Fumfer Physics 42: Geometry, Predictive Cognition, Information Theory, and the Dimensionality of Space

In this interview, Scott Douglas Jacobsen speaks with Rick Rosner about geometry, dimensionality, predictive cognition, and informational structure. Rosner begins by distinguishing the one-dimensional perimeter of a square from the two-dimensional surface of a sphere, using that contrast to explain inverse-square laws in physics. He then advances a speculative hypothesis that three-dimensional space may reflect informational complexity and non-overlapping histories across regions of the universe. The conversation expands into fractal dimensions, quantum interpretation, predictive neuroscience, adolescent social modeling, artificial intelligence, virtual reality, counterfactual thinking, and the possible relationship between hearing loss, closed captioning, and cognitive decline.

Scott Douglas Jacobsen: How does the surface of a sphere relate to the surface of a square? What does this tell us about our mental landscape?

Rick Rosner: When you refer to the surface of a square, you mean the perimeter—the boundary—which is a one-dimensional object. By contrast, the surface of a sphere is a two-dimensional object embedded in three-dimensional space. They are fundamentally different geometric entities.

A square is a two-dimensional object with a one-dimensional edge. If you double the side length of a square, you double its perimeter.

If you double the diameter of a sphere, you increase its surface area by a factor of four, because surface area scales with the square of the radius. In other words, one scales linearly, and the other scales quadratically.

This observation alone does not tell us much, but it connects to inverse-square laws. Gravitation and electromagnetism follow inverse-square behavior because forces spread over two-dimensional spherical surfaces embedded in three-dimensional space. If you double your distance from a light bulb, its light spreads over a surface area four times larger, so the intensity per unit area falls by a factor of four. That is geometry, not mystery.

The deeper question is why we inhabit three-dimensional space.

One possible explanation relates to information. Three dimensions may represent a kind of balance point—a configuration that allows complex structures without requiring the exponentially greater information needed to specify stable structures in higher-dimensional spaces. In five spatial dimensions, for example, the informational requirements for stable systems would increase dramatically.

I have suggested that the structure of space may follow from how information is arranged. Objects that share more history—more informational overlap—are effectively “closer.” As informational similarity decreases, separation increases.

As we move farther away in space, there is less shared information between systems. The question then becomes: how much variation exists in the information not shared?

That may be a more fundamental way to think about spatial structure—not merely as geometry, but as an expression of informational relationships.

The universe as a whole contains an aggregate of information, but each region of space contains a different subset of that information. When I say “point,” I do not mean a mathematical point like the tip of a pencil. I mean a vast region—perhaps tens or hundreds of millions of light-years across.

Each region has a distinct history. Within the total information content of the universe, there is overlapping information and non-overlapping information. The information that is not shared between regions varies from one location to another. That missing or non-overlapping information has structure and complexity.

My working hypothesis is that this level of informational complexity requires three-dimensional space. In other words, the variety in what is not shared—the structure of informational difference—determines dimensionality. The information that any given region does not contain appears to have enough variety to require three dimensions, but not more than three in most cases.

In situations where slightly more degrees of freedom might seem necessary, we do not observe additional spatial dimensions. Instead, we observe curvature—warped space, as described by general relativity.

Jacobsen: To what extent does this informational account of dimensionality map onto existing work in theoretical physics, such as holographic approaches, quantum information theory, or emergent spacetime models? What criteria would distinguish an informationally grounded explanation of dimensionality from a metaphorical one, so that it could be assessed as a serious physical hypothesis rather than an interpretive analogy?

Rosner: I have not considered that extensively. It is not a matter of the brain performing geometric rounding. Rather, the structures that exist are those capable of stable existence. I assume there are strong constraints preventing fractional spatial dimensions at macroscopic scales.

Mathematically, fractional dimensions exist in the study of fractals, where objects can have non-integer Hausdorff dimensions. However, those describe scaling behavior, not the fundamental dimensionality of spacetime. I suspect that true fractional spatial dimensions would introduce inconsistencies in physical law. In physics, inconsistencies prevent stable existence. Systems either exist coherently or they do not.

Quantum mechanics does describe probabilistic states—partial levels of realization—but it does so within a tightly constrained mathematical framework. The probabilities are precisely defined. That is different from proposing partially realized spatial dimensions.

My intuition is that fractional dimensions, at the level of fundamental spacetime, would introduce properties incompatible with stable matter, stable forces, or consistent physical law. If such configurations were possible, they may not permit structures complex enough to persist.

That remains speculative. It is an attempt to connect informational structure with spatial dimensionality, not an established theory.

I do not know what a specifically “quantum mechanical” manner of thinking would mean in this context. We experience the world at a macroscopic scale and generally do not notice the quantum effects occurring at very small scales. Those effects can be observed under controlled experimental conditions, but they do not define our everyday perception.

Here is what I think. Whether or not one wants to label it “quantum,” current neuroscience suggests—almost tautologically—that the brain exists to predict the future so that we can respond effectively. By “future,” I often mean the immediate future, including what we interpret as the present moment. The brain continuously models the external world to prevent harm and to guide action.

The models used by a grasshopper are far simpler than ours. Yet compared to the models humans may develop in the future, our current models are limited. Once human cognition becomes coupled to large-scale artificial intelligence systems, predictive simulations of the world may become far more intricate.

Jacobsen: Would you argue, then, that consciousness is less a passive mirror of reality than an active engine of probabilistic world-modeling, and that intelligence can be measured partly by the richness and adaptability of those predictive models? In that framework, how should we distinguish between useful simulation, maladaptive over-modeling, and outright confabulation?

Rosner: Consider ordinary examples of prediction. Sports betting involves probabilistic modeling, though its sophistication varies. A more relatable example is adolescent social strategy. Many teenagers, especially boys, spend enormous amounts of time trying to predict social outcomes—how someone might react to a confession of interest, what words or actions might produce acceptance or rejection.

In high school, I spent many hours discussing strategies with friends—trying to model possible reactions and anticipate outcomes. Today, people use the phrase “the ick” to describe subtle social rejection. We did not use that term decades ago, but we were trying to solve the same problem: how to approach someone without triggering discomfort. That involved mentally simulating scenarios and evaluating possible responses.

Most of the time, however, our predictive modeling is much more mundane. We are assessing whether it is safe to cross the street. Near one of the gyms I visit, there is an awkward intersection in a shopping area. On one side, traffic flows in both directions with a stop sign at the crosswalk. On the other side, the stop sign is positioned far before the intersection. Because this is private property, traffic enforcement is limited. Drivers are aware of that. As a result, pedestrians must engage in rapid predictive modeling: Who is likely to stop? Who is accelerating? What is the probability of risk?

Our brains are constantly performing these micro-simulations. Most are automatic and unnoticed. Only occasionally do we become aware of how much predictive work is occurring beneath conscious thought.

Most intersections are predictable. This particular one is unusually unpredictable. You do not know who will ignore the stop sign or accelerate unexpectedly.

About a year ago, I had an unpleasant experience there. I was leaving the gym and forgot to remove my mask. A fire truck driver saw me walking outdoors wearing it and accelerated abruptly in my direction, apparently to startle me. It worked. That is the only place I have ever been harassed for wearing a mask. The incident illustrates the unpredictability of that intersection. It requires more mental simulation than most crossings.

Looking ahead, as our cognitive processes become augmented by greater data-processing power—especially through artificial intelligence—we may engage in more intricate modeling of possible outcomes in everyday situations.

In a book I am writing, I explore the idea that AI combined with virtual reality could allow people to revisit moments in their lives where they feel they made mistakes. These scenarios would be populated with plausible simulations of themselves and others. One might revisit a poorly answered question on a game show or a missed opportunity in a social situation, exploring alternate outcomes in a controlled, simulated environment.

The broader point is that future AI systems may enable us to model “superimposed” possibilities in far greater detail. When considering a difficult situation—whether relational, professional, or ethical—we mentally simulate multiple potential futures. With AI assistance, those simulated futures could become more detailed and analytically rigorous.

Jacobsen: Would such AI-assisted counterfactual modeling deepen human judgment, or might it also intensify rumination, regret, and decision paralysis by multiplying plausible branches of experience? In ethical terms, how should society think about responsibility when artificial systems begin shaping not only our decisions, but the menu of futures we can vividly imagine?

Rosner: Consider a mundane example: you dent the car and anticipate your spouse’s reaction. You imagine varying degrees of frustration and your possible responses. That is simple predictive modeling.

A more serious example might involve professional misconduct. Suppose a lawyer temporarily diverts funds from a client’s estate to cover a shortfall, intending to repay them. When discrepancies are flagged, the lawyer must simulate various outcomes: disclosure, concealment, partial explanation, or legal consequences. Each path branches into further possibilities. The mind navigates these “superimposed” futures in search of the least damaging trajectory.

AI could expand the granularity and depth of such modeling, rendering potential outcomes with greater precision.

Jacobsen: Thank you very much for the opportunity and your time, Rick.

Scott Douglas Jacobsen is a blogger on Vocal with over 130 posts on the platform. He is the Founder and Publisher of In-Sight Publishing (ISBN: 978–1–0692343; 978–1–0673505) and Editor-in-Chief of In-Sight: Interviews (ISSN: 2369–6885). He writes for International Policy Digest (ISSN: 2332–9416), The Humanist (Print: ISSN, 0018–7399; Online: ISSN, 2163–3576), Basic Income Earth Network (UK Registered Charity 1177066), Humanist Perspectives (ISSN: 1719–6337), A Further Inquiry (SubStack), Vocal, Medium, The Good Men Project, The New Enlightenment Project, The Washington Outsider, rabble.ca, and other media. His bibliography index can be found via the Jacobsen Bankat In-Sight Publishing. He has served in national and international leadership roles within humanist and media organizations, held several academic fellowships, and currently serves on several boards. He is a member in good standing in numerous media organizations, including the Canadian Association of Journalists, PEN Canada (CRA: 88916 2541 RR0001), Reporters Without Borders (SIREN: 343 684 221/SIRET: 343 684 221 00041/EIN: 20–0708028), and others.