Navigating the Unseen: Math Intuition and the Power of Analogy

Unlocking the Fourth Dimension of Wealth

Building a robust financial future requires more than just basic arithmetic; it demands a shift in how we perceive the world. To master complex systems, one must develop mathematical intuition, the ability to sense and navigate patterns that exist beyond immediate physical perception.

We will explore this concept through the lens of a remarkable, short book titled Flatland, written by Edwin Abbott. Although published in 1884, this narrative provides a profound mental model for understanding dimensions we cannot see. By following the journey of its protagonist, A Square, we can learn to apply "strictly according to Analogy" logic to our own lives (Abbott, 1884).

This discussion bridges the gap between Victorian geometry and modern wealth-building. Integrating the lessons of Flatland with the principles of Personal Finance Reimagined (PFR) enables us to transition from "flat" financial thinking to a multi-dimensional strategy. We will examine how math intuition empowers you to see the invisible forces—such as compounding, risk variance, and cognitive biases—that shape your economic reality (Hulett, 2025).

“In One Dimension, did not a moving Point produce a Line with TWO terminal points? In Two Dimensions, did not a moving Line produce a Square with FOUR terminal points? In Three Dimensions, did not a moving Square produce—did not this eye of mine behold it—that blessed Being, a Cube, with EIGHT terminal points? And in Four Dimensions shall not a moving Cube—alas, for Analogy, and alas for the Progress of Truth, if it be not so—shall not, I say, the motion of a divine Cube result in a still more divine Organization with SIXTEEN terminal points? Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this—if I might quote my Lord’s own words—‘strictly according to Analogy’?

Again, was I not taught by my Lord that as in a Line there are TWO bounding Points, and in a Square there are FOUR bounding Lines, so in a Cube there must be SIX bounding Squares? Behold once more the confirming Series, 2, 4, 6: is not this an Arithmetical Progression? And consequently does it not of necessity follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must have 8 bounding Cubes: and is not this also, as my Lord has taught me to believe, ‘strictly according to Analogy’?”

- Edwin Abbott, Flatland

Beyond the Third Dimension

Abbott’s protagonist, A Square, experiences a profound cognitive shift when encountering the concept of a fourth dimension. While our biological hardware limits us to a three-dimensional physical perspective, our cognitive software enables us to transcend these boundaries through mathematical intuition. Math serves as a bridge, allowing the mind to "see" patterns where the eyes find only empty space. This process involves shifting from sensory-based observation to logic-based extrapolation.

The Role of Analogy in Mental Models

Human brains utilize analogy as a primary mechanism for learning and discovery. By identifying the progression from a point to a line, and a square to a cube, we establish a "rule of growth" (Hulett, 2024). Once the brain recognizes this pattern, it can project that logic into the fourth, fifth, or even hundredth dimension. This mental gymnastics stimulates the prefrontal cortex, the area responsible for complex planning and abstract thought. It encourages us to view challenges not as static obstacles, but as variables within a larger, dynamic system.

Decision-Making and Multi-Dimensional Thinking

In the context of Personal Finance Reimagined (PFR), thinking in higher dimensions becomes a practical necessity for wealth building. Most individuals view financial decisions through a one-dimensional lens: price. High-dimensional thinkers, however, incorporate time, risk, opportunity cost, and behavioral biases. PFR encourages this expansive view by providing a structured decision-making framework. Using tools like Definitive Choice empowers individuals to weight multiple competing dimensions simultaneously, transforming a complex choice into a manageable, logical progression (Hulett, 2023).

Neuroscience and Intuitive Growth

Developing math intuition requires more than memorizing formulas; it involves training the brain to find comfort in abstraction. When we successfully solve a problem by visualizing unseen dimensions, the brain releases dopamine, reinforcing the habit of deep, analytical inquiry. This neurochemical reward system drives the curiosity necessary to master complex financial or career landscapes. By applying the PFR framework, individuals move beyond "gut feelings" toward an evidence-based intuition grounded in economic principles and cognitive science.

Resources for the Curious

Abbott, Edwin. Flatland: A Romance of Many Dimensions. Seeley & Co., 1884. Explores the limitations of perception and the mathematical possibility of higher dimensions through a satirical narrative.

Hulett, Jeff. Making Choices, Making Money. 2nd Ed. Personal Finance Reimagined, 2025. Provides a structured framework for decision-making by integrating economics and behavioral science to improve long-term financial outcomes.

Hulett, Jeff. “The Geometry of Riches.” The Curiosity Vine, 2025. Demonstrates how mathematical intuition and geometric thinking enable individuals to navigate complex financial systems and build sustainable wealth.