A bounded interval on a scale of structural functional or conceptual complexity

'Level' originated in libella, diminutive of 'balance' in Latin. It was adapted to denote gadgets used to establish flat surfaces. That led to the use of 'level' to denote a stratum in a hierarchy, because components at the same level are considered, mostly "metaphorically, to be at the same height or rank. The question whether the "taxonomy of levels in a "system follows natural divisions or is merely a convenient "artefact of human cognition, is an issue that needs to be addressed separately in each case. Whatever the particular answer is, in real-life levels in any system are dependent on each other. But in practice, in the analysis and "modelling of systems, the borders between the levels are delineated in an attempt to optimize their apparent segregation and permit their separate treatment. This ordinarily involves the assumption that variables at other levels are for all practical means either constant or irrelevant. This is referred to as the ceteris paribus assumption (Latin for

'other things being equal'). It is a risky heuristic that must be retested from time to time by using the appropriate "control procedures.1

When neuroscientists say 'level' they refer to one of three things: level of organization, level of processing, and level of description and analysis (Dudai 1989; Churchland and Sejnowski 1992). 'Level of organization' refers to the structural hierarchy in the nervous system. It is the most common usage of 'level' in the popularization of science. A conventional top-down organizational hierarchy depicts the nervous system as composed of behavioural, brain, organ, circuit, cellular, and molecular levels. These levels differ in their physical scale, ranging from metres (behaviour) to angstroms (molecules). It is useful to note that on the one hand, a higher level of organization means a higher complexity of the system as a whole, but on the other, the complexity within each of the levels is still immense. For example, it is evident that the biophysical properties of single neurons, and the molecular networks within a single cell, are amazingly intricate (Alberts et al. 1994; Aidley 1998). Therefore, transition from the brain or the circuit to the cellular or the molecular level per se does not really imply simplification; hence one should not confuse 'reductive steps' with 'simplifying steps' (Dudai 1989; "reduction).

'Levels of processing' refer to the neuroanatomical and physiological hierarchy of information processing in the nervous system. A bottom-up view depicts them from the lower to the higher. 'Higher' means a larger distance from sensory receptors, or a more global representation of an item. Brain systems that process sensory information used to be portrayed as strictly hierarchical, whereby information from 'low level' centres converges on 'high level' centres ("homunculus). This picture is currently replaced with the one that portrays central sensory systems as concurrent streams of processing, with 'low level' "cortical areas already dealing with rather complex attributes (e.g. DeYoe et al. 1994). Picturing "perceptual systems in the brain as neu-roanatomical 'pyramids', each composed of low strata supporting higher ones, is thus considered today as a somewhat naive simplification. Still, at a certain stage the processing is expected to culminate in a more global "internal representation ("binding). 'Levels of processing' is also a concept used, initially without explicit neu-roanatomical or physiological connotations, in the theory of memory (Craik and Lockhart 1972).2 The proposal is that processing of sensory information in the brain begins with 'shallow' levels and proceeds to 'deeper', cognitive ones, and that the deeper the processing, the more robust is the resulting "engram.

For example, phonological processing of a word could be regarded as 'shallow' and semantic as 'deep', and the latter is bound to generate stronger memories than the former. A major conclusion from such a model is hence that the levels of processing engaged in the first second in the life of a memory determine much about the whole future of that memory ("acquisition, "retrieval).

'Levels of description' or 'analysis' are concepts that refer to the operation of the brain as an information-processing, problem-solving machine. An influential account of such levels is that of Marr (1982). He distinguished three levels in the operation of any machine carrying out information-processing tasks: (a) the level of the computational theory, involving the goals of computations and the logic of the strategy to carry them out; (b) the level of "representations and "algorithms, i.e. how can the computations be implemented in terms of'input' and 'output' representations and of the algorithms for the transformation of'input' to 'output'; and (c) the level of hardware implementation, i.e. the way the representations and algorithms are implemented in the 'nuts and bolts', or 'silicon and wires', or 'neurons and "channels' of the machine. For example, consider the implementation in a brain circuit of a Hebbian algorithm by an "long-term potentiation-like "synaptic mechanism that involves "calcium currents and subtypes of "glutamate receptors.

Three comments are appropriate here: first, the same computation can be performed in different species, or in different circuits in the same species, by different algorithms. Similarly, the same algorithm may be implemented by different molecular, cellular, and circuit devices. For example, an algorithm of multiplication may be implemented in an AND gate in two different systems, but the AND gates may be realized by different "coincidence detectors in each of the systems. Second, the complexity of algorithm should not be expected to be a function of the complexity of the brain or the behaviour. This means that a certain task may be implemented by a cumbersome algorithm in a simple brain but by a simple algorithm in a complex brain. In other words, "simple systems are not guaranteed to yield simple solutions. And third, the different conceptual levels of analysis, i.e. the computational, algorithmic, and implementational levels, could be identified at any level of processing or organization in the nervous system. This means that even cellular and molecular neurobiologists will soon have to learn to struggle with information-processing theories, representations, and algorithms, if they ever wish to understand what neurons do (e.g. Bray 1995).

Note that the term 'levels of analysis' is also used in the literature in a more colloquial manner, to simply indicate the level in which the research is performed by an experimenter. In this context, reference to the aforementioned 'organizational levels' is the most common. The choice of the level of experimental analysis depends on a personal "bias, anchored in philosophical attitudes, training, expertise, "paradigms, zeitgeist, opportunities, and chanceā€”not necessarily in that order. The choice of the level of experimental analysis places constraints on the expected outcome of research programmes and academic careers. For example, in the field of memory research, adherence to a molecular level of analysis means that the research will yield, if successful, insight on general building blocks of "plasticity and on synaptic information-storage mechanisms, but probably not on the specific mechanisms that embody a specific internal representation. For the latter, circuit analysis is required (Dudai 1989, 1992). And vice versa, a choice of a brain and organ level is not expected to illuminate the physiological implementation of synaptic algorithms. A research programme that aims at elucidating learning and memory as they really are, i.e. multilevel phenomena, must therefore combine the expertise of multiple subdisciplines, ranging from molecular biology to experimental psychology to modelling. How to integrate all these disciplines in a coherent project, and especially how to make their practitioners talk the same language and comprehend each other, is itself not an easy problem. It surely cannot be solved at the administrative level.

Selected associations: Binding, Homunculus, Reduction, System, Taxonomy

1The ceteris paribus assumption is further encountered in *system. For selected approaches to levels, their taxonomy, decomposability, and other assumptions required in dealing with them in a variety of system types, see Bunge (1960), Simon and Ando (1961), Simon (1962), Fisher and Ando (1963), Whyte et al. (1969), Mesarovic et al. (1970), and Yagil (1999).

2For the application of this concept in *functional neuroimaging studies, see Kapur et al. (1994).

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