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 I hope that everybody in the world gets their infinite moment of respite today. 

Wednesday, September 23, 2020

Music theorists and food critics

 So apparently music theory is racist because music theory presumes that valid music follows music theoretic paradigms. Here it is... great watch. Let's define: As Westerners, "music" here encompasses things that deal with melody, rhythm, harmony and other things that extend our set of examples, at least to the extent that we're comfortable with still calling them "music". 

Music theory engenders a certain attitude that even when we include certain non-Western sounds under the banner of "music", we only do so to invalidate it under Western music theory, as perhaps incomplete, or just "bad". The simple yet popular example being Ben Shapiro invalidating rap music because it is missing melody, harmony. 

When we reject this standpoint as inherently racist something interesting happens. We are forced to ask: what then is music, and what does "music theory" have to do with anything? 

We expand: what then is food, and what is "good food"? 

Well, now we are thoroughly confused, and perhaps that's a good thing. Confusion arises from trying, as in trying to fit something that just is into some known mental framework when it never asked to be fit... trying to fit an abstract and infinitely detailed jello peg into a two dimensional hole, if you will. 

And perhaps we should stop trying. Just eat the abstract infinitely detailed jello peg already. Take things for what they are: "Food" is definitely a word, "music" is definitely a word, and we try to associate experiences and things to them, for sure. And so these different "foods" and "musics" inspire all sorts of feelings in us, some pleasant, some not so pleasant. We'd like to assign "good" and "bad" to these things, but it's really not just about being pleasant, is it? Somehow there are all these other variables, like how "special" they feel, maybe the "complexity" of feelings they give you, all that. We're not really sure why we're assigning "good" and "bad" to things, but it seems really instinctive and useful, like understanding which mushrooms are tasty and nutritious and which mushrooms will give you diarrhea and a really bad trip when you're a hunter-gatherer in the wild. It's like a tagging system of sorts.

And we seem to take "good" and "bad" as some context-free indicator of general goodness and badness, as in "things to look for" and "things to avoid", as in "things that will generally improve my life experience" and "things that won't". This, in itself, is actually bad. I mean, at some point I'm sure the classification into "good" and "bad" is useful. I'm sure in some contexts it's meaningful and it's actually a good indicator of goodness and badness. But I fear those contexts are actually "Western music" and "French cuisine" respectively. 


How do people decode racism, and how to encode it

In the recent past I thought of racism very logically. Quite literally, I viewed racism as a proposition in classical logic, say R(x), evaluated as either true or false on the set of scenarios, say S. 

And as a result, saying things like "I'm not racist, I have black friends" wasn't anywhere near racist to me and it never made sense when people said that. In truth, I was actually quite frustrated and angry when people took scenarios that didn't seem clearly racist and insisted they were racist. What did it mean for something to be racist anyway? And how do you know what their intentions were? A non-racist could have easily said the same thing, so your accusation is unprovable, and also harmful. 

I refused to acknowledge police brutality on black people using the above logic. Effectively, I put an inordinate and large burden of proof on proving racism.

It turns out I was wrong: they (they being those people who I dismissively regarded as "SJWs") weren't trying to say that something in isolation was definitively racist or not. To them, it's very much a holistic, and sometimes probabilistic (will explain later), thing: you have to look at what has been said in context of who the person is and what they could have meant. When something is said to be racist, it means something more like "this statement provides information that, when taken in context of the situation and the person (such as: is this person white?), would suggest the person held racist views". 

It's actually quite complicated and is akin to a sort of Bayesian statistical inference, where with the new data we have (e.g. the person says "I have black friends") we extrapolate from prior information to deduce the parameters of our model (e.g. a parameter R determining whether the person holds a particular racist view or not). So the "new data" is not by itself determining R (racism), but rather it represents a positive differential flow of information that helps us determine R. However, the way we actually present the result in language is entirely misleading

The thing is, the language we use to call out racism doesn't accurately portray the complexity of the model doesn't help. In fact it further exacerbates a conflict of models: saying that some element (say of a situation, policy, or a statement/action) is racist (e.g. saying "that was racist" in response to someone saying something... well, racist), which is a common turn of phrase nowadays, suggests that said elements has some fixed quantity or quality of racism, as if racism were some kind of fungible property, like money. That is: money can be added to other money in a context free manner... because fungibility is like "a dollar here is a dollar there". It doesn't really matter where you add the dollar, it increases the value of something by $1 no matter what pile of dollars you add it to*. Further, the fungibility property is suggestive of a linear system: an increase dx always results in the same increase dy, no matter which x you're at. And as I mentioned, that's not the framework in which the "woke folks" are operating: saying something (dx) is racist (dy) is not some universal property of that thing (dx), but is rather an abbreviation for a much more complicated scenario that depends on what the situation (x) is. 

So as it turns out we're literally talking about linearity, and also as it happens, the language the woke folks use just reinforces the linear model. It's a communication problem! And the only way to resolve communication is by true understanding. This can only be achieved by proper listening and going beyond the language. The language, as we mentioned, is flawed: it confirms the linear model. 

The problem is, all of this is extremely difficult to understand. At least, it was for me! To someone who is not particularly invested in these issues (see: anyone who is not personally really affected by racism on a day-to-day basis), they have no reason to move from the simple, linear model to this complicated holistic model, especially when the language is not very helpful. It's much easier to stick with our old model, which tells us to disagree and perceive attacks and accordingly take offense when "called out". And we are surprised at this shouting match between two utterly divided sides. 

Indeed, at the core of any communication problem is a listening problem. In the wake of the Floyd shooting, I think many of us have internally recognized the importance of just listening, that it actually works. There's still a whole lot of the same old not listening, shouting, bickering, but things are getting better in the sense that we are collectively building the vocabulary and concepts required to understand the complexities. 

To further complicate matters, the detection of racist elements is entirely statistical, as nothing is certain. For example, Trump saying something kind of suspicious and racist-sounding might get a pass, but done enough times, we're pretty sure the dude is encoding racism. This is problematic because our entire culture, woke folks included, operate based on an assumption of a "linear world" where making local judgements (i.e. evaluating individual statements and taking things out of context) are "good enough" . This is, of course, in contrast to operating on a global/holistic level, taking things with context, and appreciating nonlinearity and embracing full complexity. 

A side note: Linearity seems to be especially an American way of doing things. I wonder how much of it is rooted in the predominant American culture of pragmatism, where the world is simple and straight and things just are, no fuzzy convoluted stuff. It relates to this sort of engineering philosophy of modularity, where components do what components do, anywhere and anywhen. No weird coupling effects, no mess. And perhaps this is also why Americans are less "global-oriented" and sometimes even insist on ignorance to the point of appearing to take pride in it. To continue with the geometric analogy, what might be happening is just an optimization, from an information-processing standpoint: there's no need to explore the whole manifold when you're assuming it's flat (linear), because local information (i.e. gradient) yields everything you need to know about the rest of the manifold. In short, why explore the rest of a flat hill when you know exactly how high you're going to be at every point? Indeed, to Americans, maybe the rest of the world is basically just America (just shittier).  

And furthermore, at the risk of sounding like I'm contradicting myself, it's not like just because it's statistics, there's nothing really concrete that can be said about racist statements. There are still enforceable "taboos", such as certain words and phrases that are said to be inherently racist. 

But given that we just developed this whole idea of Bayesian statistics and context sensitivity, how could we possibly go back on it and justify calling things "racist" in a context-free manner? How can "things" be "racist", regardless of  how or by whom or when it was said? Well, this is again a language problem -- "that's racist" is a pretty overloaded phrase. It's the "proliferation" argument at work: we should not say certain things simply because we don't want them to proliferate. To use a lateral example, using the word "gay" to describe something negatively isn't homophobic in the sense of the "statistical inference" thing, 


Honestly the whole thing is a little bit too complicated to express in the language of common discourse, which is why we struggle as a society today. The ironic thing is that most such things things are simple to explain in the language of mathematics. It's an unfortunate reality, but usually what happens is that over time, the public learns, effectively recreating the equivalent structure in, literally, their own words. Sometimes the resulting new language and theory reflects the obvious mathematical structure, other times it's a quite a bit different. More on these ideas later... maybe. 


*Generally in finance though, if we go beyond dollar-speak, it turns out that financial decisions are not fungible either, even though we would like to think of them as such (it's a lot easier to calculate and optimize decisions when every aspect of a decision has a fixed cost). For example, we would like to think of purchasing a home as having some sort of fixed value, and one can indeed arrive at some kind of opportunity cost number given some fixed time window like 5 years... but add in just a little pinch of reality and you can ask questions like, if you didn't buy that home and invested it, what then is the cost of the home after 5y? What if you didn't invest it? Should we use that number? Or what if you "invested" in a lottery ticket? It becomes a little ridiculous if we go on, but the point is that it's not so simple, so when financial experts talk about "opportunity cost" of a decision or equivocally the "'value' of the object being bought/sold" itself it's actually in a very particular context. It's important not to believe that $ value applies universally to every financial situation and decision context. 

Thursday, September 10, 2020

The Process

I read this interesting article the other day, real eye-opener. 
The idea is that if you just start focusing on the process, rather than the outcome, you'll start feeling much more free, much more effective. And this is true on multiple levels and for multiple reasons. 

There's so many other concepts that link with this one: 
  • Focus units -- by removing extraneous considerations, you free up focus units
    • These focus units can be used to form a global perspective, for instance. Perhaps "go meta", form a general theory, a model to understand your internal data. A model helps you interpret internal feedback in the model context and gives you hints on which points to test and explore to gain maximal information under the model assumptions. It could even help you build your own learning plan. 
  • Control and optimization -- by paying attention to internal factors (factors that are directly under your control) and less so on external factors (factors not under your control), you can run a learning algorithm to find the correct control pattern to get the desired result. The classic example/model is a smooth map between two differentiable manifolds. Outcome-fixation is like trying to control the outcome from the range directly, but it's really the domain that controls the outcome. 
    • A cute mathematical application of binary search for optimal control comes in bottle flipping. The mistake people usually make is not paying enough attention to how your kinetic chain feels when flipping the bottle, instead focusing heavily on the way the bottle flips. Once you start feeling, you can start adjusting and remembering and get pretty consistent. In the end, the most complex of movements is controlled by just a series of muscle contractions. It doesn't come from you "imagining the movement really hard in your mind and trying to do it" -- this typically results in your mind resorting to known habits, which is often the opposite of what you're trying to do when you're learning something new
  • Mindfulness -- outcome-fixation is often accompanied by looping noise and negative thoughts which ruin focus and consume mental resources. 
  • Scarcity mindset -- outcome-fixation is often accompanied by scarcity mindset. This is a well-known cause of tunnel visioning, which is almost always contrary to our complex, modern day goals. 

Global perspectives, and Steve Jobs' definition of "smart"

 Steve Jobs once defined "smart" this way:

A lot of [what it means to be smart] is the ability to zoom out, like you’re in a city and you could look at the whole thing from the 80th floor down at the city. And while other people are trying to figure out how to get from point A to point B reading these stupid little maps, you could just see it in front of you. You can see the whole thing.

Oftentimes you will find that local insights can be put into context if you have knowledge about global trends. It's good to remember that everything you do is part of a larger future, and that you yourself are a cog in the machine. 

Additionally, this perspective also helps you get out of focusing on stupid shit and keeps you reminded of other important lessons. Like:

  • Focus on what you CAN do, not the results (Stoicism, Focus, and The Process). Learn to "localize" properly. 
  • Understand your local goals in the context of your life, your life goals
  • Understand your life goals in context of how you fit into this world
  • Understand others, and others' actions and how they appear in context of their own lives, their own feelings as actual human beings (dovetails with emotional intelligence) 
  • Understand your life goals, yourself, and others in context of the world
  • Understand the world in context of long-term, large-scale, global effects -- e.g. the market, economy, historical patterns leading to rich insights (typically coded in few words but hard to understand unless you know them already) 

Keeping a global perspective prevents you from tunnel visioning, since it's easy to "drill down" into local effects but it's hard to "dig out" to see the big picture. Example: You start having troubles with your old car. You think it's really important that you to purchase a new car soon, but upon taking a global perspective, you start questioning yourself. What do you actually need it for? Frequency of use?  Is it going to increase your life satisfaction? Does it align with your values (e.g. considering environmental impact, economic waste)? 

I think what Steve Jobs defined can also be applied to "wisdom". Wisdom is making sense of everything but in a more elegant mental model. The way society is, all that. In short: Knowledge is local, wisdom is global. 


Related:

"We call the local cue knowledge and its accumulation wisdom, and the canine (and we humans) need both kinds of information to succeed." - L. Mahadevan, https://www.quantamagazine.org/l-mahadevan-finds-math-inspiration-in-the-mundane-20201026/

Learning: Importance of foundations

 I've found that a lot of people "know" things, but one you start questioning them deeply they don't really "understand" things. 

To put things in a formal perspective, you can say there's little "connectivity" and "rich graph structure" beneath that single "node". For instance, you might talk to some pop science enthusiast about the hip new discovery in particle physics. He might know all the names: Higgs-Boson, wave-particle duality, whatever. But you start asking questions and it appears that their mental model is basically the same as yours, except with special names for "very small glowy balls". 

Elon Musk says this is not so helpful. He makes sure to build the trunk first, instead of collecting the leaves. Build a core knowledge base -- what is this field actually about? And then, as you accumulate knowledge start building connections, a rich graph structure, involving the foundations, the new knowledge, to external knowledge, whatever. 

If the previous lesson regarding memory was about having the requisite nodes available, this one is about building connections between the nodes. 

Wednesday, September 9, 2020

Badminton: The whip action and loosening up to speed up

 So I noticed that especially when I get frustrated in a game, I will tend to try to "push" shots with the more initial, "bigger" parts of my kinetic chain. People call this, "muscling the shot". Meaning, say in a backhand, I will try to push harder with my arm instead of letting go and letting my wrist take care of the rest. It's this insistence on "more muscle = more power" that is absolutely false in badminton. 

As a test, try the backhand lift. How this should feel is that upon the completion of the move, the arm wants to fly up due to the momentum despite the arm being completely relaxed. That's because energy transfer occurred efficiently: nearly all the energy from the arm transferred to the racket, and the racket now wants to pull the arm up. That's how pretty much ALL shots should be. 

Why? Well try muscling a backhand tap drive. You'll notice that the while accelerating, the wrist is not nearly able to generate that speed, effectively springing off of the forearm rotationally and absorbing that energy from the forearm. That's because it requires more force to complete a shot against that acceleration. It's like jumping off of an accelerating platform. 

It's better instead to apply just the right amount of forward force with your arm so that you wrist stays stationary and absorbs the maximal amount of energy while it is uncoiling. Why? I'm not completely sure. 

All I can say is that when it comes to the stretch-shortening cycle, it's better not to fuck with the forces. For example, don't try to force pronation to go faster by either directly attempting to add additional muscle to a pronation or adding forward acceleration to your arm and trying to press the whole thing forward, which would be accompanied by either: 1. attempted additional muscling of the pronation leading to a weaker shot or 2. slowing down of the pronation movement, leading to incomplete and bad shot. 

If you do 1, you're essentially composing motions. This defeats the purpose of the whip action: the cue is to break up your motion into independent segments. Example: When the body is done rotating, it only serves as a foundation for energy transfer into the arm. And when the arm is done accelerating, it too should stop and only hold enough force to pass its energy down to the forearm, then forearm to pronation, etc. This way a slow, large bank of energy gets transferred into a small, fast bank of energy. That's how you generate speed, and that's the idea of badminton shots (and trebuchets). The SSC is the same concept, but with elasticity: it's capable of converting a lot of potential energy into speed, but only under certain conditions. If you mess with it it doesn't work. 

This idea seems to work for basically any shot: the overhead forehand, backhand, drives, lifts. The shot I'm not completely sure about is the forehand drive, the one shot that seems like more muscle rather than the stretch-shortening cycle (SSC). 

Learning: Memory as a component, and prep work in cooking

So I ran across this yesterday.

You know, a math professor I really respect liked to say that "Intelligence is just structured memory". And he's right. Memory is so important, just like prep work is an important part of cooking. 

At some point during high school though I started scoffing at the notion of memorizing things, and the attitude grew with me during college as well. I think it was when I started getting more into philosophy and mathematics that I prioritized the generating of thoughts and ideas, and processing/understanding them as way more important than memory. I rebelled hard against that Asian ideal of rote memorization, and sort of demonized it in my head.

Yes, learning is about understanding and not just about memory. But you need memory, some kind of memory, or else you'll never actually learn anything, you won't change. It's like saying that cooking is not prep work and dicing vegetables and glorifying all the master chef work, recipe research, with absolute disregard for anything that happens before.

But anyone who cooks knows that prep is extremely important, mise en place is extremely important. How you do it is important -- cutting vegetables and meat into even pieces, placing things so as to reduce cognitive load when doing the "cook" part. 

There is a direct relation to learning and thinking as well: you need to have stuff memorized, like really well-memorized, if you want to make sure you don't think in circles, waste time, miss things and misunderstand things and just learn very inefficiently in general. Memorizing provides the foundation for the processing later on, much like the processor works with bits in memory or the cook works with evenly cubed carrots for his curry. 

At some point I forgot this. Or perhaps it's better to say I never actually learned it. Either way, I got into the habit of learning like how I cook now: doing the memory part as an afterthought (most of the time less than an afterthought because I never consciously gave it any thought) only when I absolutely needed it at the time. Although I've gotten better at this, during cooking I often forget to prep and start getting the spices out, looking for stuff, chopping vegetables while something's already in the pan. There's basically no structure to that at all, no thought to optimization. Particularly because I discount the holistic important of memory and focus on the method that I feel is "right" because it appeals to my philosophy and sense of beauty. Prep work is gross, memorizing things is inglorious. Almost a Heidegger-esque revulsion to "manual" labor. 

But when I do have quick-access to things in memory, particularly the very ingrained, muscle-memory type, the processing goes a lot smoother since I don't have to shift my mental resources around trying to remember different things constantly. There's a lot less interrupts and my learning speed increases exponentially. In general, I think that although you shouldn't be stuck in the basics trying to perfect them forever, having a strong (or at least existent) foundation often exponentially increases your learning rate. 





Badminton: Learning with constraints and shortening the feedback cycle

I'm going to try constraining myself to "good form" and "solid footwork" first before allowing those "reach" shots. Honestly that's what 

This will serve the purpose of not only habitualizing proper footwork but also learning strategy and shot placement by making the consequences of poor shots more immediate, therefore shortening the feedback cycle. Also I'm pretty sure it also helps with lots of other things like racket position, general positioning, shot quality, etc. 

The idea, of course, applies to everything, not just badminton. Sometimes generalizing and de-constraining helps particularly when there is some elegant expression in the non-constrained space (for example, see "Long-term motor learning: Effects of varied and specific practice" , but oftentimes holding one variable fixed is better for working memory and feedback, and thus better for learning.

Wednesday, September 2, 2020

Classical music

 There's so much deep theory, so much deep stuff in the study of classical music. And pop music, despite being somewhat inspired by and based on the same theory, seems to just throw all that stuff out the window and start over.

But it actually kind of works, because pop music surprises me sometimes. It does new things all the time, perhaps by virtue of discarding the old entirely. And pop music is kind of fun to listen to.

This pattern happens all the time, though. Movies, shows, video games, what have you. Even food. 

It's this dynamic where a field advances to an extent and develops this massive history, culture, and depth and explores all kinds of things. It gets to a point, I guess, where it just becomes so obtuse and dense that the general populace doesn't care anymore and the popular stuff becomes relatively more "basic". 

The "snobs" look down on these works because they're basically things "they've seen before" -- I mean, not literally, because nobody has lived through thousands of years of music, but things that the "theory" has taught them.

And often it's when the pop stuff encroaches on the domain of the more complex that it often gets really good. This can be explained in terms of the dynamics, too... as the audience starts to re-learn, basically, the theory that already exists classically because they start getting numb to the "quick fix" effects and tire of the same old thing (e.g. people start getting tired of the same old superhero movies and explosions no longer give them the happy feels), they start demanding something with more substance and flavor and complexity (e.g. people actually like the new Joker). And then the classically trained folk look down on this because duh, this has already been done and you're raving about something we've known about and we've gotten over years ago (e.g. critics criticize the Joker for just being a rehash of Taxi Driver). 

And this is not just about music at all, some examples I can list off the top of my head: the rise of foodies, 

I guess this all fits into the theory of expert-layman dynamics, except we're talking about art and entertainment here and in this case the laymen are just as involved (typically in science there's no real "popular culture" around science. I mean there's pop science but that's a little different). 

Contexts and Seas

https://www.quantamagazine.org/emily-riehl-conducts-the-mathematical-orchestra-from-the-middle-20200902/

I wonder if chaos theory, or mathematics in general, had anything to do with how the dinosaurs got out. Did Dr. Malcolm know what he was talking about? Was he showboating? Both?

But then again, when does "mathematics in general" not have anything to do with anything? I wonder if mathematicians who work in dynamical systems sort of see the world differently, and they can just "see" certain things which seem magical to us.

Must be. Sometimes, knowledge global structure and dynamics yields really valuable insight about local patterns. Even things that seem chaotic locally often seem to admit some global pattern, right?  History gives us perspective into law and modern-day politics, evolutionary theory yields insights for psychology, sociology. 

It's sort of a Grothendieck-esque thing, I feel. One of my favorite analogies by Grothendieck is the following: 

"If you think of a theorem to be proved as a nut to be opened, so as to reach “the nourishing flesh protected by the shell”, then the hammer and chisel principle is: “put the cutting edge of the chisel against the shell and strike hard. If needed, begin again at many different points until the shell cracks—and you are satisfied”. He says: I can illustrate the second approach with the same image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!"

He imagined that a problem could be "submerged and dissolved by some more or less vast theory, going well beyond the results originally to be established". I think this is particularly striking, because that's how I imagine it -- a structure made of something loose, porous, and then some sea comes along which basically surrounds, marinates, penetrates, and incorporates this structure so that it's not literally the same, but rather the same thing viewed in a lager context. Something that is more "filled in" but at the same time more general, global, reaching beyond your initial world (the porous structure). 

Or maybe it's like never seeing a car before, and looking at a particular portion of it, perhaps the gearbox. You study the thing to death and do some really cool things with it, and then you are shown the whole car, the whole damn thing and you realize why the components are arranged the way they are, and why they HAVE to be like that. But I imagine that cars are not the only thing that use gearboxes, so there are even more ways to expand your concept of gearboxes. 
So I imagine that there are actually multiple "seas" that might encapsulate the same "structure" in different ways. 

Lately I've been wondering exactly how much I know, and judging by my "learning velocity" I know basically nothing. There's so many mind-opening things to be known, so many seas to immerse my models into.