## ART 0: Arithmetic Run Time. The common object files that get linked into any formal theory that's powerful enough to express arithmetic, whether you ask for it or not. And all the consequences that come along with it, one of which is something like Turing completeness, the other of which is Gödel incompleteness. 1: Hmmmm I think that's a stretch, zero. 0: What's a stretch? 1: I mean what are the chances that "art" stands for "Arithmetic Run Time"? 0: I don't know. Greater than zero. 1: But less than one? 0: Of course. I don't know who named this file but it wasn't me. 1: So what else might it stand for? 0: Couldn't say. But whoever named it seemed to know what I was about to start talking about. 1: Which is? 0: The Arithmetic Run Time. 1: Ok so if we assume for the sake of argument that whoever named this file knew what was coming up ahead, is there any other reason they might have called this file "art"? 0: Absolutely. 1: Why didn't you say so the first time I asked? 0: I didn't know we were assuming that. Add an axiom and everything changes. 1: Ok so what else might they have meant by "art"? 0: Well I was about to take you on a tour. A sight-seeing trip through some old documents. 1: Can you just answer my quest--- ## art 0: And I was thinking about how limited the medium of text is. 1: How so? 0: I mean books, and text generally, it's a pretty limited medium. 1: Can you explain more concretely? Seriously. For me? 0: For one, I can't grab you by the hand and drag you through text at the speed I want to take you. 1: Why would you want to drag me along before I'd finished read--- 0: Because not every experience requires you to absorb every character. Imagine this was a video. 1: Ok, I'm imagini--- 0: If this was a video I could take you on a tour through some old books, use excerpts from them as wallpaper, as the background. A tour. And sure you could pause and read the docs in full if you wanted. But there'd be a set pace and it'd be a pace I could set. To different values, as a function of the genre of the specific file we're in. 1: Genre? 0: You know the word right? 1: Of course. Not sure how it's relevant. 0: Well in some files you want to dig in and get technical. Go slow. Take notes. Write code. Some files last for miles, though they may be just a page. Other files may be longer as measured in lines. But they're meant to breeze by, like a road trip or a trip to a, what do you call those buildings with famous pictures of thing? 1: An art gallery? 0: Exactly. A museum full of paintings and stuff. That's a valid genre too. 1: Can you explain more about what you mean by "genre"? When I think of "genre," I think of like, "what part of the library the book is in." Genre is where you put it, and what other books it's near. So books can only have one genre. Otherwise where would you put it? 0: Maybe books are like that. But not bibles. 1: Aren't bibles, like... books? 0: Not really. They're libraries. 1: Libraries? 0: Libraries. ![[opt-art-bible-as-library-01.png]] 0: This isn't a new thought. ![[opt-art-bible-as-library-02.png]] 0: People say this a lot. ![[opt-art-bible-as-library-03.png]] 1: I thought the bible was a code bas--- ![[opt-art-bible-as-library-04.png]] 0: Have you ever heard deverlopers call their code base a library? 1: Yeah of course. 0: Same idea. ![[opt-art-bible-as-library-05.png]] 0: Many authors. Many genres. With different writing styles and reading speeds. ![[opt-art-bible-as-library-07.png]] 1: How is reading speed part of a genre? I thought reading speed was an attribute of... y'know... the reader. ![[opt-art-bible-as-library-09.png]] 0: Not always. Think of regexes. 1: What about them? 0: People say they're hard to read. 1: Aren't they? ![[opt-art-bible-as-library-10.png]] 0: Not at all. They just have a slower reading speed than normal text or normal code. 1: Doesn't that make them "hard to read"? 0: Not at all. 1: How so? 0: Regular grammars are objectively simpler than Turing complete ones. In that sense they're objective easier to read. Just slower per unit char. 1: Ok sure, I guess. What's the point of all this? 0: You asked me to rationalize why else this file might be called "art." 1: Did you answer? 0: In a sense. ![[opt-art-bible-as-library-06.png]] 0: See I'd been feeling for the last few files like these files needed metadata. Ways of signalling "Here's the rules of the game for this file, while we're here." 1: So the genre of this file is "art"? 0: No. Not at all. 1: Are you sure you're not just being confusing on purpose? 0: No. But I was about to be. 1: About to be confusi--- 0: See the genre of this file and the bits outside it, the bits before this that caused Narrator to toss us in here. That genre doesn't quite have a name. 1: Give me the gist? 0: It doesn't quite have a name. But if it did, it would be "The Anti-Gist." ## The Gist 1: The Anti-Gist? 0: The Anti-Gist. 1: Isn't that like... a bad thing? 0: Can't blame someone for thinking so. After all, it seems Narrator tossed us in here out of consideration for you. Because you couldn't be expected to entirely follow this part in every detail. At least not yet. 1: Well I'm not. 0: But that's ok. See some files in this library are more like a textbook. Or a regex. Places we'll be slowing down, being technical, focusing on every single char. 1: Can we get to some of those soon ple--- 0: Other files are more like a museum. A guided tour. Things I want to show you, as we walk by. 1: Why? 0: To set the stage for later when we'll sit down and focus and really try. 1: Try what? 0: To understand them in detail. For now it's just a tour. 1: A tour of what? 0: The Anti-Gist. 1: What's the Anti-Gist? 0: Ok, so... ![[anti-gist-0.png]] 0: On a scale from None to All. 1: None of what? All of what? 0: Anything. 1: Look it really bugs me when people don't label their axes. 0: It's more precise without labels. 1: More information please. ![[anti-gist-1.png]] 0: If you insist. 1: Ok, so the y-axis is information measured in bits? 0: If you'd prefer, I could measure it that way. 1: Ok so on a scale from None to All on the axis of Information. 0: Given N bits, this axis goes from 0 to N. 1: Ok... 0: Now, what's this point down here? ![[anti-gist-2.png]] 1: One? 0: Exactly. On a scale from 0 bits to N bits, what do we call 1? 1: I just said O--- ![[anti-gist-3.png]] 0: We call that the gist. 1: Isn't the gist of something usually more than just 1 bit. 0: Good point, but still. That's the gist of the gist. It's a small amount of information. Greater than 0. But way less than N, where N is the maximum amount of detail we can possibly say about a thing. 1: Ok, so?... ![[anti-gist-4.png]] 0: What's this? 1: "Too much information"? 0: Maybe. Depends on our goal. What would you call this point? 1: I dunno... Does this graph need an x-axi--- ![[anti-gist-5.png]] 0: That's the Anti-gist. 1: What's the Anti-gist? 0: The opposite of Gist. 1: Isn't that like... all the things you _don't_ want to know? 0: Far from it! It's the things you don't want to DO, but it's usually the things you DO want to know. 1: How so? 0: The gist is a simplification. It's the vibes. All the non-technical bits. Just analogies and stuff. 1: I still feel like the anti-gist is all the worst bits. 0: Learning a technical subject in full technical detail is a long term process. At any time during that process, you might get discouraged and quit. 1: I know the feeling. 0: Suppose you enjoyed a subject when you were just exposed to the gist. 1: Ok. 0: Why might you quit learning something like that, once you get to the technical bits? 1: Because it's too hard? 0: Right, or? 1: Because it's not fun? 0: Also a good answer, why else? 1: Because you're not getting enough out of it. 0: Say more. 1: Because the amount you're putting in is more than what you're getting out? 0: In what units? 1: Bits? 0: I was hoping you'd say "It's more precise without units." 1: What are you getting at? 0: Under what circumstances do we tend to quit learning a thing, assuming we enjoy it when we just hear the gist? 1: I don't know. 0: Here's a graph. Tell me why it's wrong. ![[the-learning-curve-of-everything-1.png]] 1: Looks about right. 0: In theory at least. Now what if I added an arrow, like this, and I said "that's the gist"? ![[the-learning-curve-of-everything-3.png]] 1: Seems basically the same as what you just drew up above. 0: Does it? 1: I think so. 0: But before I didn't tell you what the y-axis meant. 1: I thought you said it was Information. 0: You asked for a label so I gave you one. I didn't say I was happy with it. 1: Why would you be unhappy with your own label? 0: Because just saying "Information" is useless! Hell, that's more vague than putting no label at all! 1: Then why did you write it? 0: Because you said you don't like unlabelled axes, so I added a label, to see if you felt like you had learned something. 1: I thought I had. 0: You hadn't. Here's the reality. We have no use for "Information" in the abstract sense of bits. 1: Aren't we--- 0: Nor do we learn by exposing ourselves to more of them. Nor do we always simplify a topic by exposing ourselves to less of them. 1: What's your poi--- 0: And more often than not, the learning curve looks like this. ![[the-learning-curve-of-everything-4.png]] 1: Hah, I definitely know this picture. 0: We all do. Now suppose you've just learned a bit about some new topic or field. Just the gist. Nothing too technical. What do you do next? 1: Try to learn more of it? 0: Always? 1: I try to. 0: Impossible. No one's got the time to purse all the things they love. 1: Good point. I definitely wish I had more ti--- 0: So after our first exposure to a thing we think we love, we've got a choice. ![[the-learning-curve-of-everything-5.png]] 1: Why's the line dotted now? 0: That's one path that's open to us. It's where we'll stay if we only go as far as the gist. 1: Ok. Why are we talking about this? ![[the-learning-curve-of-everything-3.png]] 0: Because learning curves in real life aren't a one-dimensional curve. 1: What are they? 0: It's hard to draw them, but they need at least one more dimension. 1: Which is? 0: Information. 1: I thought we already had informa--- 0: Be precise! Don't just rest on the smug satisfaction of a labelled axis. Information in what sense? 1: Bits? Like Shannon entro--- 0: Useless measure. 1: Isn't that the definition in Information Theo--- 0: Be less precise so I know what you're talking about. 1: _(Exasperated)_ What's the question? 0: You've learned a subject. Just a bit. You enjoyed your first exposure to the non-technical bits. Maybe you found a popular book that explains the field with analogies and skips the technical details. Your goal is now to learn more about the subject by digging into the technical bits. What do you do? 1: ... Find a good textbook. 0: At what level? 1: Introductory? 0: And? 1: Read it? 0: Well congratulations, you've got a LONG road ahead. Set four years aside. And don't take this the wrong way, but you're probably gonna quit. And even if you don't, wow congrats by the end you've got an undergraduate level of understanding and four less years of life. 1: How is that bad? 0: Well you've wasted lots of time and energy if the graph looks like this. ![[the-learning-curve-of-everything-6.png]] 1: What's the part that says "Anti-gist"? 0: What's information? 1: Do you always answer questions with quest--- 0: When I asked you up above, why did you decide to start with the introductory textbook? 1: Because that's what I'm ready for. 0: And? 1: And what I can understand. 0: But the whole POINT of learning is to learn the things you aren't ready for and don't understand! 1: So I should start with an advanced book? 0: Absolutely not! 1: Intermediate? 0: No. 1: What do you want from me? 0: How will you know where you're going if you don't know where to go? 1: Didn't you get that backwards? 0: What's information? 1: Shannon entropy, measured in bits. 0: What's learning? 1: Acquiring information. 0: What's memory? 1: I don't know. Remembering stuff. 0: Learning minus memory equals... What? 1: What? 0: Data compression. 1: Learning minus memory equals data compression? 0: Exactly. How do data compression algorithms work? 1: I don't know all the details. 0: Give me the gist. 1: I think they basically count how often different things appear, in a text file or an image or whatever thing they're trying to compress. 0: Then what? 1: Then they built a little dictionary of the things that got repeated. And they assign shorter code words to things that appeared more often. 0: Right. So if we assume that understanding a technical field is like data compression. 1: What's the question? 0: What kind of textbook should you have chosen before when it came time to learn the hard bits? 1: I already said "Beginner" and "Intermediate" and "Advanced" and you told me those answers are all wrong. 0: You said a compression algorithm counts how often different things appear. 1: I think that's the idea. 0: How could we visualize those counts if I wanted to see them? 1: Like a histogram? 0: So if learning minus memorization equals data compression, and data compression goes over a corpus and builds a histogram, which of those books should you have chosen when it's time to get technical? 1: I don't--- 0: Which would you choose to get the best compression ratio? 1: All of them? 0: All of them! 1: All the books? 0: All the books. 1: As a beginner? 0: As a beginner. 1: Look we've been in this file for a while, remind me again why we're here? The Anti-Gist 0: Well as I was saying before Narrator tossed us in here... > 0: It starts off slow and you're not sure what the textbook is doing. 0: And then later on in the file we talked about learning. 1: You also talked about bibles again. 0: And about genres and museums. 1: And something about art. 0: And compression. 1: What's the anti-gist again? 0: The other side of gist. It's a map of where you're going. And it's how you start to build that great big histogram in your head, early on when you're still new to a field. 1: Say more about the histogram? 0: How will you know how to read the introductory book if you have no idea what the advanced books look like? 1: Isn't that backwards? 0: No. Until you know where you'll being going, you won't know how not to get there. 1: It would seriously help me if you'd stop speaking in riddl--- 0: Before you know what the "advanced" parts of the story look like, how will you know what to learn and what to skip? 1: Just read an introductory textbook. 0: How many times in life have you read an entire introductory textbook? 1: ...not many. 0: Right. So as I was saying before Narrator tossed us into this file: > 0: Then it increases in steady drumbeats until you're staring at this book, this book that you've made a policy of reading every word of so far, and you find yourself thinking "What am I supposed to do now?" I can't actually read all this. I mean Christ, just look at it. The density. It's unlike anything you'll ever see in a textbook upstairs. 1: Yeah I remember. Seems like the sort of problem you create for yourself when you read advanced stuff before you're read--- > 0: But eventually out of something like stubbornness or OCD or some other mental illness, you read it. 1: Did you just interrupt me _with a quote?_ > 0: Just enough to realize what's going on. 0: And once you do, you realize it's all simple and trivial and you didn't need to read it after all. But once you're there, the "reading" stops being hard work. > 0: That "terrifying math" you thought you were looking at turns out to be hilariously simple and fun.