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Mathematics and the Universe

Is mathematics simply a conceptual tool, or is it the fundamental material of the universe?

Tara Shears 38

Just what is the world made of? It’s such a short, simple question, but it’s a question that we still haven’t finished answering. Our answer has developed as our knowledge progresses – from thinking that everything is made up of “elements” at the time of the Greeks, to the idea of atoms and chemical elements, to today’s view that the building blocks of creation are subatomic, fundamental particles. It’s a view that represents the culmination of thousands of years of scientific enquiry. But is this really the final answer?  Is it possible that something deeper lies beyond our current understanding, perhaps something that shows that the fundamental fabric of the universe is not material at all?

Our current, best scientific view of the world is that it is at heart a very simple place. Look closely at anything in it, and you’ll see structure growing progressively simpler as you examine it at smaller and smaller scales. If you can detect scales a thousand million times smaller than us, you will see atoms. If you can detect scales a thousand million times smaller than that (or smaller, because we don’t know how small these smallest ingredients are), you will see the fundamental particles that, collected together, form atoms and everything else. A few fundamental forces determine the behaviour of these subatomic particles and how they stick together. Everything is bathed in an energy field (the eponymous Higgs field), that governs how strong the forces are – a delicate balance that ensure atoms are stable and that our universe looks the way it does to us.

It sounds a nice idea, and possibly on a par with thinking that everything in the universe is just a figment of your imagination. But what distinguishes this viewpoint is the way it was arrived at – through the scientific method. We have made observations, developed hypotheses to explain them, made predictions, built experiments to test those and so on in an unending cycle of testing and testing again. Now we have reached the stage where our experiments are huge five-storey structures sited around a 27 km long circular particle acceleration machine in Geneva. They are huge, complex and at the pinnacle of high tech. Their objective is to take snapshots of the fundamental particles produced in the particle accelerator, snapshots that form our data and that we use to test the predictions of our particle physics theory. This theory represents our best understanding. It is the only explanation we have that has passed each experimental test we’ve given it.

The theory is called the Standard Model precisely because of this ubiquitous success. As a theory it is compelling not just because of the continual reinforcement of experiment, but also because the universe it describes is simple – built of few components, with interconnectedness explained by symmetries, describing a landscape of mathematical, aesthetic beauty. The very neat way in which mathematics describes the universe in this theory has led some, like Peter Atkins in the debate on IAI TV, to think that mathematics itself must be the fundamental reality of the universe. To him, the universe is immaterial at heart. But to me mathematics is a tool – and a good one because it has enabled us to express our understanding in a way that is unambiguous and universal.

That’s not to say that understanding is easy. It isn’t. The quantum subatomic world is horribly non-intuitive. My internal picture of a fundamental particle is something small round and coloured, but that’s only because the real thing, a local “excitation in the corresponding field”, localised according to a set of probabilities, is something for which I have no internal picture whatsoever. Despite this and however strange it seems, these particles are physical. The reason that we claim this is that their behaviour is still described within our theory, and we understand them as material objects.

Although I think that the universe is formed of real, fundamental particles based on the evidence we have now, I know that science is a work in progress. The Standard Model is not a final theory and we certainly don’t have the last word on the underlying reality of the world. We don’t understand dark matter or dark energy (which form 96% of the universe at the last count), or antimatter, or even how to describe gravity at subatomic particle scales. Beyond that small oversight there is the question of why the universe should be made of fundamental particles at all. Perhaps the ultimate building block is not a speck of matter but a string that vibrates at different frequencies, each frequency corresponding to what we think of at the moment as a particle. Perhaps the fundamental unit of matter is something stranger still. I don’t know. But what I do know is that we will find out more, as we explore more, as we construct experiments capable of producing the data that will rule in or out improvements and replacement explanations for the Standard Model, because this is how science works. The description of the universe in the theory that ultimately survives these tests is what will become our explanation of the material nature of the universe.

 

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Dzen_o 5 November 2015

“Is mathematics simply a conceptual tool, or is it the fundamental material of the universe?”

- a next discussion on the IAI that remains be inside the mainstream-philosophical / mainstream/ physical approach; which implicitly eventually is reduced to many thousands years ontological problem “what is Matter?”. Including:

“…the very neat way in which mathematics describes the universe in this theory has led some, like Peter Atkins,…to think that mathematics itself must be the fundamental reality of the universe. To him, the universe is immaterial at heart...”

- this declaration isn’t something new , that had been clamed by Pythagoras yet 2500 years ago as some quite natural inference from evidently observed adequacy of the mathematics at describing of external (for humans) Nature; and recent versions of this claim don’t contain some additional essential features to the Pythagoras;

and such a situation occurs first of all because of that in the mainstream philosophy and physics there is no answer on the question above and so because of the absence of criterions – “what is/are material?”.

So - a next time on the IAI (see Dzen_o posts in a number of other topics):
– the questions above are Meta- mainstream- philosophical/ physical and so can be answered only in framework of the informational (“The Information as Absolute”) conception, where it is shown that everything, all what exists/ can exist / “doesn’t exist”, is/a re some informational patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set. Including Matter is only some specially organized informational system, i.e. a subset of the Set, which is observed by elements of another informational sub-Set “Consciousness” , i.e., by humans’ consciousnesses. At that Matter is the system where all elements are built and exchange by some messages when using true information exclusively – in contrast, say, to the consciousness. Just therefore mathematics that is essentially built in accordance with criterions of truth, self-consistence, etc. becomes be quite adequate at describing of Matter.

Including there is no problem in “…Perhaps the ultimate building block is not a speck of matter but a string that vibrates at different frequencies,..” – if the string theory is true then the strings are some “specks of matter” and nothing else.

That is another question, which is mostly terminological, though, – is the mathematics only a convenient language or indeed in depth any material object is some mathematical formula?

Cheers

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