### ‘Net of Indra’ Report

November 14

*A report on the work I conducted with Mike Lesser of *Autism and Computing

## Statement of problem

Autism has often been seen as a puzzling disorder, with those affected exhibiting a range of symptoms with no obvious connecting thread: Sensory abnormalities, obsessive tendencies, difficulties with social interactions and often problems using language. In recent decades a number of competing theories have been advanced which attempt to provide a coherent explanation of this complex of psychological differences, some more successful than others.

The idea of monotropism, advanced by Dinah Murray and Mike Lesser, suggests that the central feature of autism, from which all or almost all of its common features arise, is a different way of distributing attention. Those on the autistic spectrum exhibit a tendency, which we call monotropism, to focus their attention very tightly and intensely on only one or two things at a time – they are conscious of only a very small set of interests at any given time. By contrast, most people are polytropic, with several interests aroused at any moment, but seldom with the intense concentration of the autistic.

To model these different strategies of attention use, Murray and Lesser propose what they call the interest system. A computer model of this system uses reaction-diffusion type equations to model the dynamics of attention use over time. The model demonstrates complex behaviours, the spectrum of attention-use strategies being represented by variations in the rate of diffusion.

## Literature

### Explanations of Autism

Three main alternative ideas have been proposed for the ‘core cognitive deficit’ in autism **.**

*‘Theory of Mind’ deficit*. See eg. Baron-Cohen et al (1985). This posits that those on the autistic spectrum have a weakened ‘theory of mind module’, with the rest of their cognitive abilities left intact. This fails to account for many features of the condition outside of the social sphere, and has largely been abandoned.*Impaired executive function*. According to Hill (2003) ‘Executive function is an umbrella term for functions such as planning, working memory, impulse control, inhibition, and shifting set, as well as for the initiation and monitoring of action.’ It is a theorised system thought to control other processes, whose impairment, it is argued, could lead to autism.*Weak Central Coherence theory*. See Frith (1989). Posits a detail-focused processing style, with difficulty understanding context; shares various features with the monotropism hypothesis, but takes difficulty in understanding context to be the fundamental difference in autistic individuals, as opposed to its being a consequence of different use of attention.

The approach proposed by Murray *et al* was published in Autism, Vol. 9, No. 2, 139-156 (2005).

## The Model

The model can be seen as a floating-point cellular automaton, or a spatially discretised differential equation. It is essentially a reaction-diffusion system, and is derived in part from an earlier model of predator/prey interaction inspired by the Lotka-Volterra approach.

The model is intended as an analogue of the human mind. Attention is treated as a scarce resource, which is competed for by various tasks or potential actions. Action depletes attention. An interest, or concern, is a local clustering of attention; an interest with enough attention will usually lead to action. Interests are auto-catalytic, and also feed into each other. In some circumstances they are known to arise or divide spontaneously.

The original model conceived by Mike Lesser can be described by the following equations:

where

*N* is total available attention

*x _{i,j}*

_{ }is interest

*y*is activity

_{i,j}*b*is the rate at which interest is excited

*s*is the rate at which interest leads to activity

*m*is the rate at which arousal of interest decays

_{x}*m*is the rate at which arousal of activity decays

_{y}*w*is the rate of positive feedback

*f is*the rate of associational excitation of interests

*ρ*is the decay factor in resource overlap with distance

*d*(

*i,j:i’j’*) is the distance between

*x*and

_{i,j }*x*

_{i’,j’}At Mike’s request I extended this to include synapse-like dendritic connections, diffusing attention in one direction from each cell to several others, their location chosen at random on initialisation. I also simplified the term representing resource depletion, removing its dependence on distance, and added a negative cubic term to represent the exhaustion of resources on a local level. This gives us the following equations:

where

represents the dendrites attached to *x _{i,j}
D* is the strength of the dendrite connections

*q*is the cubic term