Groundless Emergent Multiverse On why and how anything exists hiveism.substack.com 2024-08-31 Overview There is nothing one can say about reality other than one’s perspective on it. Ultimate reality neither is nor is not, but the consensus of all possible perspectives. That’s the most concise and precise two-sentence summary I can think of. Of what? Of an attempt at explaining the ineffable. Since, by the nature of the matter, it is impossible to express it in words, take everything I write here as a finger pointing to something, a map, a set of tools. At some point, you will have to see it for yourself. Don’t take it lightly. Understanding it is a journey and transformation. I don’t say this to make it sound important but as a sincere warning—it takes a lot of work to understand, there are pitfalls along the way, and even more work after you get it. In practical terms, this is a framework, or way of thinking, for answering the “ultimate question of life, the universe, and everything”. At least, the metaphysical part. It is a bridge between different sciences, philosophy, and spiritual awakening. I expect that it can guide and inspire further research. Let’s unpack that summary a bit. We cannot say anything about reality without a perspective, a frame of reference, an observation, a subjective experience. All we can talk about is our perspective, our experience. There is nothing we could know about ultimate reality but our subjective observation. We have to conclude that ultimate reality in itself is devoid of any properties. Reality, rather, is the superposition of all possible perspectives. Without properties, it is indeterminate, neither truly existing nor not existing. Empty of inherent existence, it is completely transparent. Each possible perspective on reality is a view of all other perspectives. They are interdependent, with no substance, no ground to be found anywhere. Every perspective is defined through its relations to all other perspectives. Through relations, there is structure. This structure gives rise to (the local impression of) time, causality, space, locally broken symmetries, and all the rest. Following this structure from most symmetric to less symmetric, one finds that 1 structures branch, merge, or reach dead ends. This diversification and selection provide a universal evolution that selects for stable structures. Life, intelligence, self-awareness, and consensus arise through selection for stability. The universe we observe is a region within the structure of reality that allows for this level of complex stability to emerge. With nothing that reality consists of, neither real nor not real, with the biggest and smallest being the same, there is no fundamental layer to reality. It is truly a groundless emergent multiverse How to Read I have no credentials, am not a physicist, mathematician, or philosopher, and am not trying to be one. I don’t have all the answers, but I am certain that this is the right direction to look for them. To fully understand, you will have to let go of all your beliefs and assumptions because the entire point is that there is no single view that describes the truth of how the world really is. Letting go of your beliefs can be hard. Meditation and meta-rationality help. It may take years to break through. Rebuilding what you have let go will also take a lot of work. There are many layers to understanding this and many ways to misunderstand. It may require multiple readings. Language constrains me to a linear presentation, but some parts may only make sense in the light of what comes later. Don’t think you understand until it is blatantly obvious, unavoidable and self- evident to the point where you can’t un-get it, even if you tried. I don’t present a worldview, but a way to let go of any worldview so that you can utilize your ways of looking instead of being dominated by them. The core of what I am pointing to cannot be proven from within any formal system. All arguments are meant to deconstruct any unquestioned assumptions you may carry. When you firmly believe something is true, there is no harm in letting that belief go. If it is true, you will just rediscover it again and again. Don’t take this as an argument for or against any religion or belief system. If you understand or even use it that way, you will be totally missing the point. There is a danger of abandoning one way of explaining the world to fully grab onto another. Even worse when that new way is built on an incomplete understanding. Misunderstood concepts easily become beliefs. Extrapolating from these beliefs then gives wildly wrong results. Please don’t extrapolate before full understanding. Also, please don’t explain your interpretation or summary to others as long as it is incomplete—for this is how false understanding proliferates and turns wisdom into mush. 2 Contents Overview 1 How to Read 2 Introduction 4 Deconstructing 5 Why Does Anything Exist? . . . . . . . . . . . . . . . . . . . . . . . . 5 What is Fundamental? . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Foundations of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . 9 Gödel’s Incompleteness . . . . . . . . . . . . . . . . . . . . . . . . 10 Set-Theoretic Multiverse . . . . . . . . . . . . . . . . . . . . . . . 12 Russell’s Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Superposition of views . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Many Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 The Fiction of Everyday Experience . . . . . . . . . . . . . . . . . . . 16 Reconstructing 17 Blank Slate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Pure Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Perspectives and Individuation . . . . . . . . . . . . . . . . . . . . . . 19 Extrapolating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Conservation of Quantities . . . . . . . . . . . . . . . . . . . . . . 21 The Arrow of Time . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Uncertainty and Probability . . . . . . . . . . . . . . . . . . . . . 22 Frames Within Frames and Self-Similarity . . . . . . . . . . . . . 24 Stability, Evolution, and Emergence . . . . . . . . . . . . . . . . 26 Summary 28 Ways of Looking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3 Introduction Reality is that which, when you stop believing in it, doesn’t go away. — Philip K. Dick, How to Build a Universe That Doesn’t Fall Apart Two Days Later It’s easy to fool oneself and mistake for reality what, actually, is still a belief. When you develop the rare skill to stop believing in anything, you will find that no experience of reality remains. Beliefs are the means by which we experience reality. We can extend this process to logic, mathematics, and physics, questioning what we believe to be real, unchanging, and true. When we see that something is entirely dependent on our assumptions, it becomes transparent. When we let go of those assumptions, it disappears. In the first part, we will do just that and discover that there is no reality independent of assumptions. Every experience, observation, or the result of every measurement is entirely dependent on its perspective. The great breakthroughs of Albert Einstein came by letting go of assumptions. While Newton thought that space and time were absolute, like a stage on which the world happens, Einstein turned that idea on its head. Since then, we know that spacetime and the frame of reference of the observer are intimately linked. Quantum mechanics struggles with the measurement problem—the question of what constitutes an observation—and related problems like the question of locality. Here, the many-worlds interpretation again turns our expectation of reality upside down, implying that observations are entirely dependent on perspective. There is no observer or frame of reference that is preferred over any other. Absolute reality is completely described as the superposition of all possible perspectives. Surprisingly, this ultimate Copernican shift in itself allows for a metaphysical framework to make sense of many puzzling questions in physics and philosophy. For this, we have to take a look at two topics almost absent from natural science: metaphysics and subjective experience. While these topics are often avoided for understandable reasons (it’s hard), without integrating these two, our ability to grasp ultimate reality will remain limited. Importantly, this will answer the fundamental questions of metaphysics: Why is there something rather than nothing? What is reality fundamentally made of? And the second question, equally important, unavoidable through quantum physics: Why does the world look different depending on when and how I look at it? Related to the “hard problem”: How can I have coherent experiences that are different from someone else’s? Why am I me and not you? Also: What is an observer? What is existence? Do we live in a simulation? What are numbers? Does infinity exist? Am I a Boltzmann brain? Is reality fundamentally discrete or a continuum? What is THIS? And why, just WHY? But also; how? 4 The answer is surprisingly simple and requires no hidden magic. It might seem vague and opaque at first and will require quite a lot of explanation to make sense. The two main questions about the absolute and subjective are actually the same question, since you are not separate from reality—you are your most immediate experience of it. Understanding reality includes understanding yourself. For some people, an incomplete understanding can cause an existential crisis. Full understanding will be a relief, but it might take some time and effort to get there. That said, I am certain that the benefits outweigh the risk of getting stuck—on average, not individually. Keep in mind that however you see the world, you and the world didn’t change, only your view of it. If you, so far, have been able to navigate your life blindfolded, you will also be able to do it seeing. It’s okay if you don’t understand what I’m writing about. This text is aimed at the very small group of people who are almost there. I hope that it will help enough people to make the shift so that we can work collectively at filling in the details and making it more accessible. Deconstructing Why Does Anything Exist? The accepted scientific world view posits that our world is purely physical. Some physicists propose that physics consists entirely of mathematical structures. Set theory can explain all mathematical structures and can itself be constructed from the empty set—a collection without content. If we accept this, then it isn’t too far of a leap to conceive of everything that exists as variations of a reality that can only be left undefined. This does not mean that “nothing exists,” but that no thing exists independently. Every thing exists dependent on others. To be a thing is the combination of relations (relations also being things). It is hard to find an answer to the question “Why is there something rather than nothing?” because it contains a false assumption—that something and nothing are different. The whole problem evaporates when one realizes that nothing and everything are the same. Existence is no different from non-existence. Nothingness is not the absence of things; it’s the absence of differentiation, the superposition of all things. Without differentiation, everything is equivalent to everything else; there is only symmetry. To pick out any part of a symmetry is to constrain the perspective and introduce asymmetry. Those perspectives, or frames of reference, are what we call phenomena, observations, universes, moments. Structure emerges through how perspectives are related to each other. Every perspective builds on others and introduces additional constraints. Everything that can be solely defined through constraints is possible . Everything that is possible does exist. 5 In a way, one can conceive of ultimate reality as a fractal object containing all possible constraints on pure symmetry. Any moment of experience is one perspective onto that object. Differentiation is only present as such a view of each individual thing. Each thing includes and sees its own definition but not those of other things. In between the subjective and the absolute, objective reality exists as the consensus (shared definition) of multiple subjective experiences (individuated frames). With this, there is no fundamental layer of reality. When considering all pos- sible observations of reality, there is no content left other than observations. Observations, in turn, only describe their relationship to all other observations. Everything is empty of inherent existence and full of dependent existence. With- out a fundamental layer, the reductionist approach breaks down. No layer of reality is more real than any other. There is no ontological hierarchy, no up or down. Sooner or later we come to realize that perhaps the most fundamental, and most fundamentally important, fact about any experience is that it depends on the way of looking. That is to say, it is empty. Other than what we can perceive through different ways of looking, there is no ‘objective reality’ existing independently; and there is no way of looking that reveals some ‘objective reality’. — Rob Burbea, Seeing That Frees: Meditations on Emptiness and Dependent Arising In a way, this isn’t new. Similar ideas can be found as Dao in Taoism, in the Buddhist concepts of Prat ̄ ıtyasamutp ̄ ada (dependent arising) and Ś ̄ unyat ̄ a (emptiness)—especially since N ̄ ag ̄ arjuna and in the later Huáyán school. Mystics of probably all traditions talk about realizations like this on several levels of depth. Also, further developments like Nishida Kitar ̄ o’s basho or Rob Burbea’s ways of looking , as quoted above, recontextualize it by bringing together eastern with western philosophy and modern scientific insights. Several modern theories uncover aspects of it. For example, Ontic Structural Realism, the Zero Ontology of David Pearce, and the related zero-energy universe hypothesis, what James Cooke calls “non-dual naturalism,” the many-worlds interpretation of quantum mechanics, relational quantum mechanics, QBism, Wheeler’s participatory universe, Max Tegmark’s mathematical universe hypoth- esis. It seems to me that we live in a time where more and more people converge on a very similar insight from different directions. There are too many to list, read, or even know about. The main difference between them is the set of assumptions they have not yet let go of. Hopefully, this can be the common thread to show that they use different languages to talk about the same phenomena. Despite all these vaguely similar theories, the idea hasn’t found its way into mainstream discussion yet. For one, it’s hard to shift thinking into this new 6 understanding. It isn’t simply a fact that one could learn in school, but a way of thinking that has to be learned and practiced. Also, these ideas are often separated from practical and measurable aspects of the world by a great chasm. Especially the how is missing. By showing the connections between them, it will be possible to draw on previous work and provide a much more comprehensive and robust explanation. Ideally, the resulting story will span from the absolute, over the objective, to the subjective, connecting philosophy, science and spirituality, leaving no gaps along the way. By now I can only provide the framework for this project. I will avoid using specific terminology from these traditions and thinkers. Within and between those, there is already sufficient disagreement on what those terms actually mean. I can’t claim to know what others are talking about. I can only draw the obvious parallels back to what I mean. Be aware that I will use several standard English terms with a very specific, but broad, meaning that may only become clear once you understand what I’m talking about. Also, mind the gap between “every thing”/“no thing” as a quantifier of individual entities and “everything”/“nothing” as a collection or abstract concept. Another way to express the physics side of this text is this quote: Everything we know about fundamental physics may be summarized by the statement: “Nature doesn’t care about coordinate systems.” Indeed, rather remarkably, all of our most foundational theories of physics appear to have (essentially) no content *apart* from this statement. — Jonathan Gorard on X What is Fundamental? Every theory is based on assumptions (or, synonymously, axioms). These are statements that cannot be proven from within the theory but are accepted or assumed to be true. If we question these assumptions and require that they be justified and explained, then we—simply by the act of questioning—cannot be left with any unexplained assumptions. What remains cannot be questioned further, nor can it be justified or explained further. Not even a tautology. Such a theory would be groundless, though it’s questionable whether the term “theory” should still apply. As soon as we can explain some phenomena in terms of other phenomena, then a hierarchy is implied, denoting some objects as more fundamental (and therefore more “real”) than those they constitute. Your body is made of organs, which are made of cells, molecules, atoms, subatomic particles, and the elementary particles of the standard model, which are actually just fields—and that’s how far we’ve gotten so far. Fields are mathematical descriptions. The discussion 7 then is: does the math just describe something more fundamental, or are they math? Let’s start with the realization that, apparently, every thing can be ex- plained—usually in terms of smaller things. At least that’s the experience scientific investigation made so far. Whenever a fundamental, indivisible substance or mechanism was proposed, we later found an explanation and smaller parts. Should we update this all the way, and if so, what would that look like? There are a few possible answers: • Dogmatic - There is a fundamental building block or substance. We just haven’t found it yet. • Regressive - It’s turtles all the way down. There is no end to deconstruct- ing. • Circular - At some point, we end up where we began. These are known as the Münchhausen trilemma because, according to common logic, we can’t pull ourselves out of the mud by our own hair, like Baron Münchhausen did. We have to stand on some ground. However, this is like saying the earth under your feet has to be placed on some immovable bedrock layer, because everything else would be absurd. We know that reality is absurd under this logic, as the Earth floats in space, supporting its structure by counteracting forces balancing each other out. Therefore, let’s add a fourth option: • Groundless - Everything exists because symmetric counterparts cancel out the need to justify its existence. All phenomena are dependently arising. Infinite regress and circularity are usually dismissed as absurd, which leaves dogmatism and groundlessness. Before we take a look at the groundless, let’s see why the dogmatic argument doesn’t make sense either. The history of Western philosophy is to a large extent an attempt to provide an answer to the question as to what is fundamental. It is a search for the point of departure from which everything else follows: matter, God, the spirit, the atoms and the void, Platonic Forms, a priori forms of intuition, the subject, Absolute Spirit, elementary moments of consciousness, phenomena, energy, experience, sensations, language, verifiable propositions, scientific data, falsifiable theories, the existence of the being for whom being matters, hermeneutic circles, structures . A long list of candidates, not one of which ever managed to achieve a universal acceptance as ultimate foundation. — Carlo Rovelli, Helgoland The idea of a fundamental layer of reality is an assumption that has to be filled with an answer to what that layer should be. Yet by the vary nature of assuming something as fundamental, one doesn’t and can’t explain it. The process might often be the reverse: we can’t explain X, so it must be fundamental. Many great minds fall in love with the things they can’t explain. They awe in the mystery, 8 and instead of deconstructing it, they build upon that one idea, obscuring it even further. To tackle the question of fundamental building blocks, one has to be able to let go of every idea and worldview. For everything that is called “fundamental,” we can ask: What is it made of? Why does it have the properties it has? Why is it this particular thing and not something else? Is it possible to define it? If so, can you deconstruct the definition? Is it possible to define other fundamental objects? If the thing in question is truly fundamental, then it must be possible to answer these questions from within itself, with no outside reference. Yet, all these questions could be rephrased as “Why is this theory true and not another theory?” It cannot be answered from within that theory, because the theory cannot make statements outside its own assumptions. Even if a theory were consistent and complete, with a limited view, we could not know if another theory exists that is also consistent and complete, nor could we decide between them. That’s assuming an ideal case, but Gödel proved that every system has to be inconsistent or incomplete. So we don’t even get that. Within the hypothesis of “there has to be something fundamental,” we can never find a satisfying answer. It takes some courage to abandon all assumptions and beliefs. But when we do so, what remains is sufficient as a starting point. Foundations of Mathematics All mathematical structures can be described as sets. Set theory is, therefore, one way to talk about the foundations of mathematics . However, this statement is slightly circular since, with the advent of set theory, edge cases have been discovered that certain variants of set theory cannot address. According to standard (ZF) set theory, recursive sets don’t exist. The need for this restriction arose due to Gödel’s incompleteness theorems and Russell’s paradox, which will be discussed in the following sections. So, what are sets? A set is formed by the grouping together of single objects into a whole. A set is a plurality thought of as a unit. — Felix Hausdorff This description is especially useful here because it does not affirm sets as things on their own. It’s by merely thinking of a plurality as a unit that it is a set. To be precise, thinking is not required—just by the potential of drawing a boundary and grouping together, there is a set. For example, the integers from 0 to 5 form a set {0, 1, 2, 3, 4, 5} , and so do all mythical creatures. To formalize set theory and avoid paradoxes, axioms have been formulated. The most widely accepted axiomatic system is the Zermelo–Fraenkel set theory (ZF, 9 with 8 axioms, or ZFC with the addition of the axiom of choice). The selection of these axioms allows for the construction of all permitted sets, starting only with the empty set. These axioms still present assumptions, chosen for functionality. This can be seen in the debate over whether to include the axiom of choice. Other axioms are also challenged, particularly the axiom of foundation, which excludes sets that contain themselves as members (or any kind of infinite regress). By this axiom, x = {x} is not a valid set. This restriction allows axiomatic set theory to avoid paradoxes but comes at the cost of limiting what it can talk about. Set theory allows us to start from an empty set {} —a group without objects—and define all mathematical objects. Yet, there is no single way to do it. The natural numbers can be expressed as: {} = Ø {{}} = {Ø} = 1 {{}{{}}} = {Ø, 1} = 2 {{}{{}}{{}{{}}}} = {Ø, 1, 2} = 3 or: {} = Ø {{}} = {Ø} = 1 {{{}}} = {1} = 2 {{{{}}}} = {2} = 3 or several other ways. What gives identity to the natural numbers is not the sets that define them but their relationships. Sets can be constructed in a way that exhibits those relationships. This implies that the sets themselves are a language needed to talk about the structure; they are not the structure itself. Consequently, other ways exist to discuss the foundations of mathematics that are not based on sets. Most prominently, category theory describes all structures in their relations to other structures. The core insight here is that every mathematical structure can be constructed from simpler structures and that ultimately, there is no smallest or initial element (urelement), no substance needed. What is left unexplained is the set of axioms. Gödel’s Incompleteness The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot prove that the system itself is consistent (assuming it is indeed consistent). — Stanford Encyclopedia of Philosophy 10 This is a negative result in the sense that it shows us what cannot exist. Related theorems have been proven in other areas, such as computational complexity. It represents a hard limit on reality and on what we can know. It says that reality cannot be a formal system that is both complete and consistent. Of these three requirements, at least one does not hold. Truth in a mathematical system is what can be derived from that system. Gödel shows that there are statements that are true for that system but cannot be derived from it. This, however, does not mean that they are universally true, but rather that no formal system can prove all true statements because it assumes statements to be true which it cannot prove. Since no formal system can give us the perfect answer for what is true, truth is always dependent on the system used. What is true or not depends on the assumptions that have been made. No single axiomatic system can describe reality perfectly. So what if we simply accept this and realize that truth and reality are entirely dependent on our assumptions? The way we see reality is shaped by the glasses we put on. Without a formal system and no axioms (no glasses), reality may be consistent and complete, but we cannot make any statements about it—maybe not even that it is consistent and complete. Reality without constraints has no properties. Any formal system, and therefore any theory, contains assumptions that lack justification outside that theory. What is “true” in one theory may be “false” in another. The concept of true or false itself is therefore dependent on assumptions. Without assumptions, even the distinction between true and false falls away. All models are wrong. Some are useful. — George Box With Gödel’s proof, we must accept that no theory can describe ultimate reality. We, however, consider theories that describe our world better as more true. Math can be so abstract that it has no representation in our physical world. So much so that some physicists deny the existence of mathematical concepts that can’t exist in our physical universe, like infinities. Related is the idea that computation is fundamental to reality, and not math. If we accept, however, that the purpose of math is not to describe only our universe but every possible one, then the perspective changes. Infinities may not exist inside our local universe, but they exist outside it. Conversely, this has a secondary effect. We can no longer discriminate between different theories of math by how well they describe our universe. Instead, there are different models that describe different universes; none of them is fundamentally more true than the others. The model of math one uses then just depends on the particular problem one is working on. 11 Set-Theoretic Multiverse Gödel’s incompleteness proofs show that every (non-trivial) formal system has true statements that cannot be proven from within that system. Related to this is the discovery that there are statements that cannot be decided to be true or false from within a system. A prime example of this is the continuum hypothesis (CH). George Cantor observed that he could not put the infinite set of natural numbers in a one-to-one correspondence with the infinite set of real numbers. This showed that there are at least two sizes (cardinalities) of infinity. The continuum hypothesis asks whether there is a cardinality of infinity in between those of the natural and real numbers. It turns out that this question cannot be decided in ZF. Assuming it to be true gives one branch of math; assuming it to be false gives another, incompatible branch of math. Following this result, many similar statements have been found that simply are undecidable. The CH and others could be added as new axioms to ZF, but deciding this would always carry some sense of arbitrariness. On the other hand, the already accepted axioms can also be called into question. Any axiom that is introduced both constrains the possible math that can be explored and provides a foundation upon which math can build. Joel David Hamkins takes the position that we should simply accept and explore this set-theoretic multiverse. While he does not relate it to the physical multiverse, I think there is the same principle at work. Russell’s Paradox According to the unrestricted comprehension principle, for any suf- ficiently well-defined property, there is the set of all and only the objects that have that property. Let R be the set of all sets that are not members of themselves. (This set is sometimes called “the Russell set”.) If R is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell’s paradox. Wikipedia on Russell’s paradox The “unrestricted comprehension principle” is what I previously described as: “Just by the potentiality to draw a boundary and group things together, a set exists.” This is what was later called “naive” set theory, to distinguish it from axiomatic set theory. What Russell pointed out is that if this principle holds true, then one could create a set of all sets that do not contain themselves—but this leads to the above paradox. In ZF set theory, this paradox is avoided by only permitting sets that are not 12 members of themselves (the axiom of foundation). Let’s consider a thought experiment from the opposite perspective. Suppose we only permit sets that do contain themselves. In this system, x = {x, y} is permitted, while x = {y} is not. By this logic, the “set of all sets that are not members of themselves” has no elements—i.e., it is the empty set. We can also adopt a meta-perspective that includes both approaches. From this view, the Russell set is both empty and contains every other set. An apparent paradox, but we can make sense of it if we reconsider what the empty set actually is. We said that sets can be thought of as collections of objects. Then, what is a collection without objects? {} Let’s have a closer look: { } A boundary drawn around nothing. At the very beginning, we haven’t con- structed any other sets yet. So there is really nothing inside or outside the empty set. Let’s be clear about this: absolutely nothing means no space, no universe, no math, no observer, no set—there is nothing that this boundary could separate. The boundary itself is not a thing; it’s not even the assertion that nothing exists. It’s a separation with nothing to separate. “Inside” and “outside” the set are both nothing. There is no difference between inside and outside. What the set indicates is: There is nothing, and within that nothing, there is still nothing. The empty set is within nothing and contains nothing. This means the empty set is recursive With no axioms in place that prevent an empty, recursive set from existing, the set is already present without a cause. It creates itself out of unconstrained potentiality. When the empty set is recursive, then we can iterate over it, inserting the empty set into every instance of the empty set. {} {{}} {{}{{}}} {{}{{}}{{}{{}}}} These iterations are the same as the definition of the natural numbers from above. Each of those sets contains the empty set and is itself an instance of the empty set. We don’t need to stop there; we can see every set as a particular, constrained perspective of the empty set. Conversely, every set we can describe does contain 13 the empty set. Because this goes two ways, every set described this way does contain itself. The empty set contains all sets and is empty nonetheless. In this view, the set containing all sets, the Russell Set, and the empty set are all the same (V = R = {}). It’s a single fractal containing all mathematical structures. Russell’s paradox is no longer paradoxical. We achieved this by redefining differences between sets as differences in perspective. The multitude of all sets has become one emptiness with multiple ways to view this emptiness. Note that along the way, we already made at least one subtle assumption: that there is a binary contrast between existence and non-existence. Even this one will be dropped later. Russell’s paradox is paradoxical because it makes conflicting assumptions. The standard solution is to only consider those cases that are not paradoxical—that is, to limit the view (via the axiom of foundation). Another way out is to find, recognize, and drop the hidden assumption. All paradoxes point to a conflict in assumptions and can always be resolved by letting go of those assumptions. Superposition of views Russell’s paradox was resolved in the previous thought experiment because we took a superposition of all possible sets. We can drop into any particular set with our perspective but are not confined to it. This process can be described for two options as one original state 0 which contains, but is undecided about, L and R , where either excludes the other. When we constrain our view to (take the perspective of) L being true, then R is false, and vice versa. This gives us four possible ways of viewing the situation: • L is true • R is true • L & R : both are true • 0 : neither is true This fourfold view is called catus . kot .i or tetralemma . It is affirmation, negation, both, or neither. This contrasts with mainstream Western philosophy, where the law of excluded middle (either true or false, with nothing in between) is foundational to logic. However, this law of excluded middle is also just an assumption that has to be justified. To think of a justification, you have to think outside of it, taking all possible options into account. N ̄ ag ̄ arjuna, a circa 200 CE Buddhist philosopher, adds a fifth option, which is a viewless view, or openness to views—the middle way. It does not cling to any of the options as the only right one but sees all truth claims as insubstantial. The point of this kind of logic is explicitly not to establish a fixed dogma of how things really are. N ̄ ag ̄ arjuna, like Gödel, uses logic to expose the limits and vacuity of logic. Neither from itself nor from another, Nor from both, 14 Nor without a cause, Does anything whatever, anywhere arise. Chapter 1, verse 1 N ̄ ag ̄ arjuna’s M ̄ ulamadhyamakak ̄ arik ̄ a , translation by Jay L. Garfield As established above, any mathematical object can be described as nested sets, ultimately made up of, and presenting a perspective on, the empty set. That is, we could say that any object is empty. The information to describe or locate that object or perspective, however, is equivalent to that object and not reducible. That is, it exist entirely on it’s own. A third view is, that the object in isolation could not described to have any properties, it is only in relation to other objects that it can be said to exhibit properties—its existence is entirely other-dependent. Assuming any of these views as the ultimate truth would exclude the others, but we have no objective way of deciding between them. The best we can do is to not decide, but to use them only provisionally. Even the realization that all phenomena are empty of inherent existence, is only a provisional truth. “Empty” should not be asserted. “Nonempty” should not be asserted. Neither both nor neither should be asserted. They are only used nominally. Chapter 22, verse 11 Many Worlds It doesn’t stop there. In quantum logic, all combinations of amplitudes for L and R are possible. There are not only four but an infinite number of possible values. Yet, when the state is measured, only one of the options is realized. The probability of measuring either outcome is given by the square of the amplitudes (the Born rule). This leads to the question: What is an “observation” in quantum mechanics? The double-slit experiment introduced a problem into physics that sparked many interpretations but no consensus. Before measurement, the particle behaves like a wave of probability, interacting with itself. After measurement, it seems as if a particle was observed at a single location, determined by the previous probability. So, what is a “measurement”? Does observation influence reality? Where and when does “observing” happen, and who or what is observing? The question becomes even more pressing when we add the problem of non-locality through entanglement into the picture. Luckily, the many-worlds interpretation (MWI) allows us to make sense of this without the need to invoke a new fundamentally unexplained process or entity. When Hugh Everett first proposed the solution, he called it “Relative State Formulation of Quantum Mechanics” or later “The Theory of The Universal Wave Function”. The term “Many Worlds” came with a later reinterpretation and, while catchy, sometimes leads to confusion. There is no need to assume 15 that new worlds pop into existence each time we measure. On the contrary, Everett’s interpretation is very conservative, as it does not propose any entities apart from the wave function it tries to explain. The wave function does not change with measurement, but our view of it. All possible outcomes are already present in the wave function before measure- ment. It’s a superposition of possible worlds. To measure means to interact with the wave function. This interaction constrains what worlds are accessible from the observers perspective. It introduces more certainty about any particular per- spective, but without anything to choose the outcome, any possible perspective is realized. While several other interpretations of QM require hidden information or randomness to be fundamental, in MW randomness is a perceptual artifact. The chain of events only appears random from the point of view of an observer. In other words, every world is one possible view on the wave function. Like the empty recursive set, the universal wave function already contains all possible perspectives. To take one perspective is to constrain the view. The Fiction of Everyday Experience When you take any object, say your hand, you can look at it from different angles. There is no preferred angle that is more true to representing the hand than the others. Because of your experience, you have a mental model of what your hand looks like. But if you are truly honest with yourself, then looking at the hand from one side, the other side is a fiction, no matter how you turn it. To fully see your hand as it truly is, you would have to see it from all possible perspectives at once. There is also no uniquely true shape of the hand. If you make a fist, point at something, or relax it, those shapes always depend on conditions. Then there is the question of where the han