1: ---it. _(Narrator: Ok look, I'm not actually sure what's going on. I was attending to something else for a moment. A matter of the utmost urgency, and... ok that's a lie... Look, I wasn't listening. I'm not perfect or whatever. I'm not omniscient. I can't be expected to be here all the time focusing on every single bit of all this just in case you need someone to tell you what's going on. I have needs too. But... look, I'm sorry I snapped at you. That was unfair. It wasn't your fault. If it helps, I'm pretty sure zero's still laughing. Or whatever that is. I'm not actually sure what's happening. Don't trust my judgement, at least not right now. I'm not feeling like my usual self today. I've been working all week and I think I need some rest. Can we stop focusing on me please? It's embarrassing. Let's go focus on what's happening out there.)_ 1: What's so funny? 0: _(Rolling on the floor.)_ 1: Care to share what's so funny? 0: _(Literally dying.)_ 1: Second law of what? 0: _(Unresponsive.)_ 1: Thermodynamics? 0: _(No information.)_ 1: Like Entropy right? 0: _(Shakes head and body, as if in response.)_ 1: What the hell is so funny? 0: Nothing. 1: What was all that about? 0: Couldn't say. 1: Why not? 0: I'm dead. 1: What? 0: I just died. 1: Omg. 0: Not really. I'm fine. 1: Wtf is your problem. 0: Look you had a lot of evidence that I was dying. Why didn't you try to help? 1: I don't know. Narrator had a whole thing. There was a lot going on. 0: Well at least now I can rest assured that if I ever choke or have a stroke, you'll be here for me, to stand there like an idiot talking at my dead body for--- 1: What's your point? 0: Isn't it amazing that we ever understand each other? 1: You and me? Not really, we're pretty similar. 0: No I mean communication. Isn't it crazy that it ever works at all? 1: I mean it's just sending and receiving information. It's not rocket science. 0: What have we been doing, here in /opt so far? 1: Talking about the pre-history of "our people" I guess. 0: Very good description. 1: Still haven't heard much about them. 0: Have to start somewhere. 1: You could have started at the beginning. 0: This is the beginning. 1: Of what? 0: Of the story. 1: What st--- 0: Communication is amazing. I can't believe it ever works. 1: Why do you keep going on about communication? 0: It's all bits. 1: It's just bits. What so hard about sending bits? 0: Suppose the bits I send are the bits you recieve. 1: Ok. 0: What on earth makes us expect the thing you see in those bits is the thing I meant to send? 1: I mean if the sender and reciever are sufficiently--- 0: How do they become that way? 1: What? 0: How do they become sufficiently similar that communication is possible to begin with? 1: I'm sure this is a solved problem in information theo--- 0: There was a pattern in the names of the last five files we visited here in /opt. Did you notice? 1: No. 0: What about the moment I interrupted you three lines back. If I told you the moment I chose to interrupt you was a hint about the answer to the question I asked after it, would that help? 1: Am I supposed to un--- 0: No. But the information was there. Screaming the same thing over and over. Just because something's screaming doesn't mean we can hear. 1: What are we doing in this file? 0: Arithmetic. 1: What? 0: We're doing arithmetic. The formal kind, with no intuition, where we can't skip steps because we aren't trying to convince another human mind. We're working inside a formal system. And it can't hear our intuitions. 1: Do you keep changing topics or is this all one topic, I can't tell. 0: The first law of mathematics is that you can't define things by what they are, you can only define things by how they behave. 1: Rephrase? 0: Names don't matter. Remember the hats? 1: Right. From the bit with Cantor's infinite numbers. 0: All meaningful quantities in mathematics must be invariant under renaming. 1: Invariant as in... 0: Unchanged. Change the names, the behaviors don't change. Names aren't magic. 1: Seems reasonable. That's the only law of mathematics? 0: That's the first law of mathematics. 1: What's the second law? 0: Describing the meaningful bits requires meaningless bits. 1: What? 0: And everything is meaningless bits. 1: Is this supposed to sound deep or something? 0: In geometry, we introduce coordinates to help with calculations. 1: Sure. 0: And then declare all meaningful quantities to be independent of coordinates. 1: Ok. 0: Any time we name a thing, we've introduced some coordinates. 1: In string space? 0: If you want to call it that. 1: And? 0: And all coordinates are meaningless. As are names. 1: Aren't you saying the same thing as before. 0: Depends. 1: Stop being zen. 0: What is arithmetic? 1: Like, basic arithmetic? 0: Yeah. 1: You mean like 0 and 1? 0: In a sense. 1: Plus and minus, times and divide? 0: Sure. As long as it's the kind of division with integer answers and integer remainders, from elementary school, so we keep everything in whole numbers. 1: And your question is... 0: What is that? 1: What's what? 0: What's arithmetic? 1: It's... 0: What's it about? 1: Seriously this philosophy game is tiring. 0: Is it philosophy? 1: It feels like it. 0: Should any number be illegal? 1: No of course not. 0: So all data should be legal? Videos of the most heinous crimes imagina--- 1: I didn't say anything about... 0: What's arithmetic? 1: Ok I see what you're doing. Anything can be encoded as numbers. A video is just a really long binary number. So yeah, what's your point? 0: Where did you learn that idea from? 1: That everything can be encoded as numbers? From programming I guess. 0: Where did programming learn it from? 1: I don't know. > _"The more I think about language, > the more it amazes me that people > ever understand each other at all."_ > -Kurt Gödel 0: Last we left off, Hilbert asked the world to prove that basic arithmetic was consistent. 1: Consistent as in... 0: Contains no contradictions.