 I'm going to need more than just definitions, I'm going to need some evidence to back that up. And all I just want to see is, do you have the evidence to support more extraordinary things? That is beautiful. I'll go with one. Okay, let's see what happens. That's right. It's because I really love this topic so much. I wish I had more time to investigate all of this. I think mathematics are discovered and not invented. Ooh, yeah, yeah. The reason why I'm coming up with this, sorry, the reason why I said that I'm open to discuss about this is because I want to be convinced of the opposite. Well, that's not my job. That is okay, but in a conversation, because regrettably we don't have... And when I say we, maybe I'm not talking about the whole of humanity, but this beautiful opportunity of having conversations, I don't have that often. So what do you mean by mathematics? Mathematics. So it's a system, it's the way the universe is structured, and it seems that it can only be understood by rational minds. Oh, this is interesting. Oh, then you said two very interesting things here. So just back up. You say mathematics are discovered and not invented, right? Yes. Okay, and you said you define mathematics as something that can only be discovered or known by rational minds. Yes. And then you also said that mathematics, it represents the universe or truth of the universe? Well, it's a way to understand the universe, so it might be kind of, yeah, it's kind of a language in order to understand the rationality. It's a way to make models. Yes. Okay, it's a way to make models. When you say only by rational minds, does that also include other things than human minds? That is a good question. What do I mean by that? As far as we know, or let's put it this way, as far as I know, there's nothing in the universe right now that we know that can understand mathematical language and recognize a pattern in order to come up with a structure so we can understand things that are going to happen in the near future. Just throwing us out. So if I showed you a video, you're saying only humans can understand it as far as you understand it. Yeah, as far as I understand, yes. And that's why I love this conversation. If we do, for example, to show you a video of like a chimpanzee counting down on an LCD display, numbers 100 down to 1 to get a banana, and then they rearrange the numbers, and he's looking at the numbers again and he's like 199.98. And you can take some numbers out and he still knows after 68 the lowest next number is 56 and he's still going down in the right order. Are you saying that doesn't count? Well, it counts. It counts. Now, that is a good question because it takes us to the more specific. And I wasn't specific enough. That's why I love this conversation. Which is, I'm talking about the mathematics that allows us to predict things that are going to happen in the future in the universe. For example, cosmologists know that it seems that cosmologists know that the universe is going to disappear. So not arithmetic, but as a means to construct new models to determine what will happen in the future. Well, the thing about the question about the tie, the question about, you said chimpanzees? Yeah, chimpanzees can count to like 100, and even backwards. Now, they can count because they have the objects in front of them. But I don't know if, I don't know, and I mean this, I really don't know if abstractly, with abstract thoughts, they can think about the number one. Now, we can actually think about the number one without having an object that represents that number one. So it kind of brings me to the thought of kind of the Platonism of mathematics, this idea that mathematics is kind of independent of what people do with the physical mathematics, you know? Can I add something? Please, please. I saw a bee coming in here today. That bee is going to fly back to its hive, and it's going to be a little jig. And the craziest thing about bees is they have a dance-based language. So they are competing with other bees and telling them the sun's going to set in this direction, which is where I do my first wiggle. Then I'm going to rotate a degree, and I'm going to wiggle for the distance that you need to fly. Then I'm going to turn her direction again, show you where you need to turn, wiggle even harder. And if I wiggle really, really strong, that means there's a lot of pollen here. If I only wiggle a little bit, that means there's only a little bit of stuff to make nectar out of. But that's how we've constructed our language. It's pretty accurate. All these bees are flying back and wiggling, wiggling, wiggling really, really hard. And all the bees are like, we know what to do. 45 degrees from where the sun's landing, 15 kilometers that way. It's about this much pollen. Let's go where Sally took us. And they all fly out, and they figured it out. I'm not sure if it may not be expressed in Arabic numerals, but it is very much a model that we can translate into our system of mathematics to where these bees are telling each other, turn left here, fly this far, and there'll be this much stuff at this location. It's kind of incredible. It seems like even if they aren't using the same written system that we use, there is very much an impression of the same mathematics that we're both using. Yeah, definitely. Now, what do you think, Ty, about, for example, the difference of let's suppose, well, actually not let's suppose. I agree with you first of all because I don't have that kind of information about bees, but I really... I just love bees. Yes. I love bees. They're like my top one animal, basically. They're really great. He's just awesome at animals, and they fashion sense is amazing too. Yeah. Oh, yeah. Yeah, yeah. Let's go. Bees are awesome. Yeah. So, and... Hmm. Yes, yeah. This is delicious. We buy their... Insect vomit. Any other animal would be like, no. Get that away from me. Bees. Bees. Insect vomit. Yeah, of course. Yeah, bees are delicious. Put that in my coffee. Anyway, I'm sorry. No, that is more than fine. Sorry, that's okay. That is more than fine. Is there a difference between the way bees, for example, are following the patterns of a type of mathematics they are following, as you have described, to the way that humanity is able to recognize a type of mathematics that beyond the intuition. Like, for example... And I don't know how good of an example this is going to be, but for example as a human being, I know when I need to turn left or right in order to avoid X and Y. So it's kind of... We're bringing this type of pattern or maybe through communication. Sure. I'm doing certain things that are not tangible, but I'm kind of controlling something that is going to happen later with some type of arithmetic or some type of mathematics. Now, my question is, Ty, this mathematics that it seems that some mathematicians recognize which is beyond the human understanding, which is something that is beyond... You think that those types of mathematics are the same? I'm going to just easily tell you I don't know, but it was more just a way to define what you meant by mathematics. I'm going to take the opposite route. Cool. So there's a possibility that other kinds of minds might use a version of mathematics. Let's take all rational minds out of the universe. Does mathematics still exist? I think so. So why is your definition dependent on there being rational minds? Because you don't need rational minds to have mathematics. Maybe because I wasn't being very specific about my definition, because the type of mathematics I was referring to you is a type of mathematics with which you can, for example, predict things that are not happening at this moment. Can I just catch up? Of course. You said mathematics are discovered and mathematics are defined by something that can be termed by a rational mind. But if there's no rational minds, there's still mathematics. So clearly mathematics doesn't seem to be dependent on rational minds. So why is it part of the definition? Maybe that's completely my problem. I'll try to be more specific. Mathematics exists beyond the existence of rational minds. You don't need rational minds, period. Correct. So I'm just going to... Yes, yes, please, please. You know the need to understand the mathematics at the level that we understand it. It seems that there is something unique about us which is we have beyond the recognition of patterns that animals actually can do, we can actually go beyond the pattern and the intuition of living in the present in order to recognize that with mathematics we can predict things that are not happening in the present but are going to happen in the future. So I'm talking about something that it seems that the universe is rationalized and can be understood as a notebook. In mathematics, are there such things as unknowns? I believe so, of course, because you mean things that we still don't know? No, is the term undefined a valid thing to use in mathematics? For example, when you have an equation that doesn't have an answer that you can determine mathematically, typically what we write is UND or it's undetermined. It can't be solved with the current stuff. If it's possible for things to be unknown it doesn't necessarily mean that it's not an answer or that it's not zero or something like that. It just means we don't know yet we need to invent a different tier of mathematics to solve that kind of problem. Until then we just don't know. So maybe it's not so much mathematics can solve everything about the universe maybe there's just some things that mathematics are limiting. What do you think about that? I really like that. I actually approached this question humbly with the with the perspective of there's some type of mathematics that we haven't discovered. Maybe, of course. Maybe it's not. Because for example, let's bring to the conversation something I really know nothing about. I'm using arguments for people that are more intelligent than I am. I want to hear your arguments. For example, quantum theory. I know. I know. I'm not saying anything. I'm not making any statements about some things that I don't know yet. It seems that right now we don't understand what is happening at the quantum level with certain particles but I'm open with the idea that maybe with some different type of mathematics we can actually describe what is happening in the future. As we increase our resolution we'll get a better model that predicts what's going on. Here's this other weird question. I agree that mathematics is a model. Yeah. We invent the model. Wouldn't you agree? We're inventing a model to explain how the universe works. I agree with the fact that we invented a language that we can understand in order to understand the rationality of the universe but yeah. In that aspect, isn't in some part mathematics an invention? Not entirely an invention but definitely something that we construct arbitrarily to express concepts to each other and predict about things in the future or not. In that aspect, wouldn't you say mathematics is somewhat similar to it? In that aspect, the language in order to understand the mathematical reality of the universe. As a model, that's not dependent on rational minds. It's invented in the way that a language is kind of invented in order to communicate ideas. Do you think mathematics is entirely discovered and not an invention? I think that the ultimate reality of mathematics, which is beyond the existence of a mind that can understand it, is there. So I think that... You think the concepts that it's based on, the concepts that it's expressing are discovered but the tool of mathematics is definitely of meaning the language that we use and the models that we use in order to understand it. The model that we make. Correct, meaning number one, number two that didn't exist. I don't know maybe in the past. Number zero maybe could have been graphed in a different way in a different shape. That's just a different set of mathematics. But I think it's beautiful that there's a type of reality there that can be rationalized through this language that actually we are kind of creating. If someone came to the table and says I'm 100% confident that mathematics is not an invention in any way, shape or form would you agree with them? Would you repeat the question? If someone came to the table and says I'm 100% confident to the point where I know I can't be wrong that mathematics is not an invention in any way, shape or form would you agree with them now? It's not an invention in any way, shape or form. Well I would agree that mathematics is not an invention. It existed young time. Well, yeah but not the concepts that it's representing but mathematics itself. Mathematics, I would agree with him or with her in the sense of it's not an invention in the existence of mathematics but not in the language that is used. The language that we're using is kind of the only thing that we need to work on at this point was just the semantics of when we say mathematics are we referring to the concepts that they represent or the language that we construct to express and it sounded like at the beginning we're talking about mathematics as the system of expression but I agree with you that the concepts that mathematics are based on are discovered through this language that we use. Let me ask you a question today. This is actually very lucky that I have the opportunity to ask you these questions. No, seriously, too much pressure. No, because this is one of all these guys right here and you're loading this question way too much and I can't take it. No, I just love these questions so much. What does that entail for you? The facts that mathematics discovered? I am fine with us living in a system that we are slowly beginning to understand but we need to develop tools to reliably come to conclusions with what we're living with and I feel like mathematics is a tool that we use to understand reality. When you said it's a model like we use mathematics to build models to explain reality, I'm absolutely with that because that's totally what we use mathematics for because if we use mathematics and we are wrong about reality we will change mathematics so that we can better reflect reality. I think there are some expressions in math to express things only for us to realize if we were wrong to express it that way let's drop this tier of math and replace it with something better. I think, for example, I'm a big nerd for imaginary I I love I but we shouldn't have called it an imaginary number because it's very much a real number and a very much real means of expressing something and negative numbers I feel like we should have called them inverse numbers because there's nothing inherently negative about negative one it's just inverse of one but language issues aside these are things that we can change we can change tomorrow we can call imaginary number real numbers we can improve mathematics to better fit the model that we live in because we can change mathematics that tells me that it's a tool for us to understand the universe it's not necessarily the universe and while they are very much compatible now that was only through the work of many people working with mathematics to get to the point where it's at now and I'm totally fine with us using mathematics as a tool that we invent but I also think it's cool that we can use a tool to figure out how the universe works and what we're discovering here if I can discover it here and you can discover it in a different place in the world that's awesome because it means we're working towards a more objective truth that is, yeah so another question for you time so in languages my experience is that sometimes languages are always changing and developing themselves and that is actually beautiful things because is adapting to what is happening in society with humanity the way we think about things around us so sometimes people stop using certain words because the kind of connotations and definitions that they bring to the table actually for example today during my workshop Anthony asked me what was my definition of an atheist and it was an interesting question and I was very honest I didn't have one at the moment because when I think about that word it's so loaded that I when I think about an atheist the first thing that I think about an atheist is not about atheism he's just a person like me so I started with that common ground so it's not like I don't think about that division and I'm sure I understand that this is just my appreciation of the word I could choose to understand the word in a different way so these connotations and definitions that we have in languages do you think that the same is happening with mathematics which is we're trying to develop oh absolutely if you go this is more of like just a nerdy moment but say you go back to 17 we started thinking about numbers as you got one point here this represents one of something you got two points here this represents two of something three points here three something we didn't even have zero we were just counting from one up then around Greece time when we were starting to like hey numbers mean things actually in Aztec culture they figured out zero first way before even Greece but they figured out hey there's a value called zero we should include that then we started getting decimals there's numbers in between numbers that are of value and you can see like it's evolving to better reflect how the world works we didn't start with the numerical system that we have today we worked on it evolutionarily over a long period of time and who's to say that where we're at right now is where it's going to be if you were to ask me where it's at right now so the engineering firm that I work at right now we don't count we don't express ourselves with XY coordinates where it's just like oh it's XY we need a point it's two one we don't say that we say it's like three I because we need to think of things in a additional dimension that is not just with XY so sooner or later all kids are going to learn I in elementary school and I think that's going to be the new standard way of how we're going to be expressing ourselves mathematically and who knows what's going to be after that the reason why I say I is because that's an inherently a two-dimensional number it has a shape to it when you're expressing whereas XY is a point on a graph I gives like some planar qualities to it and that's really really useful when you're expressing things with curvature when you're designing a plane when you're making a wing you're going to use I you're not going to use standard numbers standard numbers are limited to one points I is like two-dimensional what if we use three-dimensional numbers in the future four-dimensional numbers in the future who knows how we're going to be counting thousand years from now we might look at a number chart and be like I don't even know what that is like it's numbers you can't count not in the year 2019 it seems that it kind of all boils down to the way we convey information yes because have you seen the movie the excellent amazingly amazing movie the name of it Tropic Punder Power Rangers not Facebook nobody cares because it was great and now we can't make that movie again we have to wait another 16 years before we can do that again but it was good when it happened this is where everyone can laugh it's crazy that I've forgotten about the name the name of the movie the aliens that come to Earth and they're teaching us a new way to speak and they teach us it's a kind of recent movie alright I'm with you it's alright you have my contact information you have my contact information oh yeah I'll contact you so they teach there's a linguist that come to the spaceship it's a lady with a ponytail I know that movie I've seen the trailer should I tell you what happened okay because it's a very good movie okay I don't know if I should tell you because it's something to discover then you want to hide it until maybe next time yeah let's do it because it's a good movie okay Pedro I had a great time talking to you I'll contact you about future opportunities okay and we'll just meet and I'll tell you everything about that so it's cool yeah national's nearby for me arrival arrival time spoiler words thank you see you I didn't have anything but I'll get to see if you got anything you want to do it real quick you have nothing you care about you're a soulless husk of a human being you want to talk about that