How does our ability to mathematically model physical phenomena relate to our ability to truly understand it?

Mathematical Modeling, Computational Tools, and SPIRITUAL Understanding

The Questions of SPIRITUAL Understanding

In contemplating how our ability to mathematically model physical phenomena relates to our ability to truly understand it, particularly in the context of computational tools like Wolfram and Jupyter notebooks for exploring physics data, we must consider both scientific and spiritual perspectives. This exploration is particularly relevant when examining data from sources such as NASA, CERN, and other sources of particle physics, plasma physics, or astrophysics data for contemplation of Physics beyond the Standard Model.

Biblical Framework

Several key Biblical passages provide insight into this relationship:

1. The Limits of Human Knowledge

  • 1 Corinthians 13:12 - “For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.” In this verse, expression “through a glass darkly” is used [and should be thought of in the context of mirrors available to the Apostle Paul] to describe the imperfect, cloudy but still useful visions of reality humans can have even with the best of tools, instruments, imaging assistance.
  • This suggests our mathematical models, while precise and even extremely useful, will always be fundamentally limited … indirect, incomplete, distorted.
  • It is impossible for us to see Reality as Reality really is, because our human view is always going to be limited in this way.

2. Divine Wisdom vs Human Understanding

  • Isaiah 55:8-9 - “For my thoughts are not your thoughts, neither are your ways my ways, declares the Lord. As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts.”
  • Even sophisticated mathematical models may not capture the full depth of divine reality.
  • This verse explores another take on why is impossible for us to see Reality as Reality really is … if only because our view is always going to be limited by all of the baggage we can’t escape cluttering up our view, ie we cannot resist reading our things into our own narrow view of our own sums.

3. God’s Mathematical Order

  • Proverbs 3:19-20 - “The Lord by wisdom founded the earth; by understanding he established the heavens; by his knowledge the deeps broke open, and the clouds drop down the dew.”
  • Mathematical order in nature reflects divine wisdom, but the underlying reality may be richer than our descriptions.
  • This verse explores yet another take on why is impossible for us to think through Reality as Reality really is, because our ability to think [even if computational-assisted] is always going to be limited.

4. The Challenge of Measurement

  • Job 38:4-7 - “Where were you when I laid the earth’s foundation? Tell me, if you understand. Who marked off its dimensions? Surely you know! Who stretched a measuring line across it?”
  • This challenges human presumptions about our ability to fully comprehend and measure creation.
  • This verse explores yet another take on why is impossible for us to comprehend the stucture of Reality as that structure of Reality really is, because our comrehension on the structure is always going to be limited.

Modern Computational Tools in Light of Scripture

These verse recognize the immense power and usefulness of human tools, while helping us think about their limitations.

Stewardship and Proper Use

  • Proverbs 24:3-4 suggests viewing computational tools as “treasures” of knowledge while using them mindfully
  • Tools should aid understanding rather than replace it

Pride and Knowledge

  • 1 Corinthians 8:1-2 warns against intellectual pride
  • Automated calculations should foster humility about our reliance on tools

Value of Contemplation

  • Psalm 111:2 encourages pondering God’s works
  • Automated tools can free mental capacity for deeper contemplation
  • This supports the notion that being freed from difficult mathematics might allow better focus on fundamental meanings

Practical Applications

Let’s break this question down … with some practical examples.

Mathematics as a Tool for Modeling

  • Mathematics is a language and a tool that allows us to describe, predict, and simulate physical phenomena with remarkable precision. From Newton’s laws of motion to Einstein’s theory of relativity, mathematical models have enabled us to formalize observations, make testable predictions, and develop technologies based on those predictions. For example: The equations of fluid dynamics can predict how air flows over an airplane wing. Quantum mechanics, expressed through mathematical formalism, predicts the behavior of particles at microscopic scales.
  • The success of these models suggests that mathematics is deeply connected to the structure of reality. Physicist Eugene Wigner famously referred to this as “the unreasonable effectiveness of mathematics in the natural sciences,” highlighting the mystery of why abstract mathematical concepts so accurately describe the physical world.

Modeling vs. Understanding

  • While mathematical models are powerful, they don’t necessarily equate to a complete or intuitive understanding of the phenomena they describe. Here’s why: Descriptive vs. Explanatory: A mathematical model can describe how something happens (e.g., the equations of gravity predict planetary motion) without necessarily explaining why it happens at a fundamental level. For instance, Newton’s law of gravitation describes the force between masses but doesn’t explain what gravity is. Einstein’s general relativity provides a deeper geometric explanation, but even that leaves open questions about the nature of spacetime.
  • Abstraction and Simplification: Models often simplify reality to make it tractable. For example, the ideal gas law assumes particles have no volume and don’t interact except through elastic collisions—assumptions that don’t hold perfectly in the real world. While these simplifications allow for useful predictions, they can distance us from a full understanding of the underlying complexity.
  • Limits of Intuition: Some phenomena, like quantum mechanics, are so counterintuitive that even accurate mathematical models (e.g., Schrödinger’s equation) don’t align with our everyday experience. Physicists can use these models to make predictions, but many admit they don’t fully “understand” the reality behind them in an intuitive sense.

Does Modeling Imply Understanding?

  • The relationship between modeling and understanding depends on how we define “understanding”: Pragmatic Understanding: If understanding means the ability to predict and manipulate phenomena, then mathematical modeling is sufficient. Engineers, for example, don’t need to know the ultimate nature of electricity to build circuits—they just need models that work.
  • Conceptual Understanding: If understanding means grasping the “why” or the essence of a phenomenon, mathematical modeling may fall short. For instance, we can model black holes with equations, but their true nature (e.g., what happens inside the singularity) remains mysterious. Philosophical Understanding: At a deeper level, some argue that true understanding requires insight into the fundamental nature of reality—questions like “Why does mathematics describe the universe?” or “What is the ultimate cause of physical laws?” These questions go beyond what mathematical models can address.

The Role of Interpretation

  • Mathematical models require interpretation to connect them to physical reality. For example: In quantum mechanics, the mathematical formalism (e.g., wavefunctions) can be interpreted in multiple ways (Copenhagen interpretation, Many-Worlds interpretation, etc.), each implying a different understanding of reality.This suggests that while the mathematics may be precise, our understanding of what it represents is subjective and evolving.

The Iterative Nature of Science

  • Our ability to model phenomena and our understanding of them evolve together. As new observations challenge existing models (e.g., anomalies in planetary orbits leading to general relativity), we refine our mathematics and deepen our conceptual understanding. This iterative process suggests that modeling and understanding are intertwined but not identical:
  • Models can lead to understanding by revealing patterns and relationships. Such understanding helps guide the development of better models by suggesting new hypotheses or frameworks.

Limits of Mathematical Modeling

  • There are phenomena that resist complete mathematical modeling, either due to complexity (e.g., turbulence, consciousness) or because they lie outside the current scope of physics (e.g., the ORIGINATOR of the origins of the Universe). In these cases, our inability to model fully reflects a limit to our understanding. Conversely, the development of new mathematical tools (e.g., calculus for Newtonian physics, tensor analysis for relativity) often precedes breakthroughs in understanding.

Examples Of Philosophical Perspectives

  • Platonism: Some argue that mathematics exists independently of human thought and that physical phenomena conform to mathematical structures because reality itself is inherently mathematical. In this view, modeling is a way of uncovering the true nature of the universe.
  • Instrumentalism: Others see mathematical models as useful fictions—tools that work but don’t necessarily reflect ultimate truth. From this perspective, modeling is distinct from understanding, as it prioritizes utility over insight.
  • Constructivism: Another view holds that mathematics is a human creation, and our models reflect how we structure our perceptions rather than an objective reality. This raises questions about whether we can ever truly “understand” phenomena beyond our constructed frameworks.

Conclusion

Our ability to mathematically model physical phenomena is a powerful tool that enables prediction, control, and technological progress, and it often leads to deeper conceptual insights. However, it simply cannot guarantee a complete or ultimate understanding of reality. Modeling provides a framework for organizing observations and making sense of the world for VERY USEFUL application, but true understanding requires more intuition, philosophical reflection, or even new ways of thinking that transcend current mathematical and scientific paradigms that can be caputured by machines or artificial intelligence. The gap between modeling and understanding reflects both the strengths and the limitations of human cognition [and accordingly the limitation of automating human cognitive steps with machines or AI], as well as the ongoing journey of scientific discovery.