Steve Patterson

Author: Steve Patterson

  • The Problem of Physical Interaction

    Reductive physicalism undermines itself and cannot explain how interaction happens at all. Let’s start with a syllogism:

    1. All interaction is relational.
    2. All relations are non-physical.
    3. Therefore, all interaction is non-physical.

    This is a valid argument; the conclusion necessarily follows from the premises. But are the premises true?

    (1) should be uncontroversial. “Interaction” is inherently relational—an interaction is the state of A affecting the state of B.

    Therefore, (2) is where the argument lies. I’m going to make the case that relations are, by definition, non-physical.

    Atoms “Bumping Into Each Other”

    Let’s take a simple example. Two hydrogen atoms colliding with each other.

    No matter how you conceive of the atoms—as probability clouds, states of space, fields—the question arises: why don’t the atoms simply “pass through” each other? Why do they interact at all? Why do the states of one field/cloud/structure affect the states of another?

    There are different ways to answer, but the answers look similar in the abstract. There are some physical objects and physical processes that give rise to other physical objects and processes, generating a regress of physical explanation. So at some point, physical interaction always ends up appealing to laws, rules, or principles—inherently abstract things that specify what happens when A relates to B in a particular way. It’s a variation of, “Specific structures behave in specific ways because of the laws of physics.” Those laws are sometimes captured with mathematical expressions.

    Even describing the elementary “behavior” of physical objects requires abstractions—the concept of “behavior” itself is relational and non-physical, as “behavior” is about how patterns are related across time.

    So “atoms bumping into each other” turns out to be a mixture of physical and abstract. Atoms are physical (let’s say), and bumping into each other is a highly complex, abstract, relational thing.

    (Note: if you are tempted to say, “The relation is itself physical; it’s like a string attached to the two atoms”, that does not work, because we’d require an explanation for how the string affects the atoms—the string would be, in effect, another atom, and therefore we’d be left asking, “By what mechanism does the string interact with the atoms connected to it?”)

    “It’s Just a Description!”

    One attempt to avoid this conclusion is to say, “No no, physical laws don’t have any causal power. They are merely descriptions of observed patterns!”

    But this only creates a bigger problem. The descriptionists are in principle rejecting explanations altogether, which is not far from a rejection of rationality. If rationality is about finding explanations for things, the descriptionist insists one should be content with no explanation for causal interaction at all.

    Ironically, this position does give credence to the syllogism at the beginning of this article. If interaction is relational, and relations are non-physical, they conclude interaction must not be happening at all, and we’re left with the inexplicable appearance of interaction.

    This leaves us at a fork in the road. When you look deeply enough at the world, it starts to look back, and the temptation is to close your eyes.

  • Geometry as Logic

    Mathematics is an extension of logic. Every domain in mathematics can be reduced to logic. Geometry is the logic of space.

    The most foundational, granular unit of any quantitative system is one bit. This is true by definition–whatever the fundamentum is, it’s the bit of that system. The granular, base unit.

    In geometry, the foundational unit is therefore one bit of space–the geometric atom. We will call these atoms points.

    All geometric structure can be reduced to sets of points. “Shapes,” therefore, refer to specific sets of points.

    Position and State

    We can build geometries out of two fundamental concepts: position and state.

    Position: where a point is located relative to other points.

    State: the state the point is in.

    These two concepts give us the most granular way of talking about any geometric structure. In other words, we can describe all the information by referring to “That point in that state.”

    It’s a Matrix

    I don’t claim to be a mathematician, but from what I can tell, this concept is best captured by matrix theory. In the simplest model (allowing only two possible states for each point) space is essentially an array of bits.

    In more complex models, the points can be in a range of possible states, not just 0 or 1.

    I know some physicists and computationally-biased mathematicians will appreciate this perspective. So let me make it more controversial. 

    My claim is this is the a priori geometry. I believe this is the way minds actually think about space, the way minds must think about space, and the only way for space to be. Since logic and existence are inseparable, in order for space to exist, it must be logical, and this is the logic of space: position and state.

    Every geometric model can be put into this framework. In fact, it’s the litmus test for geometry–if it cannot be put into this framework in principle, it’s logically incoherent.

    Computers all over the world, rejoice!

    Physics is Geometry + Time

    Physics is simply keeping track of geometry. It’s observing how geometric states change over time–and therefore figuring out how this part of the matrix connects to that part of the matrix. We discover patterns of state changes over time and infer the laws of physics from them.

    Not a Reduction of Everything

    The physical world can be reduced down to quantitative, logical analysis. That does not imply the entirety of existence can be reduced in such a way. Metaphysical pluralism allows for things like consciousness, information, and abstract stuff to exist outside of the matrix. They are in separate but related domains.

    Give it a few decades, and I expect this framework will conquer everything.

  • Everything in Discrete Space

    I’m working through the implications of discrete space and am starting to build some intriguing intuitions. I am trying to reduce the physical world down to a bunch of geometric atoms changing state—essentially, to a grid of voxels.

    I don’t claim the following is true, only that it’s a coherent way to explain a bunch of concepts, including motion, mass, fields (gravity and electromagnetism), local and non-local interaction, fluid dynamics, and even exotic things like quantum tunneling and time dilation. All of these phenomena follow from a simple model with a simple axiom.

    Model: The physical world is composed of discrete atoms of space (“voxels”) in particular states. These states are called “bits.” In the simplest model, there are only two possible states—off or on, 0 or 1, empty or full.

    Axiom: Two bits cannot occupy the same space.

    That’s the setup. Let’s see how far we can push it.

    The basics:

    “Motion” is a transmission of bits through the grid. The voxels themselves do not move; instead, their bit state transfers.

    Local interaction happens when there is a local “collision” of these bits.

    Non-local interaction happens when bit states are connected at a distance.

    Mass is a type of geometric structure in the grid. It is a pattern of voxels.

    Relative to the individual voxel, objects like atoms are incredibly large, dense structures.

    Fields, like mass, are a type of structure in the grid. The difference between mass and fields is only the configuration of their voxels. These different configurations produce different patterns when interacting with the world—e.g. the gravitational and electromagnetic fields create different “forces” because they are different geometric structures. Your car acts differently whether it’s driving on gravel or asphalt, going uphill or down.

    Objects as Extended Structure:

    Where are the boundaries of objects?

    In this model, the totality of an object includes all its geometric structure—both its mass and fields. It’s helpful to think of mass as “macrostructure” and fields as “microstructure”. A gravitational field, then, could be considered as part of the extended structure of an object—reaching beyond its dense atomic structure to interact with distant objects. So for example, the mass of your body affects the motion of the sun; therefore, your extended body reaches to the sun.

    Fields and Biased Motion:

    Motion is the transmission of bits through the grid. As the bits move, they must interact with the existing structures in the grid. This includes macrostructures (atoms) and microstructures (fields).

    The gravitational field is simply a microstructure that biases motion towards its center of mass.

    Take bowling as an analogy. You throw the bowling ball down the lane, towards a triangular structure of pins. If it lands on the left side of the triangle, it will bounce off to the left. If the ball lands on the right side, it will bounce towards the right. So we could say the triangular structure of the pins is biasing the motion of the ball (preventing it from moving straight).

    With a gravitational field, if it’s actually just a microstructure in a grid, we could say it has an inward bias. The greater the mass, the denser the field, the stronger the bias.

    If this is correct, then we could say gravity has a shape. That is, there’s a micro-structure that we call “gravity” which forms a field that interacts with passing bits and nudges them towards a center mass. Rather than space itself being distorted, gravity is a structure in space that distorts motion.

    Electromagnetic fields are more complex. Instead of simply nudging bits towards a center mass, they bias motion depending on other factors like charge and velocity (which can also be interpreted geometrically). “Field lines” would then map real biases generated by underlying geometric structures.

    Exotic Intuitions

    This model also gives a plausible reason for “time dilation.” Larger masses create denser microstructures in the field, which increases the interactions encountered by propagating bits. These interactions effectively slow the transmission of states, resulting in an observable time dilation effect—akin to moving through a denser medium.

    And the “quantum tunneling” phenomenon has a perfect explanation. In discrete space, objects have jagged edges, which means the “energy barriers” between boundaries are neither uniform nor smooth. This means, for purely geometric reasons, some bits can “hop” across boundaries effortlessly. In fact, in discrete space, lines can “intersect” without even sharing a common point!

    If space is discrete, we would expect to see tunneling. I consider the empirical discovery of tunneling to be evidence of the discreteness of space. (Imagine making such a prediction prior to the discovery of tunneling—people would think it’s ridiculous and impossible!)

    A Conceptual Toolbox

    I am early in my journey through theoretical physics and still playing with ideas. I only have a handful of strong beliefs. However, I’m slowly growing my conceptual toolbox, and I suspect some of these tools will be handy indeed.

  • Information and Spirit

    The spiritual domain heavily overlaps the informational domain—the world of patterns. I don’t think there’s a complete reduction of one domain to the other, but there is considerable overlap. Consider a few spiritual ideas.

    “Telling the truth is of spiritual importance. Lies destroy, while the truth heals.”

    This is not a claim about atoms or specific biological entities. This is a claim about general patterns. Humans act based on their ideas about the world. Lies create intrinsically disharmonious patterns, while the truth creates harmonious patterns—at least in the long run. Relationships based on deception are intrinsically unstable and dangerous to humans, while relationships based on the truth are solid and stable.

    This principle is both abstract and true—the truth is a pattern in the abstract domain which lies above the material.

    “You cannot overcome evil with evil, but you overcome evil with good.”

    This is also a claim about patterns—how some patterns relate to others. Revenge begets revenge; this is true both empirically and theoretically. I often think back to a conversation I had with Dr Hirini Kaa from New Zealand who told me about the never-ending cycles of revenge within indigenous Maori groups. These cycles were only stopped once Christian settlers introduced the concept of forgiveness to them, which was revolutionary. The pattern of forgiveness is logically incompatible with the pattern of revenge; the two cannot exist together. Therefore forgiveness, when manifested in the world, is a kind of destruction of revenge.

    “Spiritual warfare is real.”

    How humans relate to other humans is an objective pattern in the world. Some relationships are objectively harmonious (a loving marriage; a safe and healthy community) and other relationships are discordant (a spiteful marriage; a toxic and dangerous community). The reality of social harmony is dependent on an astronomical number of variables, including physical, economic, political, cultural, and psychological factors. All of these variables intersect with the spiritual.

    The health of your body is connected to your nutrition; your nutrition is connected to your ideas; your ideas are connected to a million other information structures. Controversial cultural subjects like pornography and drug use are fundamentally spiritual subjects—their effects are objective and real in the domain of patterns. Spiritual degradation will eventually manifest in the world as physical degradation.

    “The spiritual world is invisible.”

    We “see” patterns differently than we see material objects. A toxic marriage doesn’t have color, a smell, or a surface area. It’s a pattern which is grasped intellectually and felt intuitively—we “see” it in terms of understanding abstract relations and we can “feel” it in our guts.

    For example, the danger and chaos of physical warfare is easy to observe with your senses. The danger and chaos of spiritual warfare has to be grasped with the intellect or felt by the intuition.

    “The spiritual world is timeless and eternal.”

    Political leaders can be assassinated. Assassination itself, as a pattern, cannot be destroyed. Individuals can stop lying. Lying itself is not going anywhere. You can individually run away from love, but you can’t kill the pattern of love.

    Humans are creatures whose heads and hearts seem to intersect the spiritual world. We have the ability to instantiate or not instantiate patterns. There is no murder in my neighborhood, but at any point, that pattern can be instantiated. The spirit of hatred is always there; the question is whether that spirit will find a host.

    There’s a never-ending battle going on—whether or not specific patterns will be instantiated. It takes spiritual strength and discipline to fight it.

    It is important to re-iterate that the spiritual world does not entirely reduce to the informational world. The metaphysics are complex and confusing. The next article will be on Matter and Spirit.

  • Why We Need to Replace Mathematics

    I was recently impressed by a series of tweets from Joscha Bach. I’ve never heard somebody use this language before.

    https://x.com/Plinz/status/1817463746031464860
    Twitter

    That’s a wonderful and provocative notion that accords with my own quixotic ideas. Perhaps we don’t need to reform mathematics, but replace it altogether. That sounds like fun.

    What’s wrong with math?

    If you ask a computer scientist, they might explain how there’s a large gap between theoretical math and applied math—mathematicians claim they can do things which computers cannot.

    If you ask a physicist, they might tell you about the large gap between math and physics—many objects and processes in mathematics cannot exist in the real world, even in principle.

    But if you ask me, I see this as an outcome of a deeper problem: the philosophy of mathematics is a total mess and has been for more than a century.

    I recently came across a document I had written many years ago about this subject for a friend. Instead of an article, it’s a bunch of bullet points. I thought it did a rather nice job of summarization, so I’ve shared some of the points here.

    The Situation with the Philosophy of Mathematics in the 20th Century

    • The foundational crises that happened around the turn of the 20th century have not been resolved correctly.
      • Some mixture of the three dominant schools—logicism, intuitionism, and formalism—is likely correct.
        • From logicism: mathematical truth is grounded in logic.
        • From intuitionism: mathematics is a human language which is designed to capture our own concepts.
        • From formalism: we must allow the utility of mathematics to stand apart from its truthfulness; bad math (even conceptually incoherent math) is often useful.
    • The metaphysics of mathematics has not been sorted out properly.
    • Mathematics does not speak for itself, and it often does lie.
    • The meaning and purpose of mathematical axioms has to be clarified.
    • Godel’s incompleteness theorems are overrated in their significance, and the proof might be entirely sidestepped with alternative mathematical philosophies.
      • His axiomatic framework was explicitly formalist.
      • The proof is baroque and hard to follow.
      • Who said Godel numbering is a legitimate mathematical process?
    • Georg Cantor’s idea of the transfinite was logically incoherent.
      • He ultimately justified his ideas with appeals to God and Divine Revelation
        • “One proof is based on the notion of God. First, from the highest perfection of God, we infer the possibility of the creation of the transfinite, then, from his all-grace and splendor, we infer the necessity that the creation of the transfinite in fact has happened.”
    • The concepts of infinite totality and infinite sets are logically flawed and must be extricated from the foundations of mathematics.
      • Historically speaking, these concepts are new and few mathematicians from previous centuries would have accepted them.
    • The concept of continuity is therefore logically flawed and needs to be replaced with the concept of absolute discreteness—that all appearances of continuity are actually underpinned by discrete processes.
      • Computers have finally proven that we don’t need the concept of mathematical continuity anymore. All continuity is discrete continuity—in other words, the appearance of smoothness is generated by underlying discrete processes.
    • We need discrete, logical replacements for so-called irrational, real, and transcendental numbers, and for the concepts of convergence and limits.
      • Therefore, the formal theory of calculus will need to be re-worked.
      • There will likely be a discrete translation key to rescue these concepts—e.g. computers are already able to do mathematics without utilizing any of the aforementioned concepts.
        • I expect we’ll find specific examples in computer science, though I don’t think whether we’ll find a general theory or general language yet, which is the ultimate goal.

    I know there are others with similar intuitions. I’ve spoken with some of them on my podcast. I expect 20th century orthodoxies to be replaced within the next few decades. The momentum is too great on our side; computers have been too successful. The gap between “theoretical math” and “applied math” is too large to ignore.

    If we can’t reform, replace!

  • 4 Steps to the Immaterial

    Immaterial things are hard to understand, and taking their existence seriously has been unfashionable for centuries. Modern materialists have gotten comfortable simply defining them or laughing them out of existence.

    But since my philosophical conversion to Platonism, I now think that immaterial stuff is way more important than material stuff—and there’s even a meaningful sense in which an immaterial world is above the physical world—but it’s not an easy argument to make.

    Rhetorically, it’s hard for a Platonist to get his foot in the door. We can’t point to immaterial things, and we can’t Science them, so… what exactly are we talking about?

    Here’s four steps to intellectually grasp the immaterial:

    Step 1. Reduce the physical world down to geometry.

    Here’s what I mean: what are the essential components of the physical world? Atoms? Energy? Space?

    For our purposes, let’s say that the essential property of physical stuff is geometric—that is, spatial. Everything in the physical world happens within space or is a state of space.

    Step 2. Note that entities are related.

    The objects in space behave in particular ways. Their behavior is relational—the behavior of the electron is related to the nucleus. The behavior of one atom depends on neighboring atoms.

    Gravity is a thing.

    Matter-over-here affects matter-over-there.

    Step 3. Note that these relationships are not themselves geometric.

    What are—and where are—these “relationships”?

    Atoms are related to each other. The atoms are geometric entities, but the relationships between them are not. These relationships are most easily discovered by observing how the world changes over time.

    If we try to explain the universe as a purely geometric structure—maybe a big ol’ cube—we are left without explanation for why atoms behave the way they do. Pure geometry only gives us a static description.

    We can imagine a world which contains exactly the same amount of atoms, standing in exactly the same positions, without the universe progressing the way it does. Why do atoms interact with each other at all?

    Or to put it another way: why should the mere fact that entities stand in a particular geometric relationship to one another affect how they behave?

    https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
    Gliders in Conway’s Game of Life

    The natural answer is to say, “Oh, well there are laws of physics which determine how atoms behave in relation to each other.”

    This is correct, but it’s an admission of the immaterial—the laws of physics are themselves not physical. They are not composed of anything geometric. If you’re familiar with cellular automata, the rules that govern those systems are not found within the cells.

    Both the relationships among the atoms and the rules which govern their behavior are abstract, immaterial things.

    Step 4. Note these relationships would continue to exist without our minds.

    The final piece of the Platonic puzzle comes when accepting that these relationships would continue to exist even without our minds—that is to say, the universe would continue operating as a relational system. Physical objects wouldn’t suddenly blow apart and become ontologically-independent things, disconnected from each other.

    For many years, I thought all abstract stuff was mental. Relationships, I thought, were indeed non-physical but only exist within our minds.

    The problem with that position is that relationships exist in the world. Atoms don’t stop interacting with each other because we stop thinking about them. Even if Earth was destroyed by an asteroid, the laws of physics would still continue to bind the universe together into a connected system.

    There you have it. We’ve kicked down the materialist door and are now staring at the immaterial. The implications are vast, and there’s much more to be said.

    To reiterate in four easy steps:

    Step 1. Reduce the physical world down to geometry.*
    Step 2. Note that entities are related.
    Step 3. Note that these relationships are not themselves geometric.
    Step 4. Note these relationships would continue to exist without our minds.

    *Perhaps you object to Step 1. Fine, but please do not end up making my point by claiming, “But the physical world is more than just geometry! There’s all kind of non-geometric, non-spatial stuff happening too!” That’s another way of acknowledging immaterial aspects of the world.