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Space & Astronomy

Could the universe exist without mathematics ?

April 11, 2022 · Comment icon 186 comments

A universe without mathematics - is it possible ? Image Credit: NASA/ESA/ESO
Mathematics is such a fundamental part of our reality that it is difficult to imagine the universe existing without it.
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.

Since then, probably every single major scientific discovery has used mathematics in some form, simply because it is far more powerful than any other human language. It is not surprising that this has led many people to claim that mathematics is much more: that the universe is created by a mathematician.

So could we imagine a universe in which mathematics does not work?

The language of mathematics

The Sapir-Whorf hypothesis asserts that you cannot discuss a concept unless you have the language to describe it.

In any science, and physics in particular, we need to describe concepts that do not map well on to any human language. One can describe an electron, but the moment we start asking questions like "What colour is it?" we start to realize the inadequacies of English.

The colour of an object depends on the wavelengths of light reflected by it, so an electron has no colour, or more accurately, all colours. The question itself is meaningless. But ask "How does an electron behave?" and the answer is, in principle, simple. In 1928, Paul A.M. Dirac wrote down an equation that describes the behaviour of an electron almost perfectly under all circumstances. This does not mean it is simple when we look at the details.

For example, an electron behaves as a tiny magnet. The magnitude can be calculated, but the calculation is horrendously complicated. Explaining an aurora, for example, requires us to understand orbital mechanics, magnetic fields and atomic physics, but at heart, these are just more mathematics.

But it is when we think of the individual that we realize that a human commitment to logical, mathematical thinking goes much deeper. The decision to overtake a slow-moving car does not involve the explicit integration of the equations of motion, but we certainly do it implicitly. A Tesla on autopilot will actually solve them explicitly.

Predicting chaos
So we really should not be surprised that mathematics is not just a language for describing the external world, but in many ways the only one. But just because something can be described mathematically does not mean it can be predicted.

One of the more remarkable discoveries of the last 50 years has been the discovery of "chaotic systems." These can be apparently simple mathematical systems that cannot be solved precisely. It turns out that many systems are chaotic in this sense. Hurricane tracks in the Caribbean are superficially similar to eclipse tracks, but we cannot predict them precisely with all the power of modern computers.

However, we understand why: the equations that describe weather are intrinsically chaotic, so we can make accurate predictions in the short term, (about 24 hours), but these become increasingly unreliable over days. Similarly, quantum mechanics provides a theory where we know precisely what predictions cannot be made precisely. One can calculate the properties of an electron very accurately, but we cannot predict what an individual one will do.

Hurricanes are obviously intermittent events, and we cannot predict when one will happen in advance. But the mere fact that we cannot predict an event precisely does not mean we cannot describe it when it happens. We can even handle one-off events: it is generally accepted that the universe was created in the Big Bang and we have a remarkably precise theory of that.

Designing social systems

A whole host of social phenomena, from the stock market to revolutions, lack good predictive mathematics, but we can describe what has happened and to some extent construct model systems.

So how about personal relationships? Love may be blind, but relationships are certainly predictable. The vast majority of us choose partners inside our social class and linguistic group, so there is absolutely no doubt that is true in the statistical sense. But it is also true in the local sense. A host of dating sites make their money by algorithms that at least make some pretence at matching you to your ideal mate.

A universe that could not be described mathematically would need to be fundamentally irrational and not merely unpredictable. Just because a theory is implausible does not mean we could not describe it mathematically.

But I do not think we live in that universe, and I suspect we cannot imagine a non-mathematical universe.

Peter Watson, Emeritus professor, Physics, Carleton University

This article is republished from The Conversation under a Creative Commons license.

Read the original article. The Conversation

Source: The Conversation | Comments (186)

Recent comments on this story
Comment icon #177 Posted by zep73 7 months ago
Det lyder indviklet. Men Californien for helvede. Det må da være et sygt fedt sted at slå rødder!
Comment icon #178 Posted by jmccr8 7 months ago
Hi Zep Math doesn't know anything unless it shows that it is a self-aware intelligence, we were able to observe something through using math because of our intelligence.
Comment icon #179 Posted by badeskov 7 months ago
Både ja og nej. Sjovt nok, så er dk helt vildt mht tech.    Cheers, Badeskov
Comment icon #180 Posted by zep73 7 months ago
Yes of course. Didn't mean it literally.   Åbenbart. Der er mere under overfladen end Olsen Banden, Bamse & Kylling og TV-Avisen der kludrer i teknikken og må springe et indslag over 
Comment icon #181 Posted by Skulduggery 7 months ago
Mathematics is just a way to quantify things based on our perception. Numbers are invented.
Comment icon #182 Posted by Skulduggery 7 months ago
...much like the concept of hours and minutes. That is how I look at it.
Comment icon #183 Posted by lightly 7 months ago
Agreed,  hours and minutes are just measurements of the Length of our day..which is simply one revolution of our earth. (Approximately 24 hrs.).     I wanted to say this in the topic about  Time.   On any other planet the amount of ‘ time’ one revolution takes…would produce different measurements.      It wouldn’t change the speed of light…but it would be ‘written’ differently.
Comment icon #184 Posted by razman 7 months ago
I don't know but it is odd how solar systems are like giant atoms in a way with the sun like a nucleus and the planets like electrons orbiting around it , and maybe galaxies like molecules or something . They say that solid objects are mostly space between them , So if you take the universe and see it as much , much larger , like to the umpteenth degree larger than what we are , then it like this. 
Comment icon #185 Posted by Emma_Acid 7 months ago
Except the things those numbers represent actually exist. Whether it's two apples being added to two other apples, or a logarithmic spiral being used in the formation of a shell. The numbers we attach to them are made up on a semiotic level, but on the level of reality the structure exists.
Comment icon #186 Posted by Skulduggery 7 months ago
Not disputing that of course. I have a larger explanation but no time to type it all right now. Life is increasingly busy for me right now. There is probably a whimsical joke about time and numbers in this very post now that I think on it but I'm not about to sink too much thought into formulating and articulating it.

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