General · Language · Problem

A universe without math?

The context

“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.

The recap

So, I’ve written about this topic in various posts [1]: 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.[2]

Imagine a universe without math? Or, an understandable universe without math? An advanced technology without math? Globally connected, complex, pluralistic human cultures without math?

The conversation

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.

Plato’s cave

3-body problem

Chaotic systems




[1] 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.

[2] 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.

Related posts

Laplace’s demon RIP? – demons of physics

5 thoughts on “A universe without math?

  1. Mathematical posture …

    • Caltech Magazine > “Writing in the Language of Math” by Whitney Clavin (Feature, Summer 2022) – What Does Math Mean? [1]

    If math can be expressed in words, what does this say about the true nature of math? Are mathematical symbols merely human inventions used for expressing abstract ideas, or are they part of a fundamental language of the universe that exists independently of us?

    Christopher Hitchcock, the J. O. and Juliette Koepfli Professor of Philosophy, says there are two main camps when it comes to the meaning of math and numbers. The first group follows ideas put forth by the ancient Greek philosopher Plato, who believed mathematical objects are real and possess identities that exist beyond ourselves.

    Feynman … said in a lecture at Cornell University in 1964: “To those who do not know mathematics, … If you want to learn about nature, to appreciate nature, it is necessary to understand the language she speaks in.”

    But as Hitchcock explains, other philosophers believe math is merely an invented tool of science and not an inherent part of our reality. Hartry Field of New York University has gone so far as to reformulate Newtonian mechanics without references to numbers. Field argues the structures described by math are fictitious and not literally true.


    [1] Compare this YouTube video by Sabine Hossenfelder.

    • YouTube > Sabine Hossenfelder > “Are we made of math?” (Jul 31, 2021)

    We use the same notion of “reality” in physics, that something is real because it’s a good explanation for our observations. I am not trying to tell you that this is The Right Way to define reality, it’s just for all I can tell how we use the word.

    … when physicists say that space-time is real or the Higgs-boson is real, they mean that a certain mathematical structure correctly describes observations.

    But just because you have math for something doesn’t mean it’s real. … just that this is a belief-based statement, not supported by evidence.

    YouTube video screenshot

  2. 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

    Sabine Hossenfelder is a theoretical physicist and creator of the popular YouTube series Science Without the Gobbledygook. In her new book Existential Physics, she argues that some of her colleagues may have gotten a little too excited about wild ideas like multiverse theory or the simulation hypothesis.

    Multiverse theory states that an infinite number of alternate universes are constantly branching off from our own. Hossenfelder says it’s possible to create mathematical models that are consistent with multiverse theory, but that doesn’t necessarily tell you anything about reality. “I know quite a lot of cosmologists and astrophysicists who actually believe that other universes are real, and I think it’s a misunderstanding of how much mathematics can actually do for us,” she says.

    Multiverse spins
    Credit: Pixabay/CC0 Public Domain

  3. 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.

    • > “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?

    (quote) A dominant view in science is that there is a mathematical truth structuring the universe. It is assumed that the scientist’s job is to decipher these mathematical relations: once understood, they can be translated into mathematical models [1]. Running the resulting “silicon reality” in a computer may then provide us with useful insights into how the world works.

    Once these new additions [parameters and mechanisms] and their associated uncertainties are integrated into the model, they pile on top of the uncertainties already there. And uncertainties keep on expanding with every model upgrade, making the model output fuzzier at every step of the way—even if the model itself becomes more faithful to reality.


    [1] Cf. Wiki > Allegory of the cave – “A philosopher aims to understand and perceive the higher levels of reality.

    (quote) The shadows are the prisoners’ [our everyday] reality, but are not accurate representations of the real world. The shadows represent the fragment of reality that we can normally perceive through our senses, while the objects under the sun represent the true forms of objects that we can only perceive through reason. Three higher levels exist: the natural sciences; mathematics, geometry, and deductive logic; and the theory of forms.

    Plato's cave
    An illustration of The Allegory of the Cave

  4. Laws of physics as approximate gauges

    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 [1] (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.

    First things first. What we often call laws of physics are really just consistent mathematical theories that seem to match some parts of nature. … precise and consistent ways of describing the reality we see. This should be obvious from the fact that these laws are not static; they evolve as our empirical knowledge of the universe improves.

    One possible conclusion from this is that the conventional reductionist approach of particle physics, where natural laws are increasingly focused on smaller and smaller building blocks (like molecules, atoms and particles) and fundamental forces (like gravity and electromagnetism) acting between them, is no longer a fruitful way of looking at the physical world.

    I know from my 40 years of experience in working on real-life physical phenomena that the whole idea of an ultimate law based on an equation using just the building blocks and fundamental forces is unworkable and essentially a fantasy. We never know precisely which equation describes a particular laboratory situation. Instead, we always have to build models and approximations to describe each phenomenon even when we know that the equation controlling it is ultimately some form of the Schrödinger equation!

    … the standard model of particle physics, the theory of superconductivity and the theory of atomic spectra are all built using the rules of quantum mechanics, but they have little to do with each other. In addition, space and time are variables that have to be put in by hand into the theory, when space and time should come out naturally from any ultimate law of physics. This has remained perhaps the greatest mystery in fundamental physics with no solution in sight.


    String theory – the landscape problem, the multiverse


    [1] 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.

    In 2010, Das Sarma and collaborators, made a prediction that Majorana fermions will be found in condensed matter, in particular, in semiconductor nanowires. This has led to considerable experimental activity, led by Microsoft Corporation, to produce a topological quantum computer.

  5. Sabine Hossenfelder remarks in her latest book [1] that:

    It strikes me as presumptuous to think that humans have already discovered the language in which nature speaks, basically on the first try and right after we appeared on the surface of the planet.

    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. [2]

    … physics isn’t math. Physics is a science and as such has the purpose of describing observations of natural phenomena. Yes, we use mathematics in physics, and plenty of that, as I’m sure you have noticed. But we do this not because we know the world is truly mathematics. It may be mathematics – this possibility is known as Platonism, but Platonism is a philosophical position, not a scientific one. All we can tell from observations is that math is useful to describe the world.

    However, the belief that reality is math is deeply ingrained into the thinking of many physicists … Physicists may not consciously subscribe to the idea that math is real and when asked will deny it, but in practice they do not distinguish the two. This conflation has consequences, for they sometimes erroneously come to think their math reveals more about reality than it possibly can.


    [1] Hossenfelder, Sabine (2022-08-08T23:58:59.000). Existential Physics. Penguin Publishing Group. Kindle Edition.

    [2] She also notes that: “you do not need to silence rational thought to make space for hope, belief, and faith.”

    Book cover

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