Sounds of space-time, cross-modal sensory experience, and the developing nervous system
I’ve spent a considerable amount of time thinking about how, if mathematics grows out of fundamental cognitive mechanisms, it provides opportunities for seeing more. It is mathematics that allows for the tremendous expansion of empirical study – what we call science. I had the opportunity, last week, to listen to a talk given by Craig Hogan, Director of the Fermilab Center for Particle Astrophysics. Professor Hogan developed his talk around the idea that space-time is not only the stage on which the atoms of the world play, but an active and dynamic entity on its own, and now within reach of systematic study. I was quickly taken by the idea that we are beginning to look at what we live within. This is only possible through the combined productivity of existing models of the universe (requiring the stability of conceived mathematical structures) and herculean attempts at measurement.
Professor Hogan introduced his discussion with the statement that 95% of the matter of the universe does not interact with light. So we can’t see it. The promise of new experiments lies in the detection of gravitational waves that distort space-time in a way, as Hogan suggested, analogous to how sound waves distort air. Hence the title given his talk – Sounds of Space and Time.
In an article for The Observer, the hopes and the motivation for some of this work are discussed.
It is a startling paradox. Harald Lück, a scientist at Geo600, explained: “In his general theory of relativity, Einstein predicted the existence of gravitational waves, which he said would be set off by highly energetic events objects like supernovae or neutron star collisions. However, he also predicted we would never be able to observe these waves because they would be too weak to be detected by the time they reached Earth. We intend to prove him right in the first instance and wrong in the second.
The detection of effects other than the ones we see could provide a vast new territory to explore.
We are going to create a new kind of astronomy,” said Professor Jim Hough, the Glasgow physicist who leads Britain’s contribution to Geo600. “Until now, everything we have learned about the universe has been based on studies of electromagnetic radiation – from infrared to visible light to gamma ray detection. Gravity waves will create a completely new type of astronomy.
The model that shapes these investigations is the curved space-time of relativity, which rests heavily on the modern idea of a curved manifold in mathematics. But the hope of measuring a ripple in the curved space of our universe, caused by an extremely energetic astronomical event (like neutron stars colliding) was once thought outside the range of perceptible effects. I find it astonishing that technology could advance to the point that, by harnessing what we do understand of the physics of our world, instruments can be built to handle these impossible feats. This is a fact of particle physics research as well.
But this shift from light-driven perception to a kind of vibrational-driven perception, as I think about it, corresponds loosely to the current understanding in cognitive science that the body perceives cross modally, through the nervous system’s interconnectivity. My own inclination is to say that, if we take into account the laboriously constructed mathematical relationships that build these empirical possibilities, perhaps the correspondence can even be tightened. Mathematics builds conceptual possibilities using perceived relationships (of things like space and quantity) and linguistic actions like logic and metaphor. I discussed this a bit, with respect to Riemann in particular, in an earlier post. In a paper I read recently, whose purpose is to debunk simplistic and categorical brain-based ideas about how we learn, John Geake of Oxford points to the work of Charles Scott Sherrington who, in 1938, made the following observation of human cognition:
The naive observer would have expected evolution in its course to have supplied us with more various sense organs for ampler perception of the world . . .Not new senses but better liaison between the old senses is what the developing nervous system has in this respect stood for.
I found one of Geake’s references particularly interesting. In congenitally blind children, the abstractions of Braille acquire meaning through the work of the same visual cortices that are active in sighted children when they learn a written language.
To emphasize the cross-modal nature of sensory experience, Kayser (2007) writes that: ‘the brain sees with its ears and touch, and hears with its eyes.’ Moreover, as primates, we are predominantly processors of visual information. This is true even for congenitally blind children who instantiate Braille not in the kinaesthetic areas of their brains, but in those parts of their visual cortices that sighted children dedicate to learning written language. Moreover, unsighted people create the same mental spatial maps of their physical reality as sighted people do (Kriegseis et al. in press). Obviously the information to create spatial maps by blind people comes from auditory and tactile inputs, but it gets used as though it was visual.
Input information is abstracted to be processed and learned, mostly unconsciously, through the brain’s interconnectivity (Dehaene, Kerszberg, and Changeux 1998). Actually, we don’t even create sensory perception in our sensory cortices:
For a long time it was thought that the primary sensory areas are the substrate of our perception. . . . these zones simply generate representational maps of the sensorial information. . .although these respond to stimuli, they are not responsible for . . . perceptions . . . Perceptual experience occurs in certain zones of the frontal lobes [where] neurons combine sensory information with memory information. (Trujillo 2006, M9)
Can it be said that mathematics is fundamentally motivated by the quest for new perceptual experience? In a brief presentation on Penrose tiling, mathematician John Hunton proposes that “Science can’t see what it doesn’t have the language to describe.”