## Things versus Relations and Objects versus Properties

In the August issue of Scientific American, Meinard Kuhlmann addresses, yet again, the conceptual difficulties inherent in the interpretations of experimental data of modern physics.

…the particle interpretation of quantum physics, as well as the field interpretation, stretches our conventional notions of “particle” and “field” to such an extent that ever more people think the world might be made of something else entirely.

Kuhlmann is currently a philosophy professor at Bielefeld University in Germany and has dual degrees in physics and philosophy. I was happy to see that he is firmly committed to the idea that the task of understanding the physical world requires both disciplines.

The two disciplines are complementary. Metaphysics supplies various competing frameworks for the ontology of the material world, although beyond questions of internal consistency, it cannot decide among them. Physics, for its part, lacks a coherent account of fundamental issues, such as the definition of objects, the role of individuality, the status of properties, the relation of things and properties, and the significance of space and time.

Kuhlman takes the time to describe, in fairly simple terms, the content of the Standard Model which consists of groups of elementary particles and the forces that mediate their interaction. He describes how the particles blur into fields while, at the same time, the fields are quantized rather than continuous. His discussion of how the particles are not really particles and the fields are not really fields leads him to his point:

If the mental images conjured up by the words “particle” and “field” do not match what the theory says, physicists and philosophers must figure out what to put in their place.

Kuhlman then takes his article in two interesting directions. The first is to focus on the notion of structure.

A growing number of people think that what really matters are not things but the relations in which those things stand…We may never know the real nature of things but only how they are related to one another…New theories may overturn our conception of the basic building blocks of the world, but they tend to preserve the structures. That is how scientists can make progress.

I was immediately reminded of a passage in the Courant/Robbins classic What is Mathematics? When I first read the book, I was impressed with implications of this observation which appears early in the text.

The “ether” was invented as a hypothetical medium capable of not entirely explained mechanical motions that appear to us as light or electricity. Slowly it was realized that the ether is of necessity unobservable; that it belongs to metaphysics and not to physics. With sorrow in some quarters, with relief in others, the mechanical explanations of light and electricity, and with them the ether, were finally abandoned.

A similar situation, even more accentuated, exists in mathematics. Throughout the ages mathematicians have considered their objects, such as numbers, points, etc., as substantial things in themselves. Since these entities had always defied attempts at an adequate description, it slowly dawned on the mathematicians of the nineteenth century that the question of the meaning of these objects as substantial things does not make sense within mathematics, if at all. The only relevant assertions concerning them do not refer to substantial reality; they state only the interrelations between mathematically “undefined objects” and the rules governing operations with them. What points, lines, numbers “actually” are cannot and need not be discussed in mathematical science. What matters and what corresponds to “verifiable” fact is structure and relationship, that two points determine a line, that numbers combine according to certain rules to form other numbers, etc. A clear insight into the necessity of a dissubstantiation of elementary mathematical concepts has been one of the most important and fruitful results of the modern postulational development.

Fortunately, creative minds forget dogmatic philosophical beliefs whenever adherence to them would impede constructive achievement.

In the context of the Courant book, this is an important observation about the development of mathematics. But I have always thought that it can be seen as an important observation of a more general intellectual maturity. And this, I think, leads to Kuhlmann’s second alternative for interpreting the meaning of quantum physics which chooses ‘properties’ rather than ‘objects’ as having an existence.

What we commonly call a thing may be just a bundle of properties: color, shape, consistency, and so on.

This idea is consistent not only with current theories in cognition, but also has roots in 19th century philosophy and science (in the work of Hermann von Helmholtz and Johann Friedrich Herbart, for example). Kuhlmann rightly argues that our first experiences are of properties.

As infants, when we see and experience a ball for the first time, we do not actually perceive a ball, strictly speaking. What we perceive is a round shape, some shade of red, with a certain elastic touch. Only later we do associate this bundle of perceptions with a coherent object of a certain kind – namely, a ball. Next time we see a ball, we essentially say, “Look, a ball,” and forget how much conceptual apparatus is involved in this seemingly immediate perception.

With respect to physics,Kuhlmann explains

theory predicts that elementary particles can pop in and out of existence quickly. The behavior of the vacuum in quantum field theory is particularly mind-boggling: the average value of the number of particles is zero, yet the vacuum seethes with activity…A particle is what you get when those properties bundle themselves together in a certain way.

The forgetting of ‘conceptual apparatus’ to which Kuhlmann refers is the very thing that I always hope (and expect) that mathematics will remind us of – in one way or another.

Thanks for this. I will take a look.

Very interesting article indeed, Joselle! Thank you for writing about the very intriguing relationship between physics and mathematics. A classic essay that you may already be familiar with is one written by physicist Eugene Wigner and published in 1960, called The Unreasonable Effectiveness of Mathematics in the Natural Sciences found at this link: http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html.

You know, I did a poor job explaining my position above. Ignoring physics’ role in modern technology makes me look silly.

I should have clarified what I mean by ‘physics.’ What I meant was that THEORETICAL physics hasn’t given us much in 60 years. I would argue that the amazing technologies we’re seeing today are the result of experimental physicists collaborating with engineers, mathematicians and computer scientists.

But the basic picture, or ‘ontogeny’ – as Kuhlmann in the above quoted article labels it – hasn’t changed since Einstein’s generation.

My biggest complaint with theoretical physics, I think, is that the world is filled with problems that desperately need the clarification that mathematicians traditionally offered. There are numerous social and economic problems that Complexity and Chaos Theories have shown are governed by mathematical patterns. Biology is surely LOADED with a rich variety of mathematical patterns. But we are in the position that Galileo was before the advent of calculus: We simply don’t have the symbology and concepts to describe, say, visual perception in a mathematical way. But dynamical systems theory and computer science has shown us that the patterns exist! We just need more creative mathematicians to devote themselves to the problems.

Unfortunately, most CREATIVE mathematical work today is being devoted to String Theory or pure mathematics, two subjects totally devoid of the data and experiments required for understanding our world. In other words, most of the best mathematical minds don’t want to participate in the kind of science that has made modern science what it is. As a result, we have engineers who are bored with pure mathematics on one side, and pure mathematicians who are bored with experiments on the other.

Historically, though, the greatest mathematicians were also the greatest physical scientists. Most of Newton’s work was scientific, but he also made great contributions to infinite series. Euler worked on – among thousands of contributions – both complex number theory and acoustics. Poincare worked on abstract algebra, but also clarified the three-body problem. And Gauss – perhaps the most incisive number theorist in history – was actually a professional astronomer!

John Horgan argued in his book “The End of Science” that the major principles of nature have already been discovered; that no concepts as profound as gravity, energy, or DNA will surface in the future. That makes me sad, and I think he’s wrong; surely nature has many more BIG principles to discover. But I DO think science is in a cul-de-sac, and that such profound concepts as Cognition will never be explained until the professional pattern seekers of our world – the mathematicians – roll up their sleeves, turn their attentions away from the Higgs particle or the Dedekind Zeta function, and start developing new mathematics to describe the many novel patterns that science has discovered in the past century. Until then, I think, a real understanding of something as deep as cognition will be out of our reach.

I understand what you say. And I’m sure I would take exception to the way research funds are and are not distributed. But, despite the way that physics relies more and more heavily on mathematics, they are not the same thing. The extent to which physicists have been able to predict the behavior of physical phenomena (and the precision of experimental efforts) has provided some extraordinary technological advances (in communication, imaging, computing power etc, etc.) But the relationship between physics and mathematics is very interesting and still not understood. Some physicists continue to address this relationship and some have opened the discussion up to recent insights in cognitive science. The Foundational Questions Institute (http://fqxi.org/) devoted a conference to this kind of interdisciplinary discussion a few years ago. And this is the stuff I’ve come to care about quite a bit.

I like this article too, but I’m afraid for different reasons.

To those of us who studied quantum mechanics in college and found it totally unsatisfying, Kuhlmann is merely pointing out great weaknesses in physics.

I have no qualms about paying professional mathematicians to pursue topics with no basis in ‘reality’ (e.g., advanced Number Theory), but if modern physics is increasingly becoming equivalent to pure mathematics — as your totally astute reference to Courant/Robbins indicates — then I’m having trouble seeing how physicists can justify throwing hundreds of millions of taxpayers dollars into projects like CERN.

Instead of spending billions of dollars into finding another non-particle to the Standard Model, why couldn’t we pour those resources into say, neuroscience. Surely we’d understand much more about our world — or at least our brains — if we built a billion-dollar MRI.

What physics has given us over the past 60 years amounts to developments in pure mathematics. But physics is way more expensive.

Why does physics get the financial priority over the other sciences? Because the math is more complicated? Or because they’re higher status, and other scientists are second-class citizens?