But isn’t this bad news for a Theory of Everything?:

At the frontiers of theoretical physics, many of the most popular ideas have one thing in common: they begin from a mathematical framework that seeks to explain more things than our currently prevailing theories do. Our current frameworks for General Relativity and Quantum Field Theory are great for what they do, but they don’t do everything. They’re fundamentally incompatible with one another, and cannot sufficiently explain dark matter, dark energy, or the reason why our Universe is filled with matter and not antimatter, among other puzzles.

It’s true that mathematics enables us to quantitatively describe the Universe, it’s an incredibly useful tool when applied properly. But the Universe is a physical, not mathematical entity, and there’s a big difference between the two.

Ethan Siegel, “No, The Universe Is Not Purely Mathematical In Nature” atForbes

Maybe a universe that was completely explainable and provable couldn’t exist.

And how do we know that “the Universe is a physical, not mathematical entity”?

“Everything we call real is made of things that cannot be regarded as real.” Niels Bohr

…To the best of our current knowledge, all those “things” are basically just combinations of math equations with some fixed rules governing the interactions of said equations.

Better question: How did math assume the royal position of sole explainer? Math is an artificial set of symbols, with rule-governed interactions, created by the human mind. There are many other sets of human-created symbols and interactions that do a better job of explaining everything. Drama and poetry and religion and painting and 3d animations and dances…. ad infinitum.

When I first read the title, “No, The Universe Is Not Purely Mathematical In Nature”, I thought to myself, “Well this article could be good, perhaps Siegel will touch upon the fact that Mind, not matter, is now found to be the fundamental ‘stuff’ of the universe.”

But alas, Siegal merely briefly touched upon the fact that observational evidence has always had final say in modern science. More specifically, he briefly touched upon the fact that observational evidence has always had final say in which mathematical models that we use to describe what we observe are correct, and which models are incorrect.

To make matters worse, Siegal, directly insinuated that, since mathematical models have had a history of being corrected, then the universe must be ‘physical’. i.e. ““the Universe is a physical, not mathematical entity”

This is an unfortunate choice of words on Siegal’s part. Siegal is no dummy and surely he is aware that the term ‘physical’ is a loaded term that directly implies that the universe is purely material and/or ‘natural’ in its fundamental nature, with no mental component to its foundational nature.

Moreover, according to Siegal’s own reasoning, it simply does not follow that the universe we observe must be purely ‘physical’.

Just because the first mathematical models that we used to describe some ‘observable’ of the universe have had a history of being corrected, that certainly does not imply, as Siegal directly insinuated, that the universe must be purely physical in its foundational nature. It simply means that our first mathematical approximations were incorrect.

Such a history of correction to our mathematical models is far more of a testimony to our finite and fallible limitations as human beings than it is of any evidence to the notion that the the universe must be purely physical in its foundational nature.

In fact, according to Siegal’s own reasoning, if a mathematical model had no need of being corrected, then that would imply that our universe was ‘mathematical’ not physical.

And indeed, (in so far as the ‘observables’ that the mathematical models were specifically designed to describe are concerned), our current mathematical models have been perfected to such a point that they currently show no sign of presently needing any correction in their mathematical formulation whatsoever.

For most of the history of modern science in the Christian west, finding ‘platonic perfection’ for the mathematical descriptions of the universe has been a very elusive goal. This all changed with the discoveries of Special Relativity, General Relativity and Quantum Mechanics. That is to say, as far as experimental testing will allow, there is no discrepancy to be found between what the mathematical descriptions of Relativity and Quantum Mechanics predict and what our most advanced scientific testing of those predictions are able to measure.

As well, quantum electrodynamics (QED), which is a combination of special relativity and quantum mechanics, also now joins the list of perfect mathematical descriptions of the universe in which we can find no deviation from what the mathematics predict and what our best experimental testing can discern. In other words, as far as we can tell, ‘platonic perfection’ is reached for QED:

Thus, according to Siegal’s own reasoning, if a mathematical model of an ‘observable’ needed no correction in order to agree with observational evidence, (as is currently the state with the current mathematics of Quantum Mechanics and Relativity), then that would imply that our universe was ‘mathematical’ rather than being ‘physical’.

More specifically, mathematics has no possible material explanation and therefore, if mathematics can perfectly describe the universe, then, (again according to Siegal’s reasoning), our universe must ultimately have a non-material explanation for its existence rather than a ‘physical’ and/or material explanation for its existence.

Moreover, holding that our universe is purely mathematical in its foundational makeup, rather than being ‘physical’ or mental in its foundational makeup, is fraught with its own difficulties that render it untenable.

Namely, as I pointed out the other day, Platonists, as opposed to neo-Platonists, hold to a view of mathematics that mathematics exists independently of the mind of God,

As Ed Fesser recently pointed out, “There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind, including the divine mind. They occupy a “third realm” of their own, the realm famously described in Plato’s Theory of Forms.

And as I also pointed out the other day, this view that mathematics has a necessary existence, rather than mathematics being contingent upon the mind o God for its existence, is what prevented the rise of modern science in the first place and is what is currently behind the present stagnation in theoretical physics with String Theory.

It was only with the quote-unquote ‘outlawing’ of the ancient Greek philosophers’s deterministic and necessitarian view of creation, particularly mathematics, that modern science was finally able to achieve a viable birth.

And from that viable birth of modern science, that was made possible from the ‘outlawing’ of the ancient Greek philosophers’s deterministic and necessitarian views of creation, modern science has slowly descended back into that unfruitful deterministic and necessitarian view of the ancient Greek philosopher’s that had stymied the rise of modern science in the first place.

No place is this unfruitful necessatarian view of mathematics more evident than it is with the current search for a purely mathematical ‘theory of everything’ in which it is hoped that a single mathematical framework and/or model will explain “all physical aspects of the universe” (per wikipedia). All ‘physical aspects’ which apparently includes explaining everything like why I decided to have eggs, bacon and hash-browns this morning instead of cereal.

As should be needless to say, it is simply foolish for mathematicians to believe that such an all encompassing mathematical ‘theory of everything’ will ever be forthcoming.

This self-evident truth should not even be up for debate in mathematical circles. Godel, around 1931, proved that mathematics can’t possibly be a necessary form of existence that modern day physicist think that it is with his incompleteness theorems. But that mathematics itself is dependent, i.e. contingent, upon something else for any truthfulness that might be derived therein.

As the following article states, “Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous.”

Stephen Hawking himself, an atheist, honestly admitted that “Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”

That Stephen Hawking could stare Gödel’s incompleteness theorems in the face like he did, and then proceed directly to try to formulate a purely mathematical theory in spite of it, tells us just how deeply some of our biases are. Biases that apparently completely blind us in the face of evidence that directly contradicts what we would want to believe beforehand. Namely, Hawking desperately wanted to believe beforehand that mathematics has a necessatarian existence that is completely independent of the Mind of God for its existence. And as a result, Godel’s incompleteness theorem was little more than a road bump for Hawking in his fruitless endeavor to try to find a purely mathematical ‘theory of everything’.

Moreover, if we back up a step to where the Christian founders of modern science were in regards to their beliefs about mathematics,,, namely, if we hold mathematics to be contingent upon the Mind of God for its existence as the Christian founders of modern science held, rather than holding mathematics to have a necessatarian existence independent of the Mind of God, (as the ancient Greeks held), then a solution for the much sought after ‘theory of everything’ readily pops out for us.

Verse:

Of supplemental, according to observational evidence itself, (the very thing that Siegal stressed so highly in his article to try to imply that the universe was purely ‘physical’), the universe certainly is not purely ‘physical’, (in the sense of it being material and/or ‘natural’ in its fundamental nature). but the universe is to be considered ‘mental’ in its fundamental nature.