Prefrontal cerebral areas project to Purkinje cells, located in the most lateral part of the cerebellum, via mossy and climbing fibers. The latter olivary error signals reflect the attentional load of the prefrontal cortex. At the cerebral level, LTP-LTD plasticity allows these Purkinje cells to adaptively reinforce the active pyramidal cells involved in the motor sequence.

The cerebellum has been hypothesized to play a role in a variety of movement timing tasks that involve the processing of temporal information on a variety of timescales. Braitenberg, Heck & Sultan propose a new theory of cerebellar function that is able to account for movement timing on the order of a couple of hundred milliseconds. However, this theory does not account for the rôle the cerebellum plays in the acquisition and retention of adaptively timed discrete movements that are on the order of 200 to 1000 milliseconds, and therefore does not account for the entire temporal range of cerebellar dependent processing.

Precise timing of muscle contractions is an important prerequisite for motor control and one to which the cerebellum contributes. Braitenberg et al.'s detailed timing hypotheses relate only to a subset of the known features of the organisation of the cerebellum. However, the cerebellar architecture clearly supports the “tidal waves” that are central to the authors' proposal and such tidal waves are very likely to contribute to its functions.

The central hypothesis of Braitenberg et al.'s target article – that tidal waves of parallel fiber excitation precisely activate Purkinje cell spiking – is hard to reconcile with recent neurophysiological and modeling data. The assumed pattern of mossy fiber input seems unrealistic, inhibition is likely to interfere with the proposed excitatory responses, and moreover, computer simulations show that the Purkinje cell is a poor coincidence detector.

A propagator for a path space integral can be used to represent the “tidal wave function” and provides a natural way to model a control signal that is temporally segmented by placement of pairs of stimulating and recording electrodes. Although care must be exercised in interpreting the resulting measurement, the technique should prove useful to experimenters who study cerebellar functioning.

It is suggested that bifurcation of parallel fibres in the cerebellar cortex assists the spatiotemporal convergence of temporally dispersed and asomatotopic inputs to granule cells. This increases the number of combinations of inputs which can be compared for the purpose of sequence recognition.

The “sequence-in/sequence-out” model of cerebellar operation is mostly speculation. The same data can be interpreted in a very different way, making fewer assumptions. To wit, sets of Purkinje cells recognize a specific sensorimotor event and trigger a synchronous sensorimotor discharge.

Just as physics determines physically viable movements, the spatial distribution of input excitations allows the cerebellum to choose physiologically viable beams. Cerebellar–motor coherence implies that the ordering and modes of combination of cerebellar beams reflect (1) the way movement invariants are ordered and combined in movement and (2) the way physical principles are integrated in learning to move.

(1) The “timing idea” is not the only interpretation of cerebellar histology worth considering. Therefore, it is not imperative to strive for a theory of cerebellar function which gives it a prominent rôle. (2) The experiments with “moving stimuli” cannot support the tidal wave theory. (3) The notion that only “moving stimuli” can excite the cerebellar cortex is burdened with many intrinsic difficulties. (4) The common theoretical claim that the accuracy of skilled movements is due to exact pattern-matching processes in the cerebellum may be most misleading.

Mormyrid teleosts have Purkinje cells with palisade dendrites, which probably represent coincidence detectors of parallel fiber activity. Their existence strongly supports the ideas of Braitenberg et al. on cerebellar function. However, the organization of mormyrid granule cells and parallel fibers suggests that a key to cerebellar function is not in interactions within one wave, but between two opposite tidal waves.

I argue that the rôle for the cerebellar cortex is in the generation of sensory predictions, not motor sequences. This proposal may explain the allometric relationship described in Braitenberg et al.'s target article. I also point out that the parallel beam organisation may have a nontemporal basis.

This commentary reinterprets our recent data on the cerebellar contribution to different cognitive functions in light of Braitenberg and coworkers's hypothesis about the sequence-in/sequence-out cerebellar mode of operation in the motor domain. Cerebellar involvement in spatial data processing, procedural learning, verbal fluency, application of grammatical rules, and writing is dependent on sequence processing.

The sequence-in/sequence-out cerebellar machinery is considered from the computational point of view. We outline a learning framework which discriminates short-term from long-term learning and is able to explain single-trial adaptation to unexpected loads.

An adequate cerebellar theory should explain the timing and geometry of signal propagation in the molecular layer, hence Braitenberg et al.'s explanation of how parallel fibers may act as delay lines is important. The suggestion that these delay lines may generate control signals that dampen undesirable response modes during movements is merely interesting.

The notion that cerebellar cortex geometry may play a unique role in its function is explored by Braitenberg et al. in the form of a new theory about the distribution of cortical activity. The theory makes specific predictions which are not verified by an experimental study of hindlimb movement in the cat.

Random-excitation granule cells are likely to overwhelm spatiotemporal sequences described as “tidal waves” in Braitenberg et al.'s target article. A mechanism is proposed involving the Golgi cells to reinforce tidal waves against noise. The recurrent inhibition by the Golgi calls can recruit random excitations of granule cells in phase with sequences of mossy fiber input.

The tidal-wave theory is inspired by the particular morphology of the cerebellar cortex. It elegantly attributes function to the anisotropy of the cerebellar wiring and the geometry of Purkinje cell dendrites. In this commentary, physiological considerations are used to elaborate temporal and spatial constraints of the tidal-wave theory. It is shown, first, that limitations of temporal precision in the cortical inputs to the mammalian cerebellum delimit the spatial resolution of an input sequence (i.e., the minimal distance along the parallel fibers which can detect sequential input) to the range of a millimeter at best. Second, temporal characteristics of Purkinje cell postsynaptic potentials are argued to predict a distance of at least several millimeters along the parallel fiber beam in order to generate a sequence in the cerebellar output. It is concluded that the implementation of tidal waves as a general principle of cerebellar function is questionable as there exist cerebelli too small to match these constraints.

A path space integral approach to modelling the job description of the cerebellum is proposed. This new approach incorporates the “tidal wave” equation into a kind of generalized Huygens's wave equation. The resulting exponential functional integral provides a mathematical expression of the inhibitory function by which the cerebellum “sculpts” the intended control signal from the background of neuronal excitation.

This commentary reviews the basic physical principles underlying human single- and multi-joint arm movements. The potential role of the cerebellum in dealing with the physics of movement is discussed in the light of recent physiological findings and the theoretical model of cerebellar detection and generation of input and output sequences put forward by Braitenberg and colleagues.

We add evidence from functional imaging supporting the concept of activation of coronally oriented zones corresponding to parallel fibers. Braitenberg et al.'s suggestion that there is an operating mode of the cerebellum relies on the idea introduced by Eccles and refined by the concept of tidal waves which Heck found in vitro. Recent evidence from functional imaging has shown zones of activation in accordance with this model and hence provides support for Braitenberg et al.'s hypothesis from the intact and healthy human cerebellum. In a second section, we discuss vulnerability of the structures described by Braitenberg et al. with respect to slow and fast movements in the context of clinical symptoms in cerebellar disease.