Episode 183 - The Metaverse and Digits
Max and Aaron discuss Facebook's plan to develop a metaverse, and Max shares his thoughts and theories on our number system
Links
TechCrunch: Zuckerberg wants to create the metaverse
BBC: Evolution of Facebook’s interest in Virtual Reality
WSJ: Facebook’s Political Problems
Australia Under Martial Law?
Quora: If Binary is Base 2, What is Base 1?
Related Episodes
Episode 139 on Facebook’s Currency Project Diem Stalling
Episode 94 on Number Systems
Episode 79 with Timoni West on Virtual Reality
Episode 72 on Facebook’s Currency Project Libra
Transcript
Max Sklar: You're listening to The Local Maximum Episode 183.
Time to expand your perspective. Welcome to The Local Maximum. Now here's your host, Max Sklar.
Max: Welcome, everyone. Welcome. You have reached another Local Maximum. I feel like I don't have to say welcome at the beginning anymore. Because I think the woman who comes on for the intro already says welcome so I don't think that's necessary.
Aaron Bell: Well, you can never make our viewers, listeners feel too welcome.
Max: Yeah, I guess you're right. Okay, I promised the studio will have one new thing every time we do a video. Of course, it got a little frame here from Homesense or whatever that is so there you go. We'll do something a little bit more dramatic next time though. I promise you that.
Aaron: Class ended up one piece at a time.
Max: Yeah. Okay, so today, we're going to talk about some current events. We're going to talk about the metaverse and Facebook. Then, we are going to talk about the theory of digits because the metaverse will be made up entirely of digits. So why don't I just go back to basics and talk about some of Max's, that's me, my old philosophical musings on digits
Aaron: But what kind of digits? Stay tuned to find out.
Max: Yeah, exactly. Okay, so this news article we didn't read, but isn't it crazy that Australia is apparently ready to deploy their military to do the COVID lockdowns? We're still in the COVID era, alright.
Aaron: When you say it like that, it sounds scary and disastrous. I also did not read the article so I'm completely unqualified to comment on this and I will not let that stop me but yeah.
Max: Then we'll get into the real stuff. We actually did 30 seconds of research.
Aaron: I did it to very briefly steal Manet that, maybe it's less ominous declaration of martial law and it's more like post-hurricane sending out the National Guard to help with disaster relief. Until proven otherwise, I'm gonna give them a little bit of the benefit of the doubt on that one but we'll see. Got to keep an eye on the sneaky Australians.
Max: I feel it's to keep people in their homes. Imagine if you had soldiers outside of your home, in your neighborhood, making sure that no one's going out. That would be scary.
Aaron: Everyone was talking in mid to late 2020 about how nature was rebounding and plants and animals were retaking the country.
Max: Yeah, did that happen?
Aaron: I don't know how true that is but I think there were some things that did sound like...
Max: I heard a little bit more birds but it wasn't... Yeah.
Aaron: I don't think Australia needs that. I think the wildlife there is dangerous and aggressive enough as it is. How can you further weaponize scorpions and... Was it like 75% of all poisonous snakes live in Australia or something ridiculous. It's not a place that needed to be more wild and dangerous.
Max: Gotcha. Gotcha. Okay.
Aaron: Maybe that's what they're deploying the military to combat.
Max: I hope so. Have you ever heard of, and this is kind of a meme, of the great emu war?
Aaron: I have. I've not deeply researched on it but I believe that you lose one.
Max: Yes. The cartoon version of it which I prefer is that Australia deployed its military against the emus because there was a big emu problem there, overpopulating. Apparently, the emus won. So I love that description of that war. Okay, let's go on something that we know about a little bit. Let's talk about Facebook and some of Mark Zuckerberg's statements on the metaverse. Now first of all, what is the metaverse? This actually comes from a book that you and I read in high school around the same time like Snow Crash, Neal Stephenson. I'm really surprised that this idea stuck. This was a book from 1992. We weren't reading in 1992. We're not that old. I guess I was alive in 92 but...
Aaron: It was late 90s, maybe early 2000s.
Max: I think early 2000s. Basically, the idea is that it's a whole other universe that exists digitally but not like the internet. It's essentially a virtual reality world. You feel like you're there. It's a massively multiplayer game except it's you meet people there, you hang out. If I remember correctly, I don't remember the... I haven't read the book recently but I know that you spawn in waiting room areas and then you go out into the world. You travel around it, you can build things in it, that sort of thing. So it's sort of a digital meeting place, if you will. There was always an exciting chapter when you're going into the metaverse, and you're meeting other people, and then you're going back out into the real world. How would you describe it? Is that how you would describe it?
Aaron: Yeah I think it was somewhat inspired by some very early MMO-type games but it then went on to itself spawn. It served as a major inspiration for Second Life which some of our older listeners might be aware of. It didn't revolutionize the space but it captured a lot of people's imagination for what could be done in that kind of virtual worlds with avatars and people interacting. Not just for the purposes of playing a game but as being a platform or an interface for wide-spanning interactions. It wasn't that you were logging into World of Warcraft. It was that you were logging into a virtual world where you could do pretty much anything.
Max: Okay. It's not a game, it's actually a functional space. Why is Facebook trying to do... I guess the question to ask is why is he talking about this? Is this actually an imminent thing? If it's not, since spoiler alert, it's not imminent? What's their plan to bring this about? Why should we care? A part of me says "Hey, Mark Zuckerberg believes that VR, virtual reality, is the next mobile." The article also points out that Facebook was actually somewhat late to mobile. They dominate in mobile applications today but that was with the help of some acquisitions of companies like Instagram and WhatsApp. Also maybe they copied a little something from Snapchat. Just a little take a quick look and see and drag and drop.
But I almost wonder if this is based on real market data or if this is some kind of psychological compensation where not just Mark Zuckerberg, but the Facebook executive team is thinking like "Well, we want to be early to the next thing so obviously, this is a jump to mobile and so the next one is obviously the jump to VR because it's kind of the mobile of mobile." I don't know if it's based on any real data that's available or real... I don't know what the arguments are to support the idea that virtual reality is going to be the next big platform. Maybe it could be a big platform down the road but...
Aaron: It's not something that consumers are clamoring for right now. But perhaps they're taking if you build it, they will come approach here. It shouldn't be that surprising given the huge investment that they made in VR by acquiring Oculus and the disappointing output of that acquisition collaboration. It's not that it's fallen completely on its face but it hasn't revolutionized the company and the VR industry in the way that I think they were hoping with that. If consumers are not clamoring for it, then they will need to make it something that consumers clamor for. But I think you were definitely right about maybe overcompensating.
A little bit wanting to make sure that they're first actors in the space even if that means that they have to act on a bunch of spaces that never pan out just so that when the next big thing does come along, they've got a foot in the door. I think they're maybe a little bit anxious that when everyone went to... Well, not everyone, but when a huge amount of the American workforce went work from home in 2020, that they didn't have the killer solution to that. People were going to... We saw Zoom come from a no-name to be the... They became the Xerox of videoconferencing.
Max: He took some digs at Zoom in some other statements. I saw. If I could skip ahead here a little bit. It said here “he told The Verge people shouldn't live through small glowing rectangles” and then of course, my agenda is it needs to be a large glowing dome instead. But he said "Well, interactions shouldn't be just a bunch of squares with faces on them." I actually agree with that. I think that's a horrible way to interact. I'm going Zoom crazy. I don't know about you but I think part of those digs, part of them talking shit is probably about "Oh my God, Zoom had the solution and we didn't. Let's talk about those squares and faces and how ridiculous it is.
Aaron: Yeah I think there's a certain amount that they don't particularly care about in the metaverse. It's just a vehicle to make sure that people are spending more time in front of Facebook content that can be advertised to or data mined or whatever their future profit model is. They want to make sure that it's not a platform owned by somebody else.
Max: So remember? This reminds me almost of when Facebook tried to come out with their own cryptocurrency called Libra. I don't even know. They changed the name of it, didn't they? I don't even remember what it was but what they changed it to.
Aaron: Yeah, I think it got somewhat disaffiliated from Facebook. I'm sure that there's still deep ties.
Max: Yeah, that was called DM.
Aaron: But yeah, they wanted to maybe lessen the public relations linkage there.
Max: It still doesn't exist. I knew this was gonna happen.
Aaron: I think we may have made an explicit prediction about that. Oh, yeah.
Max: Yeah, yeah, exactly. Because they want a closed system. They want a walled garden for everything and almost like the government, if there's an open solution that everyone can use and that's free and fair. They're like, "Well, this isn't helping us." So they want to have their own and not everything in the world should work like Facebook. In fact, I think even Facebook shouldn't work like Facebook. Look, I'll let them have their own space.
Aaron: Well, in the notes, you made a comment about should the metaverse be open? To give some context, the original metaverse, the Neal Stephenson's metaverse, it was structured in such a way that all the real estate in the metaverse initially belonged to the global multimedia protocol group which does not actually exist. But in the fictional universe of Snow Crash, it was a subsidiary. A part of the Association for Computing Machinery which is a real nonprofit that exists.
Max: It almost sounds like... Because this is coming out in the 90s so there's a different sort of an intellectual soup you're pulling from here. So that almost sounds a media foundation type. Open source Apache or something.
Aaron: What is it? Is it iCam that handles the allocation of IP addresses? Because in the way real estate was broken up in the metaverse as I recall, it was not unlike an IP addressing scheme that... Obviously, it's the digital worlds, everything was powers of two. I think it was like they were 256 stops on... So the metaverse was spanned by a single Main Street that runs around the sphere. There's a monorail that runs along and it has 256 stops, each of which is 256 kilometers apart from each other. Each of those, there's like an express address and then a local port address for those. So that determines where you log in or log out of the metaverse from where those portals are.
Max: Gotcha. I'm guessing if he came up with it, there'd be some kind of a blockchain component to it. It almost sounds like it, right?
Aaron: Sure. Yeah. You would have to be able to prove that you legitimately owned this metaverse real estate. Although, it does sound like there wasn't really any discussion of whether the computing power that ran the metaverse was centralized or distributed. That wasn't really something that was in the forefront of people's minds at that point.
Max: Right. Right. That's a good question. I don't know how much you got into how much it worked. So okay, I don't know if there's anything else. Oh, I found this article from the Wall Street Journal about Facebook.
Aaron: Before we jump onto that, one more thing I want to throw out when we were talking about open versus closed. I think a big part of it is going to be them determining exactly what their objective with this metaverse play is. If it's purely that they want to sell more VR hardware, if they want to find a way to add value to make their Oculus hardware worthwhile, then I would expect it's going to be a proprietary closed source system. However, if their move here is that the platform is going to be a method for getting more eyes on Facebook content, getting people to spend more time in their environment, I could very much see a model where maybe the Facebook Oculus provides the premium experience for the metaverse.
But it is an open enough protocol that Samsung and every other designer of mid to high-level hardware can interface with it. Maybe there's some top-tier features that only those who buy Facebook hardware can access but the value of eyeballs is greater to them perhaps than the value of hardware sales. It remains to be seen what they're really trying to do with this space because right now it's all just buzzwords. Maybe some blend of opened and closed.
Max: Yeah, because it's not like they let you post on Facebook from other social networks.
Aaron: Yeah, with Mastodon versus something Twitter which... It gets exactly to the library versus Odyssey concept that you talked about in previous episodes.
Max: Or Odyssey versus YouTube.
Aaron: There's the Under... Sorry, not versus, but just there's the underlying infrastructure which anybody can use and then there's a specific portal that you can view it through. But that doesn't mean that only that interface can be used to add content.
Max: Gotcha. Gotcha. Okay, yeah. The Wall Street Journal article’s just about how Facebook is not just thinking about what's next in terms of technology and consumer needs which is probably what they were thinking, trying to think about 10, 15 years ago. Now, most of what they do is worrying about politics, and what the politicians are going to do to them, or what they're going to do to the politicians, or something, or other.
This is the Wall Street Journal article, it's a right-leaning article but it points out that Facebook tried to tip the scale during the election to help Biden. It maybe working with the administration now on misinformation. That was a whole big thing where Jen Psaki said "We're working with companies like Facebook to identify misinformation" but Facebook is still the biggest vector for uncensored information and they haven't been able to censor it all. They haven't been able to get it all on things like vaccines and all that. So it's one of the biggest vectors for sharing information period.
This article argues, I don't know, I'm not necessarily taking a position on it, but it's an interesting idea, argues that it's a huge risk for Facebook that the administration or the progressives turn on Facebook. Then, you have a situation where both parties want to destroy Facebook. There's been all this crazy rhetoric going on where people will say "Hey, someone on your platform posted something critical of vaccines, therefore, you, Facebook, are killing people.” That's how people go today. It's always over the top.
Aaron: It's always someone famous saying those things, the President of the United States that’s making those comparisons.
Max: Oh, was it the President? Okay. I thought it was someone more important. Nevermind. Okay. Rhetoric these days is over the top. It has been for at least, I don't know, five, six years? Something changed in 2013.
Aaron: If Facebook is not spending serious amounts of money on PR, and legal, and lobbying consultants to mitigate this risk, then I don't know what they're doing with their billions of dollars. This is a real risk but I think they're going to weather it okay. They just got to put a lot of effort in it.
Max: I feel like part of the reason for this over-the-top rhetoric that's popular these days is platforms like Facebook.
Aaron: You're not wrong.
Max: It might all come full circle.
Aaron: There's the question of... Yes, it's a partisan thing but it's not partisan in the sense that only one party has a beef with Facebook. For different reasons perhaps but they all want to take it down a notch. I am led to believe that part of this is... There's a saying that I'm sure I'm going to butcher but it's something about either executive power or deficit spending and that kind of thing that you only oppose it until you're in power. Then you forget that it was part of your platform to be against it. I think politicians are only going to rail against Facebook either until they destroy it or until they, perhaps more preferably to their view, find a way that they can co-opt it to serve their purposes. At which point Facebook will be able to do no wrong and they're model company again.
Max: Well, I think that part of the... There's an internal contradiction in that statement of like... So one of the things they want to do is break up Facebook. One of the things they're talking about doing is breaking up Facebook but they're like, "Well, we'll break up Facebook because they're not getting rid of all the misinformation we want them to get rid of" but then you break it up and now all of the constituent parts are free to not censor misinformation. So now you have an even harder problem.
Aaron: Yeah, there's perhaps an argument to be made that a larger...
Max: I want to point out, I'm going in the government point of view just to say personally, I don't want any of this stuff censored because there could be new people.
Aaron: Let's take it as a given for a moment that there is harmful misinformation out there and we want to be able to effectively remove that information.
Max: Let's jump into that point of view, yes.
Aaron: So from that perspective, you could make an argument that a larger, more consolidated, more powerful Facebook is better positioned to do that. That's the classic argument that you make when you're pitching a merger. It's that by our powers combined, we will be more effective and we can save the consumer money. The counter to that would be that by breaking the company up, you create competition, and those competing factions are then able to offer alternatives. Rather than just doing the same thing better and harder, they can take a different approach. That being said, I'm highly skeptical that any way they break up Facebook would result in groups that directly compete with each other. It's much more likely we would see a breakup like, okay, we need to separate out your Snapchat and your Facebook but it's not going to change any of these dynamics.
Max: Because we're talking about Facebook, the social network, is where all of the criticism comes and maybe a little bit on WhatsApp and Instagram. But let's talk about Facebook, the social... But you can't break up that Facebook. What do you say... "Okay, well, no, I'm sorry. You're in a different Facebook. I can't message you now."
Aaron: It's not like when they broke up AT&T and they had a bunch of different regional phone companies. You're not going to get Facebook New England and Facebook Southwest. Conferences or something.
Max: They started out like that. I remember when it was like that. College, university.
Aaron: It was never regionally restricted. You could see anyone else who was on Facebook but yeah, the rollout was very, very small.
Max: Yeah, but I think there was more of a... I remember, and I could be wrong, about this early on, whether there was an out of network section and an in-network section so you could... I was in the Yale network and it was like I could see more.
Aaron: Yeah, you're right. There was a period when you couldn't just randomly friend anyone. You needed to have degrees of connection or something. This is reaching way back into the memory of what, like, 2005, 2006?
Max: Yeah. 2004, I got out.
Aaron: So long ago.
Max: Yeah, I know. I know.
Aaron: So much more hair back.
Max: Okay, so a few other things that he mentioned before we moved on. He mentioned the idea of working on an infinite office that allows users to create their ideal workspace through VR. This is from the BBC article. I'll quote him. "In the future, instead of doing all this over a phone call, you'll be able to sit as a hologram on my couch or I'll be able to sit as a hologram on your couch. It'll actually feel like we're in the same place even if we're in different states or hundreds of miles apart." He said, "I think that's really powerful." Okay, but is that imminent? Is that five years?
Aaron: I'll believe it when I see it. I think this is one of those things that they could definitely do as a tech demo but how useful is it really going to be?
Max: How would I appear as a hologram on your couch without all sorts of equipment around me?
Aaron: Well, yeah. Either you're going to be wearing the virtual goggles or there's got to be some sort of projection setup.
Max: It would be cool if there's a room in my house I could just walk into and if you walk into a room in your house, then we're together. But if I have to set up a whole bunch of stuff, and then I have to call you at the right time, it's not as good as... I don't know.
Aaron: I think this technology may have a lot in common with the early concepts for touchscreens. That it's a technology that's found use mostly on phones and tablets. But the initial idea was something much more like Minority Report. Well, that was a gestures-based thing but people were envisioning large touchscreens that would replace monitors but no one is going to spend all day reaching out, moving their hand around on the screen because your arm gets fatigued. It turns out, a mouse and keyboard are sometimes more effective for that type of stuff. Yes, touchscreens are a very important part of our everyday technology use but not in the way that they were being envisioned for the first decade or so of development of the technology. I think we need to be prepared for some dramatic changes in how this VR tech gets used. There was one other quote...
Max: Maybe it could be something on your phone. But again, it's going to take the phone manufacturers many years to integrate something like a 3D camera that's any good.
Aaron: So there was one other quote that came up when they were talking about the metaverse that I wanted to pull out from that BBC article. It was really towards the end of it and let's see here.
Max: Is it the behavioral data part? Because that...
Aaron: It was actually after that. It was "Tech giants like Facebook defining and colonizing the space while traditional government structures struggled to keep up with the technological change could cause further issues," she added. If you couldn't tell already from the language used in that statement, this is definitely an academic talking about it with their concerns about the colonization of the metaverse. Just to be clear, there are no natives in the metaverse who are being displaced or enslaved. Just friendly ones and zeros. I don't know if you want to use that as a segue there but I think this concerns are perhaps being viewed through a strange light there. Granted if it is an environment that is fully owned by the Facebook Corporation, then I have other concerns. I don't know if I could use colonization to refer to them but the company stores is not a great model either.
Max: That's just the way people talk to them. That's just the way people think now. I don't know. The part of the behavioral data was interesting. It's a little bit kind of projecting what is now on to what will be then. I hope this prediction doesn't hold but they're like, well... They want the user data to advertise to us. I was personally involved in, not in Facebook but in an online advertising based on data, it's nuts. It's the nuttiest industry. I don't even know how to describe how nuts it is. But anyway, they're saying, "Okay, if you're in VR, it's not just going to be about where you click or where or what you share. According to this, it's how you stand, where your eyes look, what you're looking at the longest, subtle ways you physically move your body, and all of that is going to be used to advertise to you. It's a direct route to your subconscious. That sounds pretty nuts. It almost sounds like, "You seem like a nervous wreck. Here's some drugs."
Aaron: Eye tracking is already super valuable for that kind of thing. Yeah, if they're doing full-body motion capture as part of this VR, AR experience, then that's a whole lot more data that they could potentially be mining for useful insights there. Think if Facebook could basically have an always active lie detector on every interaction that you have on the platform.
Max: What would you would use it for?
Aaron: Well, I think it would be particularly useful to some groups whether they're corporate or governmental to know everything that you've said and when you were lying about it. Or being able to have a custom-tuned database. So when they want to pull you in for questioning, they can use all of that data to improve the performance of their lie detector system.
Max: Now that sounds really dystopian. I was thinking more in terms of ads but...
Aaron: If we can use it to throw you in jail, we can use it to sell you things too. That cuts both ways.
Max: "You said you wanted to block that ad but you're kind of lying. You kind of want it. You want this new couch, don't you?"
Aaron: "Would you to go into private browser mode? We think you want to go into private browser mode."
Max: "We've got some stuff to sell in there. Don't worry, no one will have to know. Only 8 billion people. It's only between you and Facebook. No one has to know." Okay, so that's what's going on in Facebook. I think just to wrap this up, I don't think this is something that's going to happen imminently but I think it's interesting that they're talking in this direction. They've wanted to go in the VR direction for this long. I think they're trying to ramp it up a little bit by going from VR to metaverse, trying to make it cooler. Facebook is almost trying to grab onto the next big thing. They're really trying to find it. They also have political issues at the same time. So very interesting predicament that Facebook is in and I feel like it's very hard to predict how this is going to play out.
Aaron: Yeah, and particularly to see what some of the...
Max: And I hope they build something good.
Aaron: The norms of such a platform would become... Because in Snow Crash's metaverse, they come right from the beginning of the explanation of this concept that... There was all sorts of wacky stuff you would see walking down Main Street. It wasn't just people dressed up as cyberpunk detectives. You literally had giant penises walking down the street because when your avatar can be anything, that's what you're gonna get.
Max: I feel like that's Twitter.
Aaron: I think he was pretty on the nose with people's online personas even before that was a thing.
Max: Yeah, yeah. I'm sure he was on message boards and things like that. People were using fake names, you could probably see... Weren't there people with numbers in their names in that book?
Aaron: Yes. yeah. It was like the leetspeak. I can't imagine he invented that but I think there was... Was it Da5id?
Max: Da5id, I called it. I feel like that's not what you're supposed to call him but it's like D-A-5-I-D.
Aaron: I think it's supposed to be just "David" but yeah, there's a 5 in there.
Max: I always call it "The Day-Five-id."
Aaron: Which, I believe, was loosely based on Sid Meier but don't quote me on that.
Max: Okay, okay. Cool. All right, so let's go into digits. Now, why am I interested in digits? I'm interested in computer science, the metaverse, the blockchain, the phone in your pocket. It's all based on these ones and zeros. Or theoretically, it doesn't have to be a binary system. It could be any digital system. It's based on digits. We're talking about people with digits in their names.
Aaron: Maybe take a step back because most of this is based on binary, a two-digit system but why?
Max: For computers. So actually, I don't really know the answer to that other than I think it has to do with it's just easier to make circuits.
Aaron: Having not researched this before the episode, I believe you're right that it's...
Max: I think you can make circuits that are zeros, ones, and twos or zeroes, ones, and twos, and threes.
Aaron: 01 and -1. You can do things like that but from a design perspective, even back in the analog days, having a basically on and off was a lot easier to design for rather than having multiple intervening levels that you then had to accurately read.
Max: If I remember correctly, I think early on, computers, there were some people who tried to design computers with base 10 digits because they're like, "Well, this is how we count in base 10 so we might as well put 10 digit numbers right into the hardware." I guess that fell out of favor because I guess binary was just more efficient or just became the standard. Something like that. But yeah, I think you're right that I'm right. Aren't we just all right today? Let's just define that as truth then. I'm more interested in the theoretical underpinning of digits and ever since I was in elementary school, one of the things that blew my mind when I was 10 was that numbers don't have to be base 10.
I don't know if you remember learning that for the first time, but the fact that base 10 is an arbitrary decision is funky. It means the way we think about numbers is from a very particular perspective that an alien might not have. It's interesting to think about what is a digit and what other number systems can be built up from those digits. I want to talk and I'll get into the core answer I gave a while back which was very interesting. I just want to say, the Wikipedia definition of digits is that a digit is a symbol used to represent values in a positional number system.
Aaron: Roman numerals would not be digits because they are not purely positional in their representation.
Max: Right, right. Right. All of the early number systems were not positional and a positional number system, you could say it was a really great innovation because it's so much easier to work with numbers that are like what we have today. Whereas Roman numerals are just "Hey, you want an extra five in there? Throw in a V. You want an extra 50 in there? throw in an L." It's basically like counting sticks and then crossing off the fifth stick but just doing it. Essentially, that is Roman numerals. They just do it more...
Aaron: Advanced version of that.
Max: Yeah, it's advanced version of that. It makes it harder to add and really hard to multiply. So positional number systems are really useful but they are, depending on what base you're in or what number system you're in. It's going to be easier for some things and harder for other things. So for example, in base 10, it's really easy to multiply by 10. It's also easy to multiply by five because five is half of 10. You could also multiply by five. You could multiply by 10 and try to half it. You have all sorts of different options. It's not so easy to multiply by seven and three even though... Maybe a base six would be a lot easier to multiply by three. Base two, binary, when you have ones and zeros. The cool thing about that is that if you want to multiply by two, you're just adding zeros to it instead of multiplying by 10. Depending on how you choose your base, certain things are easier and certain things are harder.
Aaron: Do you have a favorite base system?
Max: No, but I'm going to talk about a novel one at the end that's really complicated. I don't think anyone will ever use it but I think it's a really cool idea so hold off to the end for a second. In terms of favorite, I think, of the ones that I... Well, let's talk about the interesting ones. First of all, there's base 10, that's the one we use. Binary is not just interesting because it's used by computers, but it's really the smallest base that you could have. Now, my core answer is about what is base one and what is base zero so we'll get into that in a second. But binary is something that, I think, would be like if you wanted a universal language, it would be more acceptable than digits.
Aaron: It's not purely a computers thing because Morse code is basically a... I guess you're not doing mathematical operations, but it is, in essence, a binary system. You're representing more complex messages using ones and zeros or dits and dots. Dots and dashes.
Max: Dots and dashes, Yeah. So another one I'll mention is base seven. I like in terms of learning about bases because that's the one that gets really different from base 10 but the numbers have the same amounts of... Like if it's a three-digit number in base 10, it'll probably be a three-digit number in base seven, maybe four but it looks totally different. So I feel base seven is an interesting one for learning and it's freaky if you've ever played with that. Where to multiply by seven, you add a zero at the end of the number. It's like why is multiplying by seven so easy. It almost feels like something's wrong here.
People don't mention that one a lot but I mentioned that one because for some reason seven being a prime number and five is also a prime number but it's part of base 10 so we're used to it. So something about basing it off seven it's almost the weirdest one to use between two and ten if that makes sense. Another one to mention is hexadecimal which...
Aaron: I was going to say that's one that I run into a lot and I have failed to develop any sort of intuition for.
Max: Okay, so hexadecimal is base 16. The digits that they use are zero through nine and then A through F. Now, if you've ever seen color pickers online, that's, I think, six hexadecimal digits. So I think if you have FFFFFF, that is... is that black or is that white? It's one of those. I think it's white and I think 000000... how many zeros did I say? Six zeroes is black? Something like that. But anyway, the first two represent the red value, the second two, the green value, and the third two, the blue value. What's really great about hexadecimal is that it's still a small number of digits 16 so it's manageable. You memorize them and you can easily recognize it. If you're a programming professional such as I, you will immediately recognize a hexadecimal number by the fact that it only has A through Fs in the string. I think other people recognize that as well. It's very easy to recognize.
Aaron: It's much trickier to tell when it only has digits zero through nine because it could be hexadecimal. But usually there's some notation that will indicate that.
Max: That's the thing about digits. It's that whether you're in hexadecimal or base two, or base seven, or base ten, if I have the digit one, because all of those have a one in it, I'm not telling you is that one the decimal digit? Is that one the binary digit? Is that one the decimal digit? Which one is that?
Aaron: Yeah like one one is a valid number in all those systems but has very different meaning depending on what your base is.
Max: Yeah, it has to be... You could use notation, maybe a subscript to denote what type of digit it is but usually, the way we do it is just infer it based on the position. Like we say "Hey, this is going to be a binary number." So in other words, you have to be told what it is. But if you're a data scientist, you run across data. Oftentimes, you're not told what it is so that could happen as well. But in a good data system, you should be told what it is and if you actually try to use these things to communicate. The other thing about hexadecimal that I didn't mention is that it interfaces really well with binary because each hexadecimal digit being 16 is four bits. It's four ones and zeroes. It's almost a way to compress binary code in a very dependable way, If you want to show eight bits in a byte, it's two hexadecimal digits so it's really easy in that regard. Okay, so what was the core question? Let's get into that.
So the core question was if binary is base two, binary is ones and zeroes, so it's like okay, all of... Anytime you see a number that's 10000, you know that's a power of two whereas in decimal, it's a power of 10 which is freaky. I don't think I'll ever get used to the fact that one zero is two not ten. But they asked, "Okay, what is base one and what is base zero?" Then, some people said it didn't exist, and then, other people said that base one is tick marks. "Hey, base one means that there can only be one symbol. I know a system with one symbol.
Aaron: Makes sense that you can reduce the complexity that way.
Max: Yeah, yeah. But I would argue that that's not what base one is if you follow the pattern down from base ten. So if you think about it, every time you go down, every time you remove a digit from your base, you reduce the number of digits available for each place. So for example, if I am in base 10 and I have a three-digit number, how many different possibilities do I have for a three-digit number?
Aaron: In base 10?
Max: Yeah, I'm getting you on a spot here.
Aaron: Is this 10 factorial? No. That's too many.
Max: It's just 000 to 999. Yeah.
Aaron: Okay. Yeah, yeah, yeah. Yeah. That makes sense.
Max: 10 to the third. Then you go down to... Let's use base three. You have a three-digit number. It should be three to the third possibilities. Right? So that would be, oh my God, 27, right? Then, let's say you're using binary and now you have two to the third, right? So you have eight possibilities. I could enumerate those eight. There's 000, 001, 010, 011, 100, 101, 110, and 111. That's all linked.
Aaron: Representing zero through seven.
Max: Right, right. Exactly. Okay. So let's go down to base one. If I have three digits in base one, how many possibilities should I have? So if base 10...
Aaron: It's three to the one. Or is one to the third?
Max: One to the third. Right. One possibility. Notice, look. If you're base three, every time you go down a number, you remove the top digit. So base one, there's only one digit and that one digit is zero. Exactly, exactly. You can have a base one number system. It wouldn't be very useful but essentially, it would be something that's always zero. Now, I lied when I said it's not useful. You'd actually be surprised that in type theory in programming, this is very useful to... It's a type called a unit and a unit is a type where there's only one value available so I know the answer is zero going into it.
Now, why would you have unit? You can have unit because... Well, now I'm getting it complicated but you could have a system where it's like "Hey, I want to have a list of something" and actually it's like, "You know what, in this possibility, I want a list of strings. Over here I want a list of colors. And you know what, over here I want a list of units." I know that's going to reduced to basically a list of units is just a count of something." It could just be... Now, why would I be doing that? It's just if you have some abstract system that you want to crunch down to something else, it's good for trying to generalize stuff. Again, I'm getting into some abstract type theory here but sometimes it's very good when you have some... When you're trying to generalize ideas in computer science, oftentimes when you plug in that unit type, you can then make it something very specific and very simple.
So here's another example. Well, no. This is not a good example but I was thinking like... There's a concept called a map where I'm mapping some value to some other value. Let's say I'm mapping people to scores where I'm keeping score in a game. Maybe their scores are numbers. You're playing basketball game. Or it can map people to colors. Maybe it's like what color of jersey they're wearing. So mapping people to colors. So then, I can say, "Well, what if I map people to unit?" Well, that's something that gives me no information. Maybe there's a situation where you just don't want to put any information there so you just put unit. There's all sorts of different uses and ways of describing things.
I almost want to give it another example. Let's suppose you're exploding a three-digit number. Let's say you have 321. We often say when you teach kids how to explode that number. It's three hundreds, two tens, and one one. You're gonna have to go through this with your kids in two years so you better pay attention there.
Aaron: I'm getting there. I tried to explain multiplication the other day. Didn't go over well.
Max: Now, when they get older, it's going to be like, "Okay, this is three times ten to the two, and two times ten to the one, and one times 10 to the zero." You might be like, "Oh, why am I saying 10 to the zero there because that's one, it's not useful." It's like, no, it's really useful for completing a pattern. So anyway, I just went to a whole rant as to why unit is valuable. I'd actually argue that there's a case where we do use a unit and that is in time. So when you're talking about hours and seconds, or let's say you're doing times in minutes and seconds, right? You're using a positional notation there but each digit is a different type of digit.
So think about it this way. The ones digit on the seconds is a regular decimal digit but the second digit on seconds only goes up to five. It's a base six. It only goes up to five. you have bae six, and you have base ten, and you multiply that together to get 60, you've got 60 seconds. Okay, then, on the minute side you have the same thing going on. On the second side, you have a base-ten digit. To the right of that is a base six-digit, then in the minutes you have a base 10 digit, to the right of that is a base six-digit. Oftentimes, in between the minutes and the seconds what do you put in there?
Aaron: A colon?
Max: Okay. What if that colon is a base one digit? Think about it. It does work, right?
Aaron: I don't know if my mind is blown or not.
Max: Well, look, you wouldn't be able to tell the difference because that's just adding a base one digit to your number. Doesn't hurt anything. It doesn't give you any new information, Maybe it just helps with readability. Maybe the commas that we put are based one digits. So really, our decimal notation is 10, 10, 1. 10, 10, 1. 10, 10, 1. Something like that. So okay, that's crazy. Okay, so now, then the question is, even crazier, base zero. What happens on base zero? I'm going to let you guess.
Aaron: It's the absence of a number, right? How can we have less than a single possible value?
Max: Right. So in Scala, which is the programming language, we use it in FourSquare, I said there's a type called unit. I think there's also a type called "none type" and basically, if you say that a function returns none type, it will never compile because there's no value in that. There's no possible value that can return none type unless you pass it another function that returns none type that it assumes exists but then you can't build that one. If I tell you that I have a number that is base zero, you don't even have the zero digits. You don't have any digits.
So you could say it's like a number system but it's a no number system. There are no possible numbers that can be made through it if that makes sense. Are you taking notes on this? Is this...? Yeah, okay. So like I said, for a base one digit, you could add that colon, nothing happens. But if I add a single base zero digit, it wipes away the whole thing. It's like multiplying by zero. The whole thing explodes and you can't have a number anymore. So that's really interesting.
Aaron: It's almost like dividing by zero.
Max: Yeah, yeah, yeah. You're just multiplying by zero. You're multiplying the number of... Just like adding a base ten. When you add a base zero digit, you multiply your possibilities by zero, thus negating all your possibilities. I think the interesting takeaway is that base one and base zero are real concepts. Actually, in theoretical computer science, they do matter. Not only that but it's actually built into programming languages types like this. So they do have some practical use and that's fascinating. Now, I don't know if you have any questions before we move on to my idea of a factorial-based number system.
Aaron: I was going to ask, have you read Andy Weir's latest novel, Project Hail Mary? I will not give any spoilers but I will mention that, I believe, it's a base six number system comes into play.
Max: Okay, yeah. I think that was actually pretty common. I think those have been done in the ancient world the 6, 360, 12. Those are very divisible numbers so those are often used. Sometimes, I wonder if there could be a measure of divisibility. Some kind of an objective measure. Not just how many factors something has but why is 12 more useful than nine, say. Because nine has two threes but you have a trade-off because 12 has more digits. There's some objective way to measure how much more useful 12 is than say, 14? I'd be interested to know that.
Aaron: In getting dangerously close to a defense of the customary unit system and why it is superior to geometric.
Max: That wasn't my intent. It certainly is a good reason for having... It's probably why the customary system has that divisibility but I think they also found...
Aaron: Because it's a free digital world. Operating where things could be divided into fractions wasn't perhaps more useful than breaking things into units of 10.
Max: Yeah, yeah. But then, there's a lot of use standardized by 10 as well. I'm not going to get into that whole debate. Sometimes I like having both systems because you could then compare and contrast and think about things differently but that's a whole other thing. I posted about that once on Twitter, everyone got mad at me. All right. So here's my idea for a factorial-based number system. Okay. So imagine this number system. The ones digit is base one so it's always zero. The next digit over is base two. The next digit over his base three, the next digit over space four, so on, and so forth. At some point, you run out of digits but let's say we go A through Z. So let's say you can't make it more than 36 digits into it.
Aaron: There are other letters in other alphabets. You can stretch it.
Max: Sure, sure. You can stretch it but let's keep it way smaller than that for now. First of all, what's really interesting, if you take a certain subsection of those digits, let's say like the first four. You have a unit digit, a binary digit, a twos digit, and a threes digit. How many possibilities is that? If you multiply them together, that's three factorial. One times two times three. Now, if you look at the numbers that are 10000 whereas in binary they're, factors of two, in decimal they're factors of 10. In this system, those are actually factorials. So every factorial would be... Like seven factorial would be 1000 etc. If you wanted to up the factorial on that, all you would have to do is add a zero which I imagine that in terms of combinatorial computation there's got to be some use for that.
Aaron: I was going to say, what's the discipline where that could be particularly useful? I was thinking probability but I couldn't say exactly where within that this would be particularly.
Max: What would be nice if you have five items, five factorial is the number of permutation of those items. Now, one way to represent the permutations is to just have each of those five items represent a digit right? Then just write those digits in whatever order that permutation is but another way to represent that permutation is to say, "Okay, line up those five items" then let's say, "Okay, I'm going to take the fourth one. I have a four." Now there are four left I'm going to take the zeroth one, I'm going to add a zero.
Now, there are three left. I will take the second one and so and, and so forth. You can build up a number that way and that would be one of those binary digits and then they become addable, there's a certain sequence to them. I feel that's sort of a different way to explore permutations of items that has not been done recently. That's just an idea. I haven't written a paper on it. I haven't looked for it in the literature but I'm sure it's there. Maybe it's not there. Maybe I should write it but I don't know.
Aaron: It's vaguely reminiscent of changing coordinate systems or not necessarily changing coordinate systems, but changing geometries. Going from Cartesian to... I'm blanking.
Max: So Euclidean to non-Euclidean.
Aaron: Thank you. That's what I was thinking. Euclidean and non-Euclidean spaces. You can apply the same operations but it has completely different results.
Max: Right, right. and then, I think there's a broader question that I asked what is a digit? So we often think of digits as "Okay, there's a finite number of them. I think you still have to have a finite number of them. I think that's got to be a general rule because otherwise, they're not usable." Okay, there is a finite number of them, we feel they should have a certain order. Is that necessary? Could you build a digit system where maybe the digits don't have an order? Or maybe they have a pre-order where maybe there's... I don't know. I'm not going to speculate but there's all sorts of different takes on digits that I could see could be used to build up really interesting data structures and computer science and mathematics. I'm not going to attempt to do that in the format of a radio show today.
Although, I feel like I want to go up to this whiteboard that I have in the room and do some... I got to get a one of those detachable microphones because the sound looks good. I don't know if I could. Or I could just to hold this and do some whiteboarding up there. That wouldn't be part of The Local Maximum. That would be just another extra video I put out.
Aaron: We’d get you doing a whiteboard session soon.
Max: I hope so. I hope so. All right. Any last thoughts on today before we wrap up?
Aaron: Well, I asked previously if you have a favorite base but do you have a favorite digit?
Max: Ooh, yes. Yes I do. It's my favorite number. I am a fan of the number four and I think it's because four is the only digit that is like... Well, I guess this puts two in the equation but two plus two equals two times two, equals two to the power of two. It's like almost every... and then if you take Ackermann functions of two which is beyond power, it still goes to four. There's something about four where the symmetry of it really appeals to me. I like other numbers too but four, I think... Four is just my go-to. I don't know what that says about me. I don't know if that gets into numerology, some weird stuff. I don't know if that means I have some psychological issues but four is my number. Do you have a favorite one?
Aaron: Before we go there, I have to ask and I have no idea what this answer is going to tell me one way or the other. But when you write a four, is the top of your four a U shape or a triangle shape?
Max: A U shape.
Aaron: Okay. I still have no idea what I've learned from your answer there.
Max: But that doesn't really...
Aaron: It had no impact on the mathematical properties of the number. It's completely a typography question.
Max: I can imagine that for some people that the reason they like the four is how it's typed.
Aaron: The aesthetic?
Max: Yeah, I think I could write it as triangle and...
Aaron: I think a lot of people like eight and infinity for that. That it's an aesthetically pleasing symbol.
Max: I could see it. Well, people have realized, the ancients have realized that different numbers... it's not just a never-ending sequence and they all look the same. Each number has, especially the small numbers have a different personality because there are very different ways that they can be broken down and vary in systems. There are a lot of systems that break into two and a different type of system might break into three and four. There are qualitative differences as these numbers appear in nature based on their mathematical properties. So that could be a whole other area of exploration to talk about because I don't even know where to begin with that but definitely something people are interested in.
Aaron: Well, it just reminded me that I'm currently reading another Neal Stephenson book. So we mentioned The Metaverse and Snow Crash earlier which has several mathematical proofs sprinkled in there just because he needed to fill up the footnotes or something. Perhaps I will report back in several months when I finish reading it. What I've learned about mathematics and natural philosophy on that adventure.
Max: Alright. Perfect. Maybe I'll interview that for another episode. Alright. So that wraps it up today. I think we had a good show today. We didn't even have to... We didn't fall asleep. It's already one in the morning, 1:30 in the morning, so perfect. All right. These are the best shows, the one that we do at one in the morning. Anyway, all right. We have a lot of great topics lined up. I don't have a lot of guests so if anyone has some ideas, give me some guests but I'm finding some new ones.
Aaron: Mark Zuckerberg, if you're listening and you want to come in and talk about the metaverse, open invitation.
Max: Oh, yes. That would be a good thing because I don't want to just complain about Facebook with him. I would absolutely talk about the metaverse. All right. So that's a positive note to end on. Have a great week everyone.
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