## The Little Vulgar Book of Mechanics (v0.2.0)

Last updated: February 1st 2022

## Introduction #

The nail clipper doesn't get enough respect. I mean the good ol' nail clipper. You know it's a machine, right? Your nail clipper is a machine. A simple one, but still a machine. Technically speaking, a compound lever.

More on levers later. This is the introduction. But I don't really wanna waste your time with introductions, so, long story short, for the sake of history, I'll just say: This document started as notes and links for a science-y podcast episode. But, like everything I start, it grew too fast, and became something else, beyond its original purpose. So, instead, I'm gonna be growing this same document, throwing notes for several podcast episodes, song lyrics, troll posts, etc. It's just a collection of useful definitions, historical anecdotes, glued together by my shitty and rude commentary. Topics: Acoustics, Audio, other branches of Physics, Chemistry, Math, and also everything.

This document is for us, the vulgar engineers who are making shit. If we share a common language, we can build better nuclear reactors inside our death metal recording studios on our offshore drilling rigs, during the zombie apocalypse. So that's what this "book" is for. If we all agree on what we mean by "energy," "waves," etc. that'd be great. I think. Better communication through math and shit = Better at building shit.

Warning: My prose is bad, my english is almost as bad, and my approach is extremely vulgar and informal. We're not academics here. Finally, and importantly: We're not here to confirm our opinions, or to feel like we're smarter than our grandparents. We're here to optimize our communication so we're better at building, maintaining, and assessing shit.

## Feedback #

Let me know about any typoes, grammerz, and badder engrish you find. (Though if you do it about this specific paragraph, I will stare at you until you realize what I think of you.)

## Types I #

Let's always be as clear as possible about the types of shit we're talking about. I mean computationally. The units. The data structures. How shit is actually computed. This is the only type of feedback I will take for now: Let me know when a symbol doesn't have an explicit (or implicit from the topic of discussion) type.

## Genesis I: Mechanics #

"In the Beginning there was Mechanics." – MAX VON LAUE (1879–1960)

What we're trying to do as engineers is build shit. So we want to know how shit works. I.e. we want to understand the mechanics. The mechanics of shit. We are shit ourselves, of course. So sometimes it's about understanding the mechanics of ourselves. E.g. our ears, parts of our neurology, etc. The point is that mechanics is what we care about, to have a mechanics is to understadn how shit works.

## Genesis II: Universe #

In order to build shit, we (and the shit) need to exist somewhere. And so there's this "Universe" thing. Thankfully, for you, I'm not that kind of "science-loving" guy. I'm not gonna talk about origin of the universe and shit. You know those pop-sci rockstars who will literally tell you "Let me blow your mind with this amazing fact: ..."? That's the kinda shit I wanna avoid at all costs. The elitist, pretentious "I'ma blow your mind" horseshit, disguised as "passion for science." It's the pop-sci rockstar saying "I'm assuming your mind is tiny, so it's gonna be blown by what I'm about to say." Fuck that shit.

Back to the universe, though: You can read a million books and watch a million science-y things on tv, and follow a million astrophysicists on the web, and you will be none the wiser about the origin of the universe. So don't bother. No one knows how the universe came to be.

For our purposes, instead of "universe," think "spacetime." (Even though a lot of the shit here has a Newtonian mentality, where spacetime isn't even a word, but it'll be OK). If you don't know what that means, you will, later. I mean, think "spacetime" to yourself. But still say "Universe" to others (unless you both happen to be talking about relativity). Otherwise people will tell you "get the fuck out of here, nerd." As they should.

## Matter I: And Then There Was Shit #

"In doing this we’ll see that the nature of matter (i.e. body considered in general) consists not in its being a thing that is hard or heavy or coloured, or affects the senses in this or that way, but simply in its being a thing that is extended in length, breadth and depth." - RENÉ DESCARTES, Principles of Philosophy (1644)

"It seems probable to me, that God in the Beginning form'd Matter in solid, massy, hard, impenetrable, moveable Particles..." – ISAAC NEWTON, Opticks (1730)

Descartes had a simple, terse definition of matter: "Body considered in general." Newton, on the other hand, had a little story involving the big guy, the head honcho of all things, main founder of the Universe, who at some point decided to fill the Universe with shit.

My problem with both is: What the fuck am I supposed to do with it? In my computer program, I mean. Say I wanna program some simulation or experiment involving pieces of matter. My data type for matter right now would look like type Matter = {}. Empty. Vacuous. I don't know what type of data structure would represent a chunk of "matter." Sometimes a "definition" leaves you with nothing I think what I'm looking for is properties of matter.

Still, though, you should at least get the general, if vague, notion that matter is basically shit. Rocks, clouds, trees, water, cells, etc. As well as, of course, literal shit, such as dog poop. And mediocre shit, like Galileo.

## Motion I #

"Give me matter and motion, and I will construct the universe." – RENÉ DESCARTES.

OK so the universe is filled with shit. But why does anything happen? You couldn't even read this if you couldn't move your eyes. You couldn't listen it as a podcast, if a speaker couldn't move to disturb the air and eventually your ears and brain. So we gotta have motion. Shit needs to move. The beginning of all true study of mechanics and dynamics of sound and other forms of physics, chemistry, etc. is the recognition of motion as crucial.

Let's add a bit of mathematical salt to this already. Please hammer this into your brain, right now: Shit that moves, we imagine as an arrow. This arrow always has a direction and something else. Two data values. If the piece of matter happens to be a bullet, you never just care about "it's moving." Moving in whose direction?! A single number is never complete information about the motion of shit. You need at least two bits of data: some magnitude, and a direction.

So, Programmers: Make note. Vectors. (Normies: You make note too. You'll inevitably become a programmer too, after hanging around with me for long enough). If you slept through school, your idea of a mathematical operations is likely limited to plain, primitive numbers such x + 3 where x and 3 are some plain numbers. We're going to be doing computations with more complex data structures. We will see things like x + y but often those letters ("variables") will refer to values more complex than a simple number.

If you're a programmer, you already know this: Addition, for example, is just a function (*): add(x,y). Well, you can imagine that we'll be add()'ing, but with more complex structures for x and y, instead of just integers or something. Remember: We're not physicists. We're not mathematicians. We're engineers and programmers. We model and compute data.

(*): Or "method," in inferior programming styles, such as object-oriented programming.

## Life I #

So we have shit, also known as matter, and we have motion. That means now we can have jiggling shit. Presumably, Newton's God created some kind of jiggling soup that exploded and gave rise to this literally insane variety of shit we see (and are) today.

One of the weirdest types of shit is this one that is self-replicating, and constantly self-organizing into more complex forms, by eating each other. I.e. living shit. A.K.A. Life. This is just weird, sorry. I just wanted to say that. One of the rules we'll eventually see is that all shit should naturally devolve towards ever more disordered, meaningless shit. A.K.A. 2nd Law of Thermodynamics. And yet, we see – and are – this particular form of shit that decided, as an initial primitive simple form, to start ordering itself more and more, consuming energy, getting more complex. Weird. Does the 2nd Law of Thermodynamics conflict with the emergence of life? Let's explore that later.

Back when NASA (a big, clumsy, US government program formed during the dick-measuring contest between the US and Soviet Russia) used to at least be interesting, they sat down one day to agree upon a meaning of life. As in, the technical meaning. I.e.: What exactly will we be looking for, if we go out there to search for living shit in other planets or galaxies?

The NASA employees came up with this definition: "Life is a self-sustaining chemical system capable of Darwinian evolution." However, there are plenty of microbiologists, and other people from other disciplines, who define life differently. So there's no definition of life that is universally agreed upon. The most obvious example of this is the drama that arises among scientists with regards to the question: Are viruses a form of life?

The point is: Some shit we call "alive" and requires energy to make itself more complex. Is there a difference between shit and energy? Is energy in shit? Around shit, like a magic aura? What the shit is energy, anyway?

## Information I #

Let's not shit on the scientists who fight over the definition of life, though. Cos I'm basically an "everything is information!" guy, but when you ask me for a universal definition of information, I just... shit my pants! So I'll conveniently postpone the "what is information?" philosophical shit for... never. Mark that on your calendary. For now, to give you something, I'll say this: Information is what data becomes after a human interprets it. Shitty definition, I know. But you get the idea: If I find a paper full chinese symbols, that shit means nothing to me. It's not information. Data? Sure, maybe. Information, no.

## Problem Solving I #

You've probably heard of "divide and conquer." (Shit, you are living under "divide and conquer"!) "Divide and conquer" is a problem solving technique.

Say you have 2 problems: P and Q. But solving P and Q as they are is too hard. So you break them each into easier ("smaller") problems. You could, for example, break P into A and B. And break Q into C and D. Now you have four smaller problems. You solve those, and sum them into the final solution S. i.e. S = solve(A) + solve(B) + solve(C) + solve(D).

"Divide and conquer" splits problems into subproblems. (This is the essence of parallel computing.)

Another, less talked about technique, is the "solve a simpler version of the problem" technique (there's no cool name for it.) Like its name (which is not its name) says, it's about simplifying the problem somehow, and then dealing with that.

For example, say you have to fight a mastodon, but it's too large. One way to simplify the problem is to make it tired. Now you don't have to fight a mastodon. Now, you have to fight a tired mastodon. They are not the same problem. The latter is easier (unless you got yourself tired too, but let's pretend you did it right, with teamwork and shit.) An example in math is logarithms. Logarithms were invented in order to transform unwieldy numbers into simpler ones, operate on those simpler numbers, get a solution, and (usually) transform the solution back to the unwieldy form.

Don't get the wrong idea: This is not about "mathematical problem solving," or "thinking like a mathematician" bullshit. Mathematics is a fantasy land where religious ideas, such as the "Real numbers" and "Infinity," are treated seriously. Mathematician "thinkers" buy into those fairy tales, and then, hilariously, find themselves with all kinds of idiotic paradoxes. "The Banach-Tarski paradox! You can get a bigger circle from the smaller circle!" or whatever the fuck. Yeah, no shit: If you believe in infinity, you're one (infinitesimal!) step away from believing you can get something from nothing.

That's not a paradox, that's your fairy tales being incompatible with each other.

So no, "thinking like a mathematician" is not our goal. Let's think computationally instead. Which brings me to: Floating-point arithmetic. The floating-point number system is a system where numbers – get this – actually exist! It's how we get computers to be somewhat precise. Let me give you a primer.