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It is well known that the sensory cortex responds to peripheral input, and that sensory stimuli evoke a cortical response. In fact, in cases of myoclonic epilepsy, the response to a peripheral stimulus can be detected using standard electroencephalogram (EEG ) recording. In normal subjects, however, the responses are of much lower amplitude. The normal EEG activity and the normal “noise” in the recording devices are of high enough voltage to mask any evoked response. With the onset of averaging technology, these small potentials became detectable. The procedure is to time-lock a peripheral stimulus to another which triggers the sweep of a computer of average transients. Any evoked potential that recurs with a fixed relationship to this peripheral stimulus is summed by the computer. All non-related potentials, or random waves, are progressively diminished and eventually cancel out. Thus, with adequate averaging, smaller and smaller evoked potentials can be extracted from the background activity.

A functional nervous system must be laid down embryonically and be capable of producing adaptive movements in response to particular sensory stimuli as soon as the diminutive larval locust emerges from the ground. During embryonic development, the majority of central neurons are formed and have established their connections, as have the majority of proprioceptors at the joints. For example, all the motor neurons innervating the leg muscles have formed, all the proprioceptors at the leg joints are in place, and all the peripheral nerve pathways are established. Many exteroceptors are also formed and have established connections in the central nervous system, but others will develop postembryonically as the surface area of the body increases.

This chapter focuses on the swimming characteristics of toads. The toad tadpole presents a unique vertebrate animal model for studying the nervous control of locomotion, and has been used extensively to investigate the spinal mechanisms of undulatory swimming. The main object for studies of the cellular and network mechanisms of undulatory swimming is the embryo of the toad Xenopus laevis. The embryos can swim if released from their egg membrane shortly before they normally hatch. Swimming is due to the waves of lateral body flexion that propagate periodically, at a frequency of 10–25 Hz, from the head towards the tail. Swimming can be evoked as an escape reaction to different sensory stimuli. Swimming in the tadpole is based on caudally propagating periodical waves of lateral body flexions controlled by the spinal cord. In the escape reaction, the spinal central patter generator is activated by sensory input.

What is a ‘veridical visual experience’? This irreducibly normative notion confusingly suggests a ‘match’ between experiences and an unseen or unperceivable reality. And although the notion of an ‘optical illusion’ appears in technical discussions of the processing of sensory stimuli, it is obvious that natural science cannot supply criteria for veridicality. The Meditations seems to tell us both that all our visual experiences are radically false and that we can trust them as mostly true, but I argue that Descartes grasped the problem of understanding veridicality and provided the framework for a solution, which I develop in this chapter. Two key ideas are required: the notion of a ‘quasinormative’ animal machine whose experiences are not ‘matched’ to the world but to the behavioural outputs it needs to live, and the notion of a circumstantial ‘defeater’ of the organism’s efforts on some occasion.

This book concentrates on the regularity in how the brain perceives the world, the regularity in how the brain reacts to sensory stimuli, and most crucially, the regularity in how the brain controls the movements. It first introduces this regularity and then tries to make sense of it using theory—in particular, theory of the kind that relies on mathematics. It also reports mathematical concepts that relate to the formation of internal models in movement control and perception. In a way, this book is about mathematical models of brain models.