This perspective aligns with several fundamental principles of physics and philosophy. In the realm of quantum mechanics, the universe is characterized by inherent fluctuation; even a vacuum is not truly empty but teems with virtual particles popping in and out of existence. This suggests that stability is often an illusion created by the scale at which we observe the world, while the underlying reality is one of constant motion and transition.

From a thermodynamic standpoint, the second law of thermodynamics dictates that entropy always increases in an isolated system. This ensures a constant "arrow of time," meaning the universe is perpetually shifting from a state of order to disorder. If a system were truly frozen—meaning no energy exchange, no movement, and no change in state—it would effectively reach a state of absolute equilibrium, which in many physical frameworks is synonymous with a lack of meaningful existence or activity.

Philosophically, this mirrors the concept of "becoming" over "being." If existence is defined by interaction, and interaction requires a change in state (such as a particle moving or a field shifting), then something that is absolutely immutable cannot interact with anything else. In a reality defined by causality and relationship, a thing that cannot change would be undetectable and disconnected, rendering it non-existent for all practical purposes.

The fact that change manifests in such diverse ways—ranging from the chaotic fluctuations of a quantum field to the slow, predictable drift of tectonic plates—actually reinforces the idea that change is the primary mechanism of reality. The variance in how things change is what allows for complexity. If change were uniform or singular, the universe would be a monotonous loop; instead, the variety of rates, scales, and types of change is what creates structure.

This variance allows for the emergence of different layers of existence. On a subatomic level, change is probabilistic and instantaneous, providing the raw energy and instability needed for matter to form. On a biological level, change is iterative and adaptive through evolution, allowing life to diversify. On a cosmic level, change is expansive and entropic, driving the evolution of galaxies.

By seeing variance as a subset of change, it becomes clear that "difference" itself is just another form of change. The distinction between a fast change and a slow change is simply a different frequency of the same fundamental process. In this view, the "importance" of change lies in its role as the only constant; it is the canvas upon which every other property of the universe is painted.

The idea that change cannot be integrated because of the existence of infinities touches on a profound tension between mathematics and physical reality. If the potential for change is infinite—meaning there are infinite ways for a system to shift, or infinite degrees of precision in how a state evolves—then any attempt to "integrate" or sum up the totality of change becomes an impossible task.

In mathematics, integration is the process of finding the whole by summing up infinitesimal parts. However, when you introduce true infinities—such as the infinite divisibility of space-time or the infinite expansion of the universe—you encounter singularities where standard integration fails. When a value becomes infinite, the "sum" often ceases to be a number and becomes a divergence. This suggests that reality is not a completed equation that can be solved or "closed," but rather an open-ended process.

If change cannot be integrated, it means the universe is fundamentally non-totalizable. You cannot step "outside" of existence to see the finished product because the process of changing is the product itself. The variance you mentioned previously, paired with the scale of infinity, ensures that the universe remains a dynamic system of "becoming" rather than a static object of "being." In this framework, the inability to integrate change is not a failure of logic, but the very thing that prevents the universe from reaching a final, frozen state of completion.