“He [Einstein] could construct complex equations, but more important, he knew that math is the language nature uses to describe her wonders.” – Isaacson, Walter. Einstein: His Life and Universe. Simon & Schuster. Kindle Edition.
• YouTube > The Science Asylum > “Is Math the Language of the Universe?” (published 12-31-2016)
(video description) There is a very common debate over the nature of math. Is it something that exists as part of the universe that we slowly “discover” or is it something we make up to try and explain our crazy world?
(from transscript) Math is not the language of the universe. Even if we wanted to personify the universe and say it’s trying to communicate with a language, which I would advise against, math is only a small part of our best translation of it.
So, I’ve written about this topic in various posts : The relationship between (increasingly complex) mathematical models and our understanding of the universe. Whether – or to what degree – that entails understanding of reality or a powerful pragmatic language (predictive tool). A true, direct reflection; or, an approximate, conceptual framework. The conversation harkens back to ancient times.
Imagine a universe without math? Or, an understandable universe without math? An advanced technology without math? Globally connected, complex, pluralistic human cultures without math?
This recent article (below) highlights the role of mathematics in the scientific method.
• The Conversation > “A universe without mathematics is beyond the scope of our imagination” by Peter Watson, Emeritus professor, Physics, Carleton University (April 10, 2022) – Could we imagine a universe in which mathematics does not work?
Almost 400 years ago, in The Assayer, Galileo wrote: “Philosophy is written in this grand book, the universe … [But the book] is written in the language of mathematics.” He was much more than an astronomer, and this can almost be thought of as the first writing on the scientific method.
We do not know who first started applying mathematics to scientific study, but it is plausible that it was the Babylonians, who used it to discover the pattern underlying eclipses, nearly 3,000 years ago. But it took 2,500 years and the invention of calculus and Newtonian physics to explain the patterns.
What about chaotic systems?
But just because something can be described mathematically does not mean it can be predicted.
Examples: the 3-body problem, weather forecasts (hurricanes), social phenomena …
One can calculate the properties of an electron very accurately, but we cannot predict what an individual one will do.
A universe that could not be described mathematically would need to be fundamentally irrational and not merely unpredictable.
Mathematical universe hypothesis
(Wiki) Our external physical reality is a mathematical structure. That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well.
The theory can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical entities; a form of mathematical monism in that it denies that anything exists except mathematical objects; and a formal expression of ontic structural realism.
 For example, in quantum theory, whether the wave function is real or an approximation.
And how an effective theory is an emergent approximation to a deeper theory.
And the skill of physicists in knowing when a “cow” is like a sphere, when to treat (mathematically) a complex object as a point.
 Ethan Siegel recaps some history as well. “Good enough” orbital predictions became not enough. Conceptual elegance wanting. Improved mathematical models awaited better data.
• Forbes > “No, The Universe Is Not Purely Mathematical in Nature” by Ethan Siegel Senior Contributor, Starts With A Bang Contributor Group (May 20, 2020) – The Universe pushes back at math models of what it ought to be.
The Universe is a physical, not mathematical entity… Here’s why mathematics alone will always be insufficient to reach a fundamental theory of everything.
(graphic caption) One of the great puzzles of the 1500s was how planets moved in an apparently retrograde fashion. This could either be explained through Ptolemy’s geocentric model (L), or Copernicus’ heliocentric one (R). However, getting the details right to arbitrary precision was something that would require theoretical advances in our understanding of the rules underlying the observed phenomena, which led to Kepler’s laws and eventually Newton’s theory of universal gravitation.
[Kepler’s legacy was that] “science needed to be based in observables and measurables, and that any theory needed to confront itself with those notions. … it wasn’t simply that new mathematics told us how the Universe worked.
Mathematics will get you very far in this world, but it won’t get you everything.
• Laplace’s demon RIP? – demons of physics
5 thoughts on “A universe without math?”
Mathematical posture …
• Caltech Magazine > “Writing in the Language of Math” by Whitney Clavin (Feature, Summer 2022) – What Does Math Mean? 
 Compare this YouTube video by Sabine Hossenfelder.
• YouTube > Sabine Hossenfelder > “Are we made of math?” (Jul 31, 2021)
Mathematical models gone awry?
• Wired > “Have Some Scientists Gotten Too Excited About the Multiverse?” by Geek’s Guide To The Galaxy (9-9-2022) – Episode 525 of the Geek’s Guide to the Galaxy podcast, an interview with Sabine Hossenfelder
Credit: Pixabay/CC0 Public Domain
As noted elsewhere, physical models (and associated supercomputer simulations) keep getting bigger and more complicated. There’s an implicit mantra that “more detail is better.”
This article questions that assumption. Particularly regarding national epidemiological models, global hydrological models.
The article also reminds me of more and more articles touting the value of AI systems but bereft of an intelligible predictive model.
• Phys.org > “How a quest for mathematical truth and complex models can lead to useless scientific predictions” by Arnald Puy, The Conversation (November 5, 2022) – If more detailed models produce sharper estimates and better predictions, does that mean that they are closer to reality?
 Cf. Wiki > Allegory of the cave – “A philosopher aims to understand and perceive the higher levels of reality.”
An illustration of The Allegory of the Cave
So, here’s an article by a senior theoretical physicist, commenting on the relationship between (increasingly complex) mathematical models and our understanding of the universe. While powerful, our mathematical theories (in physics) are approximate, evolving.
• New Scientist > “Why the laws of physics don’t actually exist” by theoretical condensed matter physicist Sankar Das Sarma  (9 December 2022) – While amazing that we can make sense of some aspects of the universe through the laws of physics, it is difficult to imagine that a thousand years from now physicists will still use quantum mechanics as the fundamental description of nature.
String theory – the landscape problem, the multiverse
 Sankar Das Sarma is a theoretical physicist based at the University of Maryland, College Park. His interests are diverse, spanning the strange properties of matter to how information should be understood in the quantum realm.
Sabine Hossenfelder remarks in her latest book  that:
While her arguments “implicitly assume that mathematics itself is timeless, that mathematical truth is eternal, and that logic doesn’t change,” additional comforting beliefs are not scientific – unnecessary (superfluous) to explain what we observe. 
 Hossenfelder, Sabine (2022-08-08T23:58:59.000). Existential Physics. Penguin Publishing Group. Kindle Edition.
 She also notes that: “you do not need to silence rational thought to make space for hope, belief, and faith.”
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