General · Language · Problem

A universe without math?

John Healy
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 (increasing 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.

References

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

Ontology

Epistemology

Notes

[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

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One thought 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.

    Notes

    [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

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