Mathematics is just a form of mental gymnastics

Our neural networks often generate these little "concepts". (See motivating example in addenda)

 

The powerful thing here, is that we can write such concepts down, or otherwise name or remember it. And once we've written it or remembered it, we can do things with it that we normally can't do when it is but a fleeting pattern of signals in our neural network.

 

As a still-quite-abstract example, sometimes we retrieve a mathematical idea from a very "fuzzy" intuitive idea, or some "hunch" that we have. We just know that some mathematical description of it ought to exist, and eventually we're able to write it down and "capture it" to some sufficient degree. This is done in the exact same way a painter captures a feeling or concept in a painting.. in the sense that the image of the painting in our minds can be processed in a way that evokes the concept or emotion in our deeper mind. The simplest way to do it is by naming, which is basically the bundling together of several intuitive thoughts, feelings, experiences into one without any additional structure. Of course we usually do something more than naming, using other pre-established names and relations to build something with structure, and in effect "reducing" the thing-in-our-minds into just these other, already labelled, "known" things arranged in some combinatorial way. 

 

Anyways, once we've captured a concept as described, we can apply other little concepts to it, create more structures. In this way we build and build. Essentially we are "hacking" our own minds, conceiving of new ways to think about the same things in different ways, about different things in the same ways. Further, we often "extend" our neural network by using external memory (e.g. paper and pencil) and external processing (e.g. computers, grad students).

 

This idea of forcing our brains to do different things… this "hacking" thing…. Seems profound. It's like us trying to transcend our own minds, become greater than it by telling it how to think. But by definition… we can never transcend our own minds, right? 

 

..Or can we? We might consider that indeed, we're not just using our minds, but other things: paper, pencil, computers, and… time.

 

The summative mathematical results of our mathematical work across all memory, external or otherwise, and time… may indeed surpass anything any mind by itself would have done, ever.

I mean, that's a nice fantasy. But what do you call math that you do entirely in your head, and learn via experience over time? What if, say, a man thinks up of an addition system all on his own, just over time?

 

Well… that man still made an effort to remember stuff in his head, effectively "writing". The point is that he still used your executive function to make sure his brain "burned in" certain things, certain "gymnastics". That's when you're doing math -- you're becoming aware, conscious, and basically manipulating your unconscious mind to make it do what you want. It often involves taking bits and pieces of the thoughts from the unconscious brain, naming them and storing the labels into the conscious brain, then using them to take control of what the unconscious brain computes for you. Usually, the unconscious brain is purely functional -- like an artificial neural network, it arranges itself in the optimal way in response to reinforcing stimuli. But when one does mathematics, one might say it becomes more than just a means to an end, but a means in itself. This idea, in fact, reflects in mathematics itself at several levels: On the actual doing of mathematics level, there's often theory that just is. It doesn't really "operate" on anything, and it's more like am abstract painting than anything else, just sort of describing this object. It's sort of the part of math where you build definitions, write axioms. And then there's mathematics that "says stuff". Theorems, lemmas, applications. And on the outside-of-math level, there's mathematics that's really "pure" and doesn't seem to be inspired by or say much about much of anything. And then there's mathematics that really came to be as an abstraction of real things and experiences.

 

You might say that the conscious brain is not as powerful, but with the help of the unconscious brain and by making it "its bitch", it can do some pretty impressive stuff, something the unconscious brain by itself wouldn't have really bothered to figure out on its own.

Of course, this is sometimes less true than other times. It's like native people who speak a language vs a foreigner who learned it "by the book". As foreigners, the native people, it might appear, "know" the grammar rules! But anyone who is even slightly introspective about how they speak their native tongue knows that that's just not how it works. We will often be surprised that certain rules even exist, despite the fact that we magically seem to always follow them (e.g. order of adjectives in English).

And indeed, there are structures in our deep unconscious minds that make it so (hence why we don't observe the rules consciously), although they may not actually be represented by literal graph-theoretic components strung together in some logical structure that the grammar books seem to imply.

In fact brain research hints at the contrary (brain surgery experiment), which is that logically modular "functions" seem to be more topologically distributed rather than actually topologically compartmentalized in the brain. And indeed, this may just be a better, faster way to do things, and the componentization is just a side effect of the deep structure of how the function really works.

 

So do we say that the native speaks "does grammar"? Not really, not in the same way that the foreigner "does grammar".

 

And it's true, it's quite beautiful in a way how native speakers can speak their language so well and so effortlessly. The foreigners might be slower, limited. But oftentimes we will be surprised at how eloquent the truly well-studied foreigners are. There's a running joke on social media sites about how people who say apologize saying "sorry, English is not my native tongue" often speak English better than half the native English speakers on the site!

 

And there is an advantage to knowing conscious, compartmentalized, formal rules of grammar. And that's provability, communicability, and extensibility. That is, with provability, we can extend, scale. And we can communicate and share proofs with other minds, because the elementary objects of the proofs are, purportedly, basic concepts we can all work with and understand.

 

With only our pure, unconscious neural networks, we can only do so much. It's true that we often overthink, theorize, and generally forget to get out of our heads and just simply do the task, but at the same time we're not going to be launching spaceships based on the advice of some seasoned veteran who "knows his rockets real well". Because first of all, such a veteran isn't going to exist…. I mean, how much "trial and error" are you gonna have when it comes to building rockets (which is what you need for the training phase of the unconscious mind)

 

I mean, raw experience and ingrained skill are great for most human tasks…  maybe even all human endeavors and jobs/skills made up before some time period (hunting, farming, building). But even the slightly more complex stuff require some theory. And of course, once you're talking theory, you're talking about the conscious mind. Executive function. Rules. Logic. Legos.

 

And the two minds used together in this way, in what we call "mathematics", is truly powerful. And that's what mathematics, at its core, is really all about. Using your head real smart.

But I doubt mathematics is the only way to use your head real smart. It sure is an interesting way to do it, and it definitely seems to be the most executive-dominant method of the bunch.

Badminton Experiment, and Breadth-first search

Apply previous lesson: don't settle on the solutions that you like too easily. Imagine it's like BFS and DFS on a tree.

First a framework to keep in mind: the goal is to "learn" and"master" something. Essentially what you're doing is trying to "memorize" a solution in a solution space. We all know it's not enough to "know" what the best way to play badminton is. It's not enough to accidentally even do it and feel it once. What we're seeking is MASTERY, which has basically everything to do with MEMORY. And that's *fast*, immediately accessible memory, not some slow isomorphic representation in our minds (i.e. the ability to talk about it).

And often, we have to "cut" and partition our space in sequence to "drill down" to the solution, because often the solution must be expressed and decomposed as a series of conjunctions. This means that one common way to learn is to "learn" one or few conjunctions at a time. We all know human mental capacities are limited and sometimes we just can't do multiple things at once. In fact the very definition of "multiple" might just be those things that the mind can't handle at once.

 

Anyways, back to it. DFS is like setting a bunch of goals and attempting to satisfy them all at once, trying to immediately assume the final solution and practice that. If it doesn't work, back up and try something different. BFS is instead incrementally exploring your solution space and solving little bits and pieces at a time; not necessarily rushing and making assumptions on what the final solution is going to look like and trying to train that, but rather poking around, committing correct pieces to muscle memory and proceeding slowly and consistently.

 

Example: Badminton, statistical problem at work (exploration of intuitive concepts like "bumps and streams" instead of trying to jump into immediate abstraction)

 

Particularly, when playing badminton it's really tempting to attempt to emulate the pros without really understand what's going on, and copy everything immediately. So we might try to forcefully pronate the arm. Or do some sort of exaggerated split step motion. Or get really low to the ground and make exagerrated step motions. And we might try to practice some kind of inefficient exagerrated chassé stuff. All of these I have done.

 

The problem is exactly that: we are trying to do things without understanding them, so we are likely to make mistakes. That's because all of the solutions that the pros implemented have deep reasons and come from deep, layered reasoning cemented over years of practice. It's like seasoning on a cast iron... You can copy it but you better make sure you're seasoning correctly and slowly and thoroughly.

 

At the very least, we should pay attention to our bodies, and use our brains. If it simply doesn't make sense to chassé when you could just step or run, don't do it!

 

That's the great thing about BFS and exploration, taking it slow. You'll come to understand, layer by layer, level by level, why a particular method is good, because you've explored the alternatives. For example: with flat drives, we understood that a "pushing" motion was appropriate and proved it physically to some extent. Even if we didn't literally explore alternatives (we did, like the exaggerated backstroke method... seeing a pattern here), the very nature of analyzing motion is a process of elimination of alternatives**. In other words, understanding the bits and pieces and habits and skills that make up our final solution *in context* helps us recognize WHY we do things, thereby creating a stronger mental relevance in our minds.

 

But what about if you have a mentor? Or some kind of guide, that tells you how to master something? Basically this is more like BFS (simply because it's not like DFS where you try to master everything in one go. Although maybe for some skills this might actually BE the way to go) except at each step you know exactly what to do and what to train. And you know exactly which skills to train first (i.e. how to partition your solution space, and which partition to go to and engrain into memory, I.e. "muscle-memorize").

Is this always the best way though? Perhaps for the sake of time. Perhaps for the sake of advancing the field (you cannot have students rediscovering the wheel all the time)

But yes, a master can teach a student all of the correct routes, never letting the student fall into bad habits, wrong paths and traps. But does a student understand the fundamentals the way the master does? No, because of experience: the master UNDERSTANDS what arithmetic is simply because of all the time he's had to deal with edge cases and scenarios which force him to understand beyond the abstraction, and the student simply knows 1+1=2, quick mafs.

But does a master compare to the creator when it comes to the fundamentals? Likely not. The creator understands even more intimately the pain that he had to go through in developing his art. He truly understands fundamentally why you would even want to have a system of arithmetic since he was around before it even existed. He understands every "why" of why the fundamentals have to be the way they are. In this way, the fundamentals he has created are a part of his being because they are so entrenched; entrenched by all the reasoning and failed alternatives that make it obvious why the fundamentals are the way they are.

It's like actually understand the area because you've explored the roads vs just reading a map. It doesn't feel the same: making a right because Google maps says so (student) vs making a right because you want to go to Walmart and not the neighborhood up ahead, according to the map (master) vs making a right because you actually have explored this area and been to that neighborhood and it's really not friendly (creator).

Another analogy (there's so many) is like the user, the superuser/scripter, and developer.

As you can see this is a fundamental principle of human knowledge and learning and it explains a lot. It might even explain why Rodney Mullen is so great and nobody now is as great (because he created the fundamentals and was around during it's developmebt... Well also skaters don't practice fundamentals very properly)

 

 

Aaanyways. Back to badminton. Sure, you could have a coach train you in all the right ways. You will get to the end faster, and by virtue of real world experience you will also realize why the right ways are the right ways... To some extent. Of course, the more stringent and linear the training regimen you're ironically less likely to understand the "why" of things, which may prevent you from truly mastering things. [Also maybe badminton isn't really complete yet, and there's more weird things you can make up that don't necessarily follow the rules (but that's a maybe).]

 

That's why I want to try "coaching" myself. Use videos. Watch videos. Annotate. Watch pros. Do physics. Experiment, explore, then train.

This is a true BFS approach.

 

 

 

**[Why? Because selection of an optima can be seen as de-selection of non-optima. For analogy, remember how proved theorems work in computation. You can always do a brute force search, but if you know certain theorems you can narrow down the search greatly. As a side note, Dr. Williams said that sometimes it's just not worth it). And even the proof of that theorem eventually breaks down to physics, and the laws of physics breaks down to elimination (deduction) of un-truths.

Aaaaanyways. ]

 

 

 

 

 

 

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Definitely, by observing, accepting, and understanding my own mind, I've improved in writing, and thinking, as well. I understand my limited memory, so often as the ideas come I jot down quick notes. Instead of trying to do everything in one linear go and having to rush (and writing terribly in consequence), I let myself write more nonlinearly, and structure my sequence of words so they are more meaningful and more properly cemented into paper and mind, so as to build a stronger foundation for the next point.

 

Dovetailing off of that point, I've also understood the importance of organization, tidiness, and things I formerly disregarded. Like making your writing pretty, putting subtitles, references. Organizing your workspace. All this stuff I thought was useless because I didn't pay attention to the chaos storm going on within my mind, slowing me down.

 

 

You need to go step by step. Sure, if you have a lot of discipline and you know that your "lesson plan" is correct, you can do a DFS and learn quickly. But otherwise, you are going to have to explore.

 

To explore properly, you need data. That means listening to your mind, listening to your body, listening to your emotions -- because that is the data that goes most unrecognized. We tend to focus on only the outside world and the results. When badminton isn't going well, we focus harder on what's going on on the outside and try to force your body to go in a certain way, stare harder at opponents moves to "pay attention". We seldom think about how our body's momentum feels, about how there seems to be inefficient energy loss up our kinetic chain, about our insecure and turbulent mind that fails to recognize that our strategy and tactics are incorrect. When we fix this, wake up from our tunnel vision and start PAYING ATTENTION, suddenly the court is simple to you, just a problem that you control with your body. It becomes little more than a control theory problem, no longer a confusing mess of I-don't-know-whats-going-on. Instead you will see it for what it is: controller (your body, your mind) and feedback (the environment). Dead simple. From here, your game brain will take over.

The problem is, to get to this state, again, you have to let yourself get to it. Oftentimes you're just too caught up, too much absorbed in feeling frustrated, that you fail to admit that what you're doing isn't working, because if you're wrong then what worth do you have, right?

 

Body badminton

 

Focus on self

Looking outwards and taking advice

 I've often found it difficult to take advice from people. I used to think I was pretty open minded, and when I decide to be I really am.

I actively avoid looking outwards for advice, asking others for help. Why? Most likely it's a fear of realizing that I "suck" at things, a need to be great at everything all the time. I've come to understand myself a little bit more now and I realize that I'm hard on myself a lot of the time. 

Another symptom that supports this theory is that I tend to "rush" or "force" short-term solutions to things instead of really learning. I'm not observant of my own capabilities, preferring instead to focus purely on the outcomes, trying to make something work, at least to the extent that I can delude myself into thinking that I'm good at this. I've done this with school, with work, with relationships. I cover up problems and don't listen to my own mind, my own body. It's also a source of great stress... things are real difficult when you're not actually getting any better, improving, but still have to convince myself that you're awesome. My neurotic personality is likely associated with it, since my way of solving a problem is by thinking about something over and over, worrying, pacing around. 

Those times that I "let go" and accept the limits of my capabilities, things just get... better. My headspace seems a lot clearer. It's not that my problems magically disappear, but the problems are put into context. And as it turns out, the solutions often lie not with me but with the outside world, with others -- there are so many things I was doing sub-optimally that became drastically better after some simple changes. Yes, I suck, but it's not too difficult to not suck after all. It's a matter of opening up. 

It's difficult to admit that you're not complete. But I imagine that once you get into the habit of truly learning new things, new mindsets and attitudes that you couldn't have possibly thought of in your lifetime, there is a paradigm shift. It's not this simple "get problem, process really hard on your own, output solution" anymore. You're now part of a community of human beings, this larger organism. Problems aren't a limiting, "you've got to solve it now" kind of scarcity-mindset-inducing, urgency-inducing sort of thing. Instead, they're just... things. Opportunities? Curiosities? 

What is an interview?

Networking, interviewing blog post
-being yourself
-understand the root of things... If something seems difficult, you're likely looking at it the wrong way (ex. Talking to people just comes down to seeing them as people and not as interfaces, seeing conversation as something more than just means to an end, but rather just allowing yourself to discover things, explore others minds )
-win-win article. Honesty works for everyone except for sociopaths.
-joshua -- him and his friends see it as a game. Doing things to build up their resumes. I was the same way... But what changed? Where do I now stand? I see the bigger picture, the mechanisms. As a society we attempt to obfuscate all of our institutions. But we are not nearly to the point where we can sustainably do that. To be part of a society, we need to understand the complications, the reasons why we do things, or else we'll just be going around faking things, using these flawed APIs that only mimic the right behavior.
-try building society from the ground up. What is an interview but just a test, a communication and exchange of information to test whether you two are a good match?
-stop looking at it like a selfish thing but see the big picture of how society works. Those who see this picture and want to participate in society recognize each other. If you play games they can see right through you.
-look at it this way. In an interview, what is your goal? To get a job? That's a scarcity mindset right there. The point is not to get a job, that's an ad hoc solution that you have devised, or been told is the only solution, and decided on, without understanding the general perspective. And the general perspective is this: we're all just trying to survive. And to survive and maybe even fluorish, we need to provide services, create goods, build things, improve things. But to do those things we often need to work together, we need to trade -- what a job is is simply a function to enable you to apply your skills in the best way so that you can trade your time for other things of value.
So speaking of your skills, when you are interviewing or negotiating, what should you do? Should you overrepresent what you offer? No, because this is dishonesty! Not only that, the dishonesty will always catch up to you. But that should not be the reason you dont lie... You need to think one level deeper, go beyond the simplified scarcity mindset of "I need money and I need to find someone to trade with". Rather, you need to think about it holistically, from everyone's perspective. Rather even further, take it to the limit, and just look at the truth. Is this partnership -- yes, I mean partnership -- going to be mutually beneficial, and optimal? Is it "win-win"? Otherwise, there's deception going on.
The reason I stress honesty so much is because that's how you really should look at everything. No games, just honesty. If you're just honest, you should only have to present yourself as you are. All of these interview prep things are now cast in a different, less toxic light... Instead of you memorizing stuff to try to game them, you're learning more effective ways to communicate your honest, true self and what you can do from them. And that's the best form of marketing.
Of course on the other side there's ways you can undersell. That's why you need to practice communiction.
-communication is information transfer. If it's based on truth, then it's easier to communicate. If it's based on lies, that's deception. Deception is a lot harder to get good at since it's more natural to just be yourself and have other people believe it than to project a false image of yourself and have them believe that it's genuine. Unless of course you're a sociopath that's really good at lying. But usually people are really good at recognizing genuine-ness and non-genuine-ness. Real recognize real, I think.
-The best way to act in a certain way is to BE a certain way. That's why the best actors literally put themselves in the character's shoes. There's just so much entropy and ways you can give away your hand if you try to control everything. The subconscious mind is better at crafting a story, maybe.
-and that's the thing. If something seems difficult but not difficult for others, like you have to consciously control and force your way into it, you're probably doing it wrong and there's a different way -- you need to adopt a certain mindset. Because clearly in their mindset, it's easy. How do you get to that mindset? That's the question. The first, and most important, requirement is that you "keep an eye out". Stop fixating on those "obvious" linear solutions. Stop staying in a toxic mindset and just think about other possibilities. Explore. Talk to people. Admit ignorance and avoid assumptions. Love yourself and don't fear "mistakes", which are really just data gathering exercises. They're only mistakes to you because you put your whole self-esteem at stake on these "successes" you're chasing.
-dont play games.

Gas station, 12:30 AM

Slow numbers go up

Really just need to fill up

What the fuck ? ? 

raining trees

Trees don't weep in rain
Afterwards a gentle breeze
Sheds their tears away

birthdays

There's nothing special about being born.
Well... That's not quite true, we (humans) are pretty amazing, if only as information processors, neural networks.
But a neural network is really not all that interesting in a vacuum, is it? What does it do? What is it supposed to do? How is it useful?
In the same way, none of us come into this world with a sense of meaning or purpose (at least I didn't). The way I see it, we come into this world as painters with blank canvases. But we color each others' canvases, not our own. Every greeting, every interaction amounts to a sharing of paint on these canvases. Over the years, the empty canvas fills and transforms into a work of art.

For those who have known me, seen me, interacted with me in some way, the 11th day of April marks the day of beginning of this life, one of many that would touch and color their lives.
For me, it was the day I joined this weird drunk-painting class.

Like a violin being lifted into a dissonant, but beautiful harmony, the singular me is granted meaning through the collection of singular others.

I want to take this day to really notice this fact, really appreciate others for their contribution in creating, for lack of better words, this work of art. And, as  art, whether it's good or bad seems irrelevant. Comparing it to "other pieces" becomes meaningless to me, since there are no other works I can truly, fully see in full detail as my own.

So why not take time on your birthday to meditate on your (but not really your) painting? To open up to yourself, and then open up to others by recognizing that you are part of this beautiful collage?



I often say half-jokingly that mothers are essentially the best machine learning experts. Every child birthed is the result of future-state engineering -- hardware, firmware, software, model implementation. On top of that, mothers need to train their children using supervised learning, reinforcement learning, and sometimes unsupervised learning.
I love nature (modulo humans) as much as anybody. But humans are on a different level... in part because I am one. The complexity you can perceive even through the most basic communications channels: words, speaking, actions... it's mindblowing. And that, in my opinion, is what makes appreciating this collective of humans so worthwhile. You'll never run out of richness, depth and beauty to explore. It's the combination of complexity and the ability to comprehend that complexity.