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The human eye and brain is designed to see continuous lines and other structures. We do not see patterns of light. We see faces, bodies, chairs, tables. lines and circles. This helps us make sense of the complex patterns of light that strike our eyes.

The idea of a continuous line is simpler than the elements that make it up. We need to recognize and respond to complex structures not in detail but to their meaning. We need to recognize food, predators, escape routes and canyons that are potential traps. We recognize geometric shapes as a starting point for seeing what is relevant to our survival.

The reality that contemporary physics paints is radically different than the conceptual framework we develop naturally. What we see as continuous lines are complex structures made up of individual molecules and atoms. Light itself comes in discrete packets of energy called photons.

The mathematics of contemporary physics remains centered on continuous structures that are sophisticated versions of the concept of a continuous line that we are designed to recognize. The objects in physical space all have a discrete structure but time and space are still modeled as continuous structures.

Part of the reason physicists focus on continuous space time models is that other models are far more complex and difficult to work with. Science must use the tools it has and these inevitably have limits and shortcomings. But it is important to distinguish between decisions made for sound scientific reasons and those made for pragmatic ones. For what is practical changes with our mathematical understanding and the tools of technology.

This chapter and the next explore the possibility that time and space are discrete or digital. Could there be a smallest possible distance and a smallest possible time just as atoms and molecules form the smallest possible unit of physical substances?

A continuous line would constitute a completed infinite totality. It would imply that infinite sets exist in some physical sense. We are a long way from being able to resolve this issue. It will take experimental techniques far beyond our existing capabilities to explore the time and distance scales where contemporary physics suggests we might observe the digitization of space-time. What we can do in this and the following chapter is paint a picture of contemporary physics that suggests why we might eventually discover that the universe is digital and finite. We can also point out some of the experimental approaches that might aid in the search.

- Time and distance scales
- Waves, particles and events
- Interpretations of quantum mechanics
- Discretizing the wave equation
- Unique properties of discrete models
- Einstein's approach to physics
- Special Relativity
- General Relativity
- Quantum Mechanics
- The uncertainty principle
- Quantum Entanglement
- The real line and configuration space

Completed
second draft of this book

PDF version
of this book

**Next:** Time and distance scales **Up:** whatth
**Previous:** A philosophy of mathematical **Contents**

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