Category Archives: Mathematics

The limits of physics

Margaret Wertheim

Margaret Wertheim, science writer and co-founder of LA’s Institute for Figuring, has written an interesting piece for Aeon Magazine (here’s the link) on the limits of physics and mathematics as descriptive languages of the world. Challenging the idea that ‘physics is a progression towards an ever more accurate and encompassing Truth’, she adopts the viewpoint that, though mathematics has been extraordinarily useful in making sense of the natural world, it might still only be an imperfect framework that we have laid down on a much more complicated reality.

In order to articulate a more nuanced conception of what physics is, we need to offer an alternative to Platonism. We need to explain how the mathematics ‘arises’ in the world, in ways other than assuming that it was put there there by some kind of transcendent being or process. To approach this question dispassionately, it is necessary to abandon the beautiful but loaded metaphor of the cosmic book — and all its authorial resonances — and focus, not the creation of the world, but on the creation of physics as a science.

She talks about the development of physics as a science and a methodology and how it has been a progression in quantifying an ever increasing amount of the physical world. As more and more phenomena fall under the explanatory power of physics, there is a tendency among physicists to ‘believe that the mathematical relationships they discover in the world about us represent some kind of transcendent truth existing independently from, and perhaps a priori to, the physical world.’ But, she says, this doesn’t really give us the whole story.

We should be wary of claims about ultimate truth. While quantification, as a project, is far from complete, it is an open question as to what it might ultimately embrace. Let us look again at the colour red. Red is not just an electromagnetic phenomenon, it is also a perceptual and contextual phenomenon. Stare for a minute at a green square then look away: you will see an afterimage of a red square. No red light has been presented to your eyes, yet your brain will perceive a vivid red shape. As Goethe argued in the late-18th century, and Edwin Land (who invented Polaroid film in 1932) echoed, colour cannot be reduced to purely prismatic effects. It exists as much in our minds as in the external world. To put this into a personal context, no understanding of the electromagnetic spectrum will help me to understand why certain shades of yellow make me nauseous, while electric orange fills me with joy.

Her essay is not an argument against science, but against the obsession with quantitative measures, rigorous equations, and strict boundaries between natural elements. The universe might be messier than we give it credit for, and our attempts at categorization might lead more to confusion than to understanding.

Happy Pi Day!

As a graduate student in the sciences, especially one so heavily involved with mathematics as physics is, it’s quite natural to set aside today, 3/14, as a memorial to the number that math nerds seem to love so much. In celebration, I’ve already sampled three different kinds of pie: blueberry, peach, and egg/cheese (technically that last one was a quiche, but it was circular and had a crust, so that makes it a pie in my book). And that might not be the end of it.

As an aside, let me share something I heard once. If you take the length of the base of the Great Pyramid of Giza and divide it by its height, you get a number that is very nearly equal to 2pi, to a greater precision than the ancient Egyptians could have possibly known. At first this is a little baffling – how is it possible for them to have managed such a mathematical and architectural feat without advanced technology (perhaps given to them by some visiting extraterrestials?)

It turns out to be due to the peculiar way that the ancient Egyptians measured heights and distances: by using a wheel. Distances along the ground (such as the width of a pyramid) were measured by rolling the wheel along the ground. Heights were measured by standing the wheel on its side. Since pi is equal to the circumference of a circle divided by its diameter, anything constructed using this method will automatically have the number pi in its proportions.