First posted 21 January 2005. Questions of consciousness. Questions of the role of subjectivity. Questions of time. Questions of a Platonic reality. All still central to what keeps my curious mind busy... Penrose was the adviser of another of my scientific heroes: Julian Barbour.

Roger Penrose, the Oxford Physicist, is not convinced: quantum theory, he believes, is incomplete.  In The Road to Reality he argues that a further revolution is required in quantum mechanics, as indicated by its inability to address the reduction process for the wave function (and thereby its inability to 'join up' with classical physics) as well as troubling incompatibilities with general relativity.

The time asymmetry associated with the wave function reduction (or collapse) upon measurement of a quantum system contrasts sharply with the symmetry associated with the propagation of the wave function itself.  The latter can be made sense of moving either backwards or forwards in time; the former works only moving forward.

A more familiar time asymmetry, the one we experience every minute of every day, is grounded in the extraordinary nature of the Big Bang itself - its strikingly low entropy.  The Big Bang was so ordered that the ever-decreasing order of the universe is a probabilistic near-certainty.  This is what lies behind the 2nd law of thermodynamics and the 'arrow of time'.  It points to the peculiar behaviour of gravity at cosmological singularities - not only the Big Bang but (less spectacularly) black holes.

The presence of this time asymmetry in both the reduction of the wave function and in the Big Bang suggests that gravity might play an important role in wave function reduction. Discovering this role would amount to a revolution that could well resolve the 'measurement paradox' and render quantum mechanics consistent with general relativity and contiguous with classical physics.

According to this idea, it is the gravitational effects of the classical measuring apparatus (and other macroscopic entities in our everyday world) rather than the perceptions of any observer that bring about the collapse of the wave function.  As such, the reduction is an objective rather than a subjective one.  This takes the conscious observer from the limelight of quantum theory.  How does this happen? As the wave function propagates through time, non-uniformities develop in the distribution of energy and matter among its superposed states, and at some point become gravitationally significant. The gravitational interaction with the measuring apparatus (or other macroscopic entity) then brings a collapse into a measurable single state.

Although Penrose takes the consciousness out of quantum reduction, in The Emperor's New Mind he puts quantum reduction centre stage in consciousness, thereby turning the world (as seen by conventional quantum theory) on its head. These same quantum gravitational effects account for the difference between consciousness and artificial (computer) 'intelligence', and Penrose calls upon them in his rejection of the computational theory of mind. There are things - including non-algorithmic, non-computable ones - that the human mind can comprehend while no computer (Turing machine) possibly could. This is in keeping with Godel's theorem, which states that no formal mathematical system (or at least none of the richness required to handle even common arithmetic) can be complete.  There must always be truths that cannot be expressed without recourse to 'meta-mathematical' language that is not part of the formal system.

Penrose suggests that our access to such truths is due to quantum fluctuations, gravitationally induced, within the brain (he suggests maybe in the microtubules of the neurons' cytoskeletans).  Multiple states may exist in superposition in our brains until gravity triggers a collapse to a specific state, with resulting (possibly non-local) effects on our neural states. This is something that is not possible (at least for now) with computers.

There is a deep connection among the time-asymmetry of the wave function reduction, the behaviour of gravity at singularities and the presence of non-algorithmic (non-computable) elements - including consciousness - in the world. This helps to explain the relationship among Penrose's "Three Mysteries":

1. The ability of the human consciousness to access and understand the full Platonic world of mathematics (even the non-computable areas, because consciousness goes beyond computation, and the Platonic world is woven into the fabric of the universe at the Planck scale)
2. The remarkable resonance between the Platonic world of mathematics and the physical world (and the ability, not yet realised, of the mathematical world to explain the entire physical one)
3. The ability of a small portion of the physical world to give rise to the entire conscious world (since Penrose discounts the notion of the soul or brain-independent mind).

There is also an "Escher element" to the relationships among the three mysteries. Escher was an artist (and obviously a mathematician) whose works included paradoxical staircases and streams that seemed to always lead in one direction (up or down) yet returned to their own source.

In Penrose's three world / three mystery model, a small portion of the mental world is all that is needed to capture the mathematical one (since we obviously spend lots of time considering other things). Similarly, a small portion of the mathematical world is applied to the collected (total) formalism of physics, with much else being dedicated to other questions. And finally, only a small portion of the physical world (that part that makes up our cells) is drawn on to explain the mental one. Each part is able to 'swallow' its neighbour in an illogical, unending cycle.

Penrose believes that the secret to this mystery of the mysteries is that all these worlds are in fact one. Perhaps in a holographic, holistic, non-local sense like that evoked by David Bohm, another of my creative scientific heroes?

First posted 15 April 2006. These days, I tend to think of the brain a lot less when I'm thinking of the mind, but my sense of wonder for whatever it is that is behind our mental experience is undiminished.

Michael O'Shea's The Brain: A Very Short Introduction has shown me that my longstanding wonder with the brain has been understated.  You see, I have marvelled at the complexity inherent in a collection of 100 billion neurons - each with a thousand synapses, connections with other neurons - and the effectively uncountable number of possible brain states implied by the permutations of these on-off switches.

O'Shea is also impressed by this, but he adds several other elements of our current understanding that demonstrate that the metaphor of a network of binary electrical switches is far too simple:

1. It seems that glia, the brain cells that outnumber neurons by at least an order of magnitude, may also contribute directly to the brain's computation, by regulating neurotransmitter exchange between synapses.  This suggests even the straight combinatorials are more staggering than I have imagined.
2. Neurons do not only communicate with each other electro-chemically through their 'wiring' connections.  They also broadcast information to other neurons within certain radial volumes by releasing messenger chemicals that diffuse without regard to synaptic connection.
3. Information is conveyed not just by the firing (as opposed to non-firing) of a neuron's action potential but also by the rapidity of its repeated firing and by the duration for which the firing is repeated.
4. The neurotransmitters emitted by a synapse not only send immediate excitatory or inhibitory values to the receiving neuron, but can also trigger secondary messengers within it.  These can alter the characteristics of the neuron (creating new synapses, altering threshold levels for triggering the action potential, etc.) permanently (or until they are again altered by new secondary messenger activity).

All of this suggests that the challenges of 'porting' human intelligence to computer hardware ( a la Ray Kurtzweil) are vastly greater than I had thought.  The challenges are similarly greater for efforts such as Dan Lloyd's to eventually map mental states to brain states: the state space, already mind-bogglingly large, is vastly larger still.

It even makes me slightly more sceptical about Julian Barbour's timeless theory of time, because the asynchronous nature of the brain's neuronal (and glial?) interactions doesn't seem to fit well with the notion that particular brain states are but tiny subsets of instantaneous universe states (or Nows) that happily happen to contain records that act as bridges to other Nows.  How instantaneous is a Now?  If mental states are tied not to instantaneous brain states but are affected by the frequency of repeated neuronal firing, then can a mental state reside within a single Now, given that such a Now, by definition, can contain no change (i.e. no repeated firing)?  

But there is a way out.  I guess if the brain encodes in each instant information about its state in previous instants (as in discussion of the specious now in Dan Lloyd), then there is no necessary inconsistency between the unquestionable existence of subjective experience and Barbour's theory of time.