Reverse Engineering the Universe

The following is a sample from my work in progress on the relativity of light.

In physics, there is some tension between mathematics and philosophy. On the one hand, mathematics is arguably the unadulterated absolute truth, the language in which the universe is written and in which it reveals itself to us. On the other hand, discretion — we call it philosophy — is needed to avoid misusing the endless possibilities of mathematics to create logic through its own inner consistencies. Mathematical consistencies in themselves do not necessarily reflect the design of the universe, says philosophy.

It should be fair to say that modern physics has a mathematical bias and there is a certain mathematics-first approach. An example of how far such a one-sided emphasis can go is string theory; it searches purely in the realm of mathematics for an inner logic that matches the empirical evidence from the universe around us. We have two worlds. We are exploring the first in the hope of finding a key to the second. The by-product of this effort is a high level of mathematical complexity, together with an implicit philosophical premise: the fundamental design of the universe is complex, reserved for those capable of mastering such complexity.

String theory is an extreme example. More commonly, we turn to mathematics for reassurance. In the face of uncertainty, it allows us to test the waters and visualize the invisible. As Prof Charles Bailyn puts it, with a delightful awareness of the limits of our knowledge: When our imagination fails us we turn to mathematics.^Bai07 But the question remains: is it true? Or could the picture we paint for ourselves be a false reassurance, a professional over-focus on the task at hand? Prof Bailyn’s quote is about picturing the three-dimensional expansion of the universe – for which we have only a mathematical description. We could add to this the precise calculations of the first moments of the bang in the big bang theory. Can we really know this, given the other fundamental unknowns in our big picture? Why do we have to claim that we can?

An uninitiated outsider cannot follow the mathematics, let alone check its validity in the context of a theory where it is being used. On what basis can a philosophically minded non-physicist question professional physics? The problem with philosophy — when it comes to a detailed understanding of the universe — is precisely its naivety. Where mathematical physics loses contact with logical reasoning in a human language, the latter has no mathematical validity. In the eyes of physics, philosophy has no facts and is guilty of the same “anything goes” approach for which it blames the other side. Neither mathematics nor philosophy alone is enough.

What unites the mathematical and philosophical reasoning is the aforementioned word design. The universe clearly has a design. It applies the mathematical formulae we have discovered and written down, but the structures that use the formulae go beyond mathematics. This is where the transition to physics happens. The additional logic — which defines the structures, controls their transformation and makes them relevant to what we see is happening — is the design. So physics is in the end nothing but the discovery of the design of the universe. We try to reconstruct the mechanics of the world around us into a workable logical system and, like a tree in the ground, our efforts are rooted in mathematical consistency. There is no clear line where mathematics ends and thinking in terms of the empirical world begins. In design they transition into each other.

What makes the design question in physics difficult is the lack of feedback on our design choices. Mathematically, we are on solid ground. Any mathematical models we create are validated by the inner self-consistency of mathematics. Where we are on thin ice is in the relationship of the mathematical models to the mechanics of the empirical world. Is our design generic and adaptable enough to cover all the diverse and seemingly contradictory requirements of the universe? The problem here is one of non-testability. We cannot validate a design for consistency in the real world. At some point, both at the small elementary scale and even more so at the large cosmological scale, we can only theorize and seek logical proofs for a design. Its relevance to the functioning of the real physical universe remains largely an assumption.

We cannot change where we are in relation to the universe, but theoretical physics is not alone with the central design problem. There is a modern discipline that answers the same question in a comparable context – computer programming. The similarity is compelling. Both the universe and a computer program (1) are defined by mathematics (2) create structures together with a flow of transitions (3) have to “work” — not crash in running (4) have to correctly and optimally reflect the requirements of the real world. For a program, the last point means capturing a specific real-world problem. For the universe, it means creating a place for us to live with all the elementary and macroscopic structures and flows. This is where computer programming has an advantage over theoretical physics. Program designs are constantly validated against real-world requirements (in jargon: business requirements), and a vast body of practical experience has been accumulated in this area. Program design, with its paradigms and best practices, has become a discipline in its own right. It has much to say about what to pay attention to, what to avoid, and what to strive for in design.

References

Chris Bailyn: ASTR 160: Frontiers and Controversies in Astro-physics. Lecture 17 - Hubble’s Law and the Big Bang (cont.) 2007. URL: https://oyc.yale.edu/astronomy/astr-160/lecture-17 (visited on 09.10.2022).

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