Through cultural transmission, repeated learning by new individuals transforms cultural information, which tends to become increasingly compressible . Existing diffusion chain studies include in their design two processes that could be responsible for this tendency: learning and reproducing . This paper manipulates the presence of learning in a simple iterated drawing design experiment. We find that learning seems to be the causal factor behind the increase in compressibility observed in the transmitted information, while reproducing is a source of random heritable (...) innovations. Only a theory invoking these two aspects of cultural learning will be able to explain human culture's fundamental balance between stability and innovation. (shrink)

We address the problem of predicting how people will spontaneously divide into groups a set of novel items. This is a process akin to perceptual organization. We therefore employ the simplicity principle from perceptual organization to propose a simplicity model of unconstrained spontaneous grouping. The simplicity model predicts that people would prefer the categories for a set of novel items that provide the simplest encoding of these items. Classification predictions are derived from the model without information either about the number (...) of categories sought or information about the distributional properties of the objects to be classified. These features of the simplicity model distinguish it from other models in unsupervised categorization (where, for example, the number of categories sought is determined via a free parameter), and we discuss how these computational differences are related to differences in modeling objectives. The predictions of the simplicity model are validated in four experiments. We also discuss the significance of simplicity in cognitive modeling more generally. (shrink)

A full appreciation for Ernst Mach's doctrine of the economy of thought must take account of his direct realism about particulars (elements) and his anti-realism about space-time laws as economical constructions. After a review of thought economy, its critics and some contemporary forms, the paper turns to the philosophical roots of Mach's doctrine. Mach claimed that the simplest, most parsimonious theories economized memory and effort by using abstract concepts and laws instead of attending to the details of each individual event (...) or experiment. For Mach, the individual case never truly repeated in all of its uniqueness, nor was all of the individual detail of a physical element adequately captured in abstract laws and schemata, however necessary these were for the pursuit of science. As can be shown from specific passages, some already published, some not, Mach's elements included physical qualia in nature similar to Russell's unsensed sensibilia, which existed even where there were no conscious observers. An argument will be presented to make the case that Mach believed in the mind-independent elements from the 1870s on, while other aspects of his thought evolved over time; I have thus dated the references to reflect this historical progression. I concentrate on Mach's ontology, as it bears on economy of thought, not his epistemology per se, which might well have been restricted to observable elements/sensations. After his own conversion to neutral monism, in the 1920s, Bertrand Russell echoed Mach's call for a 'future science' capable of handling the 'intrinsic character' of qualitative data directly without the excessive abstraction of physics. (shrink)

This paper presents a computational model of the way humans inductively identify and aggregate concepts from the low-level stimuli they are exposed to. Based on the idea that humans tend to select the simplest structures, it implements a dynamic hierarchical chunking mechanism in which the decision whether to create a new chunk is based on an information-theoretic criterion, the Minimum Description Length (MDL) principle. We present theoretical justifications for this approach together with results of an experiment in which participants, exposed (...) to meaningless symbols, have been implicitly encouraged to create high-level concepts by grouping them. Results show that the designed model, called hereafter MDLChunker, makes precise quantitative predictions both on the kind of chunks created by the participants and also on the moment at which these creations occur. They suggest that the simplicity principle used to design MDLChunker is particularly efficient to model chunking mechanisms. The main interest of this model over existing ones is that it does not require any adjustable parameter. (shrink)

Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes be corrected. Such learning from “positive evidence” has been viewed as raising “logical” problems for language acquisition. In particular, without correction, how is the child to recover from conjecturing an over-general grammar, which will be consistent with any sentence that the child hears? There have been many proposals concerning how this “logical problem” can be dissolved. In this study, we review (...) recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favors the simplest encoding of the linguistic input. Results include the learnability of linguistic prediction, grammaticality judgments, language production, and form-meaning mappings. The simplicity approach can also be “scaled down” to analyze the learnability of specific linguistic constructions, and it is amenable to empirical testing as a framework for describing human language acquisition. (shrink)

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about “information compression via the matching and unification of patterns”. That is itself a novel approach to IC, couched in terms of nonmathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics reflects the facts that mathematics is almost exclusively the product of human brains, and has been developed, as an (...) aid to human thinking, mathematics is likely to be consonant with much evidence for the importance of IC in human learning, perception, and cognition. This perspective on the foundations of mathematics has grown out of a long-term programme of research developing the SP Theory of Intelligence and its realization in the SP Computer Model, a system in which a generalised version of ICMUP—the powerful concept of SP-multiple-alignment—plays a central role. This paper shows with an example how mathematics, without any special provision, may achieve compression of information. Then, it describes examples showing how variants of ICMUP may be seen in widely used structures and operations in mathematics. Examples are also given to show how several aspects of the mathematics-related disciplines of logic and computing may be understood as ICMUP. Also discussed is the intimate relation between IC and concepts of probability, with arguments that there are advantages in approaching AI, cognitive science, and concepts of probability via ICMUP. Also discussed is how the close relation between IC and concepts of probability relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that latter view may be reconciled with the all-or-nothing, “exact,” forms of calculation or inference that are familiar in mathematics and logic. There are many potential benefits and applications of the mathematics-as-IC perspective. (shrink)