Steve Patterson

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  • Our Present Dark Age, Part 1

    For the last fifteen years, I’ve been researching a wide range of subjects. Full-time for the last seven years. I’ve traveled the world to interview intellectuals for my podcast, but most of my research has been in private. After careful examination, I have come to the conclusion that we’ve been living in a dark age since at least the early 20th century. 

    Our present dark age encompasses all domains, from philosophy to political theory, to biology, statistics, psychology, medicine, physics, and even the sacred domain of mathematics. Low-quality ideas have become common knowledge, situated within fuzzy paradigms. Innumerable ideas which are assumed to be rigorous are often embarrassingly wrong and utilize concepts that an intelligent teenager could recognize as dubious. For example, the Copenhagen interpretation in physics is not only wrong, it’s aggressively irrational—enough to damn its supporters throughout the 20th century.

    Whether it’s the Copenhagen interpretation, Cantor’s diagonal argument, or modern medical practices, the story looks the same: shockingly bad ideas become orthodoxy, and once established, the social and psychological costs of questioning the orthodoxy are sufficiently high to dissuade most people from re-examination.

    This article is the first of an indefinite series that will examine the breadth and depth of our present dark age.  For years, I have been planning on writing a book on this topic, but the more I study, the more examples I find. The scandals have become a never-ending list. So, rather than indefinitely accumulate more information, I’ve decided to start writing now.

    Darkness Everywhere

    By a “dark age”, I do not mean that all modern beliefs are false. The earth is indeed round.  Instead, I mean that all of our structures of knowledge are plagued by errors, at all levels, from the trivial to the profound, periphery to the fundamental. Nothing that you’ve been taught can be believed because you were taught it. Nothing can be believed because others believe it. No idea is trustworthy because it’s written in a textbook.

    The process that results in the production of knowledge in textbooks is flawed, because the methodology employed by intellectuals is not sufficiently rigorous to generate high-quality ideas. The epistemic standards of the 20th century were not high enough to overcome social, psychological, and political entropy. Our academy has failed. 

    At present, I have more than sixty-five specific examples that vary in complexity. Some ideas, like the Copenhagen interpretation, have entire books written about them, and researchers could spend decades understanding their full history and significance. The global reaction to COVID-19 is another example that will be written about for centuries. Other ideas, like specific medical practices, are less complex, though the level of error still suggests a dark age. 

    Of course, I cannot claim this is true in literally every domain, since I have not researched every domain. However, my studies have been quite broad, and the patterns are undeniable. Now when I research a new field, I am able to accurately predict where the scandalous assumptions lie within a short period of time, due to recognizable patterns of argument and predictable social dynamics. 

    Occasionally, I will find a scholar that has done enough critical thinking and historical research to discover that the ideas he was taught in school are wrong. Usually, these people end up thinking they have discovered uniquely scandalous errors in the history of science. The rogue medical researcher that examines the origins of the lipid hypothesis, or the mathematician that wonders about set theory, or the biologist that investigates fundamental problems with lab rats—they’ll discover critical errors in their discipline but think they are isolated events. I’m sorry to say, they are not isolated events. They are the norm, no matter how basic the conceptual error.

    Despite the ubiquity of our dark age, there have been bright spots. The progress of engineers cannot be denied, though it’s a mistake to conflate the progress of scientists with the progress of engineers. There have been high-quality dissenters. Despite being dismissed as crackpots and crazies by their contemporaries, their arguments are often superior to the orthodoxies they criticize, and I suspect history will be kind to these skeptics. 

    Due to recent events and the proliferation of alternative information channels, I believe we are exiting the dark age into a new Renaissance. Eventually, enough individuals will realize the severity of the problems with existing orthodoxies and the systemic problems with the academy, and they will embark on their own intellectual adventures. The internet has made possible a new life of the mind, and it’s unleashing pent-up intellectual energies around the world that will bring illumination to our present situation, in addition to creating the new paradigms that we desperately need.

    Why Did This Happen?

    It will take years to go through all of the examples, but before examining the specifics, it’s helpful to see the big picture. Here’s my best explanation for why we ended up in a dark age, summarized into six points:

    1. Intellectuals have greatly underestimated the complexity of the world.

    The success of early science gave us false hope that the world is simple. Laboratory experiments are great for identifying simple structures and relationships, but they aren’t great for describing the world outside of the laboratory. Modern intellectuals are too zoomed-in in their analyses and theories. They do not see how interconnected the world is nor how many domains one has to research in order to gain competence. For example, you simply cannot have a rigorous understanding of political theory without studying economics. Nor can you understand physics without thinking about philosophy. Yet, almost nobody has interdisciplinary knowledge or skill.  

    Even within a single domain like medicine, competence requires a broad exposure to concepts. Being too-zoomed-in has resulted in a bunch of medical professionals that don’t understand basic nutrition, immunologists that know nothing of virology, surgeons that unnecessarily remove organs, dentists that poison their patients, and doctors that prolong injury by prescribing anti-inflammatory drugs and harm their patients through frivolous antibiotic usage. The medical establishment has greatly underestimated the complexity of biological systems, and due to this oversimplification, they yank levers that end up causing more harm than good. The same is true for the economists and politicians who believe they can centrally plan economies. They greatly underestimate the complexity of economic systems and end up causing more harm than good. That’s the standard pattern across all disciplines.

    2. Specialization has made people stupid.

    Modern specialization has become so extreme that it’s akin to a mental handicap. Contemporary minds are only able to think about a couple of variables at the same time and do not entertain variables outside of their domain of training. While this myopia works, and is even encouraged, within the academy, it doesn’t work for understanding the real world. The world does not respect our intellectual divisions of labor, and ideas do not stay confined to their taxonomies. 

    A competent political theorist must have a good model of human psychology. A competent psychologist must be comfortable with philosophy. Philosophers, if they want to understand the broader world, must grasp economic principles. And so on. The complexity of the world makes it impossible for specialized knowledge to be sufficient to build accurate models of reality. We need both special and general knowledge across a multitude of domains.

    When encountering fundamental concepts and assumptions within their own discipline, specialists will often outsource their thinking altogether and say things like “Those kinds of questions are for the philosophers.” They are content leaving the most important concepts to be handled by other people. Unfortunately, since competent philosophers are almost nowhere to be found, the most essential concepts are rarely examined with scrutiny. So, the specialist ends up with ideas that are often inferior to the uneducated, since uneducated folks tend to have more generalist models of the world.

    Specialization fractures knowledge into many different pieces, and in our present dark age, almost nobody has tried to put the pieces back together. Contrary to popular opinion, it does not take specialized knowledge or training to comment on the big-picture or see conceptual errors within a discipline. In fact, a lack of training can be an advantage for seeing things from a fresh perspective. The greatest blindspots of specialists are caused by the uniformity of their formal education.

    The balance between generalists and specialists is mirrored by the balance between experimenters and theorists. The 20th century had an enormous lack of competent theorists, who are often considered unnecessary or “too philosophical.” Theorists, like generalists, are able to synthesize knowledge into a coherent picture and are absolutely essential for putting fractured pieces of knowledge back together.

    3. The lack of conceptual clarity in mathematics and physics has caused a lack of conceptual clarity everywhere else. These disciplines underwent foundational crises in the early 20th century that were not resolved correctly.

    The world of ideas is hierarchical; some ideas are categorically more important than others. The industry of ideas is also hierarchical; some intellectuals are categorically more important than others. In our contemporary paradigm, mathematics and physics are considered the most important domains, and mathematicians and physicists are considered the most intelligent thinkers. Therefore, when these disciplines underwent foundational crises, it had a devastating effect upon the entire world of ideas. The foundational notion of a knowable reality came into serious doubt.

    In physics, the Copenhagen interpretation claimed that there is no world outside of observation—that it doesn’t even make sense to talk about reality-in-some-state separate from our observations. When the philosophers disagreed, their word was pitted against the word of physicists. In the academic hierarchy, physicists occupy a higher spot than philosophers, so it became fashionable to deny the existence of independent reality. More importantly, within the minds of intellectuals, even if they naively believe in the existence of a measurement-independent world, upon hearing that prestigious physicists disagree, most people end up conforming to the ideas of physicists who they believe are more intelligent than themselves. 

    In mathematics, the discovery of non-Euclidean geometries undermined a foundation that was built upon for two thousand years. Euclid was often assumed to be a priori true, despite the high-quality criticisms leveled at Euclid for thousands of years. If Euclid is not the rock-solid foundation of mathematics, what is? In the early 1900’s, some people claimed the foundation was logic (and they were correct). Others claimed there is no foundation at all or that mathematics is meaningless because it’s merely the manipulation of symbols according to arbitrary rules.

    David Hilbert was a German mathematician that tried to unify all of mathematics under a finite set of axioms. According to the orthodox story, Kurt Godel showed in his famous incompleteness theorems that such a project was impossible. Worse than impossible, actually. He supposedly showed that any attempt to formalize mathematics within an axiomatic system would either be incomplete (meaning some mathematical truths cannot be proven), or if complete, the system becomes inconsistent (meaning they contain a logical contradiction). The impact of these theorems cannot be overstated, both within mathematics and outside of it. Intellectuals have been abusing Godel’s theorems for a century, invoking them to make all kinds of anti-rational arguments. Inescapable contradictions in mathematics would indeed be devastating, because after all, if you cannot have conceptual clarity and certainty in mathematics, what hope is there for other disciplines? 

    Due to the importance of physics and mathematics, and the influence of physicists and mathematicians, the epistemic standards of the 20th century were severely damaged by these foundational crises. The rise of logical positivism, relativism, and even scientism can be connected to these irrationalist paradigms, which often serve as justification for abandoning the notion of truth altogether. 

    4. The methods of scientific inquiry have been conflated with the processes of academia.

    What is science? In our current paradigm, science is what scientists do. Science is what trained people in lab coats do at universities according to established practices. Science is what’s published in scientific journals after going through the formal peer review process. Good science is what wins awards that science gives out. In other words, science is now equivalent to the rituals of academia.

    Real empirical inquiry has been replaced by conformity to bureaucratic procedures. If a scientific paper has checked off all the boxes of academic formalism, it is considered true science, regardless of the intellectual quality of the paper. Real peer review has been replaced by formal peer review—a religious ritual that is supposed to improve the quality of academic literature, despite all evidence to the contrary. The academic publishing system has obviously become dominated by petty and capricious gatekeepers. With the invention of the internet, it’s probably unnecessary altogether.

    “Following standard scientific procedure” sounds great unless it’s revealed that the procedures are mistaken. “Peer review” sounds great, unless your peers are incompetent. Upon careful review of many different disciplines, the scientific record demonstrates that “standard practice” is indeed insufficient to yield reliable knowledge, and chances are, your scientific peers are actually incompetent.

    5. Academia has been corrupted by government and corporate funding.

    Over the 20th century, the amount of money flowing into academia has exploded and degraded the quality of the institution. Academics are incentivized to spend their time chasing government grants rather than researching. The institutional hierarchy has been skewed to favor the best grant-winners rather than the best thinkers. Universities enjoy bloated budgets, both from direct state funding and from government-subsidized student loans. As with any other government intervention, subsidies cause huge distortions to incentive structures and always increase corruption.  Public money has sufficiently politicized the academy to fully eliminate the separation of Science and state.

    Corporate-sponsored research is also corrupt. Companies pay researchers to find whatever conclusion benefits the company. The worst combination happens when the government works with the academy and corporations on projects, like the COVID-19 vaccine rollout. The amount of incompetence and corruption is staggering and will be written about for centuries or more.

    In the past ten years, the politicization of academia has become apparent, but it has been building since the end of WWII. We are currently seeing the result of far-left political organizing within the academy that has affected even the natural sciences. Despite being openly hostile to critical thinking, they have successfully suppressed discussion within the institution that’s supposed to exist to pursue truth—a clear and inexcusable structural failure.

    6. Human biology, psychology, and social dynamics make critical thinking difficult.

    Nature does not endow us with great critical thinking skills from birth. From what I can tell, most people are stuck in a developmental stage prior to critical thinking, where social and psychological factors are the ultimate reason for their ideas. Gaining popularity and social acceptance are usually higher goals than figuring out the truth, especially if the truth is unpopular. Therefore, the real causes for error are often socio-psychological, not intellectual—an absence of reasoning rather than a mistake of reasoning. Before reaching the stage of true critical thinking, most people’s thought processes are stunted by issues like insecurity, jealousy, fear, arrogance, groupthink, and cowardice. It takes a large, never-ending commitment to self-development to combat these flaws.

    Rather than grapple with difficult concepts, nearly every modern intellectual is trying to avoid embarrassment for themselves and for their social class. They are trying to maintain their relative position in a social hierarchy that is constructed around orthodoxies. They adhere to these orthodoxies, not because they thought the ideas through, but because they cannot bear the social cost of disagreement. 

    The greater the conceptual blunder within an orthodoxy, the greater the embarrassment to the intellectual class that supported it; hence, few people will stick their necks out to correct serious errors. Of course, few people even entertain the idea that great minds make elementary blunders in the first place, so there’s a low chance most intellectuals even realize the assumptions of their discipline or practice are wrong.

    Not even supposed mathematical “proofs” are immune from social and psychological pressures. For example, Godel’s incompleteness theorems are not even considered a thing skepticism can be applied to; they are treated as a priori truths to mathematicians (which looks absurd to anybody who has actually examined the philosophical assumptions underpinning modern mathematics.) 

    Individuals who consider themselves part of the “smart person club”—that is, those that self-describe as intellectuals and are often part of the academy—have a difficult time admitting errors in their own ideology. But they have an exceptionally difficult time admitting error by “great minds” of the past, due to group dynamics. It’s one thing to admit that you don’t understand quantum mechanics; it’s an entirely different thing to claim Niels Bohr did not understand quantum mechanics. The former admission can actually gain you prestige within the physics club; the latter will get you ostracized.

    All fields of thought are under constant threat of being captured by superficial “consensus” by those who are seeking to be part of an authoritative group. These people tend to have superior social/manipulative skills, are better at communicating with the general public, and are willing to attack any critics as if their lives depended on it—for understandable reasons, since the benefits of social prestige are indeed on the line when sacred assumptions are being challenged.

    If this analysis is correct, then the least examined ideas are likely to be the most fundamental, have the greatest conceptual errors, and have been established the longest. The longer the orthodoxy exists, the higher the cost of revision, potentially costing an entire class their relative social position. If, for example, the notion of the “completed infinity” in mathematics turns out to be bunk, or the cons of vaccination outweigh the benefits, or the science of global warming is revealed to be corrupt, the social hierarchy will be upended, and the status of many intellectuals will be permanently damaged. Some might end up tarred and feathered. With this perspective, it’s not surprising that ridiculous dogmas can often take centuries or even millennia to correct.

    Speculation and Conclusion

    In addition to the previous six points, I have a few other suspicions that I’m less confident of, but am currently researching:

    1. Physical health might have declined over the 20th century due to reduced food quality, forgotten nutritional knowledge, and increased pesticides and pollutants in the environment. Industrialization created huge quantities of food at the expense of quality. Perhaps our dark age is partially caused by an overall reduction in brain function.

    2. New communications technology, starting with the radio, might have helped proliferate bad ideas, amplified their negative impact, and increased the social cost of disagreement with the orthodoxy. If true, this would be another unintended consequence of modernization.

    3.  Conspiracy/geopolitics might be a significant factor. Occasionally, malice does look like a better explanation than stupidity.

    In conclusion, the legacy of the 20th century is not an impressive one, and I do not currently have evidence that it was an era of great minds or even good ideas. But don’t take my word for it; the evidence will be supplied here over the coming years. If we are indeed in a dark age, then the first step towards leaving it is recognizing that we’ve been in one.

  • Coming Around to Platonism

    I’ve become persuaded by a version of Platonism. The universe seems to be composed of concrete and abstract things, and the abstract things seem to exist separate from our individual minds. 

    For years, I’ve been making anti-Platonist arguments. One of my most popular articles, “No, Chairs Do Not Exist” sketches out a conceptualist position, which claims that the famous “chair-ness” of Plato isn’t an ethereal Platonic form, but rather, it’s conceptual criteria situated in our own minds. It seemed to me that all abstract stuff was situated in the mind. But now I think conceptualism is incorrect – or at least incomplete. 

    This change of mind happened since coming up with my theory of indirect interaction, which allows objects in multiple ontological categories to effectively interact with each other. If there is a distinct mental and physical realm, then perhaps there’s a Platonic one as well.

    So, for the past couple of years, I’ve been playing devil’s advocate with myself, and to my horror, the devil eventually persuaded me. I now think some kind of Platonism is a better theory to explain how the universe operates. Abstract things seem to be as fundamental as concrete things. Not only might chairs exist, but chair-ness probably does as well. 

    Seeing What You Can’t See

    Let’s begin by calling abstract things “abstracta” for simplicity.

    First of all, it’s hard to understand what abstracta are because you can’t point to them. They’re hard to clearly reference since they don’t look like anything. They don’t take up space. So, we have to be content understanding the concept without directly observing what it references. I’ll try to illustrate the idea, then re-phrase it several different ways from several different angles.

    Abstracta are things like patterns, connections, and most importantly, relations. Any metaphysical theory needs to explain the existence of objects and their behavior across time, and it turns out, relations are essential to explaining the behavior of objects.

    (Note: for idealists reading this article, you can substitute the word “objects” for “areas of experience,” and the argument still holds.)

    The general idea is this: the universe comes bundled together. There are individual objects and concrete things, and there are relations among them. These relations are abstract and independent from our minds. 

    Concrete objects in the world are not isolated from one another. Their states affect each other. Their states are related, and these relationships have a real metaphysical existence.

    Individual objects, by themselves, are not sufficient to explain their own behavior across time. Their behavior is determined in relation to other objects. Were concrete objects completely isolated from one another, then their behavior would be different. Therefore, we have to posit the existence of the concrete objects and their abstract relations.

    We observe that the fundamental building blocks of the physical world – let’s call them “atoms” – get unified into larger objects – meaning, their behavior is different than if those individual atoms existed without any relation to each other. I have previously argued that this unification is done by the mind. Now, I believe the unification is also done by the universe.

    You can think about relationships like glue. Fundamental units of matter are glued together – their states are interrelated – and this relationship exists in addition to the fundamental units. 

    To grasp these abstract relations, it’s helpful to break the physical world down to its most fundamental parts.

    Reducing the Physical World

    Take any physical object, break it apart, and you’ll end up with smaller pieces. Break those pieces apart, and you’ll end up with even smaller pieces. Keep breaking things down, and you’ll eventually end up with atoms and molecules, which you can break apart into subatomic particles, and so on. The key question is this: at some point, do you ever reach indivisible units, or can you keep breaking things down ad infinitum?

    For purposes of this article, let’s say there are indeed fundamental, indivisible units at the bottom of everything. Let’s say we can completely reduce the physical world down to different arrangements of these indivisible units. 

    At this base-level of analysis, there’s a further interesting question: what is the difference between these indivisible units and the space they occupy? What is space, at this level?

    For purposes of this article, let’s posit the following:

    The most fundamental units of the physical world are identical with units of space. They are atoms of space. They don’t “occupy” space; they are space. You can call this theory “geometric atomism.” At the bottom of everything, there are only units of geometric space in particular states. You can think of it like an extremely-fine resolution Minecraft world, where indivisible blocks form all other complex structures. Regular, large-scale atoms like “helium” would be ultimately reducible to a pattern of units of space in a particular state. 

    To keep this model simple, let’s say the geometric atoms can be in only one of two states – on or off, empty or full, 0 or 1. This allows us to represent patterns of atoms as sequences of 0’s and 1’s. For example, empty space might be represented as:


    000000

    000000

    000000

    While an atom of helium might look like:


    000100

    001010

    010100

    Or, a chair might be:

    011010

    101101

    011110, etc.

    You get the idea. Different objects are different patterns of geometric atoms. Since the metaphysics of space is not the subject of this article, we’ll just treat geometric atomism as the model for the physical world that will help illustrate the point about abstracta.

    Parts and Wholes

    In this model, what is a chair? Well at first glance, it appears that a chair is just a pattern of atoms. It isn’t something in addition to the atoms. The whole chair is not greater than the sum of the parts of the chair. The whole is the parts; it’s a shorthand way to reference all the parts. I like the way “mereological nihilists” phrase it: a chair is just “atoms arranged chair-wise.” 

    In this theory, the word “chair” merely references some patch of space which contains a pattern that meets our own conceptual criteria for being labeled as “a chair,” and nothing more. My favorite example of this is constellations. Without any humans, would there be constellations of stars? Would there be a “Big Dipper” that exists in addition to individual stars that compose it? It seems unlikely. While the individual stars have a mind-independent existence, their unification into “The Big Dipper” is something humans do. 

    I’ve previously claimed this unification of parts into wholes is always a mental function, and in the mind-independent world, there would be no unification. But I now see this argument is incomplete. It misses something important: the behavior of atoms across time. The real-world behavior of composite objects implies that the universe unifies parts into wholes, too. Abstract relationships are not all created by the mind; some of them are discovered in the universe.

    Composite Objects and Their Behavior

    Consider a metal spring. Let’s reduce it down to a purely geometric form – a pattern of 1’s and 0’s. As the spring is compressed, the pattern of 1’s and 0’s changes. As the spring returns to its original position, the pattern also returns.

    Notice, when the spring is compressed, it doesn’t fracture into a trillion isolated atoms. The atoms have a particular behavior, and their positions are determined in relation to each other. The 1’s and 0’s change across time depending on the neighboring 1’s and 0’s. The individual atoms alone do not determine their own behavior. They are stuck together in some kind of composite system, with many interrelated parts.

    Critically, these relations are not like the relations of the stars in a constellation. Distant, individual stars do not seem to affect one another’s states. However, the atoms of a spring do affect each others’ states. The universe – not our minds – seems to unify the atoms of a spring into a composite object whose behavior is different than if the individual atoms weren’t unified. 

    A hundred 1’s next to each other behave differently than a hundred isolated 1’s that are unrelated. Therefore, the fundamental units themselves are not sufficient to explain their own behavior.

    While our minds do glue seemingly-unrelated objects together – like the stars in a constellation – the universe also seems to glue things together. This “glue” is a bunch of abstract relationships that exist independent from our minds and take up no physical space themselves.

    Trees, Sticks, Families, Nations

    There seem to be many relationships and connections in the world. A tree’s top and bottom, for example, are related. When the state of the roots changes, the state of the leaves change. Two ends of a stick are related. When one gets pushed down, the other rises up. Families, too, act like composite objects. The state of the husband affects the state of the wife; were they isolated individuals without relations, their states wouldn’t affect each other. 

    Whether or not a set of individuals qualifies as a “family” might be a real metaphysical question: do the states of the individuals affect the states of the others according to the abstract criteria of “family-ness”? If not, then regardless of the last names of those individuals, they are not unified into the composite object known as a “family.” There are billions of people on Earth whose states don’t affect me; I’m not unified into any composite object with them.

    Through this lens, even nations seem to behave like composite objects. The atom of society – the individual human – is affected by the state of others who are glued together into a “nation.” These humans’ lives would be different – for better or worse – if they weren’t glued to each other. Though it doesn’t square nicely with my current libertarian philosophy, factually speaking my state is affected by the state of other people who consider themselves part of the same nation. I find myself part of a larger system, whether I like it or not. The universe seems to be a relational system, and this applies to both physical objects and humans.

    Matter, Form, and Arrangement

    Here’s another way to grasp the abstract. Let’s return to the metal spring example and compare these two statements:

    (1) Springs are just atoms arranged spring-wise.

    (2) Springs are just atoms.

    There’s clearly a difference between these two statements. What is it? What does the first statement convey that the second does not?

    Arrangement. Or, you could say structure, form, or shape. The pattern of atoms. Their states and relationships analyzed together, rather than individually. A spring cannot be described by simply “X number of atoms.” That’s not enough information.  Springs are “X number of atoms arranged in a particular way.”

    To use more traditional language, this is the difference between matter and form. (Well, actually in the context of historical philosophy, “matter” and “form” meant something different, but in contemporary English, these two words convey the correct concepts.) “Matter” is the atoms; “form” is their arrangement. Form is a bundle of abstract relations. We can distinctly reference both matter and form.

    The universe treats form as something in addition to the matter. It’s a unique, relevant feature of the universe that affects how things behave. If the form of the matter changes, its behavior changes. Thus, there is a real metaphysical difference between a trillion atoms-arranged-this-way and a trillion atoms-arranged-that-way. In fact, the difference between physical objects is precisely their atomic arrangement. Geometric structures are the fundamental objects of the physical world.

    Why should units of matter behave differently when they are in different arrangements? I don’t know, but that’s the way the universe seems to operate. We might consider Physics, then, the study of exactly which geometric structures yield which behaviors. 

    Consider the position of an individual atom. We can imagine it has an “absolute position” in space – perhaps identifiable by X, Y, and Z coordinates. But the universe doesn’t seem to care too much about absolute position. Relative position seems to be what matters – an atom’s position in relation to other nearby atoms. It’s changes in relative position that yield different behavior. It’s as if the universe says, “When atoms are arranged this way, then render out this state, and when atoms are arranged that way, render out that state.” 

    It is a mistake to consider objects in the universe as being in a state of radical metaphysical independence. They are not. They are glued together; their states are unified, and unless solipsism is true, it’s not our own minds doing the unification.

    Notice that “relative position” and “relative arrangement” are not themselves concrete objects. They aren’t atoms; they aren’t composed of atoms. They don’t weigh anything or look like anything. They are abstract. Yet, since they seem to be an integral part of the universe’s operation, I think they are both abstract and mind-independent – a metaphysical status I’m calling “Platonic.”

    Chair-ness as Universal Criteria

    Part of the reason I’ve been so skeptical of Platonism is because I’ve never been able to fully make sense of the concept of Platonic forms – the infamous “chair-ness” that Platonists like to talk about. I also couldn’t understand how our human minds might interact with these ethereal Platonic forms, since they’re supposed to be explicitly non-mental. But now, thanks to my theory of indirect interaction, I have a workable analogy.

    Let’s start with what we know. Before theorizing about the Platonic realm, we can say that, at the very least, “chair-ness” can reference our own conceptual criteria for determining whether we label something a “chair.” That criteria does exist, and it’s unique to each of our minds. We can imagine edge-cases where something doesn’t qualify as a “chair” to you, but it would qualify as a “chair” to me. 

    However, “chair-ness” might also reference something else – universal criteria. Just like we have abstract criteria that determines whether something gets the label of “chair”, the universe seems to have some criteria for determining the behavior of the things we call “chairs.”  In that sense, the “chair-ness” in our minds might actually correspond to “chair-ness” in the universe. 

    A “chair” is simply an object; a unique pattern of behavior; a particular output state or pattern of outputs across time. If the atoms of the universe stand in particular relation to each other (to form a structure that we call a “chair”) then the universe will output a unique state, keeping those atoms glued together in a specific way. 

    The best analogy is to computer code.

    Dinosaur Code and 3d Printing

    You can imagine universal criteria is like computer code which says, “If criteria A is met, then output state B.” So “chair-ness” would be that part of the universe’s code that determines when atoms behave like chairs – or when atoms are unified in a unique way that we reference as “chairs.”

    This is how “chair-ness” might exist completely separate from any chairs. The code can still exist – “If A, then B” – but since there might not be any A, there might not be any B.

    Consider dinosaurs.

    Let’s say a “dinosaur” is a particular structure and pattern of behavior of atoms across time. When dinosaurs exist, the universe is running the “dinosaur program.”

    If in 2020, atoms were arranged in a way that constituted a “live dinosaur,” then would we see those atoms behave like a dinosaur? If so, then we can say the universe’s code for dinosaurs still exists, even though there are presently no dinosaurs. The program is still out there, even if it isn’t running.

    Now, let’s call the code for dinosaurs “dinosaur-ness”, and suddenly Platonism makes sense. What is the Platonic dinosaur-ness? It’s that part of the universe’s code which determines when some arrangement of atoms is to behave like a dinosaur. Notably, there don’t need to be any actual dinosaurs in order for this Platonic form to exist.

    In fact, if we understand Platonism this way, the contrary position seems bizarre. Anti-Platonism would imply that the universe could no longer produce dinosaurs. So, even if atoms were arranged exactly like they were back when dinosaurs existed, those atoms wouldn’t act like dinosaurs. The universe somehow couldn’t run the dinosaur program or output dinosaur-states. To me, it seems more reasonable to think that even if all the dinosaurs go extinct, the “code” for dinosaurs would still remain.

    Another intuitive example is 3d printing. There is a clear difference between a computer file which contains information about how to build a physical object, and the physical object itself. The file is just a bunch of 1’s and 0’s. Well actually, to be precise, it’s not just 1’s and 0’s; it’s 1’s and 0’s in a particular arrangement. In this case, the arrangement is the whole point.

    You won’t find a physical object inside the code. And yet, it contains enough abstract information to be able to construct a physical object. Like Platonic forms, the code exists separately from any printed structures. Even if the code is never instantiated into a physical object, the abstract information – the form, the structure, the pattern – still exists.

    The Special Composition Problem

    Let’s say that fundamental units can indeed get unified into composite objects. We run into a famous problem called the “special composition problem.” Exactly when does this unification occur? Under what circumstances do fundamental units suddenly get treated as a whole thing?

    I think the easiest resolution to the special composition problem is this: new objects are composed whenever the universe treats fundamental parts as interrelated. It’s precisely the universe doing this unification, not our minds, which means we don’t know beforehand exactly what structures will yield unique behavior. I can’t tell you a simple rule. It’s a matter of empirical inquiry. Whether X and Y are related is not discovered by examining X or Y in isolation. X and Y’s state-changes are observed together across time to see if there are discoverable patterns.

    For example, a tiny asteroid trillions of lightyears away probably doesn’t form an object with my thumb; their states appear to be unrelated. The asteroid can do anything, move anywhere, and change its structure, but it won’t affect my thumb. However, my fingers and thumb do appear related. The states of my fingers affect the state of my thumb. There are a large bundle of relations between them, such that the universe outputs their behavior as a composite object I label “my hand.” My hand shares many further relations with my arm, which shares relations with the rest of my body. The universe treats the parts of my body as tightly bundled and not isolated from each other. Hence, my body also qualifies as a composite object.

    Prosthetics are an interesting case. Is a prosthetic a true part of the body? Well, it depends on the tightness of its relations. A removable prosthetic arm has far fewer relations to the body than a hip transplant. The universe treats the hip transplant as an integrated part of the body as a whole. It does not treat the removable arm the same way. Thus, it seems reasonable to say “the hip transplant is a true part of the body,” while the removable arm is not. We could say that while the arm is attached, it acts like part of the body, but when it’s removed, it becomes a separate object. Our own conceptual criteria for saying “X is a part of the body while Y is not” might actually correspond to universal criteria. 

    Divine Conceptualism vs Platonism

    As the above has demonstrated, there seems to be mind-independent relationships that are discoverable in the world. They are a distinct feature of the universe that can be referenced separately from any concrete objects. They aren’t physical things; they don’t weigh anything; you can’t see them. They are abstract. But what exactly are abstract things? I see two possibilities. Abstract things are either mental or Platonic in nature. 

    Thought it might sound odd, some mental things could be mind-independent, within the framework of “divine conceptualism.” Abstracta might exist separate from our own personal minds, but still within the mind of God. In the same way that “chair-ness” is conceptual criteria inside of our minds, the universal “chair-ness” is also conceptual criteria, but it resides inside the mind of God. The abstract categories, forms, patterns, and relations that we have direct access to are all mental objects, and they correspond to the abstract categories, forms, patterns, and relations that are mental objects inside the mind of God.

    Within the divine conceptualist paradigm, we don’t even need to posit that this “mind of God” is personal. We might simply define the mind of God as “all of the human-mind-independent abstract stuff.” It’s the universe’s categories. The mind of God is what glues individuals into groups. This fits rather nicely into the pantheist worldview I explained in my article “Understanding God as Nature or the Universe.”

    The other option is if abstract things are Platonic – explicitly non-physical and non-mental. They would reside in their own unique ontological realm: the realm of Forms. Perhaps this is where information and the laws of physics reside as well. The trouble with the realm of Forms is that we can’t say much about it, since our minds aren’t in that realm and behave according to different rules. By calling abstract stuff “Platonic”, it might just be a placeholder word that means, “in another realm that we don’t have access to.” To the extent we have direct access to it, it’s mental, not Platonic.

    I don’t know whether abstracta are Platonic or mental. Both theories seem beautiful to me. Regardless, I have become persuaded that my previous position was incorrect and that abstract relationships are a real feature of the universe.

  • Understanding God as Nature or The Universe

    It’s taken me a couple of decades, but I’m finally starting to make sense of the concept of God. I was raised in an Evangelical Christian household, but the ideas never fully made sense to me at the deepest level. When searching for clarity about God, the people I spoke with would appeal to mystery and faith rather than explain a concept I could rationally grasp. Finally, after investigating for more than twenty years, I have a concept of God that I can understand. The idea is one of the oldest in existence, and it turns baroque theological claims into true and important insights.

    We can define “God” as “all of existence,” “the entirety of the universe,” or “reality itself.” God is the whole-thing-together. God’s parts include all of the objects, their relations, and their rules for interaction. God is the biggest conceivable existent, which is the totality of existence itself. In a word, God is Nature. Not “nature” referring to trees and shrubs and rocks, but “Nature” referring to the entire system, the universe, in which we live.

    With this definition, many theological claims start to make concrete sense. I have a suspicion that this is what Christians mean (or meant) when talking about “God the Father.” In this article, I will go through and demonstrate just how powerful the concept of God is when equated with Nature or The Universe. We’ll take a couple dozen religious claims about God and turn them into something reasonable and profound by translating “God” into “Nature,” “the universe,” “existence,” or “reality.” 

    Now whether, in addition to the universe, there is a Divine Person we can call “God” is a separate question. I’m not sure the answer, but regardless, it doesn’t change the profundity of the truths we can state about the universe.

    Omni-Qualities

    We’ll start with the traditional omni-qualities of God. Take the simplest example, the claim that:

    “God is omnipresent.”

    Meaning, God is everywhere at the same time.

    If God is a person, it’s hard to understand how he can be omnipresent. If God is the Universe, then it suddenly because obvious, even necessarily true, that God is omnipresent. The Universe is everywhere. Existence is everywhere. If something exists, it’s part of reality, therefore part of God. There is no corner of the universe that’s somehow not part of the universe. You can’t separate yourself from the universe – or to sound theological, you can’t separate yourself from God. Not only is this claim true, but it also hints at a real relationship between the universe and you. There is some kind of remarkable connection between “the whole thing” and “you as part of it.” 

    Next, take the claim,

    “God is omnipotent” or “all-powerful.”

    The universe is indeed all-powerful. There is definitely nothing more powerful than it, since it doesn’t really make sense to talk about something in the universe that’s more powerful than the universe. Every thing that acts is acting within the rules of existence. The system itself is categorically more powerful than any object within the system. To put it into religious terms, everything in existence is playing by God’s rules, therefore God is all-powerful.

    Next, the claim,

    “God is omniscient.”

    Meaning, God knows everything. There’s no information that God doesn’t have. This is a true statement about the universe. There’s a sense in which all states of the existence are “known” by the universe – though not necessarily implying a conscious state of knowing. Rather, all of the information about the universe is within the universe. You cannot “hide” information from the universe. You can’t trick Nature or be somewhere that Nature can’t see you. Every state that you’re in is itself a state of the universe. Therefore, the universe cannot lack knowledge of your existence, in a similar sense that the laws of physics cannot lack knowledge of your existence.

    If you think of information as being a key part of how the laws of physics operate – part of the “universal function”, as I theorize in this article – then it makes sense to talk about the universe as “knowing” present states in order to render future states. 

    Universal Substance and Being

    Let’s examine a Biblical quote:

    “God is the Alpha and the Omega, the beginning and the end.”

    If God is a person, it’s unclear what this means or how it’s true. But if God is the Universe, then in the most literal sense, God is indeed the Alpha, Omega, and everything in between. You could also call God “the Father” of everything, which is essentially the same idea as being the Alpha and the Omega.

    How about the claim,

    “God maintains our existence every minute.”

    This is also true. The universe maintains our metaphysical existence from second to second. We don’t choose to continue being; Nature chooses for us, and if Nature stopped sustaining our existence, we would cease to be.

    Next, take the common claim that:

    “Humans are made in the image of God,” or as it’s sometimes phrased, “Every individual has a spark of the divine.”

    There is again a literal sense in which humans are an image of Nature. They are stamped with an impression of the entire universe. If you agree with the story of modern cosmology, then humans are little bits of the Big Bang, aged a few billion years. In a real sense, Nature created humans. We are inescapably of Nature – of God. You are not separate from reality. The universe is part of you, and you are part of the universe. So when you’re looking at a human, or looking at anything for that matter, you’re looking at a bit of Nature itself. Thus, if God is the Universe, then humans literally look like a part of God, and if existence is divine, then every individual has a spark of the divine.

    Take the claims that:

    “We’re all God’s creation,” and the more poetic, “God formed man from dust.”

    Just like the claim that “God made man and woman”, this is literally true. We are a creation of the universe – but not necessarily a creation in the intentional conscious sense. The material building blocks of humans are of the universe. Humans are a particular composition, a structure, that’s been created – or if you prefer, has emerged – from the universe. Again in a literal sense, the universe formed man from dust.

    Take a claim that I used to hear from Evangelicals growing up:

    “God made man and woman,” or more generally, “Things are the way they are because God made them that way.”

    Again, true and important. Nature has created men and women with different biological and psychological traits. This is a fact of the reality in which we live. It’s foolish and arrogant to pretend otherwise, and it should probably affect the way that we live in the world. 

    Submission, Satan, and Karma

    Consider the popular religious concept of “submission to God.” It makes a great deal of sense. To submit to God is to submit to reality, to Nature. To obey the system and let it operate. To establish God as ”sovereign over everything” is to admit that reality, Nature, the Universe, is king. We have no metaphysical power over the structure of reality. 

    Looking at things from a universal perspective, there’s a very real sense in which your life is not your own. It’s God’s; it’s Nature’s. What happens in your life is not ultimately controlled by you, but rather by greater forces outside of yourself. 

    In this sense, I can agree with religious people when they claim,

    “Western culture needs to submit to God!”

    Western culture does need to acknowledge the existence of objective reality and live in accordance with it. Perhaps when theologians say “humans should live by God’s law”, they’re really saying “humans should not pretend they live in an alternative universe; they should live by the laws of Nature and accept reality as it is.”

    This perspective also gives me a comprehensible understanding of “Satan.” Instead of being a really bad supernatural person, he might be the personification of non-reality, falsehood, or rebellion against reality. 

    Imagine we constructed a story about God (reality) versus Satan (falsehood), where both God and Satan were people. We could talk about how seductive Satan is, how tempting lies can be, and how deep delusions run in the human psychology. We could talk about the fundamental arrogance of Satan – the tendency for humans to vociferously proclaim they have the truth when they don’t. We could tell stories about how “listening to Satan” leads to unhappiness, since in the real world, lies and delusions end up harming people.

    With such stories, I would end up advising the same thing as my Christian friends: stay away from Satan! God is what you need! And we could translate this rationally as, “Stay away from lies and delusions! Truth and reality is what you need!”

    Furthermore, I often heard stories in my youth about the burning hatred that Satan has for God. Well, understanding God as reality and Satan as non-reality, I actually see this story play out in people. Humans that are living in delusion have an extreme hatred for anything true – even the concept of truth. Similarly, humans that are doing really bad things – think the Epstein sex ring – do not want the truth exposed. They have a strong preference for darkness and a fear of the light, so to speak.

    After hearing stories about God and Satan for so many years, and never quite grasping them, it’s stunning to see them suddenly make sense by simply translating “God” as “reality” or “existence.”

    This translation also helps make sense of the concepts of “Karma” or “cosmic justice.” Instead of thinking there’s someone personally punishing and rewarding humans for their behavior, we can conceive of the universe as possibly being intrinsically just. Perhaps the laws of physics are also coupled with laws of morality. When something bad happens in the world, perhaps it sets of up a chain of events to correct itself at a future time. “Punishment” might be built into the structure of the universe, rather than something dished out by a person.

    “God will judge you for your sins”

    might be another way of saying “actions have consequences.” 

    Now, whether or not we live in a universe which operates on principles of justice is an entirely empirical and open question. I’m not saying we do. There’s plenty of evidence that seems to suggest otherwise. However, it’s another example of the explanatory power of treating God as existence. We can seriously talk about whether God is just without invoking confusing theological concepts. We can even talk about whether God “has a sense of humor” or God is “loving.” These are all meaningful statements about how the universe operates.

    God and Culture

    Next, let’s examine the cultural criticism you might hear from a cranky old person:

    “Western society has forgotten about God!”

    This statement becomes true and important if we interpret it as, “Western society has forgotten about reality!” Especially in elite society, humans seem to have forgotten that the universe has a structure independent of them. They pretend that all of existence is a mere social construction. They are deluded about the reality of things as they are in the world. One could even interpret the fashionable claim that “there is no objective truth” as “there is no universe” or in this context, “there is no God.”

    To quote Psalms:

    “A fool in his heart says ‘there is no God.’”

    Again true and relevant to my own work. A fool says “there is no universe” or “there is no such thing as reality.” I’ve met plenty of fools and even interviewed a few on my show. Perhaps part of the reason past thinkers believed the existence of God was self-evident is because they were treating “God” as Nature or the Universe. The existence of the universe is essentially self-evident – i.e. the existence of existence – and it probably reflects on some psychological or moral problem to deny that it exists.

    Now take the crotchety old person’s condemnation of his teenager son’s behavior:

    “Don’t rebel against God!”

    It’s actually sound advice if the old man is saying “Don’t rebel against Nature!” Rebelling against reality is vain and counter-productive. You might not like Nature, but you’d better grow up and get over it. Nature is a particular way, and it won’t change just because you don’t like it.

    Instead of “rebellion” against God, I think it would be amazing to live in a society that “worshipped” God. In other words, a society in which truth and reality are sacred. Lying, for example, would be seen as seriously immoral, but at present, Western culture seems completely tolerant of lies and celebrates a myriad of human delusions.

    Next, consider the wisdom of the proverb:

    “The fear of the Lord is the beginning of wisdom.”

    That’s wise if we interpret it as “the fear of Nature is the beginning of wisdom.”

    As somebody who has experienced chronic illness for nearly a decade, I can tell you this is true. All pain, suffering, disease, and death comes from Nature. Your mental state – happy or sad, sane or insane – is an output of Nature, and at any moment it can change. Everything can be taken away from you, and this fact is outside of your control. Nature has the ability to eternally torture you or ruin your life in ways inconceivable to you. 

    Next, consider the common practice of “Thanking God” before a meal, for success in life, or for avoiding some tragedy. My old Evangelical community thanked God with the belief that they were thanking a cosmically powerful person who was responsible for their well-being. But there’s another way to understand giving thanks to God.

    In a literal sense, the universe provided you with your meal. The universe was the ultimate cause of your professional success. The universe – forces external to you – were the reason that some particular tragedy was avoided. If you have talents, wealth, or physical looks, the universe gave them to you. And as the saying goes, since the universe gives you everything, it can take everything away from you.  

    A related phenomenon is religious people “giving glory to God” when they perform things at a high level. Say we’re talking about music. Rather than merely celebrate some particular human’s musical creation, it makes sense to celebrate the whole structure that gives rise to the existence of music in the first place! It’s extraordinary that we live in a universe in which sound exists. Relatively speaking, the musician isn’t actually doing much. He’s not creating music ex nihilo. He’s creating music within the system provided to him. In this context, “giving glory to God” makes sense to me.

    These high-performers often say things like,

    “There is a higher power working through me.”

    Again, in this context, that’s true. When somebody accomplishes something, it’s some part of the entire universe operating. The actions of individual humans are just a small part of its operation.

    Now consider a few Biblical quotes. This one is of God speaking:

    “My people are fools; they do not know me. They are senseless children; they have no understanding.”

    Imagine the universe talking. It could truthfully say that humans are “my people,” as humans are constructed out of the universe itself. It could also say that humans are senseless children who have no understanding of reality. That’s also true.

    Now from Corinthians:

    “God makes foolish the wisdom of the world”

    Yes, definitely. The universe makes foolish the “wisdom” of the world. Intellectuals for all of history have been fundamentally mistaken about everything, and the present moment is no exception. The more you learn about the universe, the more you learn that humans know approximately nothing, and the greatest fools are those who profess to understand while being in a state of ignorance.

    Personal or Impersonal

    In theological discussions, whether God is “personal” or “impersonal” seems to be a big deal. Of course it depends on what we mean by these terms, but in this framework, I think God is both personal and impersonal. There’s a sense in which God is the most personal thing in existence. To the extent that there are people in the universe, then God is personal. It’s necessarily part of God’s potential to be personal, since there are people. God is the substrate out of which people are built, including yourself. What could be more personal? To the extent that consciousness is part of the universe, then at least part of God is conscious, too.

    But in this context, God is also bigger than a person. He’s a person and everything else, too, including the laws of physics. He’s the mechanical forces keeping everything in operation. Even rocks and planets are a tiny part of God.

    One of the difficulties I’ve had with thinking of God as a cosmic person is that it seems like he would still be a part of a larger system. He would be bound by the laws of logic, for example. It just seems weird to me to think of a solely-personal God that operates in a system which is larger and more powerful than he is. Instead of God being a person acting in a larger system, it makes sense to talk about God as being the system itself. Nothing is outside of it, larger than it, or more powerful than it. Nothing is higher than God if God is the structure for all of existence.

    That being said, we can also talk as if it has a kind of personality. We can meaningfully say, “God wants you to have children.” In reality, Nature pushes organisms towards procreation. You can talk about Nature having a “purpose”, as new states and structures are continually coming into existence. The universe is constructed in such a way to generate living things that have the capacity to love. That’s remarkable – staggering and absurd, really when you think about it – whether you attribute it to a Divine Person or not. You can talk about God having a “will” or a “plan.” When something happens, it was “God’s will.” In other words, everything that happens is a kind of unfolding of the entire universe towards a future state, with all parts relating to one another. Any event is merely a step towards some future state – a part of “God’s plan.”

    Now don’t get me wrong: it might be possible that the entire universe is a person. Perhaps God is all of existence, and if you put together all of existence, you get a person. That would be remarkable indeed. I don’t want to rule it out, but I have a very hard time making sense of it, so this article won’t make a claim either way. Even if the universe is ultimately unified into a person, it doesn’t change the various, true things we can say about it.

    Little Greek Gods

    This way of understanding God can also apply to lesser gods. Say we’re talking about Greek or Roman gods. Suddenly, they make sense if they are understood as real, abstract forces and patterns in the universe, rather than supernatural people. The god of Love, for example – the real force of love in the world – can be spoken about as if she had a personality. The god of Wine makes people do silly things. The god of War has his own destructive personality. There’s even a way of talking about the interplay between the god of Wine and War – as if the two gods speak to each other. I’m sure there’s a real connection in the universe between alcohol, violence, and war.

    We can make sense of the Greeks saying things like,

    “The gods might strike you with madness.”

    That’s just another way of saying “the universe, the many forces outside your control, might strike you with madness.” These gods should be feared. They are powerful and immortal. Humans can’t “kill” them. 

    With this context, you can see how clever it is to build stories about the gods – their personalities, relationships among themselves, including their various marriages, children, and partners, and about the relationship between the gods and humans. It makes sense to say,

    “The gods don’t care about the affairs of humans.”

    Contemporary minds might say “the laws of nature do not care about the affairs of humans.” 

    These lesser gods are different from the Big God. Lesser gods are specific forces and patterns in reality. They are themselves deferent to the Big God – the totality of reality itself.

    Monotheism versus Polytheism

    This way of thinking also helps me make sense of the debate between monotheists and polytheists. Are there multiple gods, or just one? I think there’s a sense in which both monotheism and polytheism could be true. Polytheism makes sense when understood in the Greek god example. There are many powerful, immortal forces that control what happens on Earth. 

    Monotheism makes sense when talking about the biggest-possible picture. We don’t need to posit the existence of multiple existences. We can say, “If something exists, it’s part of the totality of existence. Therefore, there is only one universe, one reality, one God.”

    Pantheism vs Panentheism

    Is this Pantheism? Is it Panentheism? I don’t know. I haven’t studied theology, and I’m not sure of the nuances between Pantheism and Panentheism. I don’t really care how my ideas are labeled, but from what I can tell, they are similar to both.  Pantheism is the idea that everything is divine or of God. Panentheism is the idea that everything is within God, but not everything is divine, and God might be bigger than the universe. To me, since I don’t have a theological dog in the fight, it seems to be more of a semantic distinction.

    There’s an obvious sense in which I’m saying “the universe is God”, which sounds like Pantheism, but it depends on what we mean by “the universe.” If “the universe” is restricted to four-dimensional spacetime, then I would be a Panentheist, because I believe existence is much bigger than four dimensional space. The universe studied by Physics might only be a small part of God. If, however, we treat “the universe” as “all of existence in every form”, then I would be a Pantheist, since there couldn’t be anything “outside” of existence in the biggest picture. If all parts of existence are in God, then they are still of God – as something in existence is a part of existence, from what I can tell. Regardless, I’ll let theologians handle the taxonomy.

    No Faith

    The picture I’ve just painted requires no faith to appreciate. It comes with no religious dogma. It’s just philosophy. It’s by no means an exhaustive list of religious claims that make sense if you translate “God” to “existence.” Nearly every time I encounter claims about God, I can make sense of them in this context.

    Regardless of whether there’s a Divine Person in addition to everything else, we can say really remarkable things about the universe. You are part of the entire universe; the universe is part of you. You are made up of the universe. If Nature were a painter, you would be a small part of its painting.

    As my Evangelical community was fond of saying,

    “God can fill a hole in your heart.”

    In other words, reality – the truth – can seriously fulfill you. If you don’t have it, it’s what you’re missing. Life without truth is aimless and fuzzy. This is a true statement about human psychology. People really are restless when they don’t have any grasp of reality.

    The universe provides everything for you. It is sustaining you right now. It’s been churning through various states for billions of years, with unbelievably powerful forces working together, and it’s finally reached the point of producing you at this present moment. It’s responsible for all of your positive and negative qualities. To the extent you learn, it’s always teaching you a lesson. To the extent that you are conscious, then the universe is conscious. To the extent that you love or are loved, then the universe loves. These truths seem profound to me. I believe this is the beginning of a rational theology.

  • Mind-Body Dualism | Solving the Interaction Problem

    Dualism is an attractive philosophy with an Achilles’ heel. Mind and body seem to be fundamentally separate things, yet dualists since Descartes have never been able to solve the famous problem of interaction. If mind and body are in different ontological categories, then how could they possibly interact with each other, even in principle?

    Descartes didn’t give a good answer, nor has any other dualist I’ve ever encountered. They tend to respond, “Well, we don’t know how mind and body interact, but that doesn’t mean it’s impossible!” This is not a satisfying answer, even though I agree with them, and lots of philosophers don’t find it compelling at all. In fact, many have claimed the problem of interaction is so severe, it’s a refutation of dualism. They think the problem can’t be solved even in theory.

    I disagree. I’ve been trying to figure out a plausible mechanism of interaction for many years, and finally, I’ve got one. I have a working resolution to the mind-body problem that solves the problem of interaction. It not only supports substance dualism, but substance pluralism, which doesn’t restrict the amount of ontological categories to only two. If you’re sympathetic to dualism, or are familiar with its history, this is the type of theory we wanted Descartes to figure out a few centuries ago.

    I call it a theory of indirect interaction. Mind and body do not directly interact, but they effectively interact – i.e. the state of one affects the state of the other. This theory has many favorable properties:

    1) It gives a plausible mechanism for interaction between objects in any ontological category – not just mental and physical. Even if there are a hundred more categories, the mechanism could still work.

    2) It allows for two-way causality. Physical states can affect mental states; mental states can affect physical states.

    3) It is free-will-agnostic. There is a clear opening for the role of free will, but the system works perfectly fine without it.

    4) It doesn’t break the laws of physics – or perhaps more precisely, it doesn’t break the laws of causality. It might simply broaden the scope of the laws of physics.

    The purpose of this article is not to claim that “This is the way things actually work in the world!” Rather, it’s to demonstrate that in principle there could be a mechanism for things in different ontological categories to effectively interact with each other. Whether or not I’ve discovered the “real” mechanism is a separate question.

    Examining Causality through Billiards

    The best way to illustrate the theory is by first taking the mind out of the equation and analyzing purely physical phenomena. By breaking down physical phenomena into their most fundamental form, it will elicit the concepts necessary to understand indirect interaction.

    My favorite example of “purely physical phenomena” is the motion of balls on a billiard table. Let’s take a simple scenario. Imagine that there are only two balls left on the table – the white cue ball and the black 8-ball. Imagine the cue stick strikes the white ball, the white ball rolls forward and hits the 8-ball, then the 8-ball rolls into a pocket.

    Let’s break this scenario down as thoroughly as possible. What are we really talking about when we reference “pool balls”? What exactly are such objects? What are we describing when we say, “The 8-ball rolled into a pocket”?

    Rather than give an extended analysis of the metaphysical status of pool balls (which you can read about in my article “No, Chairs Do Not Exist”), let me give you one plausible position. What a “pool ball” really is is “units of matter arranged in a particular way in a particular part of space.” Let’s call those units “atoms.” Some philosophers might put it, “A pool ball is really just atoms arranged ball-wise.”

    Let’s consider this phrase:  “The 8-ball rolled into a pocket.” What exactly are we describing? What is this “rolling” phenomenon? If the pool ball is just atoms, then we can rephrase it this way: “Some particular atoms changed their positions in space.”

    Another way to understand it would be to say, “At Time 1, atoms were in Position 1. At Time 2, atoms were in Position 2.” In fact, that’s a pretty good description of motion in general.

    That’s an abstract way to understand pool balls rolling on a table. Now let’s ask two interesting, yet difficult questions:

    1) When the white ball hits the 8-ball, why does the 8-ball start moving?

    2) Why does the 8-ball move on its particular path rather than some other path?

    Notice that when we reduced the phenomenon of motion to “atoms changing position,” it doesn’t actually communicate an extremely important piece of information:

    The changes in position are not random.

    We didn’t say, “At Time 1, the white ball struck the 8-ball, and at Time 2, the 8-ball started orbiting Jupiter.” No. There is a pattern to the motion. A predictable, observable pattern.

    Why?

    Why isn’t the motion of the 8-ball completely random? Why should the motion be predictable at all? Hell, why doesn’t the universe just spontaneously fall apart when the balls collide? What holds all of these objects into the same coherent, predictable system?

    One plausible answer is this: There are laws of the universe. Physical laws keep the whole thing together. They make motion predictable. The reason that the 8-ball rolls into its pocket instead of orbiting Jupiter is because there are laws of physics which govern the behavior of objects. These laws have a real existence.

    That’s a nice-sounding answer – and physicists might like it – but it provokes many more questions. For example:

    Are the laws of physics physical themselves? Do the laws of physics take up space or weigh anything?

    What is the relationship between the laws of physics and the objects governed by them?

    What is the mechanism for the laws of physics?

    In other words, how do laws keep objects in order?

    If our explanation for physical phenomena appeals to laws, then we’ve posited the existence of two radically different types of things: physical phenomena and the laws which govern them. Atoms in space, by themselves, are not sufficient to explain why they move in predictable ways. There must be underlying principles, or laws, which determine their behavior. By thinking about “purely physical phenomena” this way, it gets us one step closer to solving the mind-body problem.

    Inputs and Outputs According to Laws

    Let’s break down our billiard example even further. Instead of only identifying what we see, we need to identify exactly what we don’t see.

    Treat the table and balls as a whole system. We see changes in the position of the balls, which means we see the system in different states at different times. But we don’t see the glue between the states. We don’t actually see the laws that we’re appealing to in order to explain the phenomena. We’re simply inferring the existence of laws and causality to explain the patterns in our observation, but we don’t see the laws themselves.

    It’s helpful to keep rephrasing and condensing our language. Instead of saying, “At Time 1, the object was in Position 1, and at Time 2, the object was in Position 2,” we can simply talk about “states.” We can say, “State 1 was followed by State 2.”

    So another abstract way to understand physical phenomena is to say, “There is a series of states. Each state contains a particular arrangement of atoms in space. The changes between states are non-random and happen in accordance with laws.”

    This allows us to re-ask the previous questions:

    1) Why is State 2 the way that it is and not some other way?

    2) Why doesn’t State 2 include the 8-ball orbiting Jupiter?

    The answer:

    Any given state is determined by its previous state. Since State 1 was a particular way, the laws of physics determine that State 2 must follow State 1.

    Or, to put it more succinctly: Preceding states determine future states.

    Let’s consider these states of the universe from another perspective: As “inputs” and “outputs.” Inputs yield outputs. So if we call State 2 an “output,” we could say that State 1 was its “input.”

    What determines that State 2 is an output of State 1 in particular? The laws of physics. If we think about states of the universe as being inputs and outputs, we can understand the laws of physics as a kind of mathematical function – they take inputs and turn them into specific outputs!

    This is a theoretical picture in which the universe is like a gigantic computer that keeps churning out new output states. The outputs are determined by their inputs. Then, those outputs are used as inputs for the next state. The laws of physics are the specific code that determines exactly how inputs relate to outputs.

    So, we can reduce the physical universe to a very abstract formula:

    Input state + laws of physics -> output state.

    Then, that output state is treated as the next input, and the universe churns out a new state.

    Information and State

    We’ve posited the existence of two radically different types of things to explain physical phenomena – spatially-extended atoms in space, and non-spatially extended laws of physics which govern their behavior. Whether or not it’s necessary to give the laws of physics a real existence is an interesting question (and it turns out that it’s awfully hard to explain the regularity of physical phenomena without them!). Regardless, this metaphysical picture allows us to understand how objects in different ontological categories might be able to interact with each other. However, we must go deeper.

    Reduce the physical universe to “atoms in their position in space at any given time.” Those atoms themselves are not enough to determine the future state of the universe. There must also be laws. But that brings up several more difficult questions:

    1) What connects the physical states to the laws?

    Why aren’t the physical states completely separated from the laws? What’s the glue between the laws and the physical states?

    2) How do the laws of physics “know” the state of the universe? Why doesn’t the universe “get it wrong” when determining future states?

    3) How are states treated as inputs? What’s the format?

    All of these questions can be answered by the final piece of the puzzle: Information. The universal mathematical function that takes inputs and turns them into outputs has information about the physical state. This information is itself non-physical. The information is the glue between the laws of physics and the physical states themselves.

    So, what actually gets used as the “input” is information about the physical state, rather than the physical state itself. The subsequent output is another purely physical state, then information about that output is used as the new input state!

    This is an abstract way to understand the mechanics of a physical system. Crucially, it allows for real ontological differences between the physical state, the information about the physical state, and the laws of physics which take that information and generate new output states.

    Think about the relationship between ordinary objects and your knowledge about them. Take your information about chairs. There’s a categorical difference between physical chairs and your information about physical chairs. Chairs take up space, while your knowledge about chairs does not take up space. The concept of a chair is not somehow embedded inside of chairs. Information is not the same thing as what the information is about. Information about physical states does not need to be embedded within physical states.

    In this theory, the physical states are entirely concrete, not abstract. They are reducible to “atoms in space.” Yet, there can be information about those physical states which is abstract and not reducible to atoms in space.

    There’s an interesting question about the metaphysical status of information. It’s “abstract,” but what exactly are abstract things? Are they mental? Platonic? This theory doesn’t require a particular answer, but it should be clarified that it doesn’t necessarily imply consciousness. Your knowledge of chairs is within your mind; you can have a kind of conscious experience of it. The universe doesn’t need to have any internal experience of knowing information about physical states, just like your computer doesn’t have to have an internal experience of “reading and knowing” the state of your hard drive. Information is processed in your CPU without consciousness.

    So, to revise our picture of a physical system one more time:

    We start with atoms in space. The universe has information about the position of the atoms in space. That information is used as an input into a function that we call “the laws of physics.” It then generates a new output state – i.e. atoms change position. The universe has information about this new state, which then gets put back into the function to generate subsequent output states. The universe progresses.

    If this theory works, then we’ve just solved the mind-body problem and the problem of interaction. All we’ve got to do is add mind.

    Mind and Brain

    The picture I’ve just painted includes effective interaction between at least two ontological categories – the laws of physics and the spatially-extended objects that are governed by them. Now, it doesn’t matter how many ontological categories we posit; the same mechanism can still work. Instead of restricting output states to only spatially-extended physical stuff, we can expand the category of output states to include mental stuff as well – feelings, experiences, qualia, etc.

    For example, take the conscious experience of seeing red. It’s a particular kind of mental state. In this system, it’s simply another output that will get generated with the correct input. Whenever the physical universe is arranged in a particular way, the output state of “experiencing redness” is generated. That output state does not need to be physical. It can be in an entirely different ontological category!

    This allows us to expand the laws of physics to include laws of mental representation. Just like particular physical inputs yield particular physical outputs according to laws, the universe can also generate particular mental outputs with the right input. In other words, the universal function includes the informational criteria for generating both physical outputs and mental outputs.

    This theory accords perfectly with the physical mechanics of sight. When physicists talk about “light rays entering the eye, stimulating particular nerves, etc.” they’re simply talking about changes in physical states. As these physical states change, the information going into the universal function also changes, and at some point, when the correct physical state has been reached, mental states start getting generated.

    Notice: it’s not the physical state itself that’s generating mental phenomena. It’s not some mechanism in the brain. It’s information about the physical state which gets used as an input to generate a mental state in a different ontological realm.

    In this theory, brains are not some unique object that “secretes consciousness,” as some philosophers have suggested. Consciousness is not to be found within a skull. There’s nothing intrinsically special about the atoms that compose a brain. What’s important is their arrangement and the corresponding information about them.  If patterns and information about the brain are indeed what generates consciousness, then we also have no need to posit panpsychism, which suggests each atom might be “a little bit conscious” itself.

    The reason that the brain is so closely correlated with conscious states is because it’s precisely the information about the atoms in space that we call a “brain” that yields consciousness. The brain state itself is not enough; it requires brain states plus the laws of physics/mental representation. So it shouldn’t be surprising that when people get brain damage, their conscious experience changes. This isn’t because the brain loses the ability to create consciousness. It never had that ability. It’s because when the brain state changes, information about the brain state changes, which then changes the input and subsequent output of the universal function.

    This is why I call the theory a mechanism of “indirect interaction.” The brain isn’t directly generating consciousness. Instead, it’s the pattern of information corresponding to the physical state of the brain that generates consciousness. The effect is essentially the same. The state of the body affects the state of the mind, but it’s via an abstract mechanism instead of a purely physical or mental one.

    Two-Way Causality

    Our experience of the world suggests that physical states can affect mental states and that mental states can affect physical states. For example, experienced meditators can regulate their body temperatures through deliberate mental focus. Even regular people can make their mouth water simply by envisioning a juicy steak when they’re hungry. Or, take one of the most significant examples of mental states appearing to affect physical states: The placebo effect. How is it possible?

    Well, just like the outputs of the universal function can be mental or physical, so can the inputs! The universe can have information about physical and mental states. So information about mental states might also be used as inputs to generate outputs.

    Let’s take the placebo effect as an example. Simply taking a sugar pill is not enough to generate improvement in one’s symptoms. It also requires belief that the pill will help you. So, in order to generate the desired result, the universal function requires an informational input from both physical and mental states. Having only the correct physical state or mental states is not enough. Both must be in the correct state.

    Two-way causality accords with our experiences, and contrary to the claims of some philosophers, it doesn’t need to break the laws of physics. The laws of physics can simply be expanded to include mental states as well. Instead of calling them “the laws of physics”, perhaps it would be better to call them “the laws of the universe” to include governance over all kinds of phenomena.

    Free Will

    Another benefit of the theory is that it allows for the existence of free will in a rather straightforward way. If mental states are used as inputs into the universal function, then what if some mental states are volitional? If not all mental states are determined by previous states of the universe, it could allow for volitionally-determined mental states. Those volitional states would then be used as an input to generate a particular output.

    For example, whether or not you eat dinner at 6pm or 7pm might not be a predetermined fact. The universe could require a volitional state in order to determine which output gets generated. In other words, information about your choice, whether 6pm or 7pm, will determine what happens. Without your choice, you might not have dinner at all.

    Now, I don’t currently have an answer to the question of free will, but I think it’s a strong benefit of this theory that it can seamlessly allow for its existence. The mechanics of indirect interaction gives us a concrete mechanism for minds to affect the world, whether that mind is controlling its mental states or is merely a predetermined output of the universal function.

    Theoretical Flexibility

    The theory I’ve just explained is extremely flexible. It allows for the existence of arbitrarily many ontological categories. If you think the world is constituted by only physical and mental stuff, it can work. If you think Platonic objects also exist, that’s fine too. If you think there are 100 other categories, all of which interact with each other, that’s fine as well. The ontological categories can be completely separated, so long as there’s a simple fact about them: The universal function has information about their state. That isn’t difficult to imagine, since in this theory, the universal function is the thing outputting the different states into their various ontological categories in the first place!

    Indirect interaction also allows for a plausible story of emergence. If might be the case that the universe began with only physical phenomena and laws. Then, over time, as matter rearranged itself, a pattern of information yielded the very first conscious output. If this actually happened, then other types of emergence might also be waiting to come into existence with the correct informational input.

    The theory works whether the interaction is causally one-directional or two-directional.

    It also allows for the existence of free will.

    It’s also consistent with the modern conception of the relationship between body and mind that views the body/brain as fundamental. It might be that the physical state of the brain entirely determines mental states. Mental phenomena can be purely epiphenomenal. Indirect interaction simply gives a causal mechanism for brain to affect mind. So if stimulating one area of the brain causes changes in mental phenomena, it’s not because some particular gland starts secreting consciousness a bit differently. It’s because the underlying physical structure of the brain changes, which changes the information going into the universal function.

    This mechanism is even consistent with idealism. Even if one rejects the existence of physical stuff completely, the regularity of mental phenomena still requires explanation. If the laws of the universe govern only mental phenomena, because that’s all that exists, it might be that the underlying mechanics are the same: state + information + laws -> output.

    It also explains why the interaction problem has lasted so long. People keep looking in the wrong places. While there’s a tight correlation between brain states and mental states, you’ll never find consciousness within the brain. You’ll only find correlating physical states. The mechanism is not within the skull, because consciousness is simply not a physical phenomenon. You can’t see its generation from the outside. There are no levers, pulleys, glands, or fluids that contain it. That’s because the relationship between brain and mind is abstract. Information about the physical state is not to be found within the physical state.

    There are many parts of this theory that one can object to. Perhaps you think the laws of physics aren’t real, for example. Or perhaps you think the continuity of time makes this story less plausible. The details don’t matter. The point is to paint a picture of at least one conceivable mechanism for objects in different ontological categories to effectively interact with each other. If such a picture exists, then the interaction problem is not a refutation of substance dualism or pluralism.

  • Responding to Jason Brennan’s Review of Square One

    Last year, I put out a challenge to some of my academic friends. (more…)

  • Pi is a Rational, Finite Number

    Heresy comes in different levels. For the modern intellectual, the lowest levels of heresy might be about politics or economics – areas of thought where you’re allowed to have unorthodox ideas without being excluded from polite company. Higher levels of heresy might be about religion or science – disagree with orthodox assumptions here, and you’ll be seen as quite-possibly-crazy. The highest level of heresy in the modern world is mathematical heresy. Disagreement with mathematical orthodoxy is synonymous with “being a full-blown crank.” You’re simply not allowed to doubt certain ideas in mathematics without being condemned as an intellectual leper.

    Unfortunately, as with any other area of thought, there’s an inverse relationship between “acceptability of disagreement” and “likelihood of error.” The more taboo it is to challenge an assumption, the more likely it will collapse under scrutiny. Theologians might be able to tolerate disagreement about God’s properties, but they cannot tolerate disagreement about God’s existence. His existence is too foundational to revise. If God doesn’t exist, the entire theoretical structure built on top of this assumption gets destroyed.

    So it is with mathematics. Several fundamental assumptions are not allowed to be challenged and have therefore turned into dogma, which makes this article mathematical heresy.

    I’ve examined the foundations of standard Geometry and found two errors – one logical, the other metaphysical. This article will focus on the metaphysical. Essential objects described by mathematicians do not exist. Thus, any conclusions that are derived based on the existence of these objects are likely incorrect.

    In this case, the universally-accepted claim that “Pi is an irrational, transcendental number whose magnitude cannot be expressed by finite decimal expansion” is false because of a metaphysical error.

    Pi is a rational number with finite decimal expansion. This idea, that might seem inconceivable at first, will turn out to be overwhelmingly reasonable by the end of this article.

    (For the rest of this article, I’ll abbreviate “Pi is a rational number with finite decimal expansion” as “Pi is a finite number” or more simply, “Pi is finite.”)

    On Shapes

    My claims are straightforward and preserve basic geometric intuition. For example, this is a “circle”:

    2000px-Circle_-_black_simple.svg

    This is a “line”:

    Horiz-line

    And these are “points”:

    220px-ACP_3.svg

    If you believe these objects are indeed circles, lines, and points, then you too believe that pi is finite. You see, mathematicians do not believe these objects qualify as “lines” or “points.” In their minds, lines and points cannot be seen, and in fact, they’d say the above “lines and points” are mere imperfect approximations of lines and points.

    To understand why, we have to ask a set of questions whose answers people assume have already been sorted out. These are questions that are supposedly so obvious that they aren’t worth asking. And yet, when we ask them of mathematicians, we get dubious answers. Questions like:

    What is a “shape”?

    What is a “line”?

    What is a “point”?

    What is a “circle”?

    What is “distance”?

    Ask your average intellectual these questions, and they’ll likely scoff at you, because they assume, “Everybody knows what a line is!” They are wrong. I, for one, do not think that mathematicians know what lines are. And because their theories are built on their metaphysical claims about “lines and points,” the theories must be revised from the ground up.

    Without Length, Breadth, or Sense

    As pi is the subject of this article, let’s lay out the definition that we’ve all learned in school:

    Pi is the ratio of a circle’s circumference to its diameter.

    We’ve got a few key terms in here: “the ratio”, “a circle”, “circumference” and “diameter”.

    In order to understand what pi is, we need to understand what these other terms mean. Especially this one: “a circle.” Here’s one definition:

    A “circle” is a shape whose boundary consists of points equidistant from a fixed point.

    Sounds reasonable. A few more key terms we need to understand: “shape”, “boundary”, and “points.” If we want to understand pi, we must understand what circles are, and if we want to understand what circles are, we must first understand what “points” are.

    It’s here that I find the fundamental error plaguing orthodox geometry: the definition of a point, from which all other geometric objects are constructed. What is a point? Turns out, there are many different definitions. We’ll start with Euclid’s original definition, which I like.

    A “point” is that which has no part.

    We’ll come back to that definition later. Here’s another one:

    A “point” is a precise location or place on a plane.

    Not bad. They are often represented by little dots:

    220px-ACP_3.svg

    However, these intuitive definitions aren’t actually workable in modern mathematics. “Points”, in orthodox geometry, aren’t really “defined” per se. They are supposed to be understood in terms of their properties. An essential property is this:

    Points do not have any length, area, volume, or any other dimensional attribute. They are “zero-dimensional” objects.

    This is absolutely foundational to modern conceptions of geometry. Points cannot have any length, width, or depth to them. And yet, all shapes are supposedly constructed out of them. So you might ask, “Hang on, how can shapes, which have dimensions, be composed of a bunch of points that do not have dimensions?”

    That’s a very good question, and if you insist on finding a logical answer, you will end up like me: rejecting very large parts of orthodox mathematics.

    Every “line”, to a mathematician, is actually composed of an infinite number of points – yet, each point is itself without any dimension. Lines, which have length, are composed of points, which have no length. How does this make sense?

    It doesn’t.

    It’s like asking, “How many 0’s do you have to add together to get a 1?” The answer is obvious: you can’t add a bunch of 0’s together and get a 1 – not even an infinite amount of 0’s. If a point has zero dimensions, then it doesn’t matter how many you put together. You’ll never end up with a dimensional object. This is a logical necessity.

    So, we have a very big problem. The literal foundation on which the entire theoretical structure of modern geometry is built – the “point” – is dubious. Errors at this level could be catastrophic.

    Shapes Without Shape

    If consistent, the mathematician quickly forces himself into odd positions. For example, he must conclude things like, “We cannot see shapes!” Take the example of what non-mathematicians call a “line”:

    Horiz-line

    Certainly, this cannot be a line to a mathematician, because lines supposedly have only one-dimension – length. This object has both length and width – it is extended in two dimensions. What can we call this shape, then, if not a “line”? I don’t know – you’ll have to ask a mathematician.

    What about a two-dimensional object: the circle?

    2000px-Circle_-_black_simple.svg

    Certainly, this cannot be a circle. This object is composed of pixels, not points, and each pixel is itself extended in two dimensions. Therefore, the object has rough edges and isn’t perfectly smooth. Though laymen might call it a “circle,” it’s only a mere approximation of the mathematical circle, sometimes called the “perfect circle.”

    The same can be said for the mysterious “point”:

    220px-ACP_3.svg

    These objects cannot qualify as “points” either, because they have dimensions. We can see them, after all. Mathematical objects cannot be seen; they cannot be visualized; they cannot have any extended – or “actual” – shape. If an object actually has shape, if it takes up space, then it’s got to be made up of spatially-extended objects akin to computer pixels, not mathematical points.

    Note: I’m not just talking about “physical space” or “physical shape”. I’m talking about shapes of any kind. What I see in my visual field – blobs of color – have shape, but they are not physical objects. They themselves do not occupy physical space. They are mental representations, and they are made up of extended points of light – pixels on my mental screen.

    So, a natural question arises:

    Has anybody, ever, seen or experienced these mathematical shapes in any way? Has anybody encountered even one true “line” or “circle”? The answer must be an emphatic “No.” All of the “lines” and “circles” that we actually experience have dimensions. They are constructed from a finite number of points which themselves have dimensions. The objects we experience are composed of pixels.

    The importance of this point cannot be overstated.

    This means every “circle” you’ve ever seen – or any engineer has ever put down on paper – actually has a rational ratio of its circumference to its diameter. Every “circle” that’s ever been encountered has a unique “pi” that can be expressed as ratio of two integers.

    “Circumference”, for any circle we can experience, can be understood as “the shape’s outermost boundary”, which is itself composed of a finite number of pixels. It’s “diameter”, too, is a simple integer – the number of pixels which compose it. Put one integer as a numerator and one integer as a denominator, and you’ve got a rational pi.

    In fact, these truths should be uncontroversial, even for mathematicians:

    Every “circle” you’ve ever encountered, without exception, has a rational, finite pi.

    No “circle” you’ve ever encountered, without exception, has an irrational pi.

    So, that means my claims about a “rational pi” are true for at least 99.9999% of all shapes that we call “circles”. It also means that pi is unique to any given circle. This shouldn’t come as a surprise, however, when you think about the nature of ratios.

    Imagine I were to say, “What is the ratio of a table’s height to length?”

    You would naturally respond, “Which table?”

    The same is true of circles. There is no “one true ratio called ‘pi’” for the same reason there is no “one true ratio of a table’s height to length.” Each table, and circle, is constructed by a finite number of units, arranged in different ways, and therefore their ratios will vary.

    According to standard geometry, there is literally only one “circle” that my claims don’t hold true for: the so-called “Perfect Circle” – an object so mysterious that no mortal has ever encountered it.

    The Divine Shape

    This “perfect circle” does not have any measurable sides or edges. Its boundary is composed of an infinite number of zero-dimensional points. The outermost points take up exactly zero space. Its pi cannot be expressed by any decimal expansion – nor will we ever know exactly what its pi is.

    This object cannot be constructed, visualized, or even exist in our world. Our world is too imperfect for it. Instead, it lives in another realm that our minds can faintly access.

    The Perfect Circle is so great, that all other “circles” are mere approximations of it. It is the one true circle. If you ask for proof of its existence, you will find none. Yet, the mathematicians have built their entire geometric theory based upon its existence.

    I freely admit my heresy: I do not believe in the “perfect circle.”

    Therefore, I do not believe in the “irrational pi.” Nor do I have any need for such a concept. Every shape I’ve ever encountered – or will ever encounter – has edges that take up space.

    A geometry without perfect circles, and without the irrational pi, is fully sufficient to explain all of the phenomena I experience. Therefore, I’ve no need to posit an extra entity – especially one with such remarkable properties.

    In other words: I simply believe in one less circle than mathematicians. That’s all that’s required to conclude that pi is a rational number for any given circle.

    Just an Abstraction!

    I’ve heard some mathematicians claim that geometric objects are mere abstractions and are therefore exempt from the preceding criticism. But among other things, this gets the metaphysics of abstraction backwards. You abstract from concretes. You don’t concrete from abstract.

    Think about it. From what does one abstract in order to get the concept of a “perfect circle”?

    It cannot be the circles we actually see, since every one of those circles has imperfect edges. All of the concrete experiences we have are of shapes with imperfect edges, a rational pi, and are made up of points with dimension. So from these experiences, the mathematician says, “Well, I think that a true circle is one without edges, with an irrational pi, and is made up of zero-dimensional points!”

    This is nonsense, and it’s not the way abstraction works.

    Imagine we’re talking about houses and abstract conceptions of houses.

    Every house we’ve ever encountered has walls, a floor, and a ceiling. The mathematician wants to say that his conception of a “perfect house” is one without walls, floors, or a ceiling. And in fact, regular ol’ houses are mere approximations of his perfect house. Obviously, this is a mistake.

    We can have a perfectly valid abstract conception of a house, but the properties of our “abstract house” must include the properties of the concrete houses we’re abstracting from. Our “mental house” has to include the conceptual categories of “having walls, floors, and a ceiling.” The dimensions of these properties are irrelevant, so long as they are existent.

    An abstract conception of “a house without walls, floors, or a ceiling” cannot explain any phenomena we experience, because it describes no thing that could possibly exist. Imagine your friend takes you to an empty field and says, “Here’s my perfect house! It’s got no walls, floors, or a ceiling!” You’d think he was crazy – especially if he added, “And all other houses are a mere approximation of it!”

    Not Real!

    One of the more self-incriminating responses from mathematicians goes like this, “But mathematical objects are not real! They don’t exist at all!” In all my research, I can confidently say that mathematics is the only area of thought where admitting “the objects I’m talking about aren’t real and don’t exist” is meant to defend a particular theory.

    This error is a conflation of objects and their referents. For example, the concept of “my house” is supposed to refer to “my house in the world.” It would be silly to say “My house doesn’t take up space, because my idea of my house doesn’t take up space.”

    Similarly, the conception of a “point” is supposed to refer to “a precise location in geometric space.” It would be equally silly to say “points don’t take up geometric space, because my idea of a point doesn’t take up geometric space.”

    The fundamental essence of geometry is about space – whether physical space, mental space, conceptual space, or any other kind of space. Therefore, the objects of geometry must themselves take up space. There is no such thing as “a precise location in space that isn’t a precise location in space.”

    An Alternative Theory

    So, let me present an alternative geometric framework. This is just the beginning of a whole new theory of mathematics that I call “base-unit mathematics.” This is the fundamentals of base-unit geometry:

    1) All geometric structures are composed of base-units. These units are referred to as “points.”

    2) Each point is spatially extended.

    3) In any conceptual framework, the extension of the base-unit is exactly 1. Within that framework, there is no smaller unit of distance, by definition.

    4) All distances and shapes can be denominated in terms of the base-unit.

    These foundations form a logically sound foundation on which to build geometry.

    Put points together, and you can compose any shape you like, without any irrational numbers. Every object except the base-unit is a composite object, made up of discrete points. This is why I said earlier that I like Euclid’s original definition of a “point” as “that which has no part.” Base-units have no parts; they are the parts which form every other whole.

    I recognize there will be lots of objection to this way of thinking about geometry. Those objections will be addressed in detail in future articles.

    To gain an intuition about this framework, you can think of “points” as “pixels”, which we all have experience of. All of the shapes and objects you might encounter in a hi-res VR simulation are actually clumps of pixels, though they might appear “perfectly smooth” from our macroscopic perspective.

    A few of the nice implications of this theory:

    This is a line:

    Horiz-line

     

    This is a circle:

    2000px-Circle_-_black_simple.svg

     

    And it has a demonstrably rational pi:

    Pi-unrolled-720

    (Note: this GIF was taken from Wikipedia to show the supposed irrationality of pi. Yet, if you’re aware of what you’re watching, it’s actually a demonstration of the rationality of pi. You’re looking at a GIF of the logical perfection and precision of base-unit geometry!)

    What’s the ratio of this circle’s circumference to diameter? Simple: it’s one integer over another – however many base-units make up the circumference, divided by however many units make up the diameter. And, as it so happens, as long as the circle isn’t constructed from a tiny amount of base-units, pi ratios will work out to around 3.14159 (Though, if we’re being perfectly precise, we must denominate in terms of fractions, as decimal expansion can be dubious within a base-unit framework. But that’s a future article.). There is no “generic” or “ideal” circle. There are concrete, actual circles, each of which is a composite object constructed by a finite number of points.

    Among other things, this also means there’s no such thing as a “unit circle” – a supposed circle with a radius of 1. There are no diameters that have a distance of 1. You can’t create a circle using only one pixel.

    Within this theory, “circles” are exactly what you’ve encountered. “Points” are locations in space that are actual locations in space, and “lines” are what everybody knows they are.

    Base-unit Intuition

    Obviously, this topic requires a lot more explanation and work, not just in geometry, but everywhere that the metaphysics of mathematics is mistaken. I cannot cover all the objections to base-unit geometry in this article, but I will explain a few more ways of thinking about it and why it’s superior to standard orthodoxy.

    First of all, this framework fully explains all of the phenomena we experience, and it loses exactly zero explanatory power when compared to standard Geometry. Every shape, every circle, every line, every point, every spatial experience that we’ll ever have can be explained, without positing the existence of extra entities. We do not experience perfect circles; therefore we’ve no reason to theorize about them.

    Furthermore, base-unit math is more logically precise than the orthodoxy. Anybody who’s worked with “irrational pi” must use approximations. They cannot use an actual infinite decimal expansion. They are forced to arbitrarily cut off the magnitude for pi in order to use it. Not so with base-unit geometry. Perfect precision is actually possible, since there are no approximations or infinite decimal expansions to deal with. This might not be a big deal right now, but as technology approaches the base-unit dimensions of physical space, it might actually make a big difference.

    Here’s a short, interesting aside about pi’s infinite decimal expansion:

    What’s going on when orthodox mathematicians are calculating out further and further decimals of pi? Are they grasping at “the Perfect Circle’s true ratios”? No. What they’re doing is calculating the pi ratios for circles with ever-smaller base units. As the base unit shrinks – or as the circle gets larger in diameter – the ratio of its circumference to diameter changes ever-so-slightly. These calculations are immediately practical, in the same way that trig tables are practical. They are pre-calculated values that are applicable and accurate for a given circle of a given size.

    (If you want to understand why pi changes slightly, think of it this way: as the size of the base-unit increases, the area enclosed by the circumference shrinks; as the size of the base-unit decreases, the area enclosed by the circumference increases, yet at a diminishing rate. The smoother the edge of the circle, the larger the area of the circle.)

    On this note: base-unit geometry does not require an “ultimate base-unit.” In other words, every conceptual scheme will have a base-unit by logical necessity, but that doesn’t mean you’re prevented from coming up with a different conceptual scheme that has a smaller base unit.

    Think of it this way: any given photograph will contain a finite number of pixels. It will have a base-unit resolution. However, that doesn’t mean it’s impossible to take a photo with higher res. Similarly, any given circle will have a base-unit resolution, but that doesn’t mean it’s impossible to conceive of one with higher res (smaller base-units).

    We might even run into the limits of the physical world. Physical space must have a base-unit, which means within our physical system, there is no smaller unit. However, that doesn’t mean we’re prevented from talking about smaller-dimensional base units. Those objects simply won’t correlate to our universe. Who knows – perhaps we could say true things about a different physical universe that has smaller base-units.

    Note: this also perfectly correlates with my resolution to Zeno’s paradoxes. Space must have a base-unit, if motion is possible.

    A great example of base-unit phenomena is the fractal. Supposedly, fractals only make sense within the conceptual framework of “infinite divisibility.” This is not correct. Fractals make much more sense within a base-unit context. Consider this image:

    Mandelbrot_zoom

    This looks like a prime candidate for “infinite divisibility.” However, it’s an illusion. At any given time, there is a base-unit resolution to this image. As the image “zooms in”, new units are created, all denominated in terms of pixels. At no point are you looking into infinity; you’re always looking at a finite number of pixels. If you doubt this, you may count the pixels. The object is being constructed as you watch it. The same happens in mathematics; the objects get constructed as you conceive of them. Much more will be said about this in future articles.

    Polygons and Greeks

    I want to quickly address one objection that will inevitably arise – those who claim that the images of circles in this article aren’t actually circles; they are polygons. The edges are a bunch of little straight lines; they aren’t perfectly smooth. If this is true, then it’s no criticism of base-unit geometry, because all the round objects that we encounter would be polygons. Therefore, our mathematical theories should be about polygons; we experience nothing else. I want to know about the properties of this shape:

    2000px-Circle_-_black_simple.svg

    I don’t care what you call it. Base-unit geometry can tell you about the properties of that shape.

    The Greeks also made this mistake when talking about circles – as if they were constructed from an “infinite number of lines.” This is incorrect. Circles and polygons are composed of a finite number of points, not lines. Lines don’t compose anything; they are themselves composite objects.

    Imagine constructing a circle in the sand.

    circle-in-the-sand

    What is the area of this circle? I guarantee it’s a finite, rational number. You can literally count the grains of sand which compose it. The circumference is composed of grains of sand, as is the diameter, as is the area. They are all integers.

    The last argument I will address in the article will come from those who think a “circle” isn’t a shape; it’s a mathematical expression. Something like (x² + y² = r²).

    This is just another metaphysical confusion that conflates symbols with the object the symbols are supposed to be describing. It’s like saying, “’Apples’ are synonymous with the words ‘a red fruit.’” This is confused. The words “a red fruit” are a description of the object, not the object itself. The formula like (x² + y² = r²) will describe the shape of a circle – or, if you prefer thinking about it this way – it’s a rule for constructing a circle. It is not itself a circle.

    That’s where I’ll end this article. There is much more to say in the future. Mathematics is not exempt from criticism or skeptical inquiry. Nor is it exempt from the need for precise metaphysics. For all the reasons I outlined in this post, there is plenty of room for alternative – and superior – conceptions of geometry. Base-unit geometry loses no explanatory power, eliminates an infinite number of unnecessary objects, and gives a logical foundation on which to build a stronger theory.

    If you don’t believe in the existence of “perfect circles” – made up of an infinite number of zero-dimensional points – then you do not believe pi is irrational, and you’ve joined an extremely small group of intellectual lepers. You may now expect mockery and condemnation for your heresy.

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