Usually it is a matter of systematic and patient collection of data, testing hypotheses that consolidate our knowledge in the vicinity of what we already know. We record the effect of altering this or that experimental condition, and gradually the area of scientific terra firma encroaches on the ocean of ignorance: slowly but surely the shoreline extends, creating the branched causeway we regard as Truth.

Structurally, the human brain is a mess. The problem is the way in which it has evolved: the bulk of what fills our skulls – the telencephalon, and especially the cerebral cortex – is relatively new, but it has not displaced the older and simpler structures seen in reptiles. Rather, the brain has evolved through accretion (Sarnat and Netsky 1974) (Figure 5.1): the older areas are still functional – indeed they are much the more important – but they have come to be supplemented and regulated by the newer areas, which provide improved overall integration and prediction through the massive bands of associational fibres that link every part of cerebral cortex to every other. In addition, these newer and ‘higher’ areas send and receive huge nerve tracts that have elbowed the older structures aside and distorted their shapes, making the relationships between their parts hard to discern.

There are fashions in science just as in everything else, and the popularity of measuring the time required to make a response to a stimulus has waxed and waned over the years. The earliest investigators were motivated in part by a practical problem in astronomy, the difficulty of estimating the exact moment at which a star or planet reached the cross-hairs of a transit telescope (Wolf 1865, Mollon and Perkins 1996). This work revealed two striking kinds of variability. On average, different observers had very different reaction times (Henmon and Wells 1914) (the ‘personal equation’); in addition, reaction times varied greatly from one occasion to another. Later, with the rise of quantitative psychophysics in the nineteenth century, reaction time came to be seen as an objective parameter of psychological performance that could be obtained without very advanced recording technology (Boring 1929). But these data proved easier to obtain than to explain, and reaction times fell out of favour.

In the real world, it is very rare for a single target suddenly to pop into view. In general, there are many potential stimuli that compete for our attention, and the decision to select one of them is the result of competitive interactions between multiple LATER units (Mackay, Cerf et al. 2012, Tatler, Brockmole et al. 2017). But before we deal with this kind of spatial complexity, we need to consider a particular aspect of temporal complexity. How do targets interact when presented sequentially rather than simultaneously?

The fact that a large data set can be summarised with just two or three parameters is useful in itself – for instance, if we want to characterise clinical observations (examples of this are given in ). But it is obviously not a factor that will drive evolutionary change. So why do reciprocals of reaction times have a normal distribution? What sort of mechanism could account for a recinormal distribution of latency? Does it make any functional sense? The model that is about to be presented was first conceived in relation to saccadic latencies (Carpenter 1981, 1988), but appears to have a much wider applicability. It will now be described briefly and then considered in more detail.

Of all the biological sciences, it is the study of the brain that most impinges on philosophy; and like philosophers, neuroscientists need to take special care in how they name things (Smythies 2009). Most would agree that the function of the brain is to convert stimuli into responses. But what is a stimulus? Is it best considered as the pattern formed by the combined activity of all sensory receptors at a given point in time? That is indeed what ultimately determines what the brain does. But it is not at all what is being described, for instance, in the Methods section of scientific papers. Here ‘stimulus’ means something extremely localised and specific – perhaps a dot of a certain size and colour – and there is tacit complicity with the subject that nothing else counts in making the response that is to be measured. There is also complicity regarding which aspects of the stimulus will be quietly ignored.