INTRODUCTION

Infinity exists as a mathematical abstraction, but its physical realization is impossible due to finite storage and computational limits. This paper argues that no real system—whether the universe or a computational machine—can store or process infinite numbers. Using physical constraints like the Bekenstein Bound and computational limits, we demonstrate that infinity is a theoretical construct rather than a tangible reality.

This post is an analysis rather than rigor speculative theory, Don't misunderstand!!

1. Introduction

Infinity is a foundational concept in mathematics, yet its existence as a physically realizable entity remains unproven. While mathematics treats infinity as an abstract truth, our universe—being finite—imposes strict physical constraints on the storage and computation of numbers. This paper argues that infinity is an illusion from a computational and physical standpoint, as no system (including the universe) possesses infinite storage.

2. Hypothesis

If all information must be stored in a finite medium (such as the universe itself), then the concept of an infinite set, such as the digits of π, is not physically realizable. This suggests that infinity exists only as a theoretical construct, not as an observable reality.

3. Supporting Logic

3.1 The Storage Constraint Argument

Let S(x) represent the storage required to write number x.
Given a maximum storage capacity C, there exists some x for which S(x) > C, meaning that numbers beyond a certain size cannot be physically represented.
Since infinity implies numbers of unbounded size, it follows that infinity cannot be stored or computed.

3.2 The Computational Limit of π

π is an irrational number with infinite digits.
If the universe has a finite information capacity (e.g., Bekenstein Bound), then there is a limit to how many digits of π can ever be stored or computed.
This suggests that while π may be mathematically infinite, its physical realization is always finite.

4. Counterarguments & Responses

4.1 Mathematics as an Abstract System

Counterargument: Mathematics does not require physical storage; infinity exists in logical systems independent of the universe. Response: While true, mathematics without physical realization is a conceptual framework rather than a tangible reality.

4.2 Cantor’s Theory of Infinite Sets

Counterargument: Cantor’s diagonalization proves the existence of differen...

Posts

Wikitag Contributions

Comments

Posts

Wikitag Contributions

Comments