Professor Sir Roger Penrose, FRS, OM is an academic mathematician. He is the Emeritus Rouse Ball Professor of Mathematics at the University of Oxford and also Gresham Professor of Geometry, at Gresham College, London

Penrose has worked with Stephen Hawking and other notable academics and published a series of books, including

His main academic work has been to invent and develop the science and mathematics of Twistors (See below). This is an attempt to re-formulate the two pillars of 20th century physics—general relativity (gravity) and quantum field theory in terms of a new mathematics—Twistor theory. These ideas are currently incompatible, but Penrose and his colleagues aim to use Twistor geometry to unify these two fundamental ideas.

Although Twistor theory is a formidable intellectual achievement, and has won Penrose a number of very significant academic accolades (see below), Twistor theory has not gained universal respect within the academic community. Far from it.

Here is what Andrew Hodges, one of Penrose's colleagues at the Mathematical Physics research group at Oxford University has to say:

Unfortunately the scientific world has virtually no interest in this very difficult and radical approach to fundamental physics and as an academic career it has been a disaster for me.

However, when I moan about this, people rightly say that doing something serious and worthwhile is a lot more important. Also, to look on the bright side, the work I have done may now be coming into a fresh light. In 2000 Roger Penrose finally found an approach to the description of gravity in twistor geometry which seems to fit with what I found necessary to develop for the description of quantum field theory. If anything ever comes of this it will be quite enough to justify my life!

Incidentally, Hodges is a big Alan Turing fan, manages the pages and wrote Alan Turing: the Enigma, which was the basis for the play and movie of Turing's life, Breaking the Code.

So why has Penrose become one of science's B-list stars, emerging from the shadows of Hawking and Einstein?

There seem to be two main reasons. The first is his tiles, and the second are his books, which follow on from Turing's computability theories.

In Physics, Penrose proved two very significant results: the first was that any black hole which exists must have a singularity at the centre. The second (in cooperation with Hawking) was that the Big bang (if it happened) must have started form a singularity. (Thanks, unperson)

Penrose tiles

See here for a proper explanation of Penrose Tiles. But very briefly, Penrose was working with sets of tiles which can completely cover a plane surface. If you take a lot of rectangular tiles, you can do this easily. Same with regular hexagons and equilateral triangles Penrose found a whole series of different tiles which can do this, some of which required two different shapes to be interlocked, rather like an M.C. Escher drawing. However, the most interesting tiles discovered by Penrose were a strange banana-type shape which permits a non-repeating pattern to completely cover the surface. The technical term is aperiodic.

Mathematically speaking, this is a very interesting phenomenon—and the shapes are pretty as well. Combine a nerdy Oxford academic who has worked with Stephen Hawking with pretty shapes, throw in a story about Kimberly-Clark using the Penrose tiling patterns on some toilet paper, and you have a story that could have been made for the media.

The Emperor's New Mind (Oxford University Press, 1990)

There is a node about this here, The book was a best-seller, winning the 1990 Science Book Prize (now known as the Rhône-Poulenc prize). But I can't for the life of me see why. Maybe it was a thin year for science books. It appears to be a series of unrelated chapters about almost everything Penrose is interested in (except his life's work on Twistors) with no obvious continuity or link between the various sections. I think the editors were blinded by his reputation and failed to encourage him to integrate the ideas a bit more. That's just my opinion, I could be wrong.

Having said that, there are many who believe the book to be one of the most significant contributions to modern philosophy of science. The argument put forward is that the brain works in a fundamentally different manner from modern computers, and as such the quest for human-like artificial intelligence using modern digital computers is misdirected. Essentially, the argument runs, all modern computers rely on a range of specifiable algorithms to process data. Penrose argues that there are many things which our brains can do, yet which do not require algorithms.

Well, I thought that was obvious. We all know that computers are great for factoring very large numbers, but crap at picking out a face in a crowd or deciding when a writeup ought to be nuked. We all know that the all-powerful computer in Star Trek will self-destruct if you ask it some simple 'logic' puzzle, though Kirk can see in an instant whether it is true or not. I guess if you need a heavyweight scientific justification of how Star Trek plots will go, then maybe this is the book for you, but I can't say I felt any moment of great insight while reading it. It's still up there on the bookshelf, but it is not well-thumbed. Maybe I ought to put it up on The Great Grand E2 Book Lotto. In fact, I'll send it to the first person who blabs me asking for it, on condition that the person adds something worthwhile to this node.

The book covers a whole range of ideas and physical principles from the geometries of the Mandelbrot Set and Penrose tiles to cosmology and the so-called Arrow of time. Toward the end the book tackles what we can compute, what we can't compute and some philosophies of knowledge.


Born into a mathematically-inclined house in Colchester, Essex, UK on 8 August, 1931, Penrose grew up surrounded by mathematics. His mother was a doctor, his father, a medical geneticist who enjoyed recreational mathematics, a hobby which Prof Penrose inherited. The family tradition of mathematical near-geniuses is strong: one brother, Oliver is a mathematician, another, Jonathon, was ten times British chess champion.

After attending a local school, Penrose got his B Sc from University College, London and went on for a Ph D at Cambridge University (St John's College). There he started getting seriously interested in the science and mathematics of tessellations (Tiling patterns to you and me), and won his doctorate in algebraic geometry.

He has received a number of prizes and awards including the 1988 Wolf Prize which he shared with Stephen Hawking for their understanding of the universe, the Dannie Heinemann Prize, the Royal Society Royal Medal, the Dirac Medal, and the Albert Einstein prize


OK, here's the deal. Twistors are seriously heavy mathematics. I won't pretend that I can even begin to understand the first lecture in the Twistor 101 course. But here is my layman's interpretation of what twistors are all about, (relying heavily on the websites referenced below)

The aim of Twistor theory is to use these obscure mathematical constructs to describe

Once these two ideas are described in terms of mutually compatible theories, then they can be unified into a theory of quantum gravity

So why for fuck's sake would anyone want to do that?

There's a guaranteed Nobel prize for the first person who thinks up a successful theory of quantum gravity. And besides, it's the greatest intellectual puzzle of the whole 20th century, and likely to remain so for much of the 21st century. Einstein tried, and failed, Hawking, and all the others are trying to do it, and none of them is getting very far.

OK, then tell me about twistors, but spare the math, OK?

You've heard of Spinors, right? No? Hmm, me neither, but (it sez here) you need to know about them before even thinking about Twistors.

Right then let me quote you something from the academic review paper, Twistor Theory: an Approach to the Quantisation of Fields in Space-Time. by our hero and his colleague M.A.H. MacCallum:

A twistor (of the simplest type) can be pictured "classically" as effectively a zero-rest-mass particle in free motion, where the particle may possess an intrinsic spin, and also a "phase" which can be realised as a kind of polarisation plane. Such twistors form a vector space of four complex dimensions. This vector space (twistor space) in effect replaces the space-time as the background in term of which physical phenomena are to be described.

And here is another by Fedja Hadrovich who wrote down his notes following a lecture by the great man himself:

Its creator, Roger Penrose, was first led to the concept of twistors in his investigation of the structure of spacetime and it was he who first saw the wide range of applications for this new mathematical construct. Yet 30 years later, twistors remain relatively unknown even in the mathematical physics community. The reason for this may be the air of mystery that seems to surround the subject even though it provides a very elegant formalism for both general relativity and quantum theory.

Oh, you want to hear the Prof talking about his Twistor theory, and see his diagrams at the same time. OK, well fire up realAudio and go to this site. Though I have to say, I doubt it'll do you much good unless you are already familiar with Spinors (whatever they are).

Sources / further information


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