The mutual manipulability criterion (MM—Craver ) is the dominant means of assessing ‘constitutive relevance’, that is, of determining whether and when an entity is explanatorily relevant to the behaviour of a larger system. The MM’s popularity may perhaps follow from its intuitive plausibility (Baumgartner and Gebharter ). As applied to the problem at hand, one would like to know, for example, if a sensory field arising from the hairs (the trichobothria) on the cuticle of the leg of a spider, or even an external device (like the web), is constitutively relevant to the cognitive system, which is usually considered to be located within the confines of the brain. The MM helps us to understand whether the perceptual field, or the web, is part of a larger system that performs a particular cognitive function. According to the MM, if experimental changes in the external entity (the perceptual field or web) leads to changes in the cognitive system (for example, changes in the attention system) and, reciprocally, changes in the cognitive state of the system, entail changes in the external entity, then this entity can be regarded as a part of the cognitive system, and accordingly one can say that cognition extends to include the external entity (Kaplan ).
The reliable permanence of threads already laid by the spider, while web building proceeds, can also possibly reduce the computations needed to finish the structure. For example, instead of calculating in advance the number of radii needed to complete the web, the spider can proceed by filling in open spaces with new radii, until there is no open space left. By the same reasoning spiders would not need to calculate the number of viscid spiral loops before actually laying these threads, because the emerging structure itself helps to simplify the task, reducing the need for complex geometric calculations. In a way, we could say that threads simplify the problems faced by this almost blind animal by reducing the dimensionality of the navigational problem. Instead of navigating on a fully three-dimensional space, spiders basically navigate through one-dimensional draglines (even cursorial spiders leave silken lines while walking). Silken lines could shrink the effective dimension of the space that spiders navigate through, helping thus to reduce the complexity of the task. For example, when an orb-weaver is disturbed she usually jumps out of the web and hides among dead leaves in the forest litter, but later returns to the web. Finding the way back to the web could be a challenging navigational problem for a blind animal, but the task is trivial for the spider, because all she needs to do is to climb back through the safety dragline she left fixed at the hub right before she jumped away from the web. In these ways, extending cognition to the web would not only outsource information processing, but would also reduce the overall need for information, simplifying the immense navigational problem that a tiny blind animal would face so as to end up with an optimal geometrical solution to a fundamental foraging problem.
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Two further points are important here. First, at least in natural systems, information is a fundamentally relational property that pertains to particular organisms, and only exists to the extent that a communication channel is operating that allows the organism to read or extract it. Information cannot exist solely in the external environment. Second, while the notion of extended cognition inherently implies a trade-off between information stored in the brain and information distributed beyond it, any such trade-off operates within a species and not necessarily between species. Although it is hard to quantify, we envisage that different species of organisms will vary in the gross quantity of acquired semantic information that they possess, and hence that there is no reason to expect that large-brained organisms will not exhibit extended cognition: to the contrary, humans would seem a prime example.
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Miniaturisation is a common phenomenon and is perhaps becoming yet more common as the increasing temperatures in the Anthropocene select for smaller body sizes (Sheridan and Bickford ). Miniaturisation is consistently correlated with morphological simplification and novelty (Hanken and Wake ). For behavioural systems, simplification is often understood as connected to reduced behavioural plasticity, because simpler systems would have lower number of internal stable states, hence a lower number of behavioural outputs (Arnellos and Moreno ). Considering the web-building system, spiders have repeatedly evolved from orb to sheet or cob weavers (for example in Linyphiidae, Theridiidae, and Nesticidae: Bond et al. ), and this change is connected to major simplifications, with the loss of whole phases of the ancestral orb-web building algorithm (Benjamin and Zschokke , ). Nevertheless, instead of exhibiting less plastic performance, these derived species of spiders are even capable of larger adjustments in web design relative to ancestral forms. The derived forms have typically lost the stereotypic construction behaviour (Benjamin and Zschokke , ) and gained ample intra-individual, inter-individual, and species variability (Eberhard et al. ). This complexity of behavioural outputs (i.e., web variability), which arises in spite of apparent simplicity in underlying behavioural rules (e.g., a web algorithm), requires explanation. Extensive web variability and innovation appear connected to a higher behavioural imprecision in these hyper-variable spider groups (Eberhard , ; Eberhard et al. ), which could be obtained, at a mechanistic level, from the simultaneous loss of several cues for setting various web parameters, particularly the loss of an important organiser of orb-webs, the delimiting frame threads (see Eberhard et al. ). The absence of frame threads, of radial organisation, and of the whole phase of temporary spiral building turned the cob and sheet web algorithms much more dependent on the initial, exploratory phase of web building (Benjamin and Zschokke ), a phase that is much more variable, mainly involving the fixation of threads over the substrate (Hesselberg ). The dependence of the exploration phase (and independence of the remaining phases) on the substrate has been experimentally demonstrated for the ancestral orb weavers: while the length of the exploratory phase increases with the complexity of the substrate, the length of the remaining phases does not match substrate complexity (Zschokke ). Since these remaining phases are either absent or much less organised in derived cob or sheet weavers, the net result is a web much more dependent on the exploratory phase, and thus much more connected to the substrate. As a result, these webs seem to incorporate substrate organisation into the organisation of the web itself, and in this way substrate variability could help explain the large intra-individual, inter-individual and species variability in the group. What we see is a decrease in the dependence of central organisers (simplification of web building algorithm) with a simultaneous increase in the dependence of external organisers (substrate form), resulting not only in more plasticity, but also in the evolution of a huge diversity of web patterns (Eberhard et al. ). Thus, the outsourcing of information from behavioural algorithms to the environment could not only help to explain the huge success of a diverse group of spiders, but could also help to explain the taxonomic diversity of this group.