Knowledge: An Empirical Sketch

Table Of Contents

  • Introduction
    • All The World Is Particle Soup
    • Soup Texture
  • Perceptual Tunnels
    • On Resolution
    • Sampling
    • Light Cones, Transduction Artifacts, Translation Proxies
  • The Lens-dependent Theorybuilding Triad
    • Step One: Conceptiation
    • Step Two: Graphicalization
    • Step Three: Annotation
    • Putting It All Together: The Triad
  • Conclusion
    • Going Meta
    • Takeaways


All The World Is Particle Soup

Scientific realism holds that the entities scientists refer to are real things. Electrons are not figments of our imagination, they possess an existence independent of your mind. What does it mean for us to view particle physics with such a lens?

Here’s what it means: every single thing you see, smell, touch… every vacation, every distant star, every family member… it is all made of particles.

This is an account of how the nervous system (a collection of particles) came to understand the universe (a larger collection of particles). How could Particle Soup ever come to understand itself?

Soup Texture

Look at your hand. How many types of particles do you think you are staring at? A particle physicist might answer: nine. You have four first-generation fermions (roughly, particles that comprise matter) and five bosons (roughly, particles to carry force). Sure, you may get lucky and find a couple exotic particles within your hand, but such a nuance would not detract from the morale to the story: in your hand, the domain (number of types) of particles is very small.

Look at your hand. How large a quantity of particles do you think you are staring at? The object of your gaze is a collection of about 700,000,000,000,000,000,000,000,000 (7.0 * 10^26) particles. Make a habit about thinking in this way, and you’ll find a new appreciation for the Matrix Trilogy. 🙂 In your hand, the cardinality (number of tokens) of particles is very large.

These observations generalize. There aren’t many kinds of sand in God’s Sandbox, but there is a lot of it, with different consistencies across space.

Perceptual Tunnels

On Resolution

Consider the following image. What do you see?

Lincoln Resolution

Your eyes filter images at particular frequencies. At this default human frequency, your “primitives” are the pixelated squares. However, imagine being able to perceive this same image at a lower resolution (sound complicated? move your face away from the screen :P). If you do this, the pixels fade, and a face emerges.

Here, we learn that different resolution lens may complement one another, despite their imaging the same underlying reality. In much the same way, we can enrich our cognitive toolkit by examining the same particle soup with different “lens settings”.


By default, the brain does not really collect useful information. It is only by way of sensory transductor cells – specialized cells that translate particle soup into Mentalese – that the brain gains access to some small slice of physical reality. With increasing quantity and type of these sensory organs, the perceptual tunnel burrowed into the soup becomes wide enough to support a lifeform.

Another term for the perceptual tunnel is the umwelt. Different biota experience different umwelts; for example, honeybees are able to perceive the Earth’s magnetic field as directly as we humans perceive the sunrise.

Perceptual tunneling may occur at different resolutions. For example, your proprioceptive cells create signals only on the event of coordinated effort of trillions and trillions of particles (e.g., the wind pushes against your arm). In contrast, your vision cells create signals at very fine resolutions (e.g., if a single photon strikes your photoreceptor, it will fire).

Perceptual Tunneling

Light Cones, Transduction Artifacts, Translation Proxies

Transduction is a physically-embedded computational process. As such, it is subject to several pervasive imperfections. Let me briefly point towards three.

First, nature precludes the brain from the ability to sample from the entirety of the particle soup. Because your nervous system is embedded within a particular spatial volume, it is subject to one particular light cone. Since particles cannot move faster than the speed of light, you cannot perceive any non-local particles. Speaking more generally: all information outside of your light cone is closed to direct experience.

Second, the nervous system is an imperfect medium. It has difficulty, for example, representing negative numbers (ever try to get a neuron firing -10 times per second?). Another such transduction artifact is our penchant for representing information in a comparative, rather than absolute, format. Think of all those times you have driven on the highway with the radio on: when you turn onto a sidestreet, the music feels louder. This experience has nothing at all to do with an increased sound wave amplitude: it is an artifact of a comparison (music minus background noise). Practically all sensory information is stained by this compressive technique.

Third, perceptual data may not represent the actual slice of the particle soup we want. To take one colorful example, suppose we ask a person whether they perceived a dim flashing light, and they say “yes”. Such self-reporting, of course, represents sensory input (in this case, audio vibrations). But this kind of sensory information is a kind of translation proxy to a different collection of particles we are interested in observing (e.g., the activity of your visual cortex).

This last point underscores an oft-neglected aspect of perception: it is an active process. Our bodies don’t just sample particles, they move particles around. Despite the static nature of our umwelt, our species has managed to learn ever more intricate scientific theories in virtue of sophisticated measurement technology; and measurement devices are nothing more than mechanized translation proxies.

The Lens-dependent Theorybuilding Triad

Step One: Conceptiation

Plato once describes concept acquisition as “carving nature at its joints”. I will call this process (constructing Mentalese from the Soup) theory conceptiation.

TheoryBuilding- Conceptiation

If you meditate on this diagram for a while, you will notice that theory conceptiation is a form of compression. Acccording to Kolmogorov information theory, the efficacy of compression hinges on how many patterns exist within your data. This is why you’ll find leading researchers claiming that:

Compression and Artificial Intelligence are equivalent problems

A caveat: concepts are also not carved solely from perception; as one’s bag of concepts expands, such pre-existent mindware exerts an influence on the further carving up of percepts. This is what the postmoderns attribute to hermeneutics, this is the root of memetic theory, this is what is meant by the nature vs. nurture dialogue.

Step Two: Graphicalization

Once the particle soup is compressed into a set of concepts, relations between these concepts are established. Call this process theory graphicalization.

TheoryBuilding- Graphicalization

If I were ask you to complete the word “s**p”, would you choose “soap” or “soup”?  How would your answer change if we were to have a conversation about food network television?

Even if I never once mention the word “soup”, you become significantly more likely to auto-complete that alternative after our conversation. Such priming is explained through concept graphs: our conversation about the food network activates food-proximate nodes like “soup” much more strongly than graphically distant nodes like “soap”.

Step Three: Annotation

Once the graph structure is known, metagraph information (e.g., “this graph skeleton occurs frequently”) is appended. Such metagraph information is not bound to graphs. Call this process theory annotation.

TheoryBuilding- Annotation

We can express a common complaint about metaphysics thusly: theoretical annotation is invariant to changes in conceptiation & graphicalization results. In my view (as hinted at by my discussion of normative therapy) theoretical annotation is fundamentally an accretive process – it is logically possible to generate an infinite annotative tree; this is not seen in practice because of the computational principle of cognitive speed limit (or, to make a cute analogy, the cognition cone).

Putting It All Together: The Triad

Call the cumulative process of conceptiation, graphicalization, and annotation the lens-dependent theorybuilding triad.

TheoryBuilding- Lens-Dependent Triad


Going Meta

One funny thing about theorybuilding is how amenable it is to recursion. Can we explain this article in terms of Kevin engaging in theorybuilding? Of course! For example, consider the On Resolution section above. Out of all possible adjectives used to describe theorybuilding, I deliberately chose to focus my attention on spatial resolution. What phase of the triad does that sound like to you?  Right: theory conceptiation.


This article does not represent serious research. In fact, its core model – the lens-dependent theorybuilding triad – cites almost no empirical results. It is a toy model designed to get us thinking about how a cognitive process can construct a representation of reality. Here is an executive summary of this toy model:

  1. Perception tunneling is how organisms begin to understand the particle soup of the universe.
    1. Tunneling only occurs by virtue of sensory organs, which transduce some subset of data (sampling) into Mentalese.
    2. Tunneling is a local effect, it discolors its target, and its sometimes merely represents data located elsewhere.
  2. The Lens-Dependent Theorybuilding Triad takes the perception tunnel as input, and builds models of the world. There are three phases:
    1. During conceptiation, perception contents are carved into isolable concepts.
    2. During graphicalization, concept interrelationships are inferred.
    3. During annotation, abstracted properties and metadata are attached to the conceptual graph.

[Sequence] Demystifying Physics

Perceptual Tunneling


Natural History

Miscellaneous Topics

Relevance To Perception

Organisms like you are immersed in a sea of particles – particle soup, if you will. Your ability to know – your epistemology – must somehow reside in connections between your mental representations, and the soup.

Peirce: The Fixation Of Belief

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Article: The Fixation of Belief
Author: C.S. Peirce
Published: 11/1877
Citations: 1048 (note: as of 04/2014)
Link: Here (note: not a permalink)
Other Resources: Outline (found this via Google Search, but quality isn’t bad)

Summarization text is grayscale, review text (my take) is orange.


Peirce kicks off this article with a historical survey, nicely showcasing the fact that the scientific enterprise is a quite recent phenomenon on this earth. This suggests that the construction of personal epistemologies is susceptible to cultural influences. As Peirce puts it, “We come to the full possession of our power of drawing inferences, the last of all our faculties; for it is not so much a natural gift as a long and difficult art.”

Peirce also gestures towards the following question: can the reliability of our faculties be evaluated on a domain-by-domain basis? Peirce invokes evolutionary theory in an important move:

Logicality in regard to practical matters is the most useful quality an animal can possess, and might, therefore result from the action of natural selection; but outside of these it is probably of more advantage to the animal to have his mind filled with pleasing and encouraging visions, independently of their truth; and thus, upon unpractical subjects, natural selection might occasion a fallacious tendency of thought.

While many of Peirce’s views on evolution show their age, this particular insight is remarkably prescient: modern philosophers are currently exploring precisely this vein. Once this research is cast to cognitive science, neuroscientists will find themselves in a position to speak quantitatively on the matter. If the above argument is born out by data, this would be a real victory for the pragmatist camp.

Doubt vs. Belief

Doubt is a singularly important notion to Peirce: he conceives it as the primary motivator for critical thinking.

Doubt is an uneasy and dissatisfied state from which we struggle to free ourselves and pass into the state of belief; while the latter is a calm and satisfactory state which we do not wish to avoid, or to change a belief to anything else. On the contrary, we cling tenaciously, not merely to believing, but to believing just what we do believe.

The self-preservation of belief is of particular interest to me. This phenomenon is explored in detail within social psychology and memetics.

The irritation of doubt causes a struggle to attain a state of belief. When doubt ceases, mental action on the subject comes to an end.

With this definition of doubt in place, Peirce goes on to rebut three erroneous conceptions of proof:

  1. The mere putting of a proposition into the interrogative form does not stimulate the mind to any struggle after belief. There must be a real and living doubt, and without this all discussion is idle.
  2. The premises of an argument need not be grounded in some firm metaphysical strata: they merely should be free from doubt.
  3. There is, then, no practical value in arguing a point after all the world is fully convinced of it.

This contextual backdrop resonates with anyone who has tried to persuade someone not subject to real and living doubt. There are times when words move the human heart, and times when they are “just words”. However, I am largely disappointed in this dichotomy as it stands. Questions concerning what underlies, motivates, or justifies doubt are unattended. Peirce may not have been in an empirical position to cognitively explain doubt, but surely he could have afforded to provide a more detailed sketch.

Peirce goes on to detail four methods for the fixation of belief. I will summarize each in turn.

Belief Fixation Method #1: Method of Tenacity

Peirce uses examples to shed light on this way of being:

I remember once being entreated not to read a certain newspaper lest it might change my opinion upon free-trade. “Lest I might be entrapped by its fallacies and misstatements,” was the form of expression. “You are not,” my friend said, “a special student of political economy. You might, therefore, easily be deceived by fallacious arguments upon the subject. You might, then, if you read this paper, be led to believe in protection. But you admit that free-trade is the true doctrine; and you do not wish to believe what is not true.” A similar consideration seems to have weight with many persons in religious topics, for we frequently hear it said, “Oh, I could not believe so-and-so, because I should be wretched if I did.” A man may go through life, systematically keeping out of view all that might cause a change in his opinions…

How, then, are we to evaluate such a method?

It would be an egotistical impertinence to object that his procedure is irrational, for that only amounts to saying that his method of settling belief is not ours. But this method of fixing beliefs will be unable to hold its ground in practice. The man who adopts it will find that other men think differently from him, and it will be apt to occur to him, in some saner moment, that their opinions are quite as good as his own, and this will shake his confidence in his belief. This conception, that another man’s thought or sentiment may be equivalent to one’s own, is a distinctly new step, and a highly important one.

Yes! In my language, I call this Symmetry Debiasing. I intend to write more on this; it has played a role in my own worldview maturation.

Now, this first method is typically localized to the individual. The second method solves the problem of socializing belief acquisition.

Belief Fixation Method #2: Method of Authority

Here, belief is a group activity. Doxastic content is something one inherits, and its contents are to be trusted.

Uniformity of opinion will be secured by a moral terrorism to which the respectability of society will give its thorough approval. Following the method of authority is the path of peace. Certain non-conformities are permitted; certain others (deemed unsafe) are forbidden. These are different in different countries and in different ages; but, whoever you are, let it be known that you seriously hold a tabooed belief, and you may be perfectly sure of being treated with a cruelty less brutal but more refined than hunting you like a wolf.

Evidence for this sort of thing is ubiquitous; with political infighting serving as a nice example.

Thus, the greatest intellectual benefactors of mankind have never dared, and dare not now, to utter the whole of their thought; and thus a shade of prima facie doubt is cast upon every proposition which is considered essential to the security of society.

I like to play a game when I read pre-modern philosophers discuss religion: count the number of sentences wasted in defensive posturing “always remember that when I say X I do not mean Y”. Keeping your eye tuned to this kind of historical artifact, which I call the Placating Price, is a good heuristic for approximating the degree of fear behind the artful prose of the academic. And it has been considerable. Reviewing the posthumous publication of Hume’s Dialogues Concerning Natural Religion underscores this point nicely.

For the mass of mankind, then, there is perhaps no better method than this. If it is their highest impulse to be intellectual slaves, then slaves they ought to remain.

Fighting words.

Belief Fixation Method #3: A Priori Method

Systems of this sort have been chiefly adopted because their fundamental propositions seemed “agreeable to reason”. This is an apt expression; it does not mean that which agrees with experience, but that which we find ourselves inclined to believe. Plato, for example, finds it agreeable to reason that the distances of the celestial spheres from one another should be proportional to the different lengths of strings which produce harmonious chords. Many philosophers have been led to their main conclusions by considerations like this…

This method is far more intellectual and respectable from the point of view of reason than either of the others… but its failure has been the most manifest. It makes of inquiry something similar to the development of taste; but taste, unfortunately, is always more or less a matter of fashion.

Philosophy has acquired a poor reputation in many intellectual circles for precisely this reason. Certain strains of metaphysics constitute, arguably, Diseased Disciplines. Peirce also manages to anticipate modern arguments towards the refactoring of analytic philosophy.

Belief Fixation Method #4: Scientific Method

Peirce goes on to sketch a method familiar to our modern ears: the scientific method.


He also makes the interesting move in tying the method to scientific realism (the belief that things like atoms really exist, are really embedded in spacetime). His defense of scientific realism is as follows

It may be asked how I know that there are any Reals. The reply is this:

  1. If investigation cannot be regarded as proving that there are Real things, it at least does not lead to a contrary conclusion; but the method and the conception on which it is based remain ever in harmony. No doubt of the method, therefore, arise from its practice, as is the case with all the others.
  2. The feeling which gives rise to any method of fixing belief is a dissatisfaction at two repugnant propositions. But here already is a vague concession that there is some one thing which a proposition should represent. Nobody, therefore, can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. The hypothesis, therefore, is one which every mind admits. So that the social impulse does not cause men to doubt it.
  3. Everyone uses the scientific method about a great many things, and only ceases to use it when he does not know how to apply it.
  4. Experience of the method has not led us to doubt it, but on the contrary, scientific investigation has had the most wonderful triumphs in the way of settling opinion. These afford the explanation of my not doubting the method or the hypothesis which it supposes; and not having any doubt, nor believing that anybody else whom I could influence has, it would be the merest babble for me to say more about it.

If there be anybody with a living doubt upon the subject, let him consider it.

Peirce and I even share a similar sense of humor. 🙂 I love this parody of Mark 4:23!

Concluding Thoughts

After reading this essay, I do not see myself walking around and categorizing people with Method 1, 2, 3, or 4 (nor even some linear superposition of all four). I am simply not persuaded that these epistemological preferences represent natural kinds.

One might imagine combining Methods 3 and 4, and then casting the three resultant categories to personal dispositions: one based on fear/simplicity/opportunism, another on social belonging, a third on the need for cognition. With this tripartite division of epistemology based on disposition, one could then layer on cultural distinctions, such as intuitive vs quantitative philosophizing. But even this, more sophisticated, account doesn’t feel precise enough for my liking.

Why spend time on this essay if I don’t agree with its central thesis? For one, it brings key questions to the fore:

  • How does doubt affect belief construction?
  • How do individuals go about constructing personal epistemologies?

But, more importantly, the journey to our destination was interesting.

I’ll close with Peirce explaining his preference for the scientific method.

Yes, the methods [besides the scientific method] do have their merits: a clear logical conscience does cost something – just as any virtue, just as all that we cherish, costs us dear. But we should not desire it to be otherwise. The genius of a man’s logical method should be loved and reverenced as his bride, whom he has chosen from all the world. He need not condemn the others; on the contrary, he may honor them deeply, and in so doing only honors her the more. But she is the one that he has chosen, and he knows that he was right in making that choice. And having made it, he will work and fight for her, and will not complain that there are blows to take, and will strive to be a worthy knight and champion of her from the blaze of whose splendors he draws his inspiration and his courage.

A man on fire…

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