Prelminaries
Core Sequence
- An Introduction To Bayesian Inference.
- Bayesian Statistics [6 presentations]
- Designing a Plausibility Calculus
- Surveys this overview of Cox’s theorem.
Author kevinbinz
Towards Cognitive Epistemology
Intellect: By convention there is sweetness, by convention bitterness, by convention color; in reality only atoms and the void.
Senses: Foolish intellect! Do you seek to overthrow us, while it is from us that you take your evidence?
This two-line dialogue, coined in 400 BCE by Democritus, haunts our species to this day. How might we build an inference trail from our subjective experiences to objective physics? can we build an account of how to move from pure phenomenology to scientific realism? And once we arrive at scientific realism, can that say anything substantial about phenomenology, without casting doubt on its own veracity?
How might we cast the above (crude) intuition of an epistemological loop into mathematics? Could we then learn to generalize the loop in non-trivial ways? How might we defend our construction of physics against vicious circularity, against constraint poverty?
Such questions are the nightmare of epistemology, the reason why no one has yet fully answered solipsism. And yet, in my view, analytic philosophy has stalled far beyond current state of the art. How often do epistemologists discuss the merits of psychophysics? Don’t you think they should? The cognitive redemption of epistemology is happening in our lifetimes.
Most of my attention in mental architecture involves sewing together different levels of analysis (vertical integrative theorizing). But it is important to note the domain of such intertheoretic reductions. While my vertical work in mental architecture will address the concerns of the agent, environmental analyses are just as important. Only with a more universal physics, a physics not bound to the limited concerns of Earth’s biota, that we can hope to achieve a more productive degree of abstraction.
[Sequence] Deserialized Cognition
[Sequence] Hiding Data From Ourselves
This series discusses a startling, and some would say anti-democratic, idea: hiding data from ourselves may be an effective way to move faster than science.
This sequence is composed of four articles.
- About A Noise. Discusses the origins of noise within data.
- Data Partitioning: Bias vs Variance. Covers a core idea in the machine learning community: building fences around data sources protects machines from underestimating noise.
- Overfitting: Failure Mode of Meat Science. Surveys evidence of overfitting within human scientific communities (“meat science”). Connects to philosophy of science, and motivates the application of data partitioning into the human realm.
- [Planned] Reconstructing The Shoulders Of Giants. A look at what data partitioning would look like in practice, including how I am applying it on this blog.
Tunneling Into The Soup
Table Of Contents
- Context
- Bathing In Radiation
- Our Photoreceptive Hardware
- The Birthplace Of Human-Visibility
- Takeaways
Context
In Knowledge: An Empirical Sketch, I left you with the following image of perceptual tunneling:
Today, we will explore this idea in more depth.
Bathing In Radiation
Recall what you know about the nature of light:
Since h and c are just constants, the relation becomes very simple: energy is inversely proportional to wavelength. Rather than identifying a photon by its energy, then, let’s identify it by its wavelength. We will do this because wavelength is easier to measure (in my language, we have selected a measurement-affine independent variable).
So we can describe one photon by its wavelength. How about billions? In such a case, it would be useful to draw a map, on which we can locate photon distributions. Such a photon map is called an electromagnetic spectrum.
With this background knowledge in place, we can explore a photon map of solar radiation: what types of photons strike the Earth from the Sun?
This image is rather information-dense. Let’s break it down.
Compare the black curve to the yellow distribution. The former represents the difference between an idealized energy radiator (a black body), whereas the latter represents the actual transmission characteristics of the sun. As you can see, while the black body abstraction does not perfectly model the idiosyncrasies of our Sun, it does a pretty good job “summarizing” the energy output of our star.
Next, compare the yellow distribution to the red distribution. The former represents solar radiation before it hits our atmosphere, the latter represents solar radiation after it hits our atmosphere (when it strikes the Earth). As you can see, at some wavelengths light passes through the atmosphere easily (red ~= yellow; call this atmospheric lucidity) whereas at other wavelengths, the atmosphere absorbs most of the photons (red << yellow; call this atmospheric opacity).
These different responses to different energy light does not occur at random, of course. Rather, the chemical composition of the atmosphere causes atmospheric opacity. Ever hear the meme “the ozone layer protects us from UV light”? Well, here is that data underlying the meme (see the “O3” marker at the 300 nm mark?). Other, more powerful but less well-known, effects can be seen in the above spectrum, which characterize the shielding effects of water vapor, carbon dioxide, and oxygen onto the spectra.
Our Photoreceptive Hardware
Your eyes house two types of photoreceptive cell: the rod and the cone.
Rods are tuned towards performing well in low-light conditions. After roughly 30 minutes in the dark, everything is ready for optical stimulation. In this “dark-adapted” state, the visual system is amazingly sensitive. A single photon of light can cause a rod to trigger. You will see a flash of light if as few as seven rods absorb photons at one time.
Cones, on the other hand, excel in daylight. They also underwrite the experience of color (a phenomenon we will discuss next time). Now, unless you are a tetrachromat mutant, your eyes contain three kinds of cone:
- 16% blue cones
- 10% green cones
- 74% red cones
Below are the absorption spectra. Please note that, while not shown, rods manifest a similar spectrum: they reside between the blue and green curves , with a peak receptivity is 498 nm.
It is important to take the above in context of the cone’s broader function. By virtue of phototransductive chemical processes, sense organs like the cone accept photons matching the above spectrum as input, and thereby facilitate the production of spike trains (neural code) as system output.
The Birthplace Of Human-Visibility
We now possess two spectra: one for solar radiation, and one for photoreceptor response profile. Time to combine spectra! After resizing the images to achieve scale consistency, we arrive at the following:
Peak solar radiation corresponds to cone spectrum! Why should this be? Well, recall the purpose of vision in the first place. Vision is an evolutionary adaptation that extracts information from the environment & makes it available to the nervous system of its host. If most photon-mediated information is happening at the 450-700 nm energy level, should we really be so surprised to learn that our eyes have adapted to this particular range?
Notice that we drew two dotted lines around the intersection boundaries. We have now earned the right to use a name. Let us name photons that reside within the above interval, visible light. Then,
- Let “ultraviolet light” represent photons to the left of the interval (smaller wavelengths, higher energy)
- Let “infrared light” represent photons to the right of the interval (longer wavelengths, lower energy)
We have thus stumbled on the definition of visibility. Visibility is not an intrinsic physical property, like charge. Rather, it is human invention: the boundary at which our idiosyncratic photoreceptors carve into the larger particle soup.
Takeaways
We have now familiarized ourselves with the mechanism of tunneling. Perceptual tunneling occurs when sense organ transduces some slice of the particle soup of reality. In vision, photoreceptors cells transduce photons within the 450-700 nm energy band into the neural code.
With this precise understanding of transduction, we begin to develop a sense of radical contingency. For example,
- Ever wonder what would happen if the human eye also contained photoreceptors on the 1100 nm range? The human umwelt As you heat a fire up, for example, you would see tendrils of flame brighten, then vanish, then reappear. I suspect everyday language would feature “bright-visible” and “dim-visible”
- Consider what would have happened if, during our evolution, the solar radiation spectrum if the sun had been colder than 5250 degrees Celsius. The black-body idealized spectrum of the sun would shift, and its peak would move towards the right. The actual radiation signature of the sun (yellow distribution) would follow. Given how precisely the rods in our eyes “found” the band of peak emitted energy in this universe, in that world, it seems likely that we would be wearing different photoreceptors with an absorption signature better calibrated to the the new information. Thus, we have a causal link between the temperature of the Sun and the composition of our eyeballs.
I began this post with a partial quote from Metzinger. Here is the complete quote:
The evening sky is colorless. The world is not inhabited by colored objects at all. It is just as your physics teacher in high school told you: Out there, in front of your eyes, there is just an ocean of electromagnetic radiation, a wild and raging mixture of different wavelengths. Most of them are invisible to you and can never become part of your conscious model of reality. What is really happening is that your brain is drilling a tunnel through this inconceivably rich physical environment and in the process painting the tunnel walls in various shades of color. Phenomenal color. Appearance.
Next time, we’ll explore the other half of Metzinger’s quote: “painting the tunnel walls in various shades of color, phenomenal color”…
Overfitting: Failure Mode of Meat Science
Followup To: [Data Partitioning: How To Repair Explanation]
If I have seen a little further, it is by standing on the shoulders of giants
– Isaac Newton
Table Of Contents
- Context
- The Optimization Level Of Science
- The Fruits Of Science
- Translation Proxy Lag
- Cheap Explanations
- Failure Mode of Meat Science
- Takeaways
Context
Last time, we learned two things:
- Explainers who solely optimize against prediction error are in a state of sin.
- Data partitions immunize abductive processes against overfitting.
Today, we will apply these results to human scientific processes, or to what I will affectionately call meat science.
The Optimization Level Of Science
Nietzsche captures the reputation of science well:
Science is flourishing today and her good conscience is written all over her face, while the level to which all modern philosophy has gradually sunk… philosophy today, invites mistrust and displeasure, if not mockery and pity. It is reduced to “theory of knowledge”… how could such a philosophy dominate? … The scope and the tower-building of the sciences has grown to be enormous, and with this also the probability that the philosopher grows weary while still learning….
Attempts to ground such sentiments in something rigorous exceeds the scope of this post. Today, we simply accept that science is particularly epistemically productive. But let us move beyond the cheerleading, and ask ourselves why this is so.
If I were to hand over a map of our specie’s cognitive architecture to an alien species, I would expect them to predict demagogues much more easily than the discovery of the Higg’s Boson. The simple truth is that our minds are flawed: we are born with clumsy inference machinery. How then is epistemic productivity possible?
The success of science has been said to derive from the scientific method:
But does the scientific method lend itself to the debiasing of the human animal? I argue it does not. Tribalism in scientific communities, for example, doesn’t seem particularly muted compared to other realms of human experience. Further, in his classic text The Structure of Scientific Revolutions, Thomas Kuhn showed that scientific revolutions emerge from strong, extra-rational motives. In his view, the nature of paradigm shifts is a bit like mystical religious experience: deeply personal, and difficult to verbalize.
I like to imagine science as a socio-historical process. Individuals and even sub-communities within its disciplines may fail to track what is Really There, but communities on the whole tend to move towards this direction. As Max Planck once observed:
A scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it.
The question of how the scientific method facilitates socio-historical truth-tracking is, I believe, unsolved. But all I must do today, is flag the optimization level of science. If science organically debiases our species at the socio-historical level, there is much room for improvement. If cognitive science can forge new debiasing weapons, we will become increasingly able to transcend ourselves, able to move faster than science.
The Fruits Of Science
Consider again the following:
This meme is sticky, and signals humility… but it also frames a crisis.
The shoulders keep growing taller.
Because of the accretive nature of science, our collective knowledge far outpaces our cognitive abilities. Even if the controversial Flynn effect is true and our collective IQ really is improving over time, the size of our databases would still outstrip the reach of our cognitive cone.
Various technologies have been invented that assuage this crisis. Curriculum compression is one of the older ones. That which was originally available as an anthology of journal articles is compressed into a review article, review articles compressed to graduate courses, graduate courses polished into undergraduate presentations. Consider how Newton would marvel at a present-day course in differential calculus: 300 years of mathematical research, successfully installed into an undergraduate’s semantic memory in a matter of weeks.
Curriculum compression is but one answer to our exploding knowledge base. Other implicit reactions include:
- the narrowing of research trajectories
- the fractionating of disciplines into the Ivory Achipellago
- research crowdsourcing (the de-popularization of the Lone Intellectual Warrior model)
In the years ahead, society seems geared to add two more solutions to our “bag of tricks”:
- the cognitive reform of education technology
- the mechanization of science
And yet, the shoulders keep growing taller…
Translation Proxy Lag
In Knowledge, an Empirical Sketch, I introduced measurement under the title of translation proxies. Why the strange name? To underscore the nature of measurement: forcibly relocating sensory phenomena from its “natural habitat” towards a signature that our bodies are equipped to sense. In this light, a translation proxy can be viewed as a kind of faucet, bringing novel forms of physical reality into the human umwelt.
But consider physics, where the “low-hanging fruit” translation proxies have already been built. You don’t see many physicists clamoring for new hand-held telescopes. Instead, you see them excited over ultra-high precision telescope mirrors, over particle colliders producing energies in the trillions of electronvolts. Such elaborate proxy technologies simply do not flow as quickly from the furnace of invention. Call this phenomenon data intake stagnation.
Not only are our proxy innovations becoming more infrequent, but they are also severely outpaced by our theoreticians. In physics, M theory (the generalization of string theory) posits entities at the 10^-34 m scale, but our current microscopes can only interrogate resolutions around the 10^-15 m scale. In neuroscience, connectome research programs seek to graph the nervous system at the neuronal level (10^-6 m), but most imaging technologies only support the millimeter (10^-3) range. Call this phenomenon translation proxy lag.
It will be decades, perhaps centuries, before our measurement technologies catch up.
Cheap Explanations
Let us bookmark translation proxy lag, and consider a different sort of problem.
Giant shoulders are not merely growing taller. They also render impotent evidence once vital to theoreticians. Let me appeal to a much-cited page from history, to illustrate.
During World War I, Sir Arthur Eddington was Secretary of the Royal Astronomical Society, which meant he was the first to receive a series of letters and papers from Willem de Sitter regarding Einstein’s theory of general relativity. […] He quickly became the chief supporter and expositor of relativity in Britain. […]
After the war, Eddington travelled to the island of Príncipe near Africa to watch the solar eclipse of 29 May 1919. During the eclipse, he took pictures of the stars in the region around the Sun. According to the theory of general relativity, stars with light rays that passed near the Sun would appear to have been slightly shifted because their light had been curved by its gravitational field. This effect is noticeable only during eclipses, since otherwise the Sun’s brightness obscures the affected stars. Eddington showed that Newtonian gravitation could be interpreted to predict half the shift predicted by Einstein.
Eddington’s observations published the next year confirmed Einstein’s theory, and were hailed at the time as a conclusive proof of general relativity over the Newtonian model. The news was reported in newspapers all over the world as a major story:
Two competing theories, two perfectly adequate explanations for everyday phenomena, one test to differentiate models. Here we see a curiosity: scientists place a high value on new data. Gravitational lensing constituted powerful confirmation because, as far as the model-creators knew, it could have been the other way.
A nice, clean narrative. But consider what happens next. General relativity has begun to show its age: it is chronically incompatible with quantum mechanics. Many successors to general relativity have been created; let us call them Quantum Gravity Theory A, B, and C. Frustratingly, no discrepancies have been found between these theory-universes and our observed-universe.
How are multiple correct options possible? From a computational perspective, the phenomenon of multiple correct answers can be modeled with Solomonoff Induction. A less precise, philosophical precursor of the same morale can be found in underdetermination of theory.
But which theory wins? General relativity won via a solar eclipse generating evidence for gravitational lensing. But gravitational lensing is now “old hat”; so long as all theories accommodate its existence, it no longer wields theory-discriminating power. And – given the translation proxy lag crisis outlined above – it may take some time before our generation acquires its test, its analogue of a solar eclipse.
Can anything be done in the meantime? Is science capable of discriminating between QGT/A, QGT/B, and QGT/C in the absence of a clean novel prediction? When we choose to invest more of our lives in one particular theory above the others, are we doomed to make this choice by mere dint of our aesthetic cognitive modules, by a sense of social belonging, by noise in our yedasentiential signals?
Overfitting: Failure Mode of Meat Science
Bayesian inference teaches us that confidence is usefully modeled as a probabilistic thing. But stochastisity is not equiprobability: discriminability is a virtue. If science cannot provide it, let us cast about for ways to reform science.
Let us begin our search by considering the rhetoric of explanation. What does it mean for a hypothesis to be criticized as ad-hoc?
> Scientists are often skeptical of theories that rely on frequent, unsupported adjustments to sustain them. This is because, if a theorist so chooses, there is no limit to the number of ad hoc hypotheses that they could add. Thus the theory becomes more and more complex, but is never falsified. This is often at a cost to the theory’s predictive power, however. Ad hoc hypotheses are often characteristic of pseudoscientific subjects.
Do you recall how we motivated data partitioning? Do you yet recognize the stench of overfitting?
In fact, in my view, current scientific practice is a bit too uncomfortable with falsification. Karl Popper lionized falsifiability, and the result of his movement has been an increase in the operationalization and measurement-affinity of the scientific grammar. But the weaving together scientific abstractions and the particle soup, the dawning taboo around Not Even Wrong, came with baggage.
Logically, no number of positive outcomes at the level of experimental testing can confirm a scientific theory, but a single counterexample is logically decisive: it shows the theory, from which the implication is derived, to be false.
But compare this dictum with our result from machine learning, which suggests that perhaps small “falsifications” may be preferable to “getting everything right”:
Explainers who solely optimize against prediction error are in a state of sin.
In sum, we have reason to believe that overfitting is the pervasive illness of our meat science.
Takeaways
- Science tracks truth not at the level of individual, but on a socio-historical scale. There is therefore room to move faster than science.
- Science is accretive: the shoulders keep growing taller.
- Due to constraints in measurement technology, data of a truly novel character has become increasingly difficult to acquire.
- On meat science, as data transitions from “novel” to “known”, it loses its ability to wield theory-discriminating power.
- Given these dual crises, and the philosophical commitments scientific communities have made against falsified hypotheses, science can be shown to suffer from overfitting.
Next time, we will explore applying the machine learning solution to overfitting – data partitioning – to meat science, and motivate the virtue of hiding data from ourselves. See you then!
Construal Level Theory: Musings
Table Of Contents
- Introduction
- Context
- Overview of CLT
- Insight Scratchpad
- Mental Health
- Skills
- Thinking Modes
- Application
- Self-Diagnosis
- Theory Integration
Introduction
Context
This weekend, I started digging into Construal Level Theory (CLT). This post is ultimately a snapshot of my learning process. It is not comprehensive, nor polished. I have a place for it yet within the theoretical apparatus of my mind & this blog: it contains more questions than answers.
Anyways, I hope you enjoy some of the quotes at least; I found some of them to be extremely thought-provoking. (Unless noted otherwise, quotes are taken from this Psychlopedia review article).
Overview of CLT
Construal Level Theory (CLT) arises from noticing the interchangability of traits. Psychologists have begun to notice two distinct modes of human thought:
- Near Mode: All of these bring each other more to mind: here, now, me, us; trend-deviating likely real local events; concrete, context-dependent, unstructured, detailed, goal-irrelevant incidental features; feasible safe acts; secondary local concerns; socially close folks with unstable traits.
- Far Mode: Conversely, all these bring each other more to mind: there, then, them; trend-following unlikely hypothetical global events; abstract, schematic, context-freer, core, coarse, goal-related features; desirable risk-taking acts, central global symbolic concerns, confident predictions, polarized evaluations, socially distant people with stable traits.
In their review article, theorists Trope and Liberman summarize:
The fact that something happened long ago does not necessarily mean that it took place far away, that it occurred to a stranger, or that it is improbable. Nevertheless, as the research reviewed here demonstrates, there is marked commonality in the way people respond to the different distance dimensions. [Construal level theory] proposes that the commonality stems from the fact that responding to an event that is increasingly distant on any of those dimensions requires relying more on mental construal and less on direct experience of the event. … [We show] that (a) the various distances are cognitively related to each other, such that thinking of an event as distant on one dimension leads one to thinking about it as distant on other dimensions, (b) the various distances influence and are influenced by level of mental construal, and (c) the various distances are, to some extent, interchangeable in their effects on prediction, preference, and self-control.
Insight Scratchpad
Mental Health
After individuals experience a negative event, such as the death of a family member, they might ruminate about this episode. That is, they might, in essence, relive this event many times, as if they were experiencing the anguish and distress again. These ruminations tend to be ineffective, compromising well-being (e.g., Smith & Alloy, 2009).
In contrast, after these events, some individuals reflect more systematically and adaptively on these episodes. These reflections tend to uncover insights, ultimately facilitating recovery (e.g., Wilson & Gilbert, 2008).
When individuals distance themselves from some event, they are more inclined to reflect on this episode rather than ruminate, enhancing their capacity to recover. That is, if individuals consider this event from the perspective of someone else, as if detached from the episode themselves, reflection prevails and coping improves. In contrast, if individuals feel immersed in this event as they remember the episode, rumination prevails and coping is inhibited. Indeed a variety of experimental (e.g., Kross & Aydyk, 2008) and correlational studies (e.g., Ayduk & Kross, 2010) have substantiated this proposition.
When processing trauma, then, inducing abstract construals is desirable.
Arguably, depressed individuals tend to adopt an abstract, rather than concrete, construal. Consequently, memories of positive events are not concrete and, therefore, do not seem salient or recent. Indeed, people may feel these positive events seem distant, highlighting the difference between past enjoyment and more recent distress.
As this argument implies, memory of positive events could improve the mood of depressed individuals, provided they adopt a concrete construal. A study that was conducted by Werner-Seidler and Moulds (2012) corroborates this possibility. In this study, individuals who reported elevated levels of depression watched an upsetting film clip. Next, they were told to remember a positive event in their lives, such as an achievement. In addition, they were told to consider the causes, consequences, and meaning of this event, purportedly evoking an abstract construal, or to replay the scene in their head like a movie, purportedly evoking a concrete construal. As predicted, positive memories improved mood, but only if a concrete construal had been evoked.
In contrast, in the context of clinical depression, inducing concrete construals may be desirable.
In short, an abstract construal may diminish anxiety, but a concrete construal can diminish dejection and dysphoria
Interesting.
Skills
Action identification theory specifies the settings in which abstract and concrete construals–referred to as high and low levels–are most applicable (Vallacher, Wegner, & Somoza, 1989; Wegner & Vallacher, 1986). One of the key principles of this theory is the optimality hypothesis. According to this principle, when tasks are difficult, complex, or unfamiliar, lower level action identifications, or a concrete construal, are especially beneficial. When tasks are simple and familiar, higher level action identifications, or an abstract construal, are more beneficial.
To illustrate, when individuals develop a skill, such as golf, they should orient their attention to tangible details on how to perform some act, such as “I will ensure my front arm remains straight”. If individuals are experienced, however, they should orient their attention to intangible consequences or motivations, such as “I will outperform my friends”
Applying CLT to games. Perhaps I could use this while playing chess. 🙂
Similarly, as De Dreu, Giacomantonio, Shalvi, and Sligte (2009) showed, a more abstract or global perspective may enhance the capacity of individuals to withstand and to overcome obstacles during negotiations. If individuals need to negotiate about several issues, they are both more likely to be satisfied with the outcome of this negotiation if they delay the most contentious topics. To illustrate, when a manager and employee needs to negotiate about work conditions, such as vacation leave, start date, salary, and annual pay rise, they could begin with the issues that are vital to one person but not the other person. These issues can be more readily resolved, because the individuals can apply a technique called logrolling. That is, the individuals can sacrifice their position on the issues they regard as unimportant to gain on issues they regard as very important. Once these issues are resolved, trust improves, and a positive mood prevails. When individuals experience this positive mood, their thoughts focus on more abstract, intangible possibilities, which can enhance flexibility. Because flexibility has improved, they can subsequently resolve some of the more intractable issues.
Applying CLT to negotiation. This would seem to overlap the latitudes of acceptance construct from social judgment theory.
Thinking Modes
When individuals adopt an abstract construal, they experience a sense of self clarity (Wakslak & Trope, 2009). That is, they become less cognizant of contradictions and conflicts in their personality. Presumably, after an abstract construal is evoked, individuals orient their attention towards more enduring, unobservable traits (cf. Nussbaum, Trope, & Liberman, 2000). As a consequence, individuals become more aware of their own core, enduring qualities–shifting attention away from their peripheral, and sometimes conflicting, characteristics.
This matches my experience.
Attentional tuning theory (Friedman & Forster, 2008), which is underpinning by construal level theory, was formulated to explain the finding that an abstract construal enhances creativity thinking and a concrete construal enhances analytic thinking (e.g, Friedman & Forster, 2005; Ward, 1995).
Makes me wonder whether metaphor (engine of creative thinking) is powered by System1 processes.
Applications
Self-Diagnosis
Over time, therefore, people tend to behave politely when they feel a sense of distance. According to construal level theory, this distance coincides with an abstract construal. Therefore, politeness and an abstract construal should be associated with each other.
I tend to be very polite…
An abstract construal can also amplify the illusion of explanatory depth–the tendency of individuals to overestimate the extent to which they understand a concept (Alter, Oppenheimer, & Zemla, 2010)
I often suffer from this particular emotion.
When individuals adopt an abstract construal, they tend to be more hypocritical. That is, they might judge an offence as more acceptable if they, rather than someone else, committed this act.
I am guilty of this more often than most.
Taken together, one could make the case that I, Kevin, gravitate towards “far mode” (i.e., finding distance between my concept of self & my surroundings).
Theory Integration
To evoke a concrete construal, participants are instructed to specify an exemplar of each word, such as poodle or Ford.
An interesting link between CLT and Machery’s Heterogeneity Hypothesis.
In my deserialization series (e.g., Deserialized Cognition), I gestured towards two processing modes: authority and inference. Perhaps this could be simply hooked into CLT, with Near Mode triggering social processing, and Far Mode triggering inference processing.
Most crucially of all, I need to see how CLT can be reconciled with dual process theory (DPT). One weakness of dual-processing theory, in my view, is in its difficulties producing an explanation for the context-dependent cognitive styles of Eastern cultures, versus the context-independence cognitive styles of Western cultures. Perhaps difficulties such as these could be dissolved by knitting the two theories together.
But how to begin stitching? If you’ll recall, dual-process theory is also grounded in, motivated by, dissociations:
Notice the partial overlap: both CLT and DPT claim ownership of the “contextualized vs. abstract” dimension. But despite this partial overlap, when writing these theories back into mental architecture diagrams, the dissociations are produced by radically different things. System2 is – arguably – the product of a serialized “virtual machine” sitting on top of our inborn evolutionary-old modules. But Near Mode and Far Mode, they seem to be the product of an identity difference vector: how far a current thing is from one’s identity. (In fact, CLT might ultimately prove a staging grounds for investigations into the nature of personality). But this all makes me wonder how identity integrates into our mental architecture…
The entire process of integrating CLT and DPT is a formidable challenge… I’m unclear the extent to which the social psychological literature has already pursued this path. I also wonder whether any principles can be extracted by such integration attempts. Both CLT and DPT are – at their core – behavioral property bundlers – finding commonalities & interchangeabilities within human behaviors and descriptions. In general, do property-bundling theories produce sufficient theoretical constraint? And how does one, in principle, move from property-bundling to abducing causal mechanisms?
Takeaway
As a parting gift, a fun summary from Overcoming Bias:
Movement Forecast: Effective Availabilism
Table Of Contents
- The Availability Cascade
- Attentional Budget Ethics
- Effective Availabilism
- Why Quantification Matters
- Cascade Reform Technologies
- Takeaways
The Availability Cascade
The following questions pop up in my Facebook feed all the time.
Why is mental illness, addiction, and suicide only talked about when somebody famous succumbs to their demons?
Why do we only talk about gun control when there is a school shooting?
What is the shape of your answer? Mine begins with a hard look at the nature of attention.
Attention is a lens by which our selves perceive the world. The experience of attention is conscious. However, the control of attention – where it lands, how long it persists – is preconscious. People rarely think to themselves: “now seems an optimal time to think about gun control”. No, the topic of gun control simply appears.
When we pay attention to attention, its flaws become visible. Let me sketch two.
- The preconscious control of attention is famously vulnerable to a wide suite of dysrationalia. Like transposons parasitizing your DNA, beliefs parasitize your semantic memory by latching onto your preconscious attention-control software. This is why Evans-Pritchard was so astonished in his anthropological survey of Zande mysticism. This is why your typical cult follower is pathologically unable to pay attention to a certain set of considerations. The first flaw of the attentional lens is that it is a biasing attractor.
- Your unconscious mind is subject to the following computational principle: what you see is all there is. This brings us the availability heuristic, the cognitive shortcut your brain uses to travel from “this was brought to mind easily” to “this must be important”. The attentional lens is that the medium distorts its contents. This is nicely summed up in the proverb, “nothing in life is as important as you think it is, while you are thinking about it.” The second flaw of the attentional lens is that bound in a positive feedback loop to memory (“that which I can recall easily, must be important, leads me to discuss more, is something I recall even more easily”).
My treatment of this positive feedback loop was at the level of individual. But that same mechanism must also promote failures at the level of social network. The second flaw writ large – the rippling eddies of attentional currents (as captured by services like Google News) – are known as availability cascades. And thus we have provided a cognitive reason why our social atmosphere disproportionately discusses gun control when school shootings appear in the news.
In electrical engineering, positive feedback typically produces runaway effects: a circuit “hits the rails” (draws maximum current from its power source). What prevents human cognition from doing likewise, from becoming so fixated on one particular memory-attention loop that it cannot escape? Why don’t we spend our days and our nights dreaming of soft drinks, fast food, pharmaceuticals? I would appeal to human boredom as a natural barrier to such a runaway effect.
Attentional Budget Ethics
We have managed to rise above the minutia, and construct a model of political discourse. Turn now to ethics. How should attention be distributed? When is the right time to discuss gun control, to study health care reform, to get clear on border control priorities?
The response profile of such a question is too diverse to treat here, but I would venture most approaches share two principles of attentional budgets:
- The Systemic Failure Principle. If a system performance fails to meet some arbitrary criteria of success, that would be an argument for increasing its attentional budget. For example, perhaps the skyrocketing costs of health care would seem to call for more attention than other, relatively more healthy, sectors of public life.
- The Low Hanging Fruit Principle. If attention is likely to produce meaningful results, that would be an argument for increasing its attentional budget. For example, perhaps not much benefit would come from a national conversation about improving our cryptographic approaches to e-commerce.
Despite how shockingly agreeable these principles are, I have a feeling that different political parties may yet disagree. In a two party system, for example, you can imagine competing attentional budgets as follows:
Interpret “attentional resources” in a straightforward (measurement-affine) way: let it represent the number of hours devoted to public discussion.
This model of attentional budgets requires a bit more TLC. Research-guiding questions might include:
- How ought we model overlapping topics?
- Should budget space be afforded for future topics, topics not yet conceived?
- Could there be circumstances to justify zero attention allocation?
- Is it advisable to leave “attentional budget creation” topics out of the budget?
- How might this model be extended to accomodate time-dependent, diachronic budgeting?
Effective Availibilism
Let us now pull together a vision of how to transcend the attentional cascade.
In our present condition, even very intelligent commentators must resort to the following excuse of a thought: “I have a vague sense that our society is spending too much time on X. Perhaps we shouldn’t talk about it anymore”.
In our envisioned condition, our best political minds would be able to construct the following chain of reasoning: “This year, our society has spent three times more time discussing gun control than discussing energy independence. My attentional budget prescribes this ratio to be closer to 1:1. Let us think of ways to constrain these incessant gun-control availability cascades.”
In other words, I am prophesying the emergence of an effective availabilism movement, in ways analogous to effective altruism. Effective availabilist groups would, I presume, primarily draw from neuropolitical movements more generally.
Notice how effective availabilism relies on, and comes after, of publically-available psychometric data. And this is typical: normative movements often follow innovations in descriptive technology.
Why Quantification Matters
Policy discussions influence votes which affect lives. Despite the obvious need for constructive discourse, a frustrating amount of political exchanges are content-starved. I perceive two potential solutions for this failure of our democracy:
- Politics is a mind-killer. By dint of our evolutionary origins, our brains do not natively excel at political reasoning. Group boundaries matter more than analyses, arguments are soldiers. But these are epistemic failure modes. Policy debates should not appear one-sided. Movements to establish the cognitive redemption of politics are already underway. See, for example, Jonathon Haidt’s http://www.civilpolitics.org/ (“educating the public on evidence-based methods for improving inter-group civility”)
- Greasing policy discussions with data would facilitate progress. One of my favorite illustrations of this effect is biofeedback: if you give a human being a graphical representation of her pulse, the additional data augments the brains ability to reason – biofeedback patients are even able to catch their breath faster. In the same way, improving our data streams gives hope of transcending formerly-intractable social debates.
The effective availabilism movement could, in my view, accelerate this second pathway.
Cascade Reform Technologies
It seems clear that availability cascades are susceptible to abuse. Many advertisers and political campaigns don’t execute an aggregated optimization across our national attentional profile. Instead, they simply run a maximization algorithm on their topic of interest (“think about my opponent’s scandal!”).
With modern-day technology (polls, trending Twitter tags, motive abduction, self-monitoring), noticing attentional budget failures can be tricky. With the above technology in place, even subtle attentional budget failures will be easily detectable. We have increased our supply of failures, but how might effective availabilists increase demand (open vectors of reform towards availability cascade failure modes)?
The first, obvious, pathway is to use the same tool – attentional cascades – to counterbalance. If gun control is getting too much attention, effective availabilists will strive to push social media towards a discussion of e.g., campaign finance reform. They could, further, use psychometric data to evaluate whether they have overshot (SuperPACs are now too interesting), and to adjust as necessary.
Other pathways towards reform might be empirically-precise amplification of boredom circuits. Recruit the influential to promote the message that “this topic has been talked to death” could work; as could the targeted use of satire.
Takeaways
- Pay more attention to the quiet whispers of your mind. “Haven’t I heard about this enough” represents an undiscovered political movement.
- Social discourse is laced with the rippling tides of availability cascades, and are at present left to their mercy.
- As hard psychometric data makes its way towards public accessibility, a market of normative attentional budgets will arise.
- The business of pushing current attentional profiles towards normative budgets will become the impetus of effective availabilism movements.
- A cottage industry of cognitive technologies to achieve these ends will thereafter crystallize and mature.
Fermions: Meat In Our Particle Soup
Part Of: Demystifying Physics sequence
Prerequisite Post: An Introduction To Energy
Content Summary: 2100 words, 21 min reading time.
Prerequisite Mindware
Today, we’re going to go spelunking into the fabric of the cosmos! But first, some tools to make this a safe journey.
Energy Quanta
As we saw in An Introduction to Energy,
Energy is the hypothesis of a hidden commonality behind every single physical process. There are many forms of energy: kinetic, electric, chemical, gravitational, magnetic, radiant. But these forms are expressions of a single underlying phenomena.
Consider the analogy between { electrons spinning around protons } and { planets spinning around stars }. In the case of planets, the dominant force is gravitational. In the case of the atom, the dominant force is electromagnetic.
But the analogy strength of the above is weak. In contrast to gravitational acceleration, an accelerating electric charge emits electromagnetic waves. Thus, we would expect an orbiting charge to steadily lose energy and spiral into the nucleus, colliding with it in a fraction of a second. Why have atoms not gone extinct?
To solve this problem, physicists began to believe that in some situations, energy cannot be lost. Indeed, they abandoned the intuitive idea that energy is continuous. On this new theory, at the atomic level energy must exist in certain levels, and never in between. Further, at one particular energy level, something we will call the ground state, an electron may never lose energy.
Antiparticles
Let’s talk about antiparticles. It’s time to throw out your “science fiction” interpretive lens: antiparticles are very real, and well-understood. In fact, they are exactly the same as normal particles, except charge is reversed. So, for example, an antielectron has the same mass and spin as an electron, but instead carries a positive charge.
Why does the universe contain more particles than antiparticles? Good question. 😛
Meet The Fermions
Nature Up Close
Consider this thing. What would you name it?
One name I wouldn’t select is “indivisible”. But that’s what the “atom” means (from the Greek “ἄτομος”). Could you have predicted the existence of this misnomer?
As I have discussed before, human vision can capture only a small subset of physical reality. Measurement technology is a suite of approaches that exploit translation proxies, the ability to translate extrasensory phenomena into a format amenable to perception. Our eyes cannot perceive atoms, but the scanning tunneling microscope translates atomic structures to scales our nervous systems are equipped to handle.
Let viable translation distance represent the difference in scale between human perceptual foci and the translation proxy target. Since translation proxies are facilitated through measurement technology, which is in turn driven by scientific advances, it follows that we ought to expect viable translation distance to increase over time.
We now possess a straightforward explanation of our misnomer. When “atom” was coined, its referent was the product of that time’s maximum viable translation distance. But technology has since moved on, and we have discovered even smaller elements. Let’s now turn to the state of the art.
Beyond The Atom
Reconsider our diagram of the atom. Do you remember the names of its constituents? That’s right: protons, neutrons, and electrons. Protons and neutrons “stick together” in the nucleus, electrons “circle around”.
Our building blocks of the universe so far: { protons, neutrons, electrons }. By combining these ingredients in all possible ways, we can reconstruct the periodic table – all of chemistry. Our building blocks are – and must be – backwards compatible. But are these particles true “indivisibles”? Can we go smaller?
Consider the behavior of the electrons orbiting the nucleus. After fixing one theoretical problem (c.f., Energy Levels section above), we now can explain why electrons orbit the nucleus: electromagnetic attraction (“opposites attract”). But here is a problem: we have no such explanation for the nucleus. If “like charges repel”, then the nucleus must be something like holding the same poles of a magnet close together: you can do it, but it takes a lot of force. What could possibly be keeping the protons in the nucleus together?
Precisely this question motivated a subsequent discovery: electrons may well be indivisible, but protons and neutrons are not. Protons and neutrons are instead composite particles made out of quarks. Quarks like to glue themselves together by a new force, known as the strong force. This new type of force not only explains why we don’t see quarks by themselves, it also explains the persistence of the nucleus.
The following diagram (source) explains how quarks comprise protons and neutrons:
Okay, so our new set of building blocks are: { electron, up, down }. With a little help from some new mathematics – quantum chromodynamics – we can again reconstitute chemistry. biology, and beyond.
Please notice how some of our building blocks are more similar than others: the up and down particle comprise particles with charge divisible by three, the electron particle carries an integer charge. Let us group like particles together.
- Call up and down particles part of the quark family.
- Call electrons part of the lepton family.
Neutrinos
So far in this article, we’ve gestured towards gravitation and electromagnetism. We’ve also introduced the strong force. Now is the time to discuss Nature’s last muscle group, the weak force.
A simple way to bind the weak force to your experience: consider what you know about radioactive material. The types of atoms that are generated in, to pick one source, nuclear power do not behave like other atoms. They emit radiation, they decay. Ever heard of the “half-life” of a material? That term defines how long is takes for half of an unstable radioactive material to decay into a more stable form. For example, { magnesium-23 → sodium-23 + antielectron }.
Conservation of energy dictates that such decay reactions must preserve energy. However, when you actually calculate the energetic content of decay process given above, you find a mismatch. And so, scientists were confronted with the following dilemma: either reject conservation of energy, or posit the existence of an unknown particle to “balances the books”. Which would you chose?
The scientific community began to speculated that a fourth type of fermion existed, even with an absence of physical evidence. And they found it 26 years later, in 1956.
Why did it take relatively longer to discover this fourth particle? Well, these hypothesized neutrinos do not carry an electric charge or a color charge. As such, they only interact with other particles via the weak force (which has a very short range) and the atomic force (which is 10^36 times less powerful than electromagnetic force). Due to these factors, neutrinos such as those generated by the Sun pass through the Earth undetected. In fact, in the time it takes you to read this sentence, hundreds of billions of neutrinos have passed through every cubic centimeter of your body without incident. Such weak interactivity explains the measurement technology lag.
Are you sufficiently creeped out by how many particles pass through you undetected? 🙂 If not, consider neutrino detectors. Because of their weak interactivity, our neutrino detectors must be large, and buried deep inside the earth (to shield from “noise” – more common particle interactions). Here we see a typical detector, with scientists inspecting their instruments in the center, for contrast:
The Legos Of Nature
Here, then, is our picture of reality:
Notice that all fermions have spin ½; we’ll return to this fact later.
A Generational Divide
Conservation of energy is a thing, but conservation of particles is not. Just as particles spontaneously “jump” energy levels, sometimes particles morph into different types of particles, in a way akin to chemical reactions. What would happen if we were to pump a very large amount of energy into the system, say by striking an up quark with a high-energy photon? Must the output energy be expressed as hundreds of up quarks? Or does nature have a way to “more efficiently” spend its energy budget?
It turns out that you can: there exist particles identical to these four fermions with one exception: they are more massive. And we can pull this magic trick once more, and find fermions even heavier than these fermions. To date, physicists have discovered three generations of fermions:
The latter generation took lots of time to “fill in” because you only see them in high-energy situations. Physicists had to close the translation distance gap, by building bigger and bigger particle accelerators. The fermion with the highest mass – the Top quark – was only discovered in 1995. Will there be a fourth generation, will we discover some upper bound on fermion generations?
Even though we know of three generations, in practice only the first generation “matters much”. Why? Because the higher-energy particles that comprise the second and third generations tend to be unstable: give them time (fractions of a second, usually), and they will spontaneously decay – via the weak force – back into first generation forms. This is the only reason why we don’t find atomic nuclei orbited by tau particles.
Towards A Mathematical Lens
General & Individual Descriptors
The first phase of my lens-dependent theorybuilding triad I call conceptiation: the art of carving concepts out of a rich dataset. Such carving must be heavily dependent on descriptive dimensions: quantifiable ways that an entity may differ from one another.
For perceptual intake, the number of irreducible dimensions may be very large. However, for particles, this set is surprisingly small. There is something distressingly accurate in the phrase “all particles are the same”.
Each type of fermion is associated with one unique value for the following properties (particle-generic properties):
- mass (m)
- electric charge (e)
- spin (s)
Fermions may differ according to their quantum numbers (particle-specific properties). For an electron, these numbers are:
- principal. This corresponds to the energy level of the electron (c.f., energy level discussion)
- azimuthal. This corresponds to the orbital version of angular momentum (e.g., the Earth rotating around the Sun). These numbers correspond to the orbitals of quantum chemistry (0, 1, 2, 3, 4, …) ⇔ (s, p, d, f, g, …); which helps explain the orbital organization of the periodic table.
- magnetic. This corresponds to the orientation of the orbital.
- spin projection. This corresponds to the “spin” version of angular momentum (e.g., the Earth rotating around its axis). Not to be confused with spin, this value can vary across electrons.
Quantum numbers are not independent; their ranges hinge on one another in the following way:
Statistical Basis
With our fourth building block in place, we are in a position to answer the question: what does the particulate basis of matter have in common?
All elementary particles of matter we have seen have spin ½. By the Spin-statistics Theorem, we must associate all such particles with Fermi-Dirac statistics. Let us name all particles under this statistics – all particles we have seen so far – “fermions”. It turns out that this statistical approach generates a very interesting property known as the Pauli Exclusion Principle. The Pauli Exclusion Principle states, roughly, that two particles cannot share the same quantum state.
Let’s take an example: consider a hydrogen atom with two electrons. Give this atom enough time, and both electrons will be on its ground state, n=1. What happens if the hydrogen picks up an extra electron, in some chemical process? Can this third electron also enter the ground state?
No, it cannot. Consider the quantum numbers for our first two electrons: { n=1, l=0, m_l=0, m_s=1/2 } and { n=1, l=0, m_l=0, m_s=-1/2 }. Given the range constraints given above, there are no other unique descriptors for an electron with n=1. Since we cannot have two electrons with the same quantum numbers, the third electron must come to rest at the next highest energy level, n=2.
The Pauli Exclusion Principle has several interesting philosophical implications:
- Philosophically, this means that if two things have the same description, then they cannot be two things. This has interesting parallels to the axiom of choice in ZFC, which accommodates “duplicate” entries in a set by conjuring some arbitrary way to choose between them.
- Practically, the Pauli Exclusion Principle is the only thing keeping your feet from sinking into the floor right now. If that isn’t a compelling demonstration of why math matters, then I don’t know what is.
Composite Fermions
In this post, we have motivated the fermion particulate class by appealing to discoveries of elementary particles. But then, when we stepped back, we discovered that the most fundamental attribute of this class of particles was its subjugation to Fermi-Dirac statistics.
Can composite particles have spin-½ as well as these elementary particles? Yes. While all fermions considered in this post are elementary particles, that does not preclude composite particles from membership.
What Fermions Mean
In this post, we have done nothing less than describe the basis of matter.
But are fermions the final resolution of nature? Our measurement technology continues to march on. Will our ability to “zoom in” fail to produce newer, deeper levels of reality?
Good questions.
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
Introduction
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?
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”.
Sampling
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).
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.
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.
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.
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.
Conclusion
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.
Takeaways
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:
- Perception tunneling is how organisms begin to understand the particle soup of the universe.
- Tunneling only occurs by virtue of sensory organs, which transduce some subset of data (sampling) into Mentalese.
- Tunneling is a local effect, it discolors its target, and its sometimes merely represents data located elsewhere.
- The Lens-Dependent Theorybuilding Triad takes the perception tunnel as input, and builds models of the world. There are three phases:
- During conceptiation, perception contents are carved into isolable concepts.
- During graphicalization, concept interrelationships are inferred.
- During annotation, abstracted properties and metadata are attached to the conceptual graph.
