Cognitive Computing 2012 The computer and the mind 4. CHURCHLAND Professor Mark Bishop

Overview The paper looks at the neuroscience of cognition at three levels offering: a theory to explain how brain may represent aspects of the world providing a neuro-biological reduction of qualia. a powerful and novel style of computation capable of explaining sensorimotor co-ordination. an explanation of brains micro-structure that illustrates how the brain actually implements its representations of the world and how it performs computations on them. 01/04/2014(c) Bishop: The computer and the mind2

01/04/2014(c) Bishop: The computer and the mind3 An eliminative reductionist strategy of cognitive phenomena The core idea: The brain represents aspects of reality by a position in multi-dimensional state- space and performs computations on such representations by co-ordinate transformations of this point. It is an eliminativist account as it posits a world whereby propositional attitudes – hopes; desires; beliefs etc – are eliminated. As Patricia Churchland (1986) has argued, it is hard to see where in the brain we are going to find anything that even remotely resembles the sentence-like structure that appears to be essential to beliefs and other propositional attitudes. And that qualia – pains, aches, happiness etc. – is more properly reduced to the richer explanatory language of, say, a specific tuple of neural firings.

01/04/2014(c) Bishop: The computer and the mind4 The micro-physical organisation of the brain Most of brain is crinkled grey matter (cerebral cortex) White matter consists of axons projecting from the cortex to deeper regions of the brain. In humans the cortex is six layers deep. Top layer lots of inputs; bottom lots of outputs. Massive horizontal connectivity in each layer; also massive regularly organised vertical connectivity. Planar cortex divided into topographically organised Brodman areas: preserving adjacency relations but not distance. Many areas (e.g. visual striate cortex areas 17+18) have been identified. Many, but not all, areas of the brain are so organised (eg. LGN; hippocampus etc).

01/04/2014(c) Bishop: The computer and the mind5 Sensorimotor co-ordination Churchlands suggestion is that the organisation of the cortex is the solution to fundamental cognitive problem of sensorimotor co- ordination. Consider a simplified crab-like creature The crab needs to grab what is in visual field. The crab needs to map from a pair of eye angles to its gripper angles. To do this it needs to transform from eye space to gripper space i.e. The crab needs to perform a 2D => 2D co-ordinate transformation.

01/04/2014(c) Bishop: The computer and the mind6 How might the cortex perform co- ordinate transformations? The cortex needs to arrange the two grids above each other and map between them. The state-space sandwich Activation of a 2D point on the eye sensor grid; Project down onto a 2D point on the motor grid; Controlling arm angles which is required to grab object.

01/04/2014(c) Bishop: The computer and the mind7 Biologically plausible observations The state-space sandwich, (SSS), is: Resistant to localised damage; Very fast implementation of sensorimotor computations; Co-ordination is not uniform over the field of motor activity The theory predicts poor between eyes and at extremities. The state-space sandwich is one solution to the problem of sensorimotor co-ordination which is biologically plausible However it is far too simplistic a mechanism. So is cognition merely appropriate sensorimotor co- ordination? Behaviourism revisited?

01/04/2014(c) Bishop: The computer and the mind8 A cognitive hypothesis The Churchlands initial hypothesis is that scattered topographic maps in the cortex are performing cognitive processes via simple co- ordinate transforms. The hypothesis was later modified to define cognitive state, (the data to be transformed), as a pattern of activity, (a vector), rather than a simple point-to-point transformation.

01/04/2014(c) Bishop: The computer and the mind9 The superior colliculus, (SC) It has been shown that the superior colliculus actually performs such transformations on the saccadic system, (secondary to areas 17/18). It has also been demonstrated that the lower layer of the SC is a motor layer, which has also been found to be a topographic map. Hence there is some experimental evidence to back up the notion of state space sandwich for saccadic movements Albeit this experimental evidence suggested area sandwiches not point to point sandwiches. Churchland emphasizes that this is an extremely simplistic description of the function of the SC.

01/04/2014(c) Bishop: The computer and the mind10 What function might other topographic areas perform? Abstract co-ordinate transfers E.g. Echo location in bats and binaural disparities in owl hearing. There has long been a restriction amongst neurologists to reserve topographic maps for clearly known functionality… … But if the cortex is performing very abstract transformations, their function might not be obvious to the experimenter. The multi-layer cortex: More than one layer provides a multi-modal sensorimotor transforms; one that can: react to different types of stimuli; perform sensor integration to d etect and act on signals that would otherwise be too weak.

01/04/2014(c) Bishop: The computer and the mind11 Beyond state-space sandwiches Churchland suggests that the cerebellum can perform more complex - vector to vector - transformations using a simple array of MCP type cells. Perhaps to perform complex bodily movements. And further, that - unlike simple 2D sandwich where information is coded spatially - in vector notation events might be coded via neural firing frequencies With MCP like neurons effectively performing matrix multiplication to map between different spaces. Properties of vector-vector (v-v) transformations: V-V transforms need not be limited to linear transforms; Preserve the fast speed of SSS; Preserve gradual degradation to damage.

The representational power of state spaces: A point in n dimensional space can represent a system of n variables. A state-space representation preserves metrical relations and so retains notion of qualia similarity. Consider example of visual qualia: orange is more similar to red than dark blue as the distance between the points is smaller. The ability to discriminate stimuli is large. Consider Lands colour cube. If each axis quantised to 10 positions could represent 1000 colours and their relation to each other. NB. This colour relationship is not linear. 01/04/2014(c) Bishop: The computer and the mind12

The qualia cube Any sensation can more properly be reduced to - is an identification with - a specific firing triplet of neural firings. Cf. the identification of lightening and electricity. Genetic faults (e.g. colour blindness) are realised by the cube collapsing to a 2D surface. The taste system is similar, (albeit this is 4D as we have 4 taste receptors); contra Nagel this allows us to say 'what it is like to be' a cat (or rat). E.g. Cats & rats have 4D taste but their bitterness channel is more (or less respectively) sensitive Hence rats dont mind saccharin, but cats hate it (as it is too bitter for them). Similarly for the olfactory system This is at least a 6D system; in dogs it has three times the sensitivity (and is possibly 7D) which allows dogs identify everyone in the world by smell alone. 01/04/2014(c) Bishop: The computer and the mind13

01/04/2014(c) Bishop: The computer and the mind14 Qualia cubes in action Using the Qualia Cube the ineffable pink of the rose is more properly reduced to a chord/triplet of neural spiking frequencies. It seems that the Churchlands eliminative materialism leaves no room for (eliminates) folk psychology notions concerning our beliefs about the world. Because by learning to talk in terms of such neural chord firings we get more precise (better?) communication of belief (cf. mummy, I believe my tummy hurts). The Churchlands demonstrate a possible extension of the theory to describe body movements as transitions pathways in state space? Link to Dynamic Systems theory. The Churchlands last hypothesis is that the idea could be extended to describe, say, an Anglophone linguistic hyperspace which could be used to define hyperspaces for appropriate sets of belief. Memories of Skinner on language?