The following is a rough transcript which has not been revised by The Jim Rutt Show or by Forrest Landry. Please check with us before using any quotations from this transcript. Thank you.
Jim: Today’s guest is thinker, writer, and philosopher Forrest Landry. This is the fourth time Forrest has been on our show. He first appeared back in EP31 where we engaged in a broad survey of his thinking on various topics. More recently, in EP96 and EP109, we explored his immanent metaphysics that’s I-M-M-A-N-E-N-T metaphysics. Today, we’re going to do a deep dive into a theorem that arises from his metaphysics, which he calls the incommensuration theorem, which we will often abbreviate today as the ICT. There is a link on our episode page to a dialogue about the ICT, which is the best way to read about it. We were going to try and keep this episode as self-contained as we can so there’s no requirement to go listen to the previous episodes, though, I would encourage you to check them out if you find this episode mentally stimulating. So welcome, Forrest.
Forrest: Good morning.
Jim: Good afternoon. From here in Virginia.
Forrest: Good morning from Southern California.
Jim: We’re at 75 every day, right?
Forrest: Yes indeed.
Jim: Pretty much wonderful weather out there in Southern California. Well, as Forrest does in his dialogue, we’re going to start with some introductory material and we’re going to build and try to build at a reasonable pace so that those of you listening at home can follow along with what’s a pretty intricate, but pretty interesting set of arguments. So let’s start out with, you described the ICT as a statement about the nature of the relationship between what you call symmetry and continuity. While we’re going to define symmetry and continuity with some precision later, could you start off with at least a rough sense of what you mean in your usage of those two terms?
Forrest: Well, the term symmetry and continuity show up a lot in mathematics and in physics. And so when we’re looking at something that’s symmetric in either of those fields, we’re looking at a sort of constancy, like if I have a shape, for example, and I flip the shape over, then I see what appears to me to be the same shape. So there’s a kind of constancy in the shape.
Forrest: In physics that shows up in things like law of conservation of matter, that if I have a certain matter at a particular amount of time, that at some future point, there will be the same amount of matter. So there’s a kind of constancy associated with that. So that’s the symmetry notion. The notion of continuity has to do more with connectedness. So if you’re in a given place, can you move to another place through a series of infinitesimally, small steps that there’s no hard edge or boundary that you would cross that basically would prevent you from going from one place to another. So in effect, we were talking lot about the sort of connectivity patterns of things when we’re talking about continuity.
Jim: Very much like the concept of a continuous function in mathematics or a differential service in something like gradient descent.
Forrest: That’s right. And so we can tune these concepts to a pretty precise level by talking about the way in which the constancy either shows up or does not and the kind of contexts, the kind of situations or environments, in which that either happens or does not.
Jim: Now the next notion, this is one that I have struggled with in my several readings of the ICT. And that’s the notion of a domain. Talk to us about what a domain is, and maybe compare and contrast the aspects of both with a set.
Forrest: So in effect, when we’re looking at a set, we’re looking at sort of like a bag with things in it as a kind of metaphor. You could put a bunch of things in a purse or pocket book or stuff like that. And if we can abstract a way, even the notion of things and just call them points or elements, and you don’t really care, this is a toothbrush and that’s a toothpick. You could just basically say, well, there’s this first thing. And then there’s the second thing. And they’re both in the bag. So, in that sense set theory is, basically, just talking about sort of the relationship between the things that are the content and the things that are the context. When we’re talking about domains, we’re actually looking at sort of three notions.
Forrest: So rather than just the notion of content and context, we’re also looking at this notion of relationship. So we could talk about the container and in a sense, the notion of set and the notion of a container and the notion of domain more or less hold the same role, right? So, there’s a role relationship between the concept of the container and the concept of what is contained. And in the domain sense, we just basically refer to the relationship itself between the elements and the container as being a kind of relationship that is neither something that is in the content nor something that is in the context. So in effect, there’s a kind of relationship between the elements and then there’s sort of this more abstract relationship between the elements and the environment in which that element might be found. These are pretty abstract concepts.
Jim: And it did make sense. So essentially you can think of it as, let me try to play it back and maybe you can tune a little bit. If a set is essentially a non ordered bag of elements, the notion of domain extends that to include the relationships amongst the elements as, essentially, first-class objects within the container called domain.
Forrest: That’s right. And in a lot of respects, the notion of domain is just a very easy one to relate to, because we can think about a domain as not just talking about abstract elements, but basically, maybe specific instances. Like we could talk about worlds or universes that contain things like matter and energy. So, the notion of domain is also extended into the realm of physics or into the realm of ordinary discourse of talking about the domain which is the marketplace, or the domain which is the home. So in effect, when you have any constellation of concepts, those concepts can be treated themselves as content and the organizing principles that sort of collect those concepts together, and we talk about it as a topic, like we could talk about real estate or finance, and to some extent, those might be considered domains because they act as a sort of collection of concepts that are connected to one another in some fashion.
Jim: That, I got relatively clear. Now the next one is one I’m still not clear on, which is that you define domains in such a way that they cannot be included in other domains. So that there’s something about a domain that makes it different than a set, because a set can clearly be a member of a set. Right? But the way you have defined domains, as I understood it, and I may have gotten this wrong, is that a domain by its very definition cannot be included in another domain.
Forrest: So this is getting into some pretty technical things pretty quickly. So the main thing is, is that when we’re looking at physics and theories of mathematics and stuff like that, there is this sort of idea that some fields, some bodies of consideration, can be considered inside of other bodies of consideration. So in other words, there’s a specialist sort of topic within a more generalist sort of topic. And in this particular sense, I’m essentially just kind of clarifying that the way that I’m using the domain is to extend out to what is the largest enclosing set that is not itself enclosed. So for instance, rather than talking about the world of the earth and all the stuff on it as being a domain, because it’s already a proper member of the universe as an enclosing set, that we would say, well, the domain we’re actually speaking of is the universe as a totality.
Forrest: And because we think about the universe as being a totality, then anything that’s not included in the totality should actually be. And so the notion of universe is essentially to extend to the point that it does include everything. So, this is kind of a technical backstop to basically say, for convenience sake, if we’re looking at the notion of universe, I’m not trying to confuse the issue of what the notion of universe means by saying that it’s embedded in some sort of meta universe or it’s embedded in some sort of multiuniverse. That if there is a multiuniverse concept, then in effect, it would mean that those universes are in some sense, peers of one another. And that there isn’t a meta universe that somehow acts as a container in which those universes would be proper members. So in a sense, when I’m basically saying a domain is not contained by another domain, I’m just trying to clean up the way I’m using the language so that confusions of this type don’t enter in at some later point.
Jim: I could see where that would be useful when talking about universes. But one of the examples you used as an example of a domain is a computer language, like C++, as a domain. And yet at least commonsensically, it seems to make sense that the language of C++ belongs as a member of a bigger domain called computer languages. What am I getting wrong there in that usage?
Forrest: That’s a deeper language in a certain sense. And you could say, well, at what point does the notion of language become, essentially, a thing that needs to be treated as a kind of entity onto itself in relation to other entities, but that you don’t have a sort of notion that any one of these is, more or less fundamental than any other. Basically, because of the Church-Turing thesis, they all assert that all the languages are in a certain sense, equal. And so therefore you don’t have a metalanguage that includes all of them as a proper subset. So, the abstraction layer associated with computer languages isn’t itself an actual language. It’s a notion of containership that doesn’t have a definite instance. There’s no place where I can point to, or actually implement a program in all computer languages. I can only do that in a specific way, not in a general way.
Jim: Well, so that was actually a singularly bad example to get at the point that I was trying to make. Because that’s actually very good. Yeah. The Church-Turing thesis, assuming it’s true, which is not actually proven, but it’s a strong conjecture generally thought to be true, would indeed allow one to talk about all the languages essentially as equivalent, in some sense. Let’s use a better example. Suppose we were talking about the domain of baseball, which has all the aspects of a domain. And one could then say the domain of baseball seems to naturally fit in the domain of team sports. And there you don’t have something like the Church-Turing thesis to sort of squash the differences and force an equivalence.
Forrest: Well, at a certain point, we want to basically be clear as to what is inside the domain. What are the contents in the sense of relationships and identities? And the notion of identity is roughly equivalent to the notion of elements in a set, for example. But the thing here is, is that when we say baseball, there’s a kind of collection and constellation of concepts. But when we talk about team sports, again, there’s a sort of an abstraction layer that’s going on. At what point do we know whether or not something is a team sport or is not a team sport? There’s kind of a boundary condition here where we’re basically saying, okay, well, I can have this meta domain that can basically be defined as containing elements of this other domain.
Forrest: Or, I can basically say that the domain itself is being treated as an identity. So for instance, if I take team sports, the elements. We might say, okay, well, we have baseball and basketball and so on and so forth. But in that sense, the notion of baseball is treated as an element. It’s treated as an identity, not as a domain. So in effect, the contents of the baseball domain, things like baseballs and bats and the sort of equipment that occurs in that game, for example, isn’t a member of the domain team sports. The thing that’s a member of the domain team sports is this label, baseball, that refers to a domain itself, but is not in that context, a domain, it’s an element.
Jim: So essentially saying the tools of looking at domains must be operated on as if the domain is the highest level. And the way to get around that is to make the move that if there are other domains in it, we actually insert an element that points to the domain and that that pointer is then the actual element in this higher level domain. So that way we don’t get ourselves confused by having to process domains at two levels.
Forrest: Yes, that’s definitely a technique that’s used a lot in things like computer science. It’s used in language. And so in effect, what we’re disentangling here is, what are we explaining? If we’re using the notion of a domain, there’s usually a rationale as to why we would want to use that concept and what we’re doing within stuff like that. So a certain amount of clarity as to what the tools are, what we’re working with. It is kind of important just as a bookkeeping thing as we go along.
Jim: Got it. I think that’s enough for the really introductory material. Now let’s get down to the next level. We’re starting to move towards the ICT itself, which is that you put forth that a domain has exactly three necessary and sufficient concepts, the notion of creation, the notion of existence, and the notion of interaction. Tell us what you mean by that.
Forrest: Well, keep in mind that this notion of creation existence interaction in the domain of the universe. So this would be a specific example. So for instance, in the development of the ICT proof, what I’m basically trying to do is to essentially show a particular constellation of relationships around the notion of comparison. But in order to describe why we would be motivated to do this in the first place, there’s this sort of underpinning of relating it to things that we would experience in this universe. So, as part of the epistemic thing, which would be why would we be asking this question, what is it that’s possible for us to know, and things like that. I was trying to basically create a foundation that was relatable. So, in physics, for example, we study matter and forces and the kind of relationships between matter and those forces.
Forrest: And we do that within the realm of all the things that are measurable, that we can perceive, that we can interact with. And so in effect, there’s a series of background assumptions that are being implied in that. And those background assumptions are roughly equivalent to this notion of domain. So effectively, I’m just saying, well, as an example of a reason or rationale as to why we would be exploring this, or why we would even be using these concepts, the universe as a domain is something that we study and we study it through measurements. We study it through these observations of material things. You have matter. And the observations are essentially interactions between the matter. And they occur in this context, which is the universe. And so in effect, we would, if we’re using that sort of model, then we end up with kind of the classical thinking of physics. But then there’s this specific move that is being made.
Forrest: It’s basically saying, well, if the overall idea is that we’re really trying to know how the universe works, then we can stand back a little bit and we can take stock of the concepts that we’re working with. So, effectively, if I say well, to understand the universe, I would need to understand, obviously, about the nature of matter and about the nature of the interactions. But I also would need to understand how did all this get there? Like where did the matter come from? So there’s a temporal element associated with the notion of measurement itself. There’s, before you measured, you don’t know. And then there’s after you measured and you do know. And so to some extent, the information associated with that measurement is, quote unquote, coming from somewhere.
Forrest: And so in effect, we have this concept of coming from somewhere. And so this is the creation notion is, in physics, is thought of as the big bang. So in effect, there is a notion of creation, there’s a notion of things, and there’s a notion of interactions. And that these three notions taken together be the collection of notions that are needed to, essentially, understand this thing called the universe i.e. so that the domain, that is the universe, contains the concepts of creation, existence, and interaction. And obviously, in a sense, we were talking about with baseball before they are pointers to the larger field of elemental science, and the larger field of forces, and the larger field of what is basically described as big bang theory.
Forrest: So in effect, we’re saying, okay, well, if I knew everything there was to know about hypothesizing, obviously this isn’t the case. But say, for example, that we had some sort of a way of knowing everything there was to know about existence, the material universe and everything there was to know about the forces that interact between existing things. And everything there was to know about creation, about how all this stuff came to be there, where all the information came from that describes the patterns of why these forces and these elements, rather than, potentially, these other forces or these other elements.
Forrest: And so in effect, we say, well, if we knew everything about these three topics, creation, existence, and interaction, then therefore, we would know everything that was knowable about this topic called universe. And so in effect, what we’re doing here is we’re basically saying, okay, well, we can consider the relationship between content and context as a methodology of understanding the basis of our knowledge. What does it mean to know something?
Forrest: And we’re effectively shifting the notion of domain from something which is defined in terms of the content exclusively, thinking about that content as being elements, to understanding the notion of universe as a concept defined in terms of other concepts and what would be the minimum necessary and sufficient concepts necessary to define the enclosing concept, in this case, the universe. So this is essentially an example of a particular philosophical idea of going from just a content context way of thinking, to a content as concepts and context as a concept way of thinking. And at first it doesn’t seem like a very interesting move, but on the other hand, what it does is it opens up doors in terms of what kinds of questions can be asked later. And that turns out to be quite important.
Jim: Yeah. You say in the dialogue that your definition of domain is, this is a direct quote, “is fundamentally different than as is usually conceived.” And I guess I haven’t yet quite seen what is fundamentally different.
Forrest: Well, this is what I was just trying to bring out about the definition of universe. So, if you go to a textbook, for example, that that talks about physics, or it talks about astronomy, or it’s just generally in the theme, the notion of universe is conceived of as a container of content, but that content is matter. And that content is energy. And that content is, essentially, information. And when I’m using the term domain, I’m basically saying, well, I’m actually using it as a concept container for the concept of matter, the concept of energy, and the concept of information. And that if I have totalization i.e. considering all of the something in the universe, then there’s a kind of… If I take it in the first way, I define the universe, which is just basically all the stuff in the universe as a material thing, not as a concept thing, but as an embodied thing, I get a different notion of what universe means.
Forrest: Then if I take the notion of universe as a concept that contains other concepts, and, again, it’s a difference between thinking about universe as an embodied thing versus universe as an abstract thing as itself a concept, not as, I can’t point to the universe in any sort of physical way. I can’t build a rocket that’s going to go to the edge of the universe. I can basically say the notion that there is an edge. I can create a hypothesis or description. But the thing is, is that at some point another, we need to keep track of the relationship between embodied entities and abstract entities. And I’m basically defining the notion of domain in terms of the abstract entities and not in terms of the concrete entities.
Forrest: And this is, again, it’s a different way of defining the notion of domain or it’s a different way of defining the notion of universe. And, again, at the surface, it looks like, well, what’s the big deal. But actually again, because we can talk about closure of concepts in a different way than we can talk about the closure of all matter in the universe. The notion of all matter in the universe is a concept. It’s not an embodied thing.
Jim: I’m going to confess to having a fuzzy idea, but it’s time to move on because we could spend all day trying to dig into that further. The next step, as we drive down towards the ICT itself is that we want to relate the notions of symmetry and continuity to creation, existence, and interaction, at least as an example. But to do that, we need the concept of comparison. And you go into quite a bit of detail about what does comparison mean in this setting. I was going to use context, but that would get us confused. And in particularly you dig into a concept of what you call the intrinsics of comparison. So give us a good dive into how you use the word comparison in this setting.
Forrest: Well, I think that to some extent, if we’re going to go directly to the concept of comparison, I think what I would like to do instead is to just give a sort of run through of the flow of the proof or the flow of the concepts, because I think that might actually be an easier way to introduce why to consider the concepts of the intrinsics of comparison. And, if there’s a motivation that explains a little bit about what we’re looking at in that sense, it might make more sense as to what those intrinsics actually are.
Jim: Yeah. If you’ve got something that makes things more tangible, so much the better.
Forrest: So one of the questions that is motivating some of this is, how do we do physics? How do we do anything that would be increasing our knowledge? Like we were just talking about trying to understand the universe. And if I basically say, well to understand the universe, I would need to understand everything there was to know about creation, existence, and interactions, and I have a kind of program. So for instance, if I basically look at, what does it mean to know something? Well, if I say, well, what would it mean to understand the universe? And I could say, well, there’s a sort of algorithm here. If you understand, if you have a sub program that basically says, understand everything about creation, understand everything about interaction, and understand everything about existence, then you would have results of understanding the universe. So, in effect, when we say, okay, well, what would it need? What is the methodology by which we come to understanding anything? Like I could say, okay, well, I want to understand creation now. Well, how would I do that? Well, I need to observe it somehow.
Forrest: … creation now. Well, how would I do that? Well, I need to observe it somehow or another. I need to basically do something like having interaction with it. So in effect, we start to basically say, “Well, what is the nature of knowing something?” Well, as a kind of first step we can say, “Well, we’re going from the state of not knowing to knowing, and that that state of not knowing to knowing involves a flow of information from, for lack of a better word, that which is outside the self to that which is inside the self.” And we say, “Okay, is there any way to know anything without that flow of information? And is there any sense in which that flow of information isn’t going to result in a change of state?”
Forrest: So in effect, there’s a kind of a change of state from not knowing to knowing on the observer side. And there’s a flow of information that is needed to create that change of state that will definitely cause that change of state when there is a flow from, say, the objective to the subjective or from the outside to the inside. And in effect, there’s this third set of concepts that we also notice, which is the idea of a change of state is itself a kind of content within a context, that in effect, the environment in which that flow happens from the objective to the subjective is an instance of something happening. It’s an event within the larger context of whatever other events could have occurred, or it’s in the larger context of what we would think of as being some sort of container, i.e. the universe that’s enclosing the specific instances of the embodied world and the embodied subject that’s observing that world.
Forrest: So in other words, no matter how we go about thinking about what it means to come to know something, we see these same six concepts coming up over and over and over again. And so we basically say, “Well, in any sense of coming to know something, there’s a sort of objective, other than self, and a sort of subjective self.” Right? Or in other language, we might say the perceived and the perceiver. And also this process of perception, i.e. the flow from the perceived thing to the perceiver. And again, this is sounding somewhat pedantic, but it’s important to keep track of these concepts because it turns out that these concepts are recurring. They’re showing up over and over again, and that there’s really no notion of measurement or interaction, or as I say in a moment, comparison that doesn’t involve this set of concepts that recurs, that every instance of a measurement is going to occur in a context.
Forrest: It’s going to involve a flow from the measured to the measurer, that there’s going to be essentially a kind of change of state involved in that inherently. And that, in effect, if we start to sort of categorize these concepts, we begin to say things like, “Well, there’s this distinct, inseparable, and non-interchangeable notion between perceiver, perceived, and perceiving.” Or if I look at it in the sense of the subjective as the perceiver and the objective as the perceived and this flow of information of the actual perception itself, that in effect, we’re saying, “Okay, these recurring concepts happen over and over and over again.” And that to think about the notion of measurement without these concepts, it just doesn’t make any sense. There’s just no real way to have a notion of measurement that doesn’t involve these concepts in some fashion.
Forrest: So in effect, what happens is that we say, “Okay, well, if the scientific method, if the very notion of what we would call epistemic process, i.e. how do we know what we know, is to some extent contingent upon, or is actually absolutely contingent upon the notion of observation, and in the science and particularly it’s the notion of repeated observation, then we can look at what does it mean to observe something? And we can notice basically that, well, every observation is a kind of measurement and every measurement is a kind of comparison or every interaction as a kind of measurement and every interaction is a kind of comparison, or that every perception is a kind of comparison.
Forrest: We begin to sort of notice this kind of through line whether we’re using the concept of comparison or measurement or interaction, or any of these sort of kind of something happening like perception happening or information flowing, that we see these concepts of subjective, objective, content, context, and sameness and difference. Obviously, if the state doesn’t change, there’s a notion of non-changing. This is this notion of sameness. And the notion of, “The state changed. I now know something I didn’t know previously,” is a notion of difference.
Forrest: And so in effect, these notions of sameness, difference, content, context, and subjective and objective are inherently involved in every notion of measurement, every notion of comparison, every notion of interaction, and that in effect, we can’t really think about epistemic process without thinking about these other concepts. And so in that sense, I basically say, “Okay, well, just noticing this about the nature of the relationships between the concepts themselves.” And you notice we’re making a distinction here between the sort of embodied notion of a measurement as an actual fact versus the sort of abstraction of what is the concepts that basically describe the notion of measurement and what concepts would we need to have in order to be able to describe the concept of measurement in the same sort of way that we made the move earlier in the sense of what we need to understand to understand the universe. Well, I’d need to understand creation, existence, interaction.
Forrest: So if I say, “What would I need to understand to understand the notion of interaction or the notion of measurement itself?” then I notice that I need these six concepts. Again, sameness, difference, content, context, subjective, and objective. And so just as a kind of convenience of labeling these things that basically say, “These six concepts taken together are called the intrinsics because they’re intrinsic to the nature of comparison and comparison is itself a notion isomorphic, i.e. the same as the notion of measurement or the notion of coming to know something or anything that would be connected to what we would think of as epistemic process fundamentally.”
Jim: Yeah. Those four, the objective, subjective, sameness, and difference, I think, you use in ways they’re more or less accessible to people from other uses, but maybe you could dig in just a little bit on what you mean about context and content, because you use them in a little bit of a special way, particularly their relationship to each other.
Forrest: Well, one metaphor to kind of see the difference and to just sort of get at this is imagine you’re in a museum somewhere or another, and it’s a fine art museum, and you’re looking at a painting on the wall. And just for the sake of a visual, just imagine it’s a picture of a person standing next to a table or something like that. And if we were to just sort of stand back a little bit, we might notice that the picture has a frame, and that it’s on a wall, and the wall has a color, right? You’re not going to really have a situation where the wall is trying to draw your attention, obviously, because that would be distracting, but there’s no situation in which you have a painting that is not on a wall with a color.
Forrest: I mean, obviously, we can create special circumstances of maybe hanging the picture in the middle of the room, but there’s still going to be a room. There’s still going to be the sky and everything that’s around the painting that is not the painting itself. So in effect, when we talk about the content, we’re talking about the world that the painting is depicting and the stuff that’s in there. So in effect, the paint itself, but also the sort of notion that it creates an image of a man or an image that when we look at it we assume is a table or represents a table or something like that, and that this is sort of separated from the context, which would be the wall and the rest of the museum with this sort of boundary that’s the frame, right? So the frame basically represents a periphery between the notion of content, which would be what’s inside the frame and the notion of context, which would be everything else around it.
Forrest: When we perceive something, when we’re looking at something, we tend not to notice the context. And in this sense, the context isn’t just the building and the kind of environment that the picture is sitting, but it’s also the person that’s looking at it. So in effect, there’s a sense in which my state of mind is defining a little bit about how I might interpret the meaning of the painting, or it might influence a little bit about what I’m thinking about in terms of what free associations occur when I basically see that imagery. And so in effect, there’s a kind of coloring that happens from the subjective side, so to speak that, that basically acts as a context in which that meaning, the content of the painting, is being perceived by myself.
Forrest: So all of these sorts of things basically are described as a kind of relationship, right? There’s a relationship between myself and the painting. There’s the relationship between the painting and the wall. And in the same sort of way that we could talk about the relationship between the elements of the painting, we can basically say that there’s this larger enclosing relationship where the things that are basically part of the environment influence what’s basically being perceived in that environment. What is the thing we’re perceiving in that environment? And that we want to keep track of that relationship between content and context or between figure and ground.
Jim: It’s interesting. It’s not really necessary for the rest of your story, but it’s an interesting anthropological fact that apparently, people in the West and in the East relate to context and content differently, people in the West, as you basically said, “We look at content. We tend to ignore the frame and ground and figure.” Apparently, lab psychology will show us that people from East Asia in particular will have a much stronger sense of context and a much stronger sense of ground as compared to people in the West, which is kind of interesting.
Forrest: I do think so myself, and I agree that there is an awareness that having an awareness of context is essential. I mean, to a large extent, I think this is one of the weaknesses of Western thinking is that we don’t pay enough attention to the context. And so as a result, we’re disadvantaged. We end up being manipulated by the advertising or manipulated in our feelings because we’re not noticing them. We’re not noticing the context in which things are happening. And so we fail to account for that. But I believe that over time, as pain is a great teacher, that that becomes far more prevalent in Western thinking as well.
Jim: Again, this is not quite on the straight line to the ICT, so let’s not go into it in too much detail. But you have an interesting discussion about the relationship or the identity are very similar, or at least very close similarity to the notions of interaction, communications, and comparison.
Forrest: Well, again, I’m trying to just sort of underline why the notion of comparison’s important. So for instance, if I’m in a process where I’m communicating with somebody, I’m receiving messages from them, and presumably, I might say something back, and so I’m sending messages to them. And if we look at say the broader context of physics, for example, we can talk about general relativity in terms of the capacity to send messages from this place to this other place. So what is the topology of spacetime? And can we connect these two places with a ray of light that would basically create a causal relationship between those two places? And so in effect, there’s a sense here in which the notion of signaling or this notion of messaging is actually a really important and really profound concept. Even in quantum mechanics, for example, the notion of making a measurement has a very central role. It has a very central basis of what does it mean for there to be something at all.
Forrest: So in effect, if we think about communication as essentially messages going back and forth, then we can start to say things like, “Well, what happens as a result of the message?” Well, obviously there’s a change of state. We could talk about the messages being a kind of measurement, like I measure the bitstream and I see that bit number three is on or is a zero, or is a one or something. What symbols occur in which sequences, for example, is a kind of observation, is a kind of measurement. So in effect, we can start to notice that communication as a process, as a signaling process, measurement as a process, and pretty much anything that’s associated with how we come to know anything about the world or anything about anything other than ourselves is all more or less going to be the same concept showing up in different words.
Forrest: So therefore, I say things like, “If you understand the notion of comparison, then you have a really good way of understanding the notion of what perception is and the notion of what communication is and the notion of what interaction is, and that in effect, it’s the same set of concepts. It’s just showing up in different words.”
Jim: Actually, I thought of the fact that in physics and information theory, we somewhat surprisingly find that information and entropy are the same thing, and I suspect that that’s closely related.
Forrest: Yeah. There’s similar patterns. So for instance, I think that if you look at the math, for example, there’s a sign difference between entropy is showing up in information theory and entropy is showing up in say thermodynamics as a topic. But the pattern, what’s really fascinating about is that the overall pattern of what the notion of entropy means, there’s a lot of overlap. I think that there’s been some, as I said, very specific sort of elements of what that pattern is. And the fact that the same word is used in information theory and in thermodynamics, this notion of entropy, begins to give us the capacity to start thinking about things in a somewhat more abstract and therefore maybe easier way. Easier in some sense. It’s obviously harder than others, but everything has its trade-offs. Yeah.
Jim: The next one I want to talk to a little bit, again, it’s not exactly on the straight line to the ICT, but it was so interesting, which is your idea of access control limits. And you gave a wonderful example, that Newtonian mechanics really doesn’t have access control limits, but quantum mechanics does. Maybe you can take people through that again as quickly as you can. I know it’s a pretty subtle concept, but I just thought it was remarkably interesting.
Forrest: This goes back to the notion of signaling. So for instance, in the notion of physics as embodied within say, general relativity, or physics as embodied within the theory of quantum mechanics, or the theory of physics as embodied in Newtonian mechanics. So in effect, I’m making a kind of comparison between those three kind of really general theories. You can use Newtonian mechanics as a way of thinking about matter and motion and stuff like that over a pretty broad range of scales. And then we’ve discovered that over scales that are really, really big, that matter and energy have these sort of relationships with one another that go beyond what’s being described in Newtonian mechanics, and that when we look at the scale of the really, really small, we end up seeing a phenomenology closer to that as described by quantum mechanics.
Forrest: But in a very general way, we’re basically saying that each of these theories has a way of thinking about the notion of signal or the notion of causation. And this shows up probably most commonly in general relativity, that the connectivity of the spacetime continuum taken as a totality basically says what paths signal can move through and what paths therefore signal cannot move through.
Forrest: So you see this in things like the Minkowski diagram, where… And I might be pronouncing that wrong. My apologies if I am. But the idea here is that at any given moment, in any given position in the spacetime manifold, that there’s sort of this past light cone of things that are accessible. And then there’s sort of all of this space around the cone, which is outside. It’s called the absolute elsewhere. And in effect, there’s no way to get a causal signal from anywhere in the absolute elsewhere to the here and now of that moment or that position in the spacetime. So in effect, you can think of that as being kind of like in computer science, that there’s the places I can access, all of the stuff in the past light cone, and things that I can’t access, anything that’s in the absolute elsewhere.
Forrest: So in effect, if we’re looking at information flows like in computer science, for example, we think about wiring that connects one component to another, and therefore we can send signal from one component to the other. But if there’s no wire, then no signal can get from one place to the other. Or if we’re talking about memory, we can talk about a signal created by a past algorithm that is received by some future algorithm. And it’s just stored in memory in the meantime, this kind of wire that connects those two. But if I don’t have enough memory, if there’s an absence or something that erases that, then it creates a disconnection and there’s no way for the signal from the past to flow to the future. So whether we’re talking about flow of signal in space or the flow of signal and time, in general relativity, these two are kind of combined, that there is a sort of broader notion of places that are connected through which signals can flow and therefore access is possible, to places which are not connected, signal cannot flow, access is not possible.
Forrest: And so in effect, the theory of general relativity describes whole, vast networks of spaces that are disconnected. The absolute elsewhere in effect defines a kind of, as I mentioned, an access control protocol about what is accessible from any given moment or any given position. Whereas when I look at quantum mechanics, we see the same sort of phenomenology occurring. There are some signals that just cannot be received at all. And this is usually described in terms of, as I said, the scale of the very small. It shows up in the notion of the Planck constant, that beyond or below certain scales, that I can’t simultaneously know both position and momentum. There’s this Heisenberg Uncertainty Principle that basically says that if I want information about things of a scale smaller than such and such, that there are actual information access limits. If I access the information of position, that I lose access to the information of momentum.
Forrest: And so in effect, when we look at general relativity and quantum mechanics, we see that both of them describe very strong sort of access control limits on what we can know and what we cannot know as inherent in the body of the physics itself. When we look at say, Newtonian mechanics, there’s this sort of assumption of a kind of deterministic or clockwork universe. And in effect, we basically say something along the lines of, “Well, the entire universe exists and we’re just looking at patterns of change within the universe. And this idea was also taken up in general relativity.
Forrest: So in effect, what happens is that we say, “Okay, well, there’s a definite state, and we might not necessarily know that definite state at this particular moment because we’re here and now. But in the abstract sense of everything being deterministic, then in effect, we have access to the full field of information, at least in principle.”
Forrest: So there’s nothing in Newtonian mechanics that suggest, for example, that we couldn’t basically using determinism to either predict the state of all future events or to retrodict the state of any past event. And therefore, we have access to everything. If we had sufficiently good computational support, for example, that we could in principle basically access everything. Whereas when we get to say general relativity, we won’t be able to know the contents of what’s inside the black hole, for example, because there’s a kind of a one-way flow of information through the event horizon itself, and that this effectively defines a hard boundary. So this is sort of what I was getting at. And I’m sorry. It’s a fascinating thing, but it’s not easy to describe without…
Jim: It really is. I think of all the things that I pulled out of this paper, that was actually the most interesting. Sort of obviously true and something that I’d never really thought about before. And I think I’d love to get your reaction to one of the thoughts I had about it was a strong conjecture, I suppose, is that one of our access control limits is that we can’t have a causal arrow back in time. Oddly enough, standard model particle physics seems to be time-reversible with one single exception. And yet, in the actual world, no one’s been able to demonstrate clearly any time reverse causality. And perhaps it could be just that simple, is that your concept of access control, in some fashion, and which you don’t yet fully understand, limits the causal arrows from going backwards in time.
Forrest: Well, this is actually very much what this whole work is about. So for instance, the first sort of observation is that if we think of causation as a flow in time, if we think about it from the first person point of view, then we do have this sort of just inherent observation that to some extent, the perceptual mechanism of just how perception happens is itself a causal process. In that sense, there’s a kind of really strict one-way-ness associated with causation and therefore with perception itself, and that this is encoded in the notion of general relativity as a kind of fundamental idea, that the whole body of science is effectively really contingent upon or kind of a generalization of these consistent observations, these regular patterns that we use words like causation to describe that as being a regularity.
Forrest: If I have a perception of these initial conditions, then I would expect by this pattern, this sort of recurrence, that I would see these output results. And so we say, “Okay, well, causation is the concept that we would use to describe that pattern.” And we say that that pattern is a recurring pattern. So we would have this expectation that we would see it over and over again everywhere in the universe. But that notion itself is itself a kind of symmetry. It’s basically saying the same law, the same content applies everywhere in the universe, and that therefore, that regularity is something we can count on. We can treat that as something that we know. And that’s a movement from, say a first-person perspective to a third-person perspective. We go from the specific experiences of particular observations made in particular times and places to general assertions that this sort of pattern will hold in all times and places.
Forrest: And so in effect, there’s the sort of regular aspect of it, but that regular aspect also implies things like if there’s this pattern, then there isn’t this other pattern. Or if I basically say that these initial conditions occur, then these output conditions with these result conditions will for sure occur. And so I’m not going to be able to “access” things that are outside of that pattern because the perceptual process itself is based on that pattern. So anything that is not defined by these regular patterns is essentially not accessible to perception. So they define a limit on what it is possible for us to know. So anywhere that we have a sort of definition of what is knowable, we therefore have a kind of implied context, i.e. a definition of what is not knowable. So I use the notion of access limits just as a kind of way of really clarifying that and making it a part of the discussion of what does it mean to know something is partially to consider what is unknowable, what is inherently unknowable.
Jim: Yeah, I find that very, very useful. Let’s move on here because we need to pick it up just a little bit. Now, the next step, moving towards the ICT itself, and I think I found this to be very important and helped me get a sense of where the argument was going, which is the idea that the elements of comparison are inseparable. And you give the example of sameness and difference and context and content. Unpack that a bit.
Forrest: Yes. Well, so first of all, if we basically say that all epistemic process is based upon perception and all perception is based upon causation, or that all perception essentially involves comparisons, then in effect, the same way that we can say with the painting that you’re never going to have the painting by itself in an empty universe. There’s always going to be some notion of other than the painting. And so in effect, this is this inherent relationship between content and context because if you have a context like a universe that is completely empty, it has absolutely nothing in it, then how can you distinguish between the universe being there and the universe not being there?
Forrest: So there’s this sort of notion. It’s called the principle of identity, or at least that’s the language I use with it. Obviously that’s not the best way of doing this. But the notion here is that if I can’t tell the difference between there being something and there not being something, then as an abstraction, that notion that there is something can’t be asserted, can’t be supported. So in effect, we
Forrest: … then can’t be asserted, can’t be supported. So in effect, we can only know that there is context or a universe in so far as we can interact with the content. And to the extent that we can interact with the content, then we must assume that there is a universe because we’re not the thing we’re interacting with. So there’s a sort of implied relationship between content and context, that each basically needs the other in order for either to be.
Forrest: And we see the same relationship between sameness and difference. To even have a notion of what it means for something to be the same, we have to have a notion of what it means for something to be different, and vice versa. And so in the same sort of way, these two concepts are inseparable, because they are not just co-defined, but also always co-occurring. I hope that helps.
Jim: Yeah. That was good, very good. Because now we go to the next step, which is you make the distinctions about continuity, discontinuity, symmetry and asymmetry, with respect to content and context. Again, this is a very important building block, in fact, just before we get to the punchline.
Forrest: Well, again, it probably comes to, we really want to describe the relationship between these concepts. We’ve made a couple of really important observations so far, so just to sort of lead into this a little bit, because this is kind of the through line of which this overall idea of the ICT is constructed. The first thing we’ve noticed is that if we’re going to have any notion of anything at all, we need perception. And that everything that is a measurement or anything that is… To know anything at all, to basically to do science, to do physics, to do any body of knowledge, that we’re going to basically be making comparisons. And that that comparison is something that happens in the first person and has certain intrinsics. Those intrinsics are therefore embedded in, and a part of, the very notion of what it means to know anything at all.
Forrest: And so then we can say, okay, well, how do we encode that knowledge? As I mentioned earlier, we talk about regular perceptions. We see this set of conditions, and then we see that set of conditions, and we use this notion of causation. But the idea of causation is effectively a way of encoding that knowledge and the general way that we think about that. So the notion of causation is a regular perception or a regular content that occurs in all contexts. So the idea of lawfulness in the universe itself is a kind of symmetry concept. Remember when we talked about symmetry earlier, we said it was a sameness, a consistency that occurs in contexts themselves that are varying.
Forrest: So I have multiple different contexts. I perceive this set of relationships between these conditions initially and these conditions finally, over at this sector of the universe. And then I get in my spaceship and I go to some other place, and I still see the same relationship between initial conditions and output conditions. And so I basically encode that as a same content, same causal law, in different contexts, other places in the universe. So we can generalize this notion. We can say everywhere, there is a sameness of content, in all contexts and there is a difference of context, that the notion of symmetry will describe that relationship between those concepts. So in other words, we’ll say symmetry is defined in terms of where there is a sameness of content and a difference of context.
Forrest: It turns out that when we do this, when we say, the concept of symmetry is itself defined in terms of these other concepts, sameness, difference, content and context, in this specific pattern, that that notion of symmetry turns out to be actually correct to the usages of that term pretty much everywhere that it occurs. In other words, we get this confirmation that the notion of symmetry is not just central to physics and mathematics and such like that, but the very notion of what it means to think about regular lawfulness in the universe, so to have any encoding of knowledge at all, is in some sense going to be connected to this notion of symmetry. That the notion of symmetry is a general way of thinking about what does it mean to remember something.
Forrest: Again, so when I remember something there’s a sameness of, presumably, between what I remember and the “actual” events in the outside world. And so the correspondence of sameness of the internal representation versus the external reality, again, different context, myself versus the reality, but sameness of content. Whatever the pattern is. In one case, in my imagination, in another case, in, presumably, actual events.
Forrest: So the idea here is just that we’re basically starting to say something really, really primal about what does it mean to be scientific knowledge. We started talking about the notion of knowing, the notion of perception, the notion of comparison and its intrinsics, and then we were able to use those intrinsics to construct a notion of knowledge, something we now hold in the third person sense. So in effect, we’ve moved from a first person experience in the sense of perception or comparison and it’s intrinsics, to now a third person perspective, this abstraction, that we’ve described using the term symmetry. So in this particular sense, the notion of symmetry is profoundly important to, basically, the entire body of what we consider to be not just scientific knowledge or physical knowledge, but literally just knowledge, point blank period.
Forrest: And so in this sense, we’re beginning to get a real sense as to why these concepts will be worth working with in the first place, because as it turns out that, in the same sort of way that we can define symmetry as a sameness of content and a difference of context, we can start to talk about concepts like continuity as being a sameness of content, where there is a sameness of context. And this is, obviously, a little bit more difficult to imagine, but on the other hand, when we think about things like continuous functions, the value of the variable doesn’t change enormously for some infinitesimally small change in the conditions. If I move a little bit on the x-axis that I don’t have the line jump a huge amount on the y-axis. And so in effect, when we take it down to the level of infinitesimals and stuff like that, we’re starting to see the notion of continuity as being critically important to thinking about things like what happens at the scale of the very microscopic.
Forrest: And so when we’re starting to think about access control limits, and what does it mean to have knowledge and what does it mean, therefore, to have things that are unknowable, it begins to show up in places where continuity and discontinuity happen. So in other words, if we say, well, we can know this and we can represent this idea, that representation happens in a form of symmetry, but then we start to think about the connected tissue of these ideas, like what is possible to know and what it is possible not to know. When we go from the knowable to the unknowable, there’s a kind of discontinuity that’s implied. So in effect, these notions of continuity and discontinuity, symmetry and asymmetry, start to become profoundly important in terms of understanding what does it mean to be essentially epistemic process or in this case, the scientific method, at all.
Forrest: So when we begin to start to say things like, there’s this irreversibility in the perceptual process. We can say, well, that shows up as a sort of asymmetry in the change of state, of going from unknown to known. And that there’s a kind of discontinuity in the state of what is knowable versus what is unknowable. And so in effect, we’re starting to see a concrete relationship emerge between the known, the unknown and the unknowable, as a consequence of the very nature of the epistemic process itself. And this turns out to have some surprising implications.
Jim: I spent more time on these four lines in the dialogue, probably, than almost the rest of it put together. And once I had gotten my head around these four statements, the rest seem to flow naturally and just straight downhill.
Forrest: Downhill? I don’t know. That sounds scary. What are you telling me?
Jim: Eventually said, that once one understood those four concepts, continuity is in reference to a sameness of content where there is sameness context, discontinuity is different content, same context.
Forrest: Oh, so the four definitions?
Jim: Yeah. The four definitions. Once I had those four, and to really be able to visualize them, then from there to the ICT itself, it was pretty straight forward.
Forrest: Yes. Yes. Well, that’s just it. There’s a lot of things happening when we’re talking about the ICT. The actual idea is really straightforward. There’s a simplicity underneath all of this, which is, it’s this basic flow of saying, hey, epistemic process is going to be measurement. Every measurement is going to be a comparison. Any form of knowing is going to be a comparison. Comparison has these intrinsics, and we can use these intrinsics to define these four really interesting concepts, symmetry, asymmetry, continuity, and discontinuity.
Forrest: At first, this seems really straightforward. But these are abstractions and obviously people sometimes can relate to that and others not so much, but that’s okay. The main thing is that for the people that would care about such things, the inherentness of the relationship between comparison and anything to do with epistemic process, the totality of anything of what it means to know is subsumed by this notion of comparison. And the notion of comparison is subsumed by these six intrinsics. And these six intrinsics, by themselves, are completely adequate. They’re both completely necessary, but completely sufficient to describe the concepts of symmetry, continuity, asymmetry, and discontinuity completely.
Forrest: So we’ve just gone from kind of vague notions of what symmetry means, to now this really explicit, really exact, precise, totally inclusive definition of symmetry in a mathematically precise way. And the nice thing about that is that it turns out that, as I said, when we look at these four concepts, as they occur in mathematics and in physics and in every other domain in which these concepts are used, that the use of these intrinsics to define these four concepts turns out to be, as I said, empirically consistent with the natural usages of these terms in all of these fields. And so in effect, it’s like we have this empirical confirmation, at least at a kind of linguistic level, that the way people are thinking about these concepts is itself inherently consistent with this underlying abstract absolute definition.
Forrest: And so in effect, we kind of say, we’ve just learned something really important about the nature of epistemic processes in a fundamental way, because these definitions are now concrete. And so in effect, we can take these definitions and we can start to use them as ways of clarifying literature that happens to use these concepts, or we can use them as tools to start to think about epistemic process in a much more fundamental and much clearer and complete way. But then it turns out that as we start to manipulate these concepts and to use them as tools to understand other fields of knowledge and so on, so forth, that certain meta patterns start to begin to appear as well.
Jim: Yep. So do you think you need anything else to take it home to the actual ICT itself? My sense is from these four definitions, it’s a pretty short jump to the actual statement of the ICT.
Forrest: Yeah. It’s a pretty short jump.
Jim: Why don’t you take the roll from the definitions and ride right through the explicit statements of the ICT. You don’t need to show every detail in how you get there, but I think we’re ready to roll.
Forrest: At this point we have the infrastructure, right? And this is enough, so this is the next couple steps. We basically say, we have this notion of comparison in the first person sense. We have these four abstract concepts that now have very explicit and very, very concrete meanings in this third person sense. Can we use these concepts to say anything about what’s happening in the first person sense if we combine them with each other?
Forrest: So in the same sort of way that I took the intrinsics of comparison, and I used them as a definitional basis to create these four concepts, these new concepts, symmetry, continuity, asymmetry, and discontinuity, I can then say, well, can I use these concepts, symmetry, asymmetry, continuity, discontinuity to construct any higher order concepts? So maybe what happens if I apply symmetry to itself? Does that generate anything? Well, typically, no, because, if it’s already there, it’s still there. So in effect, if I apply the concepts to themselves, I don’t really get anything new.
Forrest: But on the other hand, if I say, can I have a situation, can I look at measurement that is basically perfect in the sense of being both represented by symmetry and represented by continuity? Can I have perfected symmetry and perfected continuity at the same time? And so, in effect, what that would basically be saying is something like, can I really know something and can I know everything there is to know about that something? It’s sort of been hinted at when thinking about things like quantum mechanics and general relativity vis a vis Newtonian mechanics, is that some of these theories imply that there is an access control of things that are knowable and things that are inherently unknowable. So if we’re talking about these concepts as emerging out of epistemic process itself, then can we use these concepts to describe the boundary between the known and the unknowable in a really concrete way? And it turns out that we can.
Forrest: For example, if we look at the four concepts that are each defined in terms of the intrinsics, but the intrinsics themselves have certain definite relationships with one another. For example, we don’t ever have content without context. We don’t ever have sameness without difference. And obviously because epistemic process is going to involve a flow in the first person sense as just how do we come to know anything, the notion of going from unknown to known is inherently going to involve subject of an object. If there’s going to be a measurement, there’s going to be a perception.
Forrest: So in this specific sense, we can start to say, anywhere that I have a sameness, I’ll need to have a difference, and anywhere that I have a difference, I’ll need to have a sameness. So if I apply, say, the notion of symmetry and continuity together, well, because each of these concepts themselves is defined in terms of sameness and difference and content and context, we can begin to just add up how many samenesses there are and make sure that for each one there’s a pairing with a difference. But if you do this, we basically notice that for some pairings, that we don’t end up with a correspondence between sameness and difference that’s matched. We end up with imbalances.
Forrest: So for example, if I basically say, I’m going to just make a table and in the columns I’m going to put the first entity, which would be symmetry and then in the next one, I’m going to put symmetry and then I’m going to say, how much sameness is in this and how much differences in this for each of these two elements? And I’m just going to add them up and put them in another column. And I’m going to show whether or not that column is essentially adds up to the same number of sameness and differences.
Forrest: So if I take every combination of the four concepts, sameness, difference, content and context, against the four concepts of sameness, difference, content and context, and I’m just looking at the conjunctions of these. So I have 16 entries in this table, and I basically just track how many times does the notion of sameness occur in symmetry or the notion of sameness occur in continuity or discontinuity, et cetera, for both of those columns. I notice that there are actually only two combinations that meet the requirements of having matched sameness and difference, and that all other combinations are effectively rejected on this basis.
Forrest: So in the sense that you can’t have sameness without difference and content without context or subjective without objective, in any first person measurement process, then effectively we come to notice that, as a result, that there is literally only two possible combinations that are valid as far as epistemic process itself. And that is, essentially, not, unfortunately, inclusive of continuity and symmetry at the same time. If we want to have perfect symmetry, we must allow for perfect discontinuity. And if we want perfect continuity, we have to allow for perfect asymmetry. And that in effect, the combination of symmetry and continuity together is just as conceptually impossible as saying that something is symmetric and asymmetric at the same time.
Forrest: So in effect, there’s a notion of contradiction when we say that there is something that’s symmetric and something that is asymmetric, and that if we’re saying that it’s symmetric, we’re not also going to be able to say that it’s asymmetric. This shows up, this contradiction, shows up in the fact that the number of samenesses and the number of differences is mismatched. So in other words, the conceptual notion of these two concepts are saying the opposite thing is represented in the notion that sameness and difference is not properly paired.
Forrest: So in effect, what happens is that we, basically, now all of a sudden realize that there are essentially two kinds of epistemic knowledge. There is things which have symmetry and discontinuity, IE the discreet universe, what we think of as the digital world, to some extent, consistent of particles that have this boundary notion that this particle is distinct from this other particle, even though electrons in the universe, for example, are in some senses equivalent to one another, there’s still this identity distinction that this electron over here and that electron over there, they’re in different spaces at different times. And therefore they’re in some sense, different.
Forrest: So in effect, there’s a notion that if we are looking at symmetry, we’re going to see these notions of discontinuity. So the notion of symmetry of electrons all have the same properties. And the notion of discontinuity is there’s a lot of them, there’s multiple electrons and they are somehow different from one another in space and time. But we don’t have a way of basically showing a connection between one electron and another except through some sort of intermediating protocol that is something else.
Forrest: For example, if we start to say things like, there’s a way of understanding the universe in terms of symmetry, that this notion of discontinuity is going to inherently be involved. But on the other hand, if we say, let’s go back from the third person perspective and we go back to the first person perspective, then in the sense that the subjective and objective is connected through the process of observation, in the first person sense for there to be a notion of measurement is to imply a notion of connectivity, to imply a notion of that there is a singular process that involves these six intrinsics inherently. To now all of a sudden we’re going to say, there is actually this asymmetry that tags along. That in the sense of the connectivity between the observer and the observed, in order for measurement to be possible at all, access actually happening, it’s not just that there are access controls, but there are times where I actually log in and access something.
Forrest: So in effect, if I’m making the measurement, I’m implying a connectivity between the measurer and the measured. That’s just an inherent aspect of the notion of measurement itself. And there’s this asymmetry that comes in with it, which is to say there’s literally a before state of not knowing and then an after state of knowing. And so in effect, the asymmetry of time is effectively bound into the measurement process itself. So in effect, we now have these two fundamental characteristics that describe the relationships between symmetry continuity, asymmetry and discontinuity, to say that in the first person sense that the description of epistemic process, now, keep in mind that this is now a comprehensive, inclusive, all encompassing, because we’re talking about the fundamental nature of what it means to be epistemic process itself. We said all epistemic process is effectively going to be described by comparison. All comparison is going to be described in terms of intrinsics. These intrinsics describe these four concepts in an absolute way. We’ve confirmed that these absolute descriptions are actually consistent with real usage of those terms. And we’ve basically said that these four concepts only combine in specific ways, that therefore those observations of how they combine actually are descriptions of the epistemic process, taken in totality as a fundamental concept in and of itself.
Forrest: So in effect, we’re basically saying that there is now this notion of epistemic process in the first person sense, which inherently is defined in terms of continuity and asymmetry, and then epistemic process that, or the result of epistemic process, which is the notion of knowing as opposed to the process of knowing which is going to be described in terms of symmetry and discontinuity. And that in effect, because we can’t have both symmetry and continuity at the same time, that to some extent, these two fields of knowledge or these two ways of thinking about epistemic process are in effect incommensurate with one another, hence the notion of the name of the theorem in itself.
Jim: All right. You did it.
Forrest: I did.
Jim: We got there. We decided to have this episode when, I think it was after one of our other episodes, you asked me what was the most surprising thing in my readings of your various writings? And I said, it was the ICT. And I still stick by that. This is not an intuitively obvious concept. And it actually seems to have some interesting implications.
Jim: So now, I don’t know if we can do this, but we’ll try. Perfect. You actually laid it all out. I think we took all the right steps to get there. Nothing more than we needed, maybe a little bit more, nothing less. Is there a good homey example, call it an everyday example, where the ICT is relevant? If not, we can leap over to some of the physics examples that we’ve talked about before.
Forrest: Well, I don’t know how homely it is, but in effect there’s this huge body of literature that’s talking about the relationship between first person perspective and third person perspective. And so in effect, what we’ve done is, we’ve shown how to go from a first person perspective to a third person perspective.
Forrest: What I think is even more interesting is how to go back from a third person perspective to a first person perspective. So in effect, there’s a set of tools now that we have to basically think about that relationship. In effect, it basically, in a sort of homely example describes, why is it that we, in the first person sense, experience consciousness as a kind of continuum, having an inherent to symmetry. We don’t have access to the future. We can’t predict with certainty, absolutely everything that’s going to happen and that there’s really this experience that we have of sequence of this happened, then this happened, and this other thing happened.
Forrest: So in effect, the very notion of knowing in the first person sense has this felt immediacy of the notion of continuity of an I am still myself from one moment to the next. And this notion of asymmetry in the sense of what we think of as the subjective flow of time. But that in effect, that’s a firsthand experiential realization of this continuity, asymmetry way of relating. And then we have this sort of abstract body of knowledge. So in the first person sense, we say, well, science can’t describe this, or at least it doesn’t seem to, and there’s this first person experience that I feel like I have choices or that events occur in time and I can’t seem to get outside of that. Otherwise, I’d be able to just dip into tomorrow and predict lottery numbers and stuff like this. So in effect, there’s this very visceral embodied sense of continuity and asymmetry.
Forrest: And then when we go to, say, a body of mathematics where the subjective is factored out, we’re just talking about the math and there’s no observer effect. There’s no sense of any kind of relationship between the subject and the object. There’s just the pattern. There’s just the content. So mathematics as a study of pure relationship is just going to consider the relationships and we’re in a sense going to lose the notions of what’s related and we’re going to lose the notions of who’s observing these relationships, or that there’s even a container in which these relationships occur. We’re just going to say, there’s this equation and we don’t necessarily know what x and y represent, but they’re related in this way. And so in effect, there’s this abstract notion of these patterns, and these patterns are floating in a disconnected way. Each statement, each equation is a discrete thing. It has discrete symbols, chosen from a discrete alphabet, that represents specific relationships that have a…
Forrest: … represent specific relationships that have a sort of quantized aspect in the sense that it’s this symbol and not this other one, and the symbols aren’t fuzzy, because if they were, we wouldn’t be able to read them with clarity. We’d say, “Well, I just don’t know what that symbol is. It could be an A, or it could be a B.” So in effect, there’s this sort of firsthand experience when doing mathematics, when thinking about physics in the abstract way that these notions of laws and so on and so forth are not in a continuum, that they represent discreet ideas, and that these ideas themselves are abstracted from the here and now experience. They are generalizations. So in this sense, we can basically say something along the lines of, “Well, this is really describing something which is so connected to the firsthand experience of how people actually live in the world that it’s impossible for there to be anything at all which is not an example of the incommensuration theorem.”
Jim: I think that’s pretty good for a Forrest Landry homely enough, everyday example, because I think I’ll try and translate it into more Philistine rock talk, right? You hit it in passing, is it’s essentially the difference between the first person and the third person, between the broken symmetry in time, if nothing else, that we have as first person conscious entities, and I suppose you could say it supports the fact that in standard model physics, things seem more symmetrical than they do in a first person perspective.
Forrest: That’s right.
Jim: There’s nothing in basic physics that seems to rule out time going in reverse. Yet with the broken symmetry that we get with continuity, we have access control that does not allow us to make that move. How’s that?
Forrest: That’s exactly right. That’s great. That’s why this discommensuration theorem is kind of important, because it gives us the tools to really consider the relationship between first person and third person, and also second person, but that’s another story. The idea here is that there’s a profound level of clarity, of reification of the relationship between these concepts in and what would normally be thought of as a philosophical way that allows us to get really at the meat of the relationship between, say, physics and mathematics or between epistemic process as scientific method and science knowledge taken as a collection or as a body of knowledge. So in effect, at first it seems like these things are, “Okay, well, these abstractions, they’re really cool. They help us to think about these things.” But most scientists would say, “Well, that’s philosophy, and it’s not really relevant. Show me the equations.”
Forrest: So in effect, we start to notice is that, well, actually, it’s already there. It’s already been part of the process all along. By the way, it is actually showing up. It shows up in things like the Bell theorem, which basically say that you can have theories of reality, but that there’s going to be a limit on the theory of reality that you have that’s going to be based upon epistemic process itself, that, in effect, we can have theories of reality that essentially are everywhere causal and everywhere connected, but that there’s going to be phenomenology that, for the most part, that that just is not going to describe, that there’s going to be places where there’s going to be limits to the notion of lawfulness that is conceived that way, or you can say, “We’re going to describe the notion of lawfulness. We’re going to take a third person perspective and say these laws apply everywhere,” but now you’re going to have things which cannot be described in terms of causal connectedness anymore.
Forrest: So you have to take your pick. You can basically say, “Well, we’re either going to emphasize symmetry and accept discontinuity or we’re going to emphasize continuity and accept asymmetry. In effect, the Bell theorem at first, although it seems to be kind of this independent observation about quantum physics type process and things like entanglement and such, it turns out to be a special case of this more general notion of the ICT and is exactly consistent with it.
Forrest: So in other words, if you think about what does the notion of lawfulness even mean, then you say, “Well, ultimately, the notion of lawfulness is exactly the same as, if not contingent on the notion of symmetry.” When we say something like the notion of locality, what we’re actually talking about is this connectedness thing, and this connectedness thing is itself strictly isomorphic with the notion of continuity. So in this specific sense, now all of a sudden we can basically say, “Well, the notion of the ICT basically is a way of understanding the Bell theorem that completely supports that the Bell theorem is in fact abstractly necessary based upon the intrinsics of the epistemic process itself” and that there’s zero ambiguity about any part of that.
Jim: Let’s dig into this a little bit, because we did this before on one of the earlier shows, and I think as you know, we’ve talked about the fact that quantum interpretation is one of my hobbies, right? One of the maddening things about quantum mechanics, which is one of our basic ways of knowing the world, is you can shut up and calculate, run the numbers in the Schrodinger wave equation, and you can get results.
Jim: But what does it actually mean about things like causality and reality are so far unresolved. There are a couple of dozen so-called quantum interpretations, i.e., what does this mean, right? There’s one, the standard Copenhagen interpretation that says, “We have no fucking idea and we never will,” right? Bell’s inequality and Bell’s theorems bind this a fair amount, but they don’t actually rule out any of the other theorems. What you were stating is a somewhat overly strong statement of Bell’s inequality, which essentially rules out local hidden variable theories, which isn’t quite the same as forcing the resolution to causality, but no locality.
Jim: Now, it does in many cases, but there’s at least, it turns out, two interpretations where you can have … and not violate Bell’s inequality, where you can have both causality and locality, surprisingly enough. One of them is becoming more and more popular, and that is the many worlds hypothesis or many worlds interpretation of quantum mechanics. This is shall we say the opposite of a parsimonious theory. It basically says every time there’s a quantum event, the universe forks and there’s another universe, and the universe went in both, if it’s a binary fork, and if it’s a nonbinary quantum event, into all the possible alternative universes. So there’s some staggering number of universes going down this tree of forking, and everything that could occur does occur.
Jim: It turns out you run the math, and you can have locality and causality in quantum multi-verse interpretation. Then when I did a little research for the show, I came across another interpretation, which I did not even know about, called super determinism. Bell himself admitted when confronted with super determinism that you could have both a causality and locality if the universe is utterly clockwork and there is no fundamental randomness to it and there is no free will. Basically, it’s a Newtonian universe, and that has not yet been ruled out by experiment. It’s still possible that there is some deep, deep clockwork which is not stochastic at all and there are no forks at all.
Jim: So if you believe that the ICT supports a stronger version of Bell’s equality than Bell’s equality itself in such a way as to mandate that causality and locality can’t coexist, then if you can actually connect that to the physics, you will have ruled out a couple of the quantum interpretations, which nobody else has. So that’s, to my mind, a really interesting question, and I’d like to see a physicist with a good grounding in philosophy take your work and see if he can move from the ICT to this stronger version of Bell’s inequality. If he does, they’ll actually be able to make progress that nobody else has been able to make in almost 100 years, which is to actually knock out at least two of the possible quantum interpretations.
Forrest: So just as as a thing to sort of do as in connection to that, so if, again, we’re using these concepts as tools, right? So the question is a fair one. What do these tools say about this sort of thing? One approach that we can take to sort of look at something like this or to address a question like that is to sort of look at the different interpretations of quantum mechanics in the point of view of what is the notion of measurement? How does the notion of, say, sameness and difference, content and context, subject and object, how do they show up? So in effect, when we look at the many worlds interpretation, for example, we can ask, “Well, what degree of connectedness exists between the worlds?”
Forrest: This is just a sort of exploratory thing. You can start with that, and you can say, “Okay, well, the worlds are somehow disconnected from one another.” In some sense, in the “past,” right, at some earlier position, we could say they were connected, and we can start to sort of step back and look at the whole network of branching that happens and say, “Well, they’re connected here, but they’re disconnected here.” Then we can start to say, “Well, what is the content?” The content is the pattern, and the context is the entire field of all of the different branches in the many worlds interpretation. So we’ve got the notions of sameness and difference. We have a way of thinking about those. We have a way of thinking about the notions of content and context, but you notice that all of this is very third person. There’s no notion of subjective or objective. There’s no actual flow.
Forrest: So in effect, there’s this sense of, “Okay, well, if I basically pin the epistemic process in just the third person sense,” then you can ask, “Well, in what way is that knowledge grounded? Where did that knowledge come from? Where did the information field that describes this branching pattern, not the abstract branching pattern as a concept, but even the detailed information of there is this lamp sitting on this table in terms of this particular universe, and in this other universe, the lamp is sitting on the floor?” So in effect, there’s a notion of information that is implied, but there’s no way for that information to have actually come into being, because we’re looking at a sort of third person perspective, a kind of atemporal thing where there’s essentially absence of flow fundamentally.
Forrest: So then you can say, “Well, if there’s no first person perspective, in what sense does this represent scientific knowledge? How would we have grounded this knowledge in anything that would resemble the scientific method?” That would be kind of like one whole thing, and I know all these arguments have been made already, so I’m not really going to try to keep going in that direction. So then I step back and I say something like, “Okay, well, can we even really think about the notions of this process in maybe some more general way, like we have all these different interpretations, and we have this thing called the incommensuration theorem. Does the incommensuration theorem allow us to sort through these interpretations in any specific sense?
Forrest: It turns out that there is a kind of thing that we observe when we do this, is, first of all, that the notion of asymmetry in the sense of there being kind of this inherent temporal arrow, and I’m not talking the temporal arrow associated with entropy, but essentially the deeper temporal arrow associated with the irreversibility of perception or the irreversibility of change of state or any notion of irreversibility itself taken as the notion of asymmetry is inherently connected to the notion of subjectivity as distinct from objectivity and the notion of hard randomness.
Forrest: So, for instance, if you look at all of the interpretations of quantum mechanics as described by the math, then in effect, what you sort of see is kind of in the background or implied in this field of interpretations is specific assertions about the concepts of hard random, subjectivity, and the arrow of time and that those three concepts are in effect distinct, inseparable, and non-interchangeable. They show up as a kind of triple and that in effect the very meaning of what it is to, in a sense, describe quantum mechanics essentially rests on this platform of what are the relationships between … In the same sort of way we could talk about what are the inherent relationships of observation itself in the first person sense versus in the third person sense, we can start to notice that there are these sort of projections that result at a fundamental conceptual level that describe the interdependence between these three things and that, in effect, if I say, “Well, there’s no hard randomness,” as the many worlds interpretation is concerned, we also notice that there’s no subjectivity and there’s no arrow of time.
Forrest: So we’re basically dealing with a perfected third person point of view, whereas if you look at something like the Copenhagen interpretation, it essentially makes the complete opposite assertion. It says, “Yes, there is hard randomness. Yes, there is subjectivity. Yes, there is an arrow of time,” in the sense there’s the born distribution of the results of the shorting or evolution of wave state and so on. So in effect, what we’re looking at here is that there are basically two kinds of interpretations, interpretations that assume that all three elements of subjectivity, hard randomness, and temporality occur, or that none of them do.
Forrest: Then in effect, we’ve now partitioned the total field of interpretations of quantum mechanics into ones that are either inherently first person or ones that are inherently third person and that, again, we see the incommensuration theorem being represented in the sense that there is now this sort of philosophical distinction between is the basis of knowledge on the principle of the scientific method, is that the ground of epistemic thing, or is the basis of knowledge just that which can be derived from, say, some sort of basic underlying math, i.e., are we living in a platonic universe where there is no change, the notion of subjective experience is essentially just not accounted for and not describable at all because there’s literally no sense of, again, surprise temporal arrow or continuity of experience or that we basically assert that there is the notion of first person measurement and that the scientific method is something like hypothesis, observation, and the recording of results in some sort of third person form?
Forrest: So in effect, if we basically describe the science itself as depending upon the scientific method, then you end up with one set of interpretations being valid, and if you basically describe something as there’s no such thing, as physics as distinct from mathematics, then you end up with another set of interpretations. But on the other hand, you would say, “Okay, well, that doesn’t really help us that much,” but then we have this other thing in mathematics itself which is called the Godel theorem. Again, I may be mispronouncing that, but-
Jim: Yeah, Godel. Yeah, Godel’s incompleteness theorem.
Forrest: Yeah. I’ve heard both. I don’t know. I used to say Godel. Sometimes I’d say Godel. I’ve heard Godel a bunch of times. Honestly, I have no idea which it is.
Jim: Yeah, I think it’s somewhere between Godel and Godel, I believe. But anyway, it doesn’t matter. We know who we’re talking about, that dude.
Forrest: That dude.
Jim: That dude who broke math.
Forrest: Exactly. Well, he’s one of my favorite characters, and I definitely admit that regardless of any embarrassment I have in referring to him properly, I definitely have a huge respect for his work. So in effect, we can say, “Okay, well, even if we were to regard physics and mathematics as being strictly equivalent,” that we’re going to try to basically just talk about the universe in terms of pure math, it turns out that there’s a projection of the incommensuration theorem into the body of mathematics as a domain or field of knowledge itself. So then we say, “Okay, well, let’s see. What does that show up as?”
Forrest: Well, the theorem basically says that you can either have completeness or you can have consistency, and one of the observations that we can make is that the notion of consistency is strictly isomorphic to the notion of symmetry, i.e., I don’t have in one position of all the theorems something that says that a statement is true and somewhere else a thing that says that it’s false. A is true versus A is false is a contradiction and that, in effect, that represents a kind of fundamental asymmetry, whereas we’re going to say symmetry. We’re going to say it’s the same content, even in different contexts. So once you sort of look at the concepts of symmetry and consistency and you really dig at what does consistency mean, then you can see that there is essentially a strict isomorphism, actually zero ambiguity that there is no notion of consistency that isn’t absolutely and exactly the notion of symmetry. So in effect, we can say, “Okay, well, those two words effectively mean exactly the same thing.”
Forrest: Then you can say, “Well, what does the notion of completeness mean?” Well, completeness would basically say that from any position in the sort of space of possible axioms that if I basically have a specific set of axioms that I can reach all of the provable theorems that those axioms would connect to and that, effectively, that would subsume the totality of all mathematical knowledge. So in effect, we are saying that there’s not multiple fields of mathematics, that there is one domain of mathematics and that that domain of mathematics essentially includes the totality of all true knowledge. So all true knowledge is essentially connected to all other true knowledge in this one field.
Forrest: So in effect, when we start to really dig into what is the notion of continuity and what is the notion of, as I said, completeness in mathematics, we see that, again, there’s this strict isomorphism, that these two concepts are, in fact, the same concept and that they can’t be regarded distinctly. Again, these are fixed, absolute definitions. The notion of completeness can’t be conceived of as other than a representation of the notion of continuity. So once you get these two sort of really hard, absolute sort of definitions, then we can see that the theorem, the Godel theorem or the Godel theorem, however you pronounce it, is itself a projection of the underlying incommensuration theorem, which basically asserts that you can’t have perfected symmetry and perfected continuity at the same time.
Forrest: The main benefit, of course, is that by doing it through the incommensuration theorem that the proof itself is vastly simpler than the one that Godel or Godel himself had to use, which required a kind of reflectivity of the number system representing equations that describe the number system and, to some extent, the reflectivity between those two, whereas in this particular case, the same reflectivity sort of shows up as that we are conceptualizing about perception when perception is a kind of concept or it’s a kind of dynamic of conception. So we’re talking about how do we perceive perception, or how do we conceive of concepts?
Forrest: So we can talk about perceiving concepts or concepts of perception, but, again, there’s a sort of dynamic reflectivity between these two domains, the embodied one and the abstracted one, or, in this case, the first person and the third person. So in effect, when we start to really look at the relationships between these things, we begin to notice that there is this recurring pattern of the incommensuration theorem showing up at the really deep foundations of what it means to know anything at all as represented in the Godel theorem. So if we basically say something along the lines of there are inherent discontinuities in the field of mathematics, because obviously we would prefer that we don’t end up with inconsistent results, then in effect, if we’re saying, “Okay, we’re going to prefer symmetry,” then we’re going to live with discontinuity.
Forrest: So in effect, if we go up into the now mathematics and physics as the same thing, then we would say, “Well, if we require that there is essentially going to be symmetry preferred,” we’re going to prefer lawfulness,” then in effect we’re going to live with discontinuity and that, to some extent, because of the Godel theorem that now we’re forced into a position where on a conceptual level, we’re required to essentially look at the symmetry, discontinuity, or in this particular case just the third person point of view. But on the other hand, that now has essentially degrounded the notion of epistemic process itself, and, in effect, what you now end up with is this huge contradiction, because, in effect, the very way in which the method was arrived at when we look at this whole thing, it was based upon perception. It was based upon epistemic process itself.
Forrest: So somehow or another, we end up with this sort of projection of if there is epistemic process, then this thing is going to require us to look at it in both the first person point of view and the third person point of view, because there’s no concept of the third person point of view that isn’t itself in some way based upon or derived on the first person point of view, and it shows up in the Godel theorem even still. So therefore, we can start to say, “Well, as much as from a purely mathematical or symmetry point of view, it might make sense for us to regard this as that the many worlds interpretation would be aesthetically pleasing, it doesn’t actually make conceptual sense,” because it effectively goes against the underpinning of even the notion, because even in the mathematical sense, we still end up with these discontinuities and therefore these incompleteness, which now basically is saying that there are portions of the many world interpretation which are not described by the many world interpretation.
Forrest: In other words, that there are worlds out there that aren’t just as connected in the sense of I can’t access this branch from this other branch, but that there are literally required to be other universes, which are inherently unmeasurable and inherently unknowable and that they’re not in any way causally connected to this universe at all, which therefore says, “Well, the many worlds interpretation can’t be a complete description, because there’s phenomenology that aren’t described by it, and therefore, it’s not a complete theory.”
Jim: I like it. I wish I knew the right guy to take that to. I did know the guy. Murray [inaudible 01:44:17] had a strong opinion about that, but unfortunately, he passed away recently. I’ll have to scratch my list of quantum guys I know who are also philosophically open-minded enough to read your ICT and say, “All right. Does this provide me a tool to actually rule out many worlds?” That would be a big move, and it’d be big news in physics if they could do it. I think on that note, we’re going to end it. Congratulations, Forrest. I had my doubts on occasion whether we could get through this thing coherently and draw a relatively clear picture of the ICT. I think you did it. So job well done, and thanks for coming back on the Jim Rutt Show.
Forrest: Awesome to be here. Thank you so much for the kindness of your attention and to anybody who’s listening to this, and if you want more information, check the links. Curious to know kind of how this lands for folks and so on. Again, I’m not going to try to convince anybody of anything, but on the other hand, this is one of the more interesting things I feel that I’ve ever even encountered. So I’m hoping that other people find it to be of interest as well.
Production services and audio editing by Jared Janes Consulting. Music by Tom Muller at modernspacemusic.com.