|I' foon laid for doot.
Thocht and scrievit – bit nae mind'nt?
Gye near. Ebsent freens.
- James Reid
| Foundation of doubt.
I thought and wrote - but I forgot?
So close. Absent friends.
|Glymur dansur í høll,
Dans sláið ring,
Glaðir ríða Skotskur menn,
til Waterloo Gym!
- his joke about the Faroese
saga Ormurin Langi
| Dance resounds in the halls,
dance! form a ring!
Brave Scots, ride
to Waterloo Gym!
Q: Roughly how long would it take for you to explain to a lay crowd what part of the world your physics work deals with?
JR: Not as long as you might imagine! Although I'm really more of a mathematician, I'm active in two fields: Mathematical Relativity and Quantum Gravity. The first uses pure mathematics to study the structure of space and time. Although Quantum Mechanics is purported to have a particularly strange ontology - inasfar as particles may be in two places at once (as indeed, they are!) - to me, Relativity is by far the richer theory, both mathematically and conceptually. That answer's a bit of a cop out, but the next isn't:
Quantum Gravity is (arguably) the deepest theory of fundamental physics. Quantum Mechanics and General Relativity are two physical theories which describe the nature of very small- and very large- scale phenomena, respectively. QM describes phenomena subatomically, whilst General Relativity describes physics astronomically. By virtue of their mathematical formulations, the two theories are completely incompatible. Thus, the regime at which quantum effects become important at gravity is completely unknown. These are the smallest fundamental scales in the universe, and (I believe) ALL the deep theories predict very strange behaviour there.
The most popular, best-developed theory of Quantum Gravity is String Theory. String Theory asserts that the elementary particles we see in linear accelerators are in fact different vibrational "modes" of a more fundamental object - a Superstring. To be consistent, String theory must exist in either 11, 12 or 26 dimensions. I'll happily write you an extensive comment about it, since I don't believe in String Theory. It's mysticism gone wrong. We have a wondrous gift in mathematics - it's truly the occult science - but String Theory is the paragon of our being misled. This would make a very good article in itself actually, let me know if you'd like to discuss it!
Q: Me saying "lay crowd" isn't far off, either; you've some mystical beliefs about physics, in the Pythagoras/Spinoza/Pauli/Penrose tradition. How much of this can you express in language?
JR: Yes, I'm somewhat mystical. At face value, mathematics is a "game". One stipulates a set of rules, according to which notional "objects" may be manipulated. One then examines the consequences of the axioms, and quickly find the that game is remarkably well-suited for describing nature.
(Aside: Penrose talks about this fairly extensively about the relation between a mathematically idealised thing, say a circle, and the thing itself - although I've only ever skimmed what he's written.)
(Aside: I didn't know Pauli had mystical beliefs. He had a strong friendship with Carl Jung, and they had many dialogues that were published in a book. That would be great to read!)
In the course of asking natural mathematical questions, you uncover new structures which are sometimes found to have application in nature. Until the twentieth century, mathematics was only really employed aposteriori in physical theories. The natural philosopher would effectively 'check' that his insight stood up the rigors of mathematics. e.g. In the C19th, there was great interest in electromagnetic phenomena. Following the work of Ampere, Faraday, Kirchoff, Coulomb and numerous others, James Clerk Maxwell succinctly described all electromagnetic behaviour in terms of two equations. Decades of sickeningly complicated calculations were reduced to:
d(*F) = J
Hidden in these equations are the principles underlying almost ALL developments in C20th theoretical physics. If we only had eyes to see, Einstein's Special Relativity was implicitly described herein in its entirety.
It was astonishing. The physical structure of the universe was written in mathematical structure. The nature of a conception constrained what "could be". I hope I'm adequately conveying the magnitude!
I think this is what started the new strain of mathematical mysticism. There've been a good many more developments along these lines recently, following the most "beautiful" mathematical structures. The one I use most extensively is the "Fibre Bundle". Here's a quote from the famous 20th century theoretical physicist Chen Ning Yang discoursing with the equally famous mathematician Shiing-Shen Chern:
Maxwell's equations and the principles of Quantum Mechanics led to the idea of gauge invariance. Attempts to generalize this idea, motivated by physical concepts of phases, symmetry and conservation laws, led to the theory of non-Abelian gauge fields. That non-Abelian gauge fields are conceptually identical to ideas in the beautiful theory of fiber bundles, developed by mathematicians without reference to the physical world, was a great marvel to me. In 1975 I discussed my feelings with Chern, and said 'this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere'. He immediately protested: 'No, no. These concepts were not dreamed up. They were natural and real.'"
There's a lot of instances of this, centred mostly around Geometry (: what I'm into), although there are similar notions in Algebra. Hermann Weyl once commented that "The angel of Geometry and the Devil of Algebra compete for the soul of any theory" - quite true!
This grand reduction is, in a sense, a mystical knowledge. The nature of the universe is being engendered, and is made manifest, in oneself whilst one's doing mathematical physics. The cardinal difference between this and canonical mysticism is that the mathematical physicist may choose to acknowledge this as divine action or not. Those of us who continue to be astounded by it ascribe to the notion of its divinity. It's the avatar of Spinoza's god. Infinitely more special that any anthropomorphic sociopath [cf. Yahweh].
It tempers and calms us, like Buddhism or other mystical disciplines. The element of neurological temperance is there - but more tangibly, since one is looking at the universe as it is in a sense, and not at the mind as it is.
Some have been led astray by these notions. You see, identifying a branch of mathematics as physically relevant motivates physicists to explore it to it's full, often thus forgetting the concept that motivated the discovery. Penrose's Twistor theory is the archetypal example of trying to practice this mysticism properly. He appeals to only the most beautiful concepts, and, somewhat ironically - having envisioned that Twistor Theory may be the road to Quantum Gravity - it has turned out that Twistor Theory has allowed every other theory to be described much more efficiently! Calculations that took ten years on a parallel computing system now take minutes on the back of an envelope with twistor methods. Consequently, there are many strains to it being researched by folk with varying degrees of volition to his mystical reasonings.
Guided by this sense of unity, Penrose is, in my mind, the second best mathematician in the world - and has done more for theoretical physics in this century than anyone bar Einstein.
These concepts are much easier to illuminate while teaching mathematics, since the concept is impressed upon you in its pure form. I'd imagine you're very familiar with the quiet catharsis that comes about as after a long night philosophising. When you're open to the luminous minds of your friends and are invigorated. You can find that in mathematics too. Ask Johnny what his views are: he's studied complex analysis, which is like sorcery! In any case, mathematics as it pertains to physics offers the most pronounced of cultivations - at least to me, and a few others.
I think that its important to note that the mysticism I embody is a very passive one. Whilst rituals often serve to prime the mind for natural truth in canonical mysticism, "metanoia" is achieved through hard work in mathematics. I think a lot of mathematicians are of this school of thought without realising they are. They seldom feel the need to philosophise on other topics, since they (often unknowingly) engender deep knowledge about concepts underpinning the nature of the universe - they're satiated, and that brings a lot of reconciliation. One of my lecturers, a mad Russian, says "I might be rich, I might be poor. I don't know - it doesn't exist to me." He does very hardcore stuff, and it's reflected in his temperament. He talks to god.
Q: There's an old cliché about how scientists see the world that always goes round: the eyes that translate or transform everything into formulae. Do you keep your work compartmentalised from the rest of your life?
JR: Both yes and no, depending on mood! I certainly adhere to the cliche, but it's nowhere near as pronounced as you'd imagine in the scientific community. Many scientists are neurologically stale individuals: wholly uninvigorating. They strive away on whimsical applications because "that's what science is". While I can see where they're coming from - it's very good fun to immerse yourself in an application (say, making a better engine using physical arguments) - these people are technologists rather than natural philosophers. They tend to never think about the nature of things, and even if they do, it's regurgitation of a notion they had once. They're devoid of spontaneity, and are content with their pre-meditated cop-out.
Consequently, very few scientists can look at the world like in that picture. It's immensely enrichening to do so - and very hard to see more than one facet at once! Each requires consideration in it's own regard, so I had to look at each of the equations and relate them to see what the illustrator meant - they're all correct and appropriate, which is refreshing!
The more fundamentally a scientist wishes to look at nature, the less of a partition there is between work and reality. That's a generalisation though: there's a lot of nuance to consider.
Q: Given your interest in mythology, any chance of a book on interrelations of Norse symbolism and Minkowski space?
JR: Haha! I don't think so, I'm afraid. I think this would be just about achievable in a book about mathematical mysticism, but it would be a stretch to accomodate Norse mythology. I really like Norse mythology for it's pragmatism and metaphor. It really appeals to the Western mind. Baldr's myth is my favourite: "He [Baldr] will only return when all living creatures mourn for him".
Which all creatures do, except Loki! Here - in constructing their gods as facets of the psyche - the Norse have summed up the impediment we all face to enlightenment: "Being wise would be ace, except I love fucking about and enjoying myself."
Hahaha! There's more to it, but I think that's the salient point.