Steve Patterson

Author: Steve Patterson

  • Is Everything Quantifiable?

    There’s an ongoing quest to reduce everything to mathematics. It’s part of the reason we’re in a dark age. Seems like a good time to ask the question: is everything quantifiable? Were the Pythagoreans correct in saying that “All is number”?

    Consider three statements:

    1 Alice is taller than Bob.

    This claim is easy to quantify. Alice and Bob have bodies that are composed of atoms which take up space—they exist in the geometric realm. To figure out whether Alice is taller than Bob, count the number of geometric units from the bottom of the feet to the top of the head. If A > B, then Alice is taller than Bob. Simple.

    2. Alice is happier than Bob.

    This claim is harder to quantify. “Happiness” does not seem to exist in the geometric realm—it’s more mental than physical, and the mental is notoriously hard to quantify. There aren’t happiness-units that we know of. But let’s try.

    Suppose that we create a new type of scanner. By pointing it at someone, you can “see” some underlying brain and neurological activity and detect chemicals like dopamine and serotonin. Perhaps there isn’t a specific happiness-unit that you can count, but there are a bunch of corresponding things you can—good enough to reliably predict that somebody is “happy” or “not happy” depending on the readout of the scanner.

    In that situation, we could say that for practical purposes happiness is quantifiable, because we have a happiness-meter which could reliably measure the quantifiable aspects of happiness.

    3. Alice is more virtuous than Bob.

    This claim is quite difficult to quantify. Virtue does not appear to be geometric nor a description of a body-state. It’s very abstract.

    When we say that Alice is virtuous, what does that mean? What are we describing?

    I don’t know how to describe it precisely. It’s an abstract relationship between a person, their actions, and their environment. It rests in the moral, ethical, spiritual, and intellectual dimensions that intersect with the geometric/physical but is not reducible to it.

    Can we imagine scanning Alice with a virtue-meter, like we scanned her for happiness? Are their enough corresponding physical states? Instead of dopamine, might we find virtuamine?

    Probably not. Perhaps we could some day, but it’s so speculative that it feels silly. I think the reason is this:

    The more abstract something is, the more difficult it becomes to quantify.

    Virtue is more abstract than happiness; happiness is more abstract than height. The further up the abstraction chain, the less quantifiable—perhaps by definition.

    Being abstract and non-quantifiable doesn’t imply being less real. Virtue is just as real as height. Abstract stuff is just as real as concrete stuff. It just isn’t quantifiable.

    It’s one thing to say, “In theory, we might some day be able to quantify virtue.” It’s quite another to say, “Hey guys, here’s my virtue scanner that I developed with the most sophisticated modern technology!” Anybody claiming such a thing in 2023 does not understand the complexity problem.

    Unfortunately, that’s the type of mistake that is currently plaguing modern thought—the premature application of mathematics to domains which are too complex for quantification. Biology, economics, epidemiology—scientists are way too quick to develop mathematical models, and they end up oversimplifying the world to an absurd degree. Statistical reasoning generally is shot throughout with these kind of abstraction/quantification errors.

    Non-mathematical reasoning is far less impressive to the modern mind, but it accounts for more complexity; it sits higher in the abstraction hierarchy. Eventually we’ll figure this out.

  • Sensations and Interpretations

    As I returned from my morning walk, I saw a bright green note attached to my front door. Odd, I didn’t notice it when I left only 20 minutes prior. Maybe the mailman came early.

    As I got closer to the door, the note seemed to vibrate then suddenly disappeared.

    “Oh.” It wasn’t a note. It was a reflection from my neighbor’s colorful ATV parked in their driveway.

    This banal experience actually points to some deeper truths about the relationship between our minds and the world.

    Feeling and Thinking

    There is a difference between your sensations and your interpretations of them. Usually, sensation and interpretation are seamlessly unified—we automatically blend our sensations and interpretations together. When you say, “I stubbed my toe on the table,” we really believe that we stubbed our toe on the table—that is, we believe we inhabit a world of three-dimensional space filled with tables and toes that are stubbable.

    Normally, this system doesn’t cause too much trouble. We probably do live in a 3D world where our theories about “toes” and “tables” are good enough for practical purposes. However, sometimes it is critically important to distinguish sensation from interpretation—it’s a matter of life or death, guilty or not-guilty.

    Sensation and interpretation are often so tightly synced, it takes deliberate practice to de-sync them. It’s natural to feel like our sensations are just as “real” or “true” as our interpretations of them, but sensations cannot be wrong in the same way that interpretations can. My morning walk provides us with a nice illustration.

    What Do You See, Really?

    As I returned from my morning walk, what did I see?

    Clearly, I did not see a note on my door. It’s tempting to say, “I really saw a reflection,” but even this is not solid enough. I might be mistaken about it being a reflection.

    What I really saw was a patch of green. A green blob in my visual field, surrounded by other blobs of color. I interpret these blobs as physical objects—a “note” or “reflection” on my “door,” but I might be wrong in my interpretations (for example, if I mistook my house for another).

    Even if I was hallucinating or dreaming—if there was no door at all—I really did see a green patch of color. I might be wrong about my theoretical interpretation of my sensation, but I can’t be “wrong” about the facts of my sensation, assuming my memory is reliable.

    Even in Court

    Martha takes the stand and testifies that she really heard gunshots at 9pm sharp. The defense asks, “Walk me through that evening. What exactly did you hear?”

    She responds, “I heard people yelling, a loud BANG, followed by people screaming.”

    The defense responds, “How do you know it was a gunshot and not, say, fireworks? It was the 4th of July, after all.”

    “Well… I guess it could have been.”

    Shoulder or Kidney?

    Until the age of 21, I dealt with nasty shoulder pain that seemed to be caused by exercise. I saw a bunch of doctors, but nobody could figure it out. (I distinctly recall my basketball coach thinking I was making it up.)

    The closest I got to a satisfactory explanation was a doctor who ran an MRI and said I might have a micro-tear that wasn’t showing up on the scans.

    Fast forward to January of 2011, when I discovered that I had a congenital abnormality with my kidney. I got laparoscopic surgery and then noticed, over the following months, I was no longer getting shoulder pain. I had no idea why, until I talked to a nurse who told me she experienced the same thing. For some reason, the congenital abnormality was irritating my phrenic nerve, which caused referred pain up to my shoulder. The phrenic nerve is connected to the diaphragm, which explained why the pain was exercise induced.

    Here’s another example where the interpretation is critically important. For years, nobody could figure out what was wrong, and at least one person thought I was making the sensation up—that it was in my head—because they lacked an interpretation that made sense to them. But I wasn’t making it up; I was not wrong about the existence of the sensation. I just didn’t have the right interpretation of the sensation; in fact, I would have sworn under oath that something was wrong with my shoulder, when in reality the problem was with my nerve.

    This pattern repeats itself over and over across different domains and aspects of life. In most cases, we can keep our sensations and interpretations in sync without too many problems. But sometimes, it becomes necessary to de-sync and carefully distinguish between an experience and the theoretical interpretation of it.

  • Theoretical Pluralism and Chess

    I am drawn to a weak form of religious pluralism. 

    The strong form says, “All paths lead to the same God. All approaches are equally valid. There is no right or wrong way.”

    The opposite extreme says, “There is exactly one denomination of one religion which is the correct path to God. All other paths are heretical and wrong.”

    I think the truth is somewhere in the middle. Many paths do lead to the same God; many approaches work, but the different paths are not equally true or sophisticated. Some paths you can sprint down; other paths are dangerous and will take you in the opposite direction of truth.

    In other words, there are indeed many ways to skin a cat. But there are many more ways to do it wrong. Chess provides us with a great analogy.

    There are different schools of thought in chess, different theoretical perspectives. Around a century ago, there was a notable tension between the classical (or “modern”) school and the hypermodern school. On a few critical points, the moderns and the hypermoderns had radically different perspectives.

    Perhaps the key disagreement was this: how should you exert influence over the center of the board in the opening? The classical approach says that you should occupy the center with your pawns. Here’s an example of the Queen’s Gambit Declined, where black has responded to 1. d4 with … 1. d5, putting his own pawn right in the center.

    The hypermoderns took a different approach. They said the center can be influenced indirectly, from the flanks and from distant pieces. They even invited their opponent to occupy the center, so they could undermine their pawn structure later. Here’s an example of the same opening from white, but a very different approach from black in the Queen’s Indian Defense:

    Notice that black has no pawns in the center and is instead exerting influence with his knight and bishop. These are two very different approaches. So who is right?

    The answer is: it depends. There is truth in both perspectives. Even though the principles are opposite of one another, they both work when skillfully executed. Right now, it looks like the most advanced chess theory is some hybrid of modern and hypermodern (perhaps the “hyper-hyper-modern”?) Both modern and hypermodern openings are still used today at the highest levels.

    Returning to the question of pluralism. It would be an obvious mistake to conclude, “Since the modern and hypermodern openings work, there is no truth in chess! All openings are equally good and valid!”

    Just like it would be a mistake to conclude, “There is only one opening that works. All other openings are wrong and lead their users to hell.”

    The truth is somewhere in the middle. Many different openings work. In fact, with the usage of AI in chess, openings that were recently considered broken are being resurrected.

    Different chess principles and theories can also work, even if they are directly opposed to each other. And yet, despite this degree of pluralism, there are still obviously superior and inferior chess moves. There are openings with objectively higher levels of success than others.

    There really is truth to be discovered in chess. These truths might eventually be synthesized into the One True Theory, which explains the nuances of why the classical and hypermodern openings work and when they don’t. Some day, we might even have powerful enough technology to solve chess and tell us, once and for all, whether White can force mate from the opening, or whether perfect play ends in a draw.

    But chances are, for the foreseeable future, we are not going to have the One True Chess Theory. We’re instead stuck with lesser theories which vary in their level of sophistication.

    So it is, I claim, with philosophical, religious, and scientific theories. A weak form of pluralism is the right approach to capture the most truths.

  • A New Paradigm to Explain Chronic Illness/Inflammation

    Douglas Kell is a systems biologist with a phenomenal new theory. He calls it “The Iron Dysregulation and Dormant Microbes hypothesis.” Everybody who in interested in chronic illness and inflammation, Lyme disease, ME/CFS, COVID/long COVID, and nutritional immunity needs to read his article. I’ve read it twice in the last couple days, but it’s extremely dense and will require many more attempts to digest the whole thing.

    Over the past decade, my wife and I have been forced to develop our own, eccentric theory of chronic illness. Our theory includes a ton of different concepts from different researchers, practitioners, and from our own experiences, but we had not seen anybody else synthesize them together until reading the Kell paper.

    He’s connecting the dots on a huge range of different conditions. As he says from the abstract: “These diseases include neurodegenerative (e.g. Alzheimer’s, Parkinson’s), vascular (e.g. atherosclerosis, pre-eclampsia, type 2 diabetes) and autoimmune (e.g. rheumatoid arthritis and multiple sclerosis) diseases.”

    The breadth and depth of the IDDM hypothesis is extremely impressive, and it accords with our own independent research. It’s not perfect or complete, but it’s superior to any other theory I’ve read, and it gives researchers/practitioners a thousand different testable hypotheses.

    The article is long and extensively referenced. At the end, he summarizes it into seven main points. I’ll share six of them:

    (1) A systems biology strategy was used to show that chronic, inflammatory diseases have many features in common besides simple inflammation.

    (2) The physiological state of most microbes in nature is neither ‘alive’ (immediately culturable on media known to support their growth) nor ‘dead’ (incapable of such replication), but dormant.

    (3) The inflammatory features of chronic diseases must have external causes, and we suggest that the chief external causes are (i) inoculation by microbes that become and remain dormant, largely because they lack the free iron necessary to replicate, and (ii) traumas that induce cell death and the consequent liberation of free iron; these together are sufficient to initiate replication of the microbes.

    (4) This replication is accompanied by the production and shedding of potent inflammagens such as lipopolysaccharide or lipoteichoic acid, and this continuing release explains the presence of chronic, low-grade inflammation.

    (5) Recent findings show that tiny amounts of these inflammagens can cause blood to clot into an amyloid form; such amyloid forms are also capable of inducing cell death and thereby exacerbating the release of iron.

    (6) Additional to the formal literature that we have reviewed here, it seems to be commonly known that infection is in fact the proximal cause of death in Alzheimer’s, Parkinson’s, rheumatoid arthritis, multiple sclerosis, etc. It may, for instance, be brought on by the trauma experienced following a fall. Such infections leading to death in chronically ill patients may involve the re-awakening of dormant bacteria rather than novel exogenous infection.

    Every point deserves extensive elaboration.

    If Kell is right, it’s a condemnation of the methods of modern medicine, which assumes “If I can’t culture it, it doesn’t exist.” If we live in a world where most microbes are dormant… the implications are staggering.

    The connection between LPS, amyloid clots, and inflammation is also promising. It might give us a glimpse into the cyclical inflammatory patterns that so many practitioners describe—and it might explain why COVID’s spike protein was particularly nasty in triggering CFS.

    Within this framework, widespread supplementation and fortification of food with inorganic iron might end up being the next public health scandal.

  • Three Confirmed Paradoxes in Mathematics

    Outside of mathematics, it’s considered a problem when a theory generates paradoxes. But within mathematics, some paradoxes are accepted and celebrated—as if they are special insights into the magical and mysterious world of math.

    The concept of the infinite totality is the #1 generator of mathematical paradoxes, and over the course of a few centuries, instead of rejecting the concept as flawed, mathematicians enshrined it at the foundation of their theories. Today, most people cannot imagine that this concept is flawed—in fact, given the intellectual social hierarchy, people are more willing to accept patent absurdities (i.e. real paradoxes) than to entertain the idea that mathematicians are wrong.

    Endless criticism can be directed at the concept of the completed infinity, but rather than engage in philosophical analysis, I thought it would be helpful to list a few uncontroversial paradoxes—that is, those paradoxes that are actually accepted by the mainstream.

    Don’t take my word for it. The mathematicians speak for themselves:

    1. Hilbert’s Hotel

    Perhaps the most famous of the paradoxes of infinity, Hilbert’s Hotel is a thought experiment where a hotel has an infinite number of rooms, all of which are occupied. Yet, it can still accommodate additional guests, simply by moving them around in a clever way. In fact, even if every room is full, the hotel can accommodate an infinite number of new guests.

    If that doesn’t make sense, then good for you. You have not lost your mind yet, unlike the producers of this informative TED video with 23M views:


    2. Gabriel’s Horn (the Painter’s Paradox)

    Gabriel’s Horn is an object with an infinite surface area yet only a finite volume, which leads to the famous Painter’s paradox where these two propositions are simultaneously true:

    (A) The horn can hold a finite amount of paint within it (exactly π units of paint). Yet,
    (B) The surface of the horn cannot be painted with a finite amount of paint

    Listen to this video explaining it. Or skip to the 16 minute mark to see this mathematician embrace the absurdity by saying, “That’s the paradox! I tried to think about that and was like [mind blown].”


    3. The Banach-Tarski Paradox (BTP)

    The BTP is supposed to demonstrate that it’s possible to deconstruct a sphere into a finite number of parts, and simply by re-arranging the parts, you can end up with a duplicate sphere of the same size. The sphere gets doubled.

    (I know, I know, your textbook told you that the BTP follows from the axiom of choice, not the axiom of infinity. But infinity does still make its way into the paradox, because it requires the spheres to be broken down into a finite number of sets composed of an infinite number of points.

    If you want to attribute the paradox to Choice instead, that’s fine, but then it becomes a demonstration how concepts other than infinity can draw mathematicians into self-evident absurdity.)

    This explainer video by the popular VSauce has a whopping 40M views:

    For more than a century, mathematicians have gotten away with accepting paradoxes, celebrating them, and even using them as demonstrations of their formidable intellect. But this situation will not last forever. As we emerge from our present dark age, cherished assumptions in math will be revisited, revised, and the discipline will be put on discrete foundations. And lots of people will rightfully be embarrassed.

  • The Objectivity of Structure Outside our Concepts

    I am guilty of having been a conceptualist for most of my life. I believed that the patterns and relationships we see in the world are actually part of our own minds—they exist only as abstract concepts. My favorite illustration of this idea is constellations. To the conceptualist, constellations would not exist without minds, though the individual stars that compose them would. The universal principle is that parts get unified into wholes by concepts. Simple substances are glued together into pluralities in our mind, but they are not glued together in the world.

    I now believe that conceptualism is false. The world outside our mind is actually glued together; relations are mind-independent; and patterns are objectively real.

    The famous Ship of Theseus is a great thought experiment that helps us generate the right intuitions. Imagine the ship is deconstructed, plank by plank, until every piece of wood has been replaced. The ancient philosophical question is asked, “Does it remain the same ship?”

    This question touches on important issues in the philosophy of mind, language, and metaphysics. I want to use it to illustrate the differences between concepts and structure. To think clearly about the ship, it’s helpful to slice it into three pieces:

    1. The atoms which compose the ship
    2. Our concepts about the ship
    3. The abstract form (the pattern) of the ship*

    (1) The atoms are easiest to understand. There are a bunch of individual atoms and molecules which compose the ship. As the planks get removed and replaced, the atoms themselves get removed and replaced. If we say, “The ship is identical to its atoms,” then the ship obviously changes when the atoms change.

    (2) We have ideas about ships. We have our own conceptual criteria for determining whether we label something as a “ship” or “not a ship.” Within this conceptual criteria, we find a complex set of different ideas—notions about shape, buoyancy, purpose, etc—that have to be bundled together in the same object. A life jacket, for example, is buoyant and intended to float, but it isn’t the right shape to be called a “ship.”

    (3) I claim that the form of the ship stands apart from its atoms or our concepts. The atoms stand in a particular geometric relationship with each other. They are arranged a particular way. There is a pattern of atoms, and even if the atoms are replaced, the pattern remains the same. Regardless of our personal linguistic habits or conceptual criteria, the pattern remains the same.

    Finding Clarity

    These three concepts are powerful enough to think clearly about the Ship of Theseus. As the planks are replaced, whether the ship changes or not depends on what we’re focusing on. Consider three possible perspectives here:

    1 Atomism / Nominalism

    Atomists are the most extreme of the materialists, claiming that the universe is entirely composed of atoms and the void. In this view, the Ship of Theseus does not exist over and above the atoms; the “ship” is really just a way of talking about atoms. It’s just a name, with no corresponding or underlying pattern.

    More generally, composite objects cannot really exist, as their atoms are constantly in flux—by merely blowing on the ship, the atoms move and shift.

    2 Conceptualism

    The conceptualists add more stuff to the picture. They want to connect the atoms somehow. They want to recognize a pattern, in addition to the atoms. But this pattern is mental or conceptual, not physical. What turns “a bunch of atoms” into “a ship” is our own abstract conceptual criteria, and without minds, “ships” do not really exist.

    The conceptualist has a good explanation for why The Ship persists over time, even if the atoms change. Ship-ness is about our own mental classification scheme, not about particular atoms. This classification scheme can even vary between individuals. We might disagree about whether [Object X] qualifies as a “ship” because of the ambiguities in our own concepts, not because of ambiguities in the physical world.

    3 Realism / Platonism

    The realist adds even more stuff. In addition to the atoms and the concepts, there is also a mind-independent structure “out there” in the world. The atoms really are glued together; the relationships between the atoms exist outside of our minds.

    The realist has a good explanation for the behavior of the ship. For example, why don’t ships disintegrate when placed into water? What makes the atoms cohere?

    If all that exists are individual atoms, then it’s not clear why the behavior of atoms is so coordinated. Atoms do not appear to be isolated from each other; they are connected in the world. Even if our minds disappear, atoms still behave relative to other atoms—meaning, their relationships are mind-independent.

    The geometry of the ship is also objective. The atoms stand in a particular spatial relationship with each other, regardless of our concepts. The form/arrangement really is “out there.”

    The realist has an excellent explanation for the persistence of The Ship. There is some objective, abstract pattern of a ship, and even if the atoms change along with the planks, the form remains the same. The structural pattern is not physical, yet it is mind-independent.

    To (most) realists, we humans do have our own conceptual criteria and classification schemes. Patterns do exist in the mind, but sometimes, the patterns in our mind correspond to patterns in the world. Sometimes, the abstract forms in our mind match the abstract forms in the world. In fact, when we have “true beliefs”, it means our mental structures are mirroring real-world structures.

    This is not meant as a rigorous defense of realism, rather it’s just a helpful way to understand the argument. A longer defense can be read here.