something that expands and deepens our views, eliminates assumptions about reality, increasing complexity but freeing us from the assumptions and constraints which previously bound us. 

And perhaps we can be lulled into a false sense of security that this is always possible. That for any problem, there is some model, just a deeper, better model that we haven't understood yet, available "out there", not too far away. But I think reality is a bit scarier, in the sense that a lot of times, we just don't know. We are never actually guaranteed any deeper structure that will solve anything. We just have no guarantee in general, period. Taking this up a notch, we don't know that our reality will devolve into some kind of incoherent mess that doesn't respond to us the way we expect it to, like something out of an acid-fueled nightmare. We do not know that the ground will not shift under our feet. 

This isn't really just a philosophical ponderance, but something that just happens in reality. I think everyone really has to face it several times in their lives: starting a new business in an industry that doesn't even exist yet, moving to a place where you don't know anyone, having a kid (from what I hear). It's this visceral feeling, that you're treading actually new ground with guarantee of success, and you're sort of making it up as you go along with only your brain to guide you. This feeling that you're outside of the bubble that is the orderly system which society would have you participate in. Most likely, you're actively expanding that bubble for everyone else. Kind of like a frontiersman, treading new ground and building civilization from the ground up. I like to see that as the basic imagery of the central task and obligation of every generation to the generations succeeding it. We are expanding that sphere of orderly influence, bringing order to a chaotic world. And it brings to light the nature of the bubble we live in -- it's extremely difficult to take it for granted knowing that flawed beings just like myself hand-built this system, and it wasn't "God-given" (for lack of better words) and uncertainty and entropy could be lurking everywhere (and not just at the quantum-philosophical-acid-trip level). 

Being trained somewhat in mathematics, I have always seeked guarantees, proofs. I wanted to live in a universe where there was solid footing. But as it turns out, not even mathematics is like this. The first time I had to come to terms with it was when I read about Godel's Incompleteness Theorems. As it turns out, mathematics isn't as systematically complete and safe as I had once thought it was. Even further, the theory behind the Incompleteness Theorems itself -- mathematical logic, formal logic -- turns out to be only just a model of how mathematicians did mathematics. It describes a fragment of what mathematicians really do. And who knows what mathematicians really do, or what mathematics is -- every professional mathematician works at the frontier, constantly defining what mathematics is. It is an innately human endeavor, something we do because we need to, want to. An act of imposing order against the chaos of the universe (at least a good attempt), but distilled purely down to that act, an attempt to capture at describe at least an ever-expanding fragment of the universe in an orderly way. Kind of like mathematical logic does for mathematics itself, I suppose. 

Maybe this visceral feeling of chaos and uncertainty in just casual, everyday reality has always been so much more obvious to everyone else who tend to get out more. But me... I feel absolutely terrified. It's like I'm in Plato's allegory of the cave, but there's no guarantee that there is some final, terminal Sun outside that represents the level of the Forms or anything like that. Instead, having seen that wacky stuff with the fire, I go outside and see a Sun, but I've played this game before. I look around and indeed, the Sun is actually a huge mirror. And in fact behind this mirror there's a whole constellation of mirrors and lenses among what seem to be other Suns, stars. And depending on where you look from it looks entirely different! Moreoever, I see other people coming out of the cave and talking about stuff, but I can't be sure that they're seeing the same thing I'm seeing, although it seems to be similar, up to some sort of geometric transformation I guess. So where's the real Sun? Is there a real Sun? Are there multiple? It's massively chaotic. 

Though chaotic, I suppose it's only distressing for people like me who were taught the "Platonic dogma" so to speak, and expected something like that in reality. Consider a hypothetical individual who never really expected order in the first place. This is someone who truly embraces the state of the world for what it is -- simply perception (because, what else is there?) -- and has no reason to feel distressed, because again, they never expected otherwise. But I think most people aren't like this, and expect the world to obey some sort of order, because that is the what is presented to us as children. So how do we handle it?

Some people might get out of their caves and face this complexity in a special way; they choose a particular interpretation and believe, say, in a single Sun, in a blissful, non-chaotic, orderly world not filled with mirrors and lenses and weird shit. Religion, for instance, is one obvious way this is done. This does sometimes require some curating and filtering of contradicting information, particularly with interpretations that aren't so consistent with the data, but that's neither here nor there. Or others might avoid complexity altogether, choosing to pretend it is not there. Many others handle it step by step, modifying their theories as they are forced to but still believing that they must be at some terminal point every step of the way. 

Another way to put it is this: There is no "canon" in life, reality. There is only a known complex ordered network of fanons, fan theories. Multiple fanons, generalizing other fanons simultaneously, and other fanons that further explain this fanon as inconsequential side stories, or even mere dreams of some character. 

Some very deep and vast fanon might tie in all these other fanons in my mind, and bring me peace temporarily. But that peace will soon be disturbed again when I start asking new questions. What about the backstory of this other character? What about this other event that happened, how does it tie in? And then again I am in uncharted territory, realizing that the fanon that granted me respite was just that; yet another fanon. The attempt to fanonize seems neverending, and one is never sure that their fanon is quite "right", whatever that means. 

Wisdom

As we grow older we do two types of things: 

1. We learn and understand the orderly world built by our predecessors, retracing their footsteps as we understand the deep structure and meaning behind all these rules and stuff they left behind. For example, maybe going from "I need to get a job" to "What do I really want to in life, and what is the optimal way to get there?" to picking up a book on existentialist philosophy and never actually doing anything about it
2. We face "chaotic frontiers" of our own, actually expanding our domain of order. We make efficient, we optimize, we automate. We create rules, laws, systems. We build families, homes, business, empires, governments, or things totally inconceivably new, etc. And in doing so we understand our domains in a deep way that isn't apparent from just looking at the things we have built, just like our forefathers. 

We crystallize this kind of deep intelligence, often called wisdom. We talk about the "wisdom of the ancients", for instance. The funny thing is though, we're not that great at communicating wisdom to our children, even though it just seems extremely necessary: imagine if society was made up of people who lived forever. But then imagine that they forgot 90% of the stuff they learned every few decades. That's basically us.

Maybe it's just not possible, given our resources and the complexity of the ideas. Or perhaps we just don't think it's possible and choose not to. Perhaps our constant failure is that we have always underestimated both our children's capacity for complexity and our capacity to formulate and communicate knowledge. Instead, we have been teaching them those simpler, surface level "heuristics" -- get an education, get a job, get a family -- rather than showing them the deep-level structure of why  and how. Isn't it telling that we are exasperated by our children persistently asking us "Why?" to every subsequent answer? Why do we choose to forget and hide the difficult trail we traveled to get to where we are, when such ready and willing minds exist? Should we not prepare them for the trails ahead, even if those trails may be different?

In that way we are just like those prideful mathematicians, carefully erasing all of the messy tracks and waylays they took to get to a beautiful proof. And the children are like the poor undergraduates just trying to understand what convoluted piece of logical fuckery got the professor from step 3 to step 4. But in real life, our "proofs" are not so beautiful, or even proofs at all. Proofs have to be correct, after all... and I certainly didn't have to graduate from Princeton to be fulfilled with my life. 

Side note: Chaos as randomness

Earlier I brought up the weak Pinsker conjecture. Technically, it's about randomness + order, not chaos + order. But as some may know, chaos can be modeled as randomness. When we're too "lazy" to actually understand those deep-rooted variables that affect significant change, we typically just write down a probability distribution and call it a day. To use a cliche example, a coin flip results is often modelled as a random 50-50 thing, but we know that technically, it's a (mostly) deterministic system, and if we had the time and computing power we could actually predict if it lands heads or tails.

Tangentially related stuff, in spirit and motivation???

https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/

https://arxiv.org/pdf/1002.1410.pdf

Anti-realism

Point-free approaches to topology, and intuitionistic mathematics