Julian Barbour, from metaphysics to mathematics to us

Julian Barbour is a theoretical physicist with a clear interest in tackling foundational issues and the errors of judgment that can lead physics theories astray.  One of these candidates for a mistaken judgment is time itself, and in 1999  Barbour authored the book The End of Time published by the Oxford University Press. He wrote an essay on time for one of the Foundational Questions Institute’s essay contests and answered some questions about his ideas in an Edge interview when the book was first published.

Back in July and I wrote a blog about how some modern thoughts point back to Leibniz’s view of the universe.  And Julian Barbour has found new value in Leibniz’s philosophy as well.  The value comes, in part, from the fact that key aspects of his philosophy can be translated into mathematical models.  Barbour published a paper in The Harvard Review of Philosophy entitled The Deep and Suggestive Principles of Leibnizian Philosophy.  The paper can be found at this website under the heading: Papers on Maximal Variety.

It is, in fact, the way Leibniz accounted for the infinite variation in our universe, that Barbour uses to suggest a new direction for modern theories in physics. And this line of thought will lead, again, to the significance of perception in the creation of these theories.

Barbour first takes note of the transition from the notion that the universe is ordered, to the insight that its order changes from instant to instant.

Before the scientific revolution, the instinctive reaction of thinkers to the existence of perceived structure was to find a direct reason for that structure. This is reflected above all in the Pythagorean notion of the well-ordered cosmos: the cosmos has the structure it does because that is the best structure it could have….Kepler and Galileo were no less entranced by the beauty of the world than was Pythagoras, and they formulated their ideas in the overall conceptual framework of the well-ordered cosmos. However, both studied the world so intently that they actually identified aspects of motion (precise laws of planetary motion and simple laws of falling bodies and projectiles) that fairly soon led to the complete overthrow of such a notion of cosmos. The laws of the new physics were found to determine not the actual structure of the universe, but the way in which structure changes from instant to instant.

Barbour raises the question of whether modern science lacks a key idea, like a “structure-creating principle that has hitherto escaped us,” which might also address problems with time since as he notes,

the highly flexible and relational manner in which time is treated in Einstein’s theory of gravity is extremely difficult to reconcile with the role that time plays in quantum mechanics, since in the latter, time is essentially the external, absolute time that Newton introduced. In fact, some researchers in the field doubt whether time has any role at all to play in quantum cosmology, arguing that time is an emergent phenomenon.

Barbour points out that Leibniz critiqued Newton’s notion of an absolute space and time by asking the question:  How would God decide to put the universe ‘here’ rather than ‘there’?  The notion of absolute place must be incorrect.  Leibniz argued that space is no more than the order of coexisting things, whose place is understood solely by their positions relative to each other. Barbour finds in Leibniz’s philosophy “the seeds of a structure-creating first principle—and much more.”  Barbour believes that while Leibniz’s philosophy can look “quite fantastical,”

it is the one radical alternative to Cartesian-Newtonian materialism ever put forward.  It possesses enough definiteness to be cast in mathematical form—and hence to serve as a potential framework for natural science.

For Leibniz, Descartes’ idea was flawed.  It couldn’t address the variety of what we see. And Barbour points out that it is roughly Descartes’ perspective to which physics lines up, although “on a much more secure empirical basis.”

Through much of the last century, one of the main goals of physics was to find the fundamental particles of nature. Even at the time when quantum mechanics was discovered, in 1925–1926, physicists believed that all matter was composed of only two fundamental particles—the electron and the proton. This picture does indeed look like a minimal extension of Cartesian reductionism. But during the course of the century, the number of so-called fundamental particles grew in a somewhat disconcerting manner, though our understanding of the way in which they interacted also progressed impressively…… if the superstring enthusiasts are correct, we are almost back to Descartes.

Leibniz’s thoughts went in another direction.  His fundamental entity was a monad not an atom.  In the atomic idea, while there were different classes of atoms, within each class only their positions and speeds, in space and time, distinguished them.  Since for Leibniz, space and time did not have an independent existence, position in space and time could not be used to distinguish objects.

Leibniz held that the entire world consists of nothing but distinct individuals, and that the sole essence of these individuals is to have perceptions (not all of which they are distinctly aware of)…. The most radical element in the Monadology, postulated rather than explained or made directly plausible, is the claim that the perceptions of any one monad—its defining attributes—are nothing more and nothing less than the relations it bears to all the other monads. The monads exist by virtue of self-mirroring of each other; they all define each other.

Barbour points out that, aside from their being intrinsically interesting, Leibniz’s ideas have the potential to contribute to modern theories because they are ‘relational’ like general relativity and quantum mechanics, and Leibniz seems to provide the way to give the idea a mathematical structure.  Barbour has explored these mathematical structures with Lee Smolin and the models can be found in their paper.

But Leibniz’s monads are metaphysical points that are real (like physical points) and exact (like mathematical points).  The cosmos that emerges from this unfamiliar world will not be what we expect.  Barbour’s maximal variety models were developed with the aim of creating new physical theories.  And he finds that the models have two “intriguing aspects.”


First, if this model is ever transformed into some kind of fundamental description of the universe, physics will come to resemble biology: all of the entities in a maximal-variety configuration are created in a kind of ecological balance between competing individuals. Each is trying to be as individualistic as possible, but in a curious way this selfish behavior is necessary if anything is to exist at all (for to exist is to become differentiated and hence to emerge from the mist of nothingness).

There it is again, “physics will come to resemble biology,” (which, in my opinion, mathematics already does).  But then pushing a bit further, it seems clear that any significant progress in ‘ideas,’ or models in physics will have to take us into account.

The second aspect warrants a lengthier discussion. Consciousness in a material world is so baffling that idealism has always seemed more cogent than materialism. But hitherto nothing significant in the way of mathematical support to rival the triumphs of physics based on the hypothesis of an external world has been forthcoming….. To make idealism plausible, one needs laws that act directly and transparently on the raw stuff of consciousness: perceptions. (emphasis my own).

There are many things about the way Leibniz characterizes monads that are provocative.  And this one, which Barbour quotes is one of them:

And just as the same town, when looked at from different sides, appears quite different and is, as it were, multiplied in perspective, so also it happens that because of the infinite number of simple substances [monads], it is as if there were as many different universes, which are however but different perspectives of a single universe in accordance with the different points of view of the monads. And this is the means of obtaining as much variety as possible, but with the greatest order possible; that is to say, it is the means of obtaining as much perfection as possible.



3 comments to Julian Barbour, from metaphysics to mathematics to us

  • happyseaurchin

    my current method of inquiry
    is for me to be sensitive to mathematics
    specifically how the arithmetic operations actually operate mentally

    if there is validity to my stance
    i have had the intuition
    that we may need to develop different mathematical techniques

    at a crude level
    i’ve made some progress wrt economics
    using subjective enumeration and then applying standard math tools like google page rank

    i’ve also come across an alternative way to capture un/certainty
    though only first steps

    but these are crude steps
    and my intuition suggests a new mathematics
    as significant as newton’s calculus was to physics

  • Joselle

    Yes. It does make sense. And my impulse is to say that mathematics already has this potential. I’m interested in how mathematics is sensitive to consciousness (to use your words).

  • happyseaurchin

    apart from the context of physics
    my mind kept interpreting monads as consciousness
    pure and simple

    rather than try to see how physics meets consciousness
    it may be easier to develop a mathematics that is more sensitive to consciousness
    derive a relational mathematics
    (which may not be representative)
    and if that is found to be useful or interesting or whatever we consider valuable
    then we might be able to conjoin it to our explorations of “physics” and our physical reality of objects

    does this make sense?