I imagine this event being more originally of a lot of outsiders coming in to like want to know about what's going on, but actually we have more insiders here. So it might actually just be like a joint venture type sharing information scenario. Our chain gets to sort of present what they're doing to Exa and sort of vice versa. So does that make sense, Ed? Did you hear me? You were saying something at the end that didn't quite catch about collaboration scenarios. Maybe more Q&A or more conversational as opposed to presentation. Yeah, I think it could be that actually. Conversation. Okay, I do have my time is somewhat limited. So, you know, I'll go through the slides really quickly. Also, we may be joining 4 o'clock. I'm sorry, 7 o'clock here. George Soder was doing business development and marketing for our team as well. So he can, you know, carry on the conversation too. Should I just launch it? Yeah. Okay, awesome. Well, and to see, to see more people instead of the back of the laptop. So I'm Ed Eichel. I'm the CEO of our team. And I'm the founders of our team. Operating as well as the board director for seven or eight months. So there are a few slides. We'd like to leave lots of time for conversations. So I'm going to go through these very quickly and happy to see my slides. Okay, great. So our team value propositions of our change is that we're building a whole blockchain platform that is scalable and trustworthy. I'm going to assume some familiarity with blockchains. Otherwise, you know, you may not be attracted to the media tonight. But as we all believe that blockchains are going to reshape how the economy works. This is not just a new technology. It's not just an experiment. But this is really going to be revolutionary in a lot of ways to change many things. The opportunity that blockchains provide us as innovators, as investors and honorable of life in societies is sort of a kind of a multi decade kind of thing. We look back over what's created in the initial confusion, the anticipation of good applications and equal systems in the bubble that followed in the late 90s and in the dot com bust, but some survived. Right. And so many great things. And then of course the internet was intended to be a decentralized or shared information more and more centralized. So blockchain helps build a what I call a trust player over the internet. It's a little bit familiar with this model. Maybe we can dive deep into why is Ethereum centralized? Well, I wouldn't call Ethereum centralized, but let me just keep going. Okay. Yeah. I'm going to go faster. Ethereum has some challenges. This is Vitalik.com to see scale the cost latency and Ethereum and all the blockchain projects are working to as well as new startups creating brand new blockchain. Just to kind of set the position of our chain relative to there have been Bitcoin transaction 40,000 transactions a second. We're pretty confident we're going to get there. We are implementing state signed on the top. Sorry. I'm glad Sam here as our director of the R chain cooperative and secret, but it's not necessarily well done either. We have we are going to have a current model similar to Ethereum. We're programmably complete territory. Our team also have content delivery. And we'll have, of course, our tokens are the primary one after this launch is called the red or EV launch. We have a ERC 20 token called the rock or ECOC and chain cooperative is actually just in the process of wrapping up a membership drive and a private token sale of the rock to its memberships. So how can we make these claims? We're we're driving the R chain platform around concurrent processes, obviously around cryptography and also around game theory. The state protocol is essentially a type of game theory to to drive consensus and the mathematics around the concurrent processes. And the specifics are called high calculus and row calculus are really quite a big driver of why we make the claim of scalability. And I'll get into it. I was mentioning the cooperative and the holding company and the private sale that we've got going on. There's a time relationship between the R chain holding company and the cooperative. And the mission of the cooperative is to build out the platform and some membership for the benefit of its members. The members will make the major governance decisions. And then the holding company is an incubator that will foster startups and joint ventures and projects and is a for profit company. And so we're looking for opportunities there. The cooperative is also looking for developers. The platform developers understand functional programming programming language and that have an appreciation and wants to learn more about formal cement. Architecture looks something like this that an R chain node will run on the Java virtual machine. It will have its own execution environment for written in layers of that as shown. We're in the process of building that out. We have the programming language specification. The lightening database in the storage model and initially the same communication model as the Ethereum runs this RL EXI. And so some of the initial plumbing is working already. There's a draft programming language. There's a virtual machine that's running. That provides also a lot of work in front of us. It is specified at some level but there's quite a bit of work to finish that. We're about six months away from an output. We'll be able to demonstrate pretty high transaction volume and consensus across many nodes about one year from launch. And we're calling that launch. In terms of what we'll build on top, just about every blockchain solution you can imagine, many of the concepts that are being built both by servers as well as enterprise organizations, they're really across the whole board of innovation and they're waiting for a scalable blockchain or Ethereum to fix scalability issues. So this is just a long list of potential things that can be built. But the whole company will especially encourage initially applications to really foster this ecosystem. So already we're working identity solutions but we will either go on to partner with those, building those as well as these other initial applications like time stamping services, private messaging, content delivery, name registration and what I call a personal blockchain. And I'm actually going to pause here because that's the primary content. And then go as deep technically as this group would like to in terms of what things are scalable and so forth. We should probably say, I'm casting this on a Hangout on Air. So you've got no releases or nothing like two formal with anybody. Is that not okay with anybody? Okay with everybody? Okay. If that changes, tell me. Even if there's anything for me, I'll need you to review it. Yeah. So I'll start with a question. So this is I think a practical question. So what about rolling concurrency relates to X's concurrency. So you're calling it fabric but it's, I think it's very similar here. So yeah, you guys have both expressed to me that you're building concurrent platforms. Yours is calling it. There is a little uncertain exactly in how the concurrency model is established. I know it's good to use the label algorithm, but maybe you can go into that a little bit. Sure thing. So concurrency happens at several parts of the system in the protocols level of the virtual machine. In contrast to, you know, the Ethereum virtual machine, which is sequential at the EM level. So this is really a key aspect of the mathematics driving this is that is all about processes running for this, that the channels over which the processes are communicating or can be changing the psychology of the network can be changing. So that's a really good applicability to decentralized systems. And so the programming language row line is a direct mapping of that calculus. And the programming language itself is concurrent in the virtual machine. So at a given node level, if there's, you know, dual quad core or whatever the local machine is, it will take advantage of all the processors. And then when we look at concurrency, for example, consensus protocols of work, is to not over constrained. And so thinking back at a user level, I have a transaction in Seattle to buy something with, and you have a transaction in New York to buy something else. They don't need to be both through the same consensus algorithm, unless they're involved in the same vendor addresses or the same payer addresses. And this is where it gets a bit difficult for me to explain exactly how we can make those claims. But let me extend a bit about the node topology and what the blockchain shape looks like overall. So as you all know, that both big portion of Ethereum, all the transactions around the world are put into Fox and are essentially sequentialized or stacked on one block chain. So all the nodes have a burden of synchronizing the blockchain. And it's brilliant, but it doesn't scale particularly well. So what our chain does is it relaxes that constraint and it allows different nodes to care about different sets of transactions and contracts, and it does that through the use of namespaces. And then namespaces are a traditional computer science thing. You can think of it similar to a URL or a past hierarchical where you can address a particular name by its past. Or by its first, that name is given context based on its past. But with this high calculus, it doesn't have to be just a tree and have a name that only in one namespace, a name actually in multiple sets, which is also another aspect of namespaces. So going back to nodes is a node then can be configured to care about a particular set of contracts, a particular set of user accounts. And then only care about the interactions with those accounts. And as long as there is not validators in the consensus cycles so that the double spend is prevented and given the surety of blockchain, that will all scale. And then, you know, most of New York's transactions, and then occasionally there'll be some that aren't, and those will be built through a different level of consensus requiring nodes that care for particular addresses and contracts about both of those sets. So that's the simple way that I think about how our chain will scale. And we're still working through both explaining this as well as building the mathematics for the territory. You guys have a follow up about that? So with that concurrency model and your data structure is a series of blocks where each block is a list of sequential transactions. Maybe I missed this, but can you talk in a high level way about what sort of the actual data structure is? Are you still calling it a blockchain? Are you not? Did you hear that? So you're just wondering how would you call it a blockchain if it's not sequential or series transactions? Exactly. I appreciate the question. In a sense, there are some aspects of our chain that aren't blockchain in the data structure sense. You know, in similar to Ethereum, there's a tree structure, PRID, in terms of serializing what's on a node. And from a transaction perspective, it looks more like a graph, actually. And it's not, I don't think it's even a directly signal graph. It's a more general graph. And these things can be independent of each other for sections of the block. Our chain is not precisely a blockchain in the sense of Bitcoin and Ethereum in technical ways. In that data structure way where you are allowing this concurrency in relative independence. But there's another way as well which is in our chain, the storage will actually be leased. So, you know, some transactions will be kept in the system for a long time because of the redundancy that's needed and the eventual finality as you go through the census. But especially for larger content, its place in the blockchain will require to have this guarantee of immutability that once it's on the blockchain, it will never change or that the storage will never change. Our chain actually won't make that guarantee unless it's made for it. So, this is another way in which the our chain will actually scale because there again, it's a great interesting promise but it's not agreed. It's a transaction quite a burden on Ethereum and our blockchain. Bitcoin nodes to not only run all the transactions but keep all of them forever. So, who would pay for that lease? So, it will be paid for upfront actually during the transaction. So, some small part of the fee will go to that storage component that lease and who will reap the benefit of that will be the node operators that will prove they're storing that data over time. So, how does that relate to before maybe you want to weigh in here, how does that relate in terms of your current fabric model? We can say like each VM is incorporating event loop in each other VM or is there a different concurrency model? It's more granular. You already understood part of that you were talking about how VMs communicate and I didn't understand the whole sentence, sorry. Before we go into the that structure looking like that structure what's the concurrency model that each VM that each node in the network follows in order to coordinate state transitions? So, like a state channel? Yeah, I understood the essence of the question. It's actually a challenging technical question for me personally to answer but let me just give you a flavor and this is exactly the mathematics of the current processes where the VMs at a particular time are evaluating a particular contract or a program. The program may have a dependency on another program that's not even necessarily on its own node. So, it needs to pass a message or a transaction to another contract. And whether it's on the same VM or separate VM the same thing is happening where all of these interactions are asynchronous. There's a call out the calling contract will essentially go to sleep in other words this state will be serialized and stored on the blockchain as its next state. The other contract will receive that call essentially a secrecy that will wake up run that transaction that transaction may be a callback to the first and then the first one will wake back up and continue. So, the notion of a transaction in our chain is much more granular involving all of the messages that are initiated from the user or the account.  Yes, it does. So, in order to practice something that initiates this transaction they need to become aware of each other. What is the the security model? What is it that enables them to know that this VM is authorized to communicate with this VM? Is it like permission as it's permission? What's the security model? Yeah, I actually don't know how to answer that one. So, let me make sure I help paraphrase the question to see what is the security model between contracts or programs? How do they know about each other? How do they call each other? You know, they find each other through namespace resolution and the nodes can be configured such that they have permissions which namespaces they even listen to that even with the same software with some configuration you can say this node is truly a public blockchain or a public node it can be open to any of these namespaces or even with that you can say but it doesn't want to take on namespaces that require gigabytes of storage or for news short movies and music, for example it's not to want to work at that it only wants to work with very small financial transactions The namespaces are the nodes to declare what namespaces or what qualities of namespaces they care about and inside of a corporate setting or a consortium setting it may be very restrictive to say these nodes only want to listen to these IP addresses and these only these namespaces so that it can be defined that way at least that's neat, my understanding of the initial design We're talking public blockchain first and then tightening through ACL like permission systems Yes, so our goal is that it's the same architecture and it's just configuration through access control etc. My question is that I agree That's good, go ahead My time is getting a bit tight I've got a lot of demand so with this membership drive and private token sales let's maybe just take one more question I want to know what's going on with the what's the how do you do it I didn't hear the question We have a membership drive like Oh that's awesome Yeah, so we've been having this membership drive and private token sale for about three, three and a half weeks now We've closed and we've closed about a big point and a little bit of US dollars We're still calling you know the submissions and requests from it's been in terms of membership numbers we have at least 300 members or 250 to 300 members total and a large chunk of that amount has come in the last several weeks and so that's awesome Our chain cooperative is a membership driven organization so having that group of folks that care about the future of blockchain is really important to us and our decisions in the future In terms of the fundraising we still have yet to close several of our rock purchasers and our individuals also that are coming back sort of a second time as they realize the opportunity so someone that maybe started three weeks ago at 50,000 dollars sometimes they're coming back for another 50,000 dollars etc so it's exciting it's a bit crazy frankly but it's a good credit That sounds great, congratulations That's a great result Thank you so much I really enjoyed the meeting with you I was out of this space at the end of May and would love to come out with PencilWorks soon again When can those of us that don't have 50,000 dollars Is there going to be like a smaller When can people who aren't a credit investor get in on the crowd sale? Yeah, I need to run but so we don't have a locked in crowd sale I expect it's likely that rocks will be listed on an exchange although that's kind of up to the exchanges that Bob's not pushing that The launch of the platform is approximately a year from now it will convert or redeem the rock token certainly at that time if not before at that time, REV would be on an exchange but I think there's going to be opportunity Okay guys, great Thanks so much for your time Now that we've sort of virgined our population Hey Kevin, what's up? So you can pick that up Yeah, to get on EtherDelta it's not a really intuitive interface which kind of sucks for most people Yeah So we're going to transition into EXA so we're taking a moment of tech setup time That was Kevin Hey Kevin If you don't mind Could you maybe give us a little bit more details on how we could do that It's on the Github On Archance Github Yeah, I listed it out It's under the issues I don't know what the issue number is but it's on that I'll find it and then I'll reply to their current response of the meter I'll find it and I'll send it They have a 1-4 hour to go in a sale that has a $50,000 minimum Oh yeah, let's go I think we're supposed to do a little networking or something between the two and then keep going at 730 Yeah, it's kind of loose We can say some clothes Maybe we'll get to know each other in the room just so we know who's here This is a nice interface Yeah, thanks again to to pencilworks for doing this Nathan, this space is awesome It's become quite a blockchain hub so it's really special to be able to do this here Thank you so much for everyone that's here We're in rare air We just heard from what could be the next big smart contract platform I believe we're about to hear from even the next one and what these guys and girls are putting together is global it's powerful it's passionate and what really stands out to me about we're going to hear about incredible technology just one thing I wanted to say that really stands out to me about gravity is that they really think about right and wrong and about creating a better world and that's what's going behind the architecture of the platform I personally I've got finance background and economics degree in Northwestern I was an investment banking and private equity and I said Sayonara about a year and a half ago to focus on the well-being space and I helped incubate platform-oriented well-being companies and now I'm coming to help people improve their quality because God knows we work too hard so that's me my name's Chris I'm I'm as Greenwood, three words a beast innovation innovation it's a lot of it's a lot of it's a lot of it's a lot of it's a lot of it's a lot of it's a lot of it's a lot of Bader I'm talking about another part of the foreign word, the other part of the word, three words. Um, Canadian, economics. So Eric Rood, disruption, wealth management.  I'll go on brand. I work in real estate and I'm interested in justice. Accommodation. Retire. I'm going to pass the letters down to the next one here. My name's Corey Levinson. Uh, usually I'm not in New York. I live in Berlin but I'm here now. And you all are here now so I can, um, I, three words for you. I, let's say I'm a developer, mathematician, slash geoscientist, Canadian. Eric, based in Montreal, cultural theorist, and art, philosophy, and activism. I'm Scott. Um, I'm a self-taught, an activist, uh, troublemaker in SAX. Something, uh, pretty familiar that I've been through. It's powered by bicycle. I'm James, a software developer, uh, JavaScript, and trust. I'm Axeli from the exit group. Also, open source finance. I'm Jacob. I'm Jacob. You, me, and the pure joy of semantic metamorphosis. Multi-hypnosis. Pure joy of semantic metamorphosis. Uh, I'm Anya, uh, also Dexter. So, future of humanity, economics, data science. My name's Kevin. I'm a, uh, an activist at the Ayala Foundation. I'm doing office development strategy. And three words, it will be, uh, beyond blockchain. It was to, uh, engineer, uh, machine learning, and vegan. My name is Kristen. I'm an archivist. I'm an X7 organization from Cuba. And I don't know what, I heard three words. I'm not sure what the three words was supposed to describe. It's me, uh, concerned with my family, uh, friends, food, and that sort of thing. You've got some great seeds up there, so you don't have to stand there. You don't want to. You can start, you can start a bit early. Yeah. And then you can tweak the world that we're starting early at no additional charge. Please, can you guys speak up for the meager mic? So, okay. What's going to happen is I'll just give a very brief, like it's not even an introduction, but kind of for, I passed the ball to Jorge, with our main course. Uh, so Jorge is the, the, the, the social architect and, and designer, creator of gravity. And we want to spend today the, the, the, uh, most of the time there. We had a real nice event yesterday at E-Flux. There was a lot of, um, it was a full house, a lot of people. And we were there concentrating a little bit more on the, on the social, political, and technological, uh, economical sides of, of, of what we're doing. And here we would like to concentrate on the technology. Technology side, which means really gravity. So that's the, that's the, that's the number one thing. So the second important thing is that we are here to, we're thinking that this event, we are here like just among friends. We're not trying to pitch or sell anything, uh, uh, because we are, we're not ready for that either. So we are just, we, it's like a little bit, like a special moment. We've been, we've been really working hard with the team to get, uh, token launch ready. Uh, we're almost there, but not quite. So this is like a special moment to, to peek a little bit behind, uh, the curtains, what is going on. And, uh, yeah, that's the, that's what the attitude was. We were, we were talking like, how we'd like to approach it. So we're a little bit also testing some things, our communication, the messaging, and, and any ideas, feedback. That would be like, like really great. Um, and I thought that I would just quickly run through, um, what is going on at the moment. So with the team, uh, just like the five minutes, I said, so we are economic space agency. And it's really important to understand that this morning I was thinking, what I should have said yesterday. Uh, and yeah, one of the things really is that it's important to understand that it's not a metaphor. It's not metaphor, but we are really thinking that the, like Ed was saying also in the beginning that the new network technologies will potentially, potentially produce a radically different economy. And what economic space agency is trying to do, we are trying to give people, create and build the tools for people to start exploring and operating this new economic space. Give agency to people into this new economic space. That's, that's what it is. It's one simple form at least to me. So, so with the team, we've been really, we have, we are distributed team. Uh, basically the headquarters are, we came from Oakland. We have a house and a garage in Oakland. The team lives in the house and we work, works in the garage and live elsewhere too. Uh, it's pretty intensive. But the garage door is always open. You're really welcome to, to come and join. There are a lot of people are hanging around just in the garage to, to, it's hard work, but fun too. Yeah, but we are distributed. So we have some core team members also in, in Finland, uh, New York, Washington, Berlin, Rio de Janeiro, Athens, Greece. So, so that's, that's, we're distributed already and we work like a, like a virtually, functions pretty much Montreal, also Philadelphia. So, so with the team, we've been working really hard on, on getting, um, token launch or token generation event ready. And it has meant like five things and I'll just quickly run you through. So number one has been that we've been really working on the, on the, building credibility around the technology, the gravity and the claim that we are making. So one of the key things is the white paper. So the white paper is not yet publicly out. We have our internal version and we are working on it. What I was just locked away for two weeks to, to get the technical, uh, documentation, design documentation ready. And it's, it's, it's working, I think. Do we need to lock you back there? I don't know. I don't know. But so, so we are adding the technical specification to the white paper. The narrative is there and we are, we are, um, if there are people who would like to review, um, um, take a first look, just, just, uh, let us know. But it's looking very promising. We're working, one of our key advisors is, is Mark, Mark as Miller, who is, I don't know if you know, one of the old, uh, crypto guards, really important to smart contracts, like as important as Nick Savo and, uh, uh, I think, and, uh, with his, his, um, good friend, his technical, built to lock. So they're helping us with the, with the, with the white paper. And it's, it's, yeah. So it's coming together, but it's not how to get, and we're getting there. Then we had a one really good event in San Francisco, like a month ago with, with Mark Miller, who was there, mixed, um, uh, Zucco Wilcox, um, Brian Warner from Tahoe Labs, um, um, Arthur Breitman from Tezos, kind of a, where it was called, blockchain meets object capabilities. And we are, we are hopefully with the white paper, uh, organizing other events. So basically that means some of the key technicals, singular people around us reviewing the white paper and kind of, uh, um, uh, getting, giving it legitimacy, basically. Then, then the second thing we've been working on that we, uh, just like, I don't know if how many of you followed the Sunero and, and Archang drama. I think it was super exciting. I was watching like this four hour, uh, meetings in the Hangouts with the, with the, with the other drama going on and I, I must say that Ed and the Archang team really handed it really well. I was, and, uh, I, they really got my respect, uh, through that process. And for them it worked also really well. They started to like, just to, to their weekly meetings. They were in Hangouts, like, transparent publicly. And suddenly you see that there was more and more every week, a little bit more people, like, they, uh, both, that's one of the reasons why we're here too. So, so we're hoping with Chris and Jonathan we have some really good base here in New York that, that we could have a meetup and people interested in join the project, um, and, and becoming involved. So we are planning to have a, a big, good hub here in, in the East Coast too. That's one that we've been meeting here with our, um, advisors and Econauts. We have Jonathan, Ben, Dick, some really good people here, like, uh, uh, who I respect a lot and we are consolidating their, their support, um, Brian Masumi, Erin Manningway yesterday, some other really, really important people, the people who I, I respect them. Um, I like a lot. We've been having meetings with them. But to, to try to consolidate our close advisors and collaborators around us, um, uh, at the moment, then the events we, we, this week, or this week we are here in New York. We were, Deanna was at MIT. We had a team in Macau, in China, Hong Kong, London. So we are like getting out to be uh, certain events a little bit so that people would also know that we, we exist. So that's the second thing. The third thing we've been working on is, is like key messaging. Just like Ed said, it's not so easy to, to, to like, to message about this. And we've been like really trying things out and we have like failed like, badly most of the time, but we are also getting there. There are some, some, uh, this is something what we would like to test today. So at the moment, what do you think? So the key slogan is gravity, deep interoperability for our decentralized future. I think it's pretty good. I think it's pretty good. Well, we have other candidates too like smart contracts unchained. It's pretty catchy. Let's see, let's see. But that's one, one thing and uh, uh, yeah how do you get the messaging and communication and uh, like, right it's, it's, it's, it's hard but also really interesting, interesting work. So we've been working on that and one of the important things so we have like, how do we message about this post-blog chain this, this technology which is taking it beyond blockchain. How do, how do you talk about it? That's one thing. Then the team which is another part of key, key part of the messaging classes and that's easier. So, so we are really we've been explicitly building the team to, to uh, from the learnings from the uh, Bell Telephone Laboratories Cerox PARC from the 70s like how they, how they built these teams where there were like people from different areas of, of expertise like sociologists computer scientists software architects economists, finance theorists because we need to like bring expertise and everybody needs to overcome their own comfort zones and step out in this new emerging space because we need everybody there to create it so this is how we've been building it and that's part of the messaging also that we, that we are like the Cerox PARC of the 21st century distributed version of what they were able to do. Yes. Then then just like Ed was saying it's really interesting the diagram he had about the how there are TG the token how do they call it kind of a hybrid structured also like in legally with the cooperative and the holding company so we've been designing the actual uh, structure of the, of the of the token generation event so so we have different organizations we have one we have just set up the foundation in Switzerland in the Swiss crypto fund with the with MME which is the same legal council that originally set up Ethereum and now recently Bezos and and a lot of different foundations like operating on the protocol level so that's set up there now then we it's a really good team I like I like the team a lot just in fact and we got to talk about that today I will call with Lowell Ness from Prokess Coit with our legal council here in the US really interesting call about the how to deal with the US situation at the moment and how they are how they've been talking with about so it's really interesting also like how do you design it in a way that these things are changing so we were really working on the token economy design, the legal design like what is the structure and how it plays out then we've been working on on the on on on finding the right like to distribute and distribution channels so this is what Ed also mentioned there we are thinking that we want to build an ecosystem not only the protocol not only the product but ecosystem and it's a different logic it's a different logic how you need to do it we need a wide distribution which fosters the healthy healthy ecosystem and what we've seen before like this far how many people are taking part in the token sales I think it's really ridiculous like from 800 to 3000 if the big sales are like 10,000 people it's like ridiculously small amount so we're looking forward to a wide distribution maybe 100,000 people so how do you pull that through we're cooperating with Blockfolio which is one of these really good apps I like it too so they're hoping to turn the Blockfolio app into into a ICO token launch platform and they would like to they have more than 600,000 active users at the moment so I think that would be a major could be an important play with the eFlex yesterday eFlex is also important different audience opens a different channel to reach really smart people who are maybe not so familiar with the crypto world the last thing we've been designing the fundraising and we are just about to start the early contributor period for our close networks and strategic contributors which basically means that we want to bring our people who we trust and who have already trusted us close to us and we want to give them the most favorable deal at the moment there are now already some momentum and some more traditional money is lining up but we would not like to take it first then the second layer of the onion we are looking for really particular kind of people who understand the importance of creating this kind of cyber social infrastructure for the future this fundamental technology and project we are not looking for the speculators but kind of for people who would like to consciously want something like this to be built it's a long term commitment this is the group we want to reach and then there are some singular investors with whom we are talking I'm thinking that we are bringing maybe one to three when the time is right and here we are yes my name is Jorge Lopez and I want to invite you personally why I'm here is because I want to share with you guys what the project is about and I think it has enough technical beef to engage with a highly technical audience so I want to get an idea of in the room who of you can consider yourself highly technical concurrency models to get a sense of where I need to go the other who else in the room knows enough about blockchain implications models why they are important but not sorry about that so I'm going to meet you guys in the middle most of the talk opens highly technical questions and I'm happy to result but I'll sprinkle around a lot of why why we take those technicals what our design goes regarding we want safety privacy scalability and security privacy is particularly important for what we are trying to do most of the offerings that we are seeing are fully open fully self funded fully transparent their structures public but also visible to everyone which leaves outside the element of privacy of these platforms which is neutral technology with no economy of its own mostly funded by private corporations and because they don't have the constraint of the token as funding model they have more freedom of movement in terms of how they design their platform to allow for privacy permission of blockchain by separating very clearly concerning the layers I think we are able to accomplish the best of what we want to talk about that is that better so what our design principles and we apply this both the microkernel all the way to the building of the network is extreme modularity why do I mean by extreme modularity we already understand that modularity is good allows for suppression of concerns allows for testable code and in the terms of blockchain allows for small pieces that are more easy to verify both formally and just to review but it has another angle which is security who is familiar here with the object capability model so in the object capability model extreme modularity is taken to extreme by following what is known as the principle of this authority basically each agent each node grants another agent or model even only as much authority as it needs in order to perform its function what this allows us to do is both design software that is resistant or more resistant to attack by virtue of reducing the surface area of its what it makes public but also internally makes less body software particular confirmed systems by virtue of reducing opportunities for even unintentional destructive interference among components so this privilege is super important and another one is rough activity so we go to great lengths to make sure that the whole platform in every layer is reflected that means it can introspect in itself change itself, update itself heal itself so that means that we are bringing in a lot of the lessons and the philosophy of reflected language like JavaScript but really the grandfather is a small talk so what makes gravity's approach distinct so we see blockchains not only as in English and not as an atomic thing that is but we see them as a subset of a much wider taxonomy of distributed verifiable data structures when seen in that way, when constructed in that way, it really allows us to look at the field differently in which we no longer need to bias our minds towards logical centralization and we can also decentralize the logical layer while still bringing in full consistency of present memory so the role of verifiable data structures is really the role to preserve the interior of the state we set this trigger to also preserve the interior of course of computation by including computation in the same data structures as all reflected languages do access control following object capabilities principle of this authority and messaging by virtue of having reliable computation be able to create reliable message so what this allows us to do is it allows it to shift from verifiable states where most blockchains are focusing on into verifiable state to a state full protocol so really we're using, or we're using state in our current solution space in which our approach to concurrency coordination, collaboration, cooperation among different processes is it possible in which everyone puts their notes and everyone is able to see who put them, verify that they have been modified, we're getting there and this is a poor replacement really for good protocol, reliable protocol there's reasons for that that we inherent from the design motivations for bitcoin which needed to be like a state persistent distributed ledger system and we've been carrying them through as necessary design constraints so we need to start seeing in discerning where we see that such design decisions need to be made and what is actually justifying them so we need to start the threat model of our distributed application and be able to see that different applications have different requirements there's totally useful applications for something like architecture like bitcoin for more than bitcoin and there's such a large landscape of verifiable applications trustworthy applications that need to be enabled that the current platforms are really leading out by virtue of relying over relying on the state there's a reason for this obviously solutions like ORDA, like ORDA is proposing they are not relying on the state, actually they are more protocol centric but the reason they can do that again is not to protect their token so for other solutions the home on the leading blockchain approach is really incentivize by virtue of wanting to preserve the value of the token the network built on top of this architecture but the design principles of the token become the design constraints of whatever you build so we've taken the approach of not having those incentives at this layer so there's no naked token in the micro kernel as itself although we can build such things on top we build then a micro kernel that allows us to create a verifiable virtual machine which allows us to verify executions, transitions and access control from that we can create networks of verifiable VMs by virtue of being able to have protocol among them and with that logic decentralize applications that are still trustworthy and fully verifiable in different dimensions instead of one blockchain and a means of bringing a city that means atomic consistent, isolated and durable transactions we do distributed transaction protocol, two phase protocol charted however at the top gravity is trying to enable these things it's not trying to bake them in so gravity has a protocol center so we go beyond to create resilient multi-party protocols most of the protocols that we have today assume either one-to-one or like just broadcasts but how do you create secure reliable, stateful multi-party protocols to grab these goals so hopefully these conversations bring questions, the questions from natural transfers are going to come at the end feel free to ask any later so the constructing consensus when you have the capacity to create reliable, stateful protocols you can start breaking consensus apart and this might get a little bit too technical but this is what really gets me excited and if there's a word I'm happy to describe them but we can the construct consensus into like message ordering for instance how do you solve the problem of message ordering and there's this concept of event queue circuits that can be done with these multi-party reliable multi-party protocols we can check the execution integrity by having again computation verification circuits and state transition integrity having state verification circuits for those that are familiar with concurrency our concurrency model is cooperating event loops among very reliable agents and this is how we are able to do this across different elements of an application a gravity application is really a gravity network of applications microservices each one reliably servicing the others in a fully verifiable way so the end goal is to create a global, open, decentralized scalable and high performance trusted execution environment that supports privacy but I'm not an expert in the book although I haven't been reading papers for the last six months I'm trying to explain this and I they basically classify a bunch of different actors to sort of filter out one of the first things that I was that my understanding of polka dots is like they are doing something very similar to us except we're doing it at the level of computation not data strategies so we're like caching the state transitions of the state of the program itself not state transitions on a data structure so the way that it does auditing verifying minors and whatnot it's very similar to what we're doing but we're doing it at the level of computational state more flexible I don't know if there's much difference in speed we're doing at the level of generalized computation so it's not just smart contracts or blockchains it's any program you would want to run on if you shoot it in the cloud and there's a question that I see over in the paper are they talking about economic groups saying whatever it is that is not fundamental basically we should stop at their point that I know that brings incentives precisely trying to get away from because I know where they live and the other one is they mention again, the coin and if they're talking about ledgers or transactions or financial instruments I just go like alright, next one because I know there's a lot of development and I think there's lots of application for specialization at that state but using a state for solving the double-spend problem which is nothing else and reliable execution and building on top of using state as the only way of bringing about reliable execution I think it's taking things into a direction that is very constrained for what you can deal with unnecessarily so if instead you focus on being reliable execution on the bottom you don't need that so why not upgrade on a private database what do you mean? like reliable execution happens in a private database so what's the well from reliable execution to even locally where you don't trust your own power they might not trust your own power and all the way to distribute execution precisely by making sure in this one we might need to go very technical but now we see that if you don't play according to the protocol you can't keep participating so the incentive isn't there to keep playing and going to the protocol has to do with event queues, refileable event queues, message ordering, refileable computation, utilizing replication for instance to make sure that nodes are not trying to lie but the basics are the same principles that are being utilized by blockchain we're still utilizing them we're just utilizing them in a more granular way and more composed way is there a question that Archie would give me talk about what the data structure is what is the data side of all this is it which is the data side which structure you have what is known as your local obi-perfect graph you have your root scope which is like namespits really which internally inside of the runtime has a root scope chain a scope chain and from there you can create enclosures your variables you have your data so if you look at this data structure from the top what do you see a tree right so if you want to scope are inherently immutable only their variables, the values change but not the structure at least it's one of the rules that many of these programming languages hold and by allowing within gravity itself to hash your references sign your references and create your objects at that level what you can create is this verifiable distributed data structure where each reference to another object that has been marked immutable has in the metadata the hash of the object that it references but what it means is that you can have any data structure that can be created with objects that still has the same verifiable immutability semantics that blockchains do but not only for languages it's any structure we include also functionality of signing being able to send your references and being able to encrypt your objects your actions so at the low level transactional computing it's approachable if you have the same two phases basically the DM the micro-felons in here transactional you send a message everything is message-standing you send a message to your micro-services which is running like a simulated traffic secure environment because the whole system has been bootstrapped to verify the hash of every element that it executes precisely to make sure that that integrity of that encoded computation has not been compromised but what the first... oh yeah two phase commit protocols so these micro-servers can be made transactional by doing something like here's message here's a continuation because everything has to convert to actually land a calculus more like high processes and the DM sends a message out saying this is my stage change here's a write a continuation for you to commit or a write to robot with those element blocks you can create networks of these transactional micro-services and your protocol your coordination they can come up with reliable state transition but that's something you build at the next layer so so would you say then the idea of coins and wallets as like primitives actually aren't part of this equation at all but they're rather something that can be built on top by the defendant protecting double spending is nothing else than doing very viable computation very viable state transition to make sure that the truth is preserved that means that the system integrity is preserved so we call low level we get rid of all these roadblocks and do whatever we can to preserve state integrity computation integrity not only among one micro-service but networks of micro-services this is what I'll be talking about because these micro-services may only be communicating with each other through their introduction creation or initial transition so embedded into that is already a security model also things that are not introduced are like dynamically impossible to find each other so they cannot guess where they are so that's the principle should you speak to the use cases I mean the parts of this again but you made that you mentioned the other purposes for mistake in terms of the differences so grab a state to enable a future where not only do you have like the main technologies for the main network issue in tokens but when everything and everyone is an issue of whatever and it's trying to tokens financial instrument assets it doesn't matter and to enable those like millions or billions even of transactions we need to first of all logically decentralized so you cannot keep thinking in terms of blockchain you need to still maintain system-wide computational integrity that's why we go to that lane computing it's very high about the structure separating concerns permissions, it's very high it's very high this one is data state transition very high this one executes a redundant computation to catch up on any of those all of those microservices have been isolated in such a way to allow us to preserve state integrity and to also detect state integrity violation instead of using economic logics or incentives to direct behavior or this is device behavior these nodes basically if you play by the rules if you don't play by the rules you just can't continue in the play because everyone can tell this basically shifting to message strings what right now we're keeping a state like for instance with message queue circuits when you have a her message in order what you can do is allow every node in the queue to be able to receive incoming messages when you have like the whole transition of the messages on all of the nodes which by the way doesn't have to be linear they can cross, cross, cross you can say like when three of my previous nodes confirm of four next four nodes in this channel and when it completes the then loop basically or when received back from the other side I consider it queued but you need to be able to rely on and create that product that self then you'll have message ordering on at her event basis so there is no need to block them or have like funny leader selection algorithms it's on through protocol through collaboration so there was one about incentive so by not needing the token and instead relying on protocol the incentive to play is the incentive to use the protocol like if you're using the protocol it's because you want to use the protocol and also as microservice can have like five nodes, five hundred thousand nodes centrally to survive five hundred nodes but certainly I cannot think of a microservice that could need 100,000 nodes for instance there's waste so yeah now I remember so in the message stream each message also references the previously approved message in the hash so you have it there, you have like a blockchain but it's message stream so this part of bringing what right now is seen as protocol, you can actually project a protocol into blockchain when you see that the blockchain is a message stream that is retrospectively verifiable and retrospectively joinable so but it's really a buffer what's going on in there I'm sure that's going to merge this is not where my mind is so you're thinking maybe somebody will fill like a token center on top of it as an application and there's this other platform that the Economic Space Agency this sort of project that is intubated by this Economic Space Agency which is called SPACE and SPACE is precisely it's an economy, it's not a currency it's an economy, so it has distributed exchange network offer, you know Economic Spaces which is in hand to let people to issue self-governance, voting all that sort of stuff but to really create this decentralized fabric there's not one chain to rule them all you need to go all the way on the protocol that's the last decentralization of our so well that talks also about our next project the first Economic Space that we're launching is called the WORP the WORP is precisely a global distributed trusted execute environment where basically what you get is a hierarchy machine that you can do whatever you want with, but it's private it's your data, you control it it runs there, you don't know right, but it's reliable and it's elastic and whatnot, I mean it all comes down to protocol there's a lot of work to do like to build another for those who are technically inclined the programming philosophy of these protocols where the higher layers of abstraction the programming language that you can build a lot of gravity, allows the creation of what they're called like IO-free protocols where even message box buffers are objects and what that allows you to do is recreate protocol reusable components so obviously part of what our effort towards building space and the WORP is creating a collection a library of these protocols but what we want to create again is this global namespace with lots of utility and stuff and not only that, it's an economic space with an economic logic that is a device developer to keep contributing into the economy, but also users to provide their data so will users and developers monetize on the information in gravity in the very network the WORP information is mass, right that's why it's gravity and that keeps value and I have to say it's related information intercontinental information just go along with that so for the case as a user so today I go on Facebook where I use Google Chrome and they track my data and they sell my identity to marketers and is what you're saying in the future you're talking about I would own my data and you would help me monetize it yes, and we don't want to write flags yet in regards to that, but yeah you can do that and the end goal is not only data self sovereignty but it's preservation of privacy you share your data according to the rules of the content that you share if you are sharing your main oversold that doesn't mean you give access to your whole history it's like a conflict of interest between your doctor and your insurance company the job is to distribute risk not to share a bit and that's what models like that of privacy and preservation and sharing of contacts where you can reliably verify that you only get to share as much as needed for XY and after that is forego so you can enforce the relation of data you can enforce this connection you can enforce a revocation of capabilities it's all derived from being able to construct and synthesize a extended trusted execution environment yes, you need to go like lower level and you don't need to worry about double spending it's like all these other stuff so it's rapidly you can run on different code nodes or like be in different nodes like you can spin off for example a big one over here and you have to also spin off like a gravity node and if so what would the node contain all the data structures and also all the verification that the company has or is there some kind of a shortage where you have a bunch of code nodes that contain a portion yeah, there's no concept of full node in gravity there's no central state but what you have is a bunch of nodes that have either an open initial state that you have full privilege over that you can constrain and modify over time and get to share with other nodes or give contracts or you can simply install the work contract in which you are a node that speaks the work protocol fading through like the distributed execution environment according to its rules which are fully dynamic it's not something that you just can't bake into one machine ahead of time and you can make special nodes in which you say like K node don't you can never run because because again the capacity to create new environment the capacity to communicate with network, they are all capability so you can constrain it as much as you want if you want to learn more about this insecure model you can go to iraq.org it's a treasure trove it's heavily influential the whole thing E as a language is heavily influential so I'm guessing you're working with some kind of color models no what I think by dynamic rules I guess when you're working with the probability model you jump to the developer each VM is capable of modifying itself so as a developer I can go and create new rules and I get to share these rules with other nodes there's rules that generate rules let's say there's code that generates code so this all comes about the virtue of the language itself and the whole VM to be fully reflected so what I mean by dynamic rules is that you can ahead of time determine what is going to be running under this machine that's kind of the point once you have the node you want the network to keep evolving from the developer perspective and with the programming languages they look to them as they're writing contracts or they're writing programs the thing they know is that they're going to rely on the execution so one example for instance for reliable execution that you guys are familiar for instance is a replicated virtual machine right here if I install my contract in a replicated virtual machine I can trust that it's going to execute correctly but when you have constructed these more basic rules that is all about preserving the interior of everything you just said you do every minute the state transition that you do you can then derive the record you can even formally prove that all of these programs can only run because they're building themselves in this app it's based on something it's kind of like from the point of view that since you have how then organizations those are forms of organizations organizations are made of programs so they are just programs that create a micro service that runs an AI program just like you find very clear what's found it's inputs and outputs and you will be able to speak with the rest of the members at the border of each micro service however there is an object capable protocol basically every micro service every even within these micro services every everything is an object so you're always talking to others so that's why at the programming language level you're just proving an object-oriented program you can always cook out external services somewhere down the street it's important but then you are outside of the trusted institutions and that's something that the other nodes can know taking into account who interact with which AI it's often how so if anyone wants to talk after these more technical stuff like the state because that's a core if you think of the state everything else doesn't want it to end speak to the vision higher level but now so what got me in this track and pursuing these goals was the fact that I'm from Mexico as many Latin American countries is known to be highly corrupted and because of that corruption among many other problems almost every six years there's no guarantee that the person is going to appreciate because each one's corruption on the best one on paid loans loans that's never meant to be paid that the government officials and themselves so I started thinking of how is it that we can create a distributed monetary system that is encouraged and perhaps as we should say like in currency but with a global unit of account that is not controlled by anyone and in order to accomplish that if I'm serious about that I cannot just create like a Facebook or whatever it has to be something lower level so that our organizational government structures were never meant to scale to the point where they are right now and one of the side effects of that need to scale but not be designed for such a thing is that internal loss is internal system corruption so to fix that you have to relieve those social structures because they just can't I cannot see a way in which a human operated legal and financial economic system could ever sustain what we really are capable of doing and we need to go like super low level into how do you perceive system integrity in order to be able to enable different structures so at the same time I don't claim to know which one is the right economic system the right financial system or the right governance system but I know what the problem any proposal will have so what I want to focus on what I am focusing is in giving everyone a first start for all these proposals for them to be able to interpret to influence each other to copy each other to evolve to adapt into what is going to become whatever it is the substructure of how human organizes these kind of features can you talk about implications for the degree you can see for the big well what you are talking about the big distribution problems distribution of resources goods and services decision making authority design implications for some of the big issues that are foreseeable the side effects is to the threat of force as a way to bring in order so however you can envision that doesn't rely on being scared of each other at the state that already opens a design space more playful for instance more safer asset distribution I think that a lot of inequality we see what we do with asymmetry of information so it's just like this self feedback self feeding feedback loop in which those that have information and get more information those that have the least they give it all so I think like when you have information or asymmetry what you are doing you are actually you don't need to bring down the current power structure or redistribute what exceeds you can actually create that actually all the votes work so it's also a way like an orthogonal way of approaching how to scale humanity that doesn't rely on conflict like from the ghetto they say hey this is conflict free it's protocol so you don't need to have all these checks and balances and incentives in order to make sure that the social programs get executed according to I'd like to pose a question about that which is so let us assume that the journey will be successful and we can use gravity in space and go war now that we can compose rules and structures to behave and interact that do not require these checks and balances and external enforcement meant mechanisms what types of rules and behaviors and systems of interaction you envision we would be possible because I imagine they wouldn't be quite the ones we're used to I think that's a good point of space in which economy economy essentially theoretically is a game it's a game that goes beyond the work capacity to comprehend because it's a nonlinear system but they think what we're going to bring is games that also feel like games different ways get together produce together value things together instead of relying on whatever authority is telling you we should value we can define our values how much we increase our agency we can choose to engage or not to engage with certain individuals we can choose to engage according to certain rules or not to engage but that's precisely why these to be leveraged probably it needs something like space which is this meta economy it's an economy of economies and you get to speak much more to that thank you I to highlight one point is that we have this sense of value of revenue within us the sense that we might at one moment value of privacy of an empty room it might be highly valuable and then two hours later not being valuable at all so we're working with the practical infinitely of different valuations that constantly change and that's actually a much more natural state of value but in a way I think we have been made pervert by working in a very very monotheistic system of packaging that is well we have many currencies but they're essentially the same structure with very very different so if we get away from that which is also kind of getting that launching a new economy is putting on yet another token and that's the economy it's a range of operations it's a field of how ever it is so if we get to that I would expect that our behavior will start to resemble also an economy a variety of values that change dynamically maybe not with quite the speed that we do in our environments but much closer to that than what we currently understand about it because to be honest I think we will look like weirdos hopefully for people in 15 or even hopefully 30 years who actually might be in a different economy we would look like this sort of some crazy tribe cult that behaves according to some very ordinary people but I don't think it's a utopia we'll make the world in some ways very problematic maybe in games but we'll still find ourselves being bad at times it's not a utopia but it's let's say a more interesting place is possible with this construction that's my two cents so I think that's it thank you guys for doing it we're gonna close it out next time if you guys want it seems like everyone's sort of overlapping here there's people from other countries that are sort of overlapping I think we should probably have a computer with emails that people want to give that email there's a lot sort of happening and there's a lot of people online as well I guess we could sort of join your Slack channel right? that's probably the easiest way to do it what do people do? how do we do it? where do we go? you can ask from the end you gotta come up here cause you can't hear ya and then like your loudest Vienna voice real close our chain has their Slack channel open you're good you're perfect so I don't have to be as loud as I can economicspace.slack.com you can request for access from our website economicspace.agency second of all we have a meetup group called meetup.com slash economy OS if there is enough demand which maybe I can survey now we can possibly push like Chris and John to organize some meetups in New York City too like let me just look at do a little survey who will attend say a meetup once a month it's upside down world I see you okay so Chris is gonna tell me if you guys are actually gonna turn up maybe if you wanna sign up on the email list so that we can stay in touch on that and I also wanna ask who are of you guys here after listening to the presentation today could think of like a use case that you might want to work on okay cool that's what we call the economic space program and the ones who raise your hand is an Econoc an Econoc and he's gonna create a legal space just so you know Daza is working at MIT on MIT future legal stuff of future law so and there's gonna be an AI blockchain conference in MIT on 30th and 31st October 30 and 31 if you want more economic space agency come to the media lab come back east and a whole bunch of other super freaks for blockchain and AI refactoring the law for a digital age so come help us like of course we have facebook as well we have twitter accounts so yeah that's it thank you alright on the slack there's a channel that's just NYC meetup so join slack hop in that channel let's party thank you space so I think that pretty much we're up here in New York it's a much shorter chair than we're used to at law.mit.edu so if you want to know more about the conference it's go to mit.edu forward slash law that's right not a law school way better or engineering you want to know more about economic space agency it's what's the website xa.io xa.io xa.io alright see Tuesday at 1pm eastern time for future law at mit.edu


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So we saw that given any single vector, we can find a vector orthogonal to it by solving the equation, making the dot product equal to zero. What if we want to find a vector orthogonal to two given vectors? Or what if we want to find a vector orthogonal to three given vectors? And the easy answer to that is, well, this is mathematics. If in doubt, set up and solve an equation. So let's try to find a non-zero vector, we'll call it x, y, z. It is orthogonal to both 1, 4, negative 1, and 3, 1, 4. So let's think about this a moment. The vector x, y, z is going to be orthogonal to 1, 4, negative 1 if the dot product is zero. Well, we know how to find the dot product, and that gives us an equation. We also want x, y, z to be orthogonal to 3, 1, 4. And again, this is orthogonal if the dot product is zero, and that gives us a second equation. And so whatever the values x, y, and z are, they have to satisfy a system of two equations and three unknowns. Now there's a number of ways of solving systems of equations, but the most efficient is by addition. And what that requires is getting the coefficient of a variable in one equation equal but opposite to the coefficient of the variable in another equation. And so in this case, we can solve this by multiplying the first equation by minus three and adding it to the second. So multiplying our equation by minus three, and we add our two equations. And we no longer need all three equations. We can drop one of them, and let's get rid of this one. So talking about systems of equations is something you'll spend a lot more time on in linear algebra. But here's a preview. If you have more equations than variables, you might be able to choose values for some of the variables and solve for the rest. So here we have two equations and three unknowns. We might be able to choose a value for some of the variables and find the others. So the other strategy that you'll see in linear algebra is it helps to work backwards. So our last variable is z. We can choose a value for z and solve for y. So let's choose z equal, how about zero? If z is equal to zero, our last equation becomes nv solve. Then since z is zero and y is zero, our first equation becomes, and so our vector x, y, zero has x equals zero, y equals zero, z equals zero. Except this is a trivial solution and we don't want that. We want a non-zero vector. So let's choose something else. And here's something that'll work. We'll choose z equals 11, y11. Well, notice that our coefficient of y is negative 11. And that means at some point we're going to be dividing by 11 to solve for y. Choosing z equals 11 helps us avoid fractions. So if z equals 11, we can solve the first equation for y. But now we know z is equal to 11, y is equal to 7. So we can solve our first equation for x and that gives us a value of x, y, and z. And consequently, we have our orthogonal vector. So let's try and find a vector perpendicular to 3, negative 1, 3, and 2, 5, negative 4. So again, we want the dot product to be zero, so that gives us the equations. And in this system of equations, notice that if we multiply the first equation by 5, then our y coefficients will be equal but opposite to the y coefficient in the second equation. So if we add the second equation, now since we got this third equation by combining the first two equations, we don't actually need both of the first two equations. We can get rid of one of them and let's get rid of the second one this time. So again, we'll choose a value for z and notice that we'll be dividing by 17 and so to avoid fractions, we'll let z equals 17, the coefficient of x, and this gives us negative 11. And if x equals negative 11, z equals 17, we find y. And that gives us our orthogonal vector. Or let's find a vector perpendicular to both negative 5, 3, 8, and 3, 2, negative 9. So again, we want the dot product of our vector x, y, z with the two vectors to be zero, and so this gives us the equations. We'd like to eliminate one variable from one equation, so let's get rid of the x and make our x coefficients equal but opposite. And we could do that by multiplying the first equation by 3 and the second by 5. And if we add the two equations, and again since this new equation combines the first and second equation, we can get rid of one of those first two equations, so let's get rid of the second one. Now for variety, we'll pick y this time. And if we look at our equation, we see that if we're going to solve for z, we're going to need to be dividing by 21. So since we're going to be dividing by 21 divided z, we'll let y equal 21 and solving for z. And with y equal 21, z equals 19, we can solve for x and we get our solution, the vector 43, 21, 19. And we'll make the same observation we did with the dot product. Notice we're always doing the same thing, forming an equation where one dot product is zero, forming a second equation where the other dot product is zero, adding the two equations to eliminate a variable, and then choosing a value for a variable and finding the values of the other two. And remember, because we're always doing the same thing, what we can do is we can write down a formula to do all the steps at once. And fair warning, in contrast to the dot product where there was an advantage to using the dot product to find the angle between two vectors, our formula is a little bit more opaque. We'll take a look at that next.