Is Consciousness Computable? Quantifying Integrated Information Using Algorithmic Information Theory

In this article we review Tononi's (2008) theory of consciousness as integrated information. We argue that previous formalizations of integrated information (e.g. Griffith, 2014) depend on information loss. Since lossy integration would necessitate continuous damage to existing memories, we propose it is more natural to frame consciousness as a lossless integrative process and provide a formalization of this idea using algorithmic information theory. We prove that complete lossless integration requires noncomputable functions. This result implies that if unitary consciousness exists, it cannot be modelled computationally.Comment: Maguire, P., Moser, P., Maguire, R. & Griffith, V. (2014). Is consciousness computable? Quantifying integrated information using algorithmic information theory. In P. Bello, M. Guarini, M. McShane, & B. Scassellati (Eds.), Proceedings of the 36th Annual Conference of the Cognitive Science Society. Austin, TX: Cognitive Science Societ

A Computational Theory of Subjective Probability

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We argue that classical probability cannot be applied in such cases, and that subjective probability must instead be used. In Experiment 1 we show that, when judging the probability of lottery number sequences, people apply subjective rather than classical probability. In Experiment 2 we examine the conjunction fallacy and demonstrate that the materials used by Tversky and Kahneman (1983) involve model uncertainty. We then provide a formal mathematical proof that, for every uncertain model, there exists a conjunction of outcomes which is more subjectively probable than either of its constituents in isolation.Comment: Maguire, P., Moser, P. Maguire, R. & Keane, M.T. (2013) "A computational theory of subjective probability." In M. Knauff, M. Pauen, N. Sebanz, & I. Wachsmuth (Eds.), Proceedings of the 35th Annual Conference of the Cognitive Science Society (pp. 960-965). Austin, TX: Cognitive Science Societ

On the Measurability of Measurement Standards

Pollock (2004) argues in favour of Wittgenstein’s (1953) claim that the standard metre bar in Paris has no metric length: Because the standard retains a special status in the system of measurement, it cannot be applied to itself. However, we argue that Pollock is mistaken regarding the feature of the standard metre which supports its special status. While the unit markings were arbitrarily designated, the constitution, preservation and application of the bar have been scientifically developed to optimize stability, and hence predictive accuracy. We argue that it is the ‘hard to improve’ quality of stability that supports the standard’s value in measurement, not any of its arbitrary features. And because the special status of the prototype is tied to its ability to meet this external criterion, the possibility always exists of identifying an alternative, more stable, standard, thereby allowing the original standard to be measured

Investigating the difference between surprise and probability judgments

Surprise is often defined in terms of disconfirmed expectations, whereby the surprisingness of an event is thought to be dependent on the degree to which that event contrasts with a more likely, or expected, outcome. We propose that surprise is more accurately modelled as a manifestation of an ongoing sense-making process. Specifically, the level of surprise experienced depends on the extent to which an event necessitates representational updating. This sense-making view predicts that differences in subjective probability and surprise arise because of differences in representational specificity rather than differences between an expectation and an outcome. We describe two experiments which support this hypothesis. The results of Experiment 1 demonstrate that generalised representations can allow subjectively low probability outcomes to be integrated without eliciting high levels of surprise, thus providing an explanation for the difference between the two measures. The results of Experiment 2 reveal that the level of contrast between expectation and outcome is not correlated with the difference between probability and surprise. The implications for models of surprise are discussed

On the Measurability of Measurement Standards

Pollock (2004) argues in favour of Wittgenstein’s (1953) claim that the standard metre bar in Paris has no metric length: Because the standard retains a special status in the system of measurement, it cannot be applied to itself. However, we argue that Pollock is mistaken regarding the feature of the standard metre which supports its special status. While the unit markings were arbitrarily designated, the constitution, preservation and application of the bar have been scientifically developed to optimize stability, and hence predictive accuracy. We argue that it is the ‘hard to improve’ quality of stability that supports the standard’s value in measurement, not any of its arbitrary features. And because the special status of the prototype is tied to its ability to meet this external criterion, the possibility always exists of identifying an alternative, more stable, standard, thereby allowing the original standard to be measured

Investigating the difference between surprise and probability judgments

Surprise is often defined in terms of disconfirmed expectations, whereby the surprisingness of an event is thought to be dependent on the degree to which that event contrasts with a more likely, or expected, outcome. We propose that surprise is more accurately modelled as a manifestation of an ongoing sense-making process. Specifically, the level of surprise experienced depends on the extent to which an event necessitates representational updating. This sense-making view predicts that differences in subjective probability and surprise arise because of differences in representational specificity rather than differences between an expectation and an outcome. We describe two experiments which support this hypothesis. The results of Experiment 1 demonstrate that generalised representations can allow subjectively low probability outcomes to be integrated without eliciting high levels of surprise, thus providing an explanation for the difference between the two measures. The results of Experiment 2 reveal that the level of contrast between expectation and outcome is not correlated with the difference between probability and surprise. The implications for models of surprise are discussed

Consciousness is Data Compression

In this article we advance the conjecture that conscious awareness is equivalent to data compression. Algorithmic information theory supports the assertion that all forms of understanding are contingent on compression (Chaitin, 2007). Here, we argue that the experience people refer to as consciousness is the particular form of understanding that the brain provides. We therefore propose that the degree of consciousness of a system can be measured in terms of the amount of data compression it carries out

In search of the frog’s tail : investigating the time course of conceptual knowledge activation

Slot-filling theories of conceptual combination assume that both constituent concepts are activated before they are combined. However, these theories have difficulty in explaining why combined phrase features are sometimes more available than the features of the constituent nouns. In this study, we investigate the time course of conceptual knowledge activation. Using three verification tasks of varying complexity we demonstrate that basic taxonomic knowledge is retrieved more quickly than modal specific conceptual features. Applying this finding to conceptual combination, we demonstrate that participants take longer to reject combinations requiring the activation of instance specific features (e.g. frog tail) than those that can be rejected based on more generalized taxonomic knowledge (e.g. daffodil tail). These findings provide convergent evidence that conceptual knowledge is activated dynamically and selectively rather than all at once. We discuss the implications for existing theories

Factors Influencing the Interpretation of Noun-Noun Compounds

The Competition Among Relation in Nominals theory (Gagné & Shoben, 1997) asserts that the relation frequency of the modifying noun is the primary determinant of ease of interpretation for noun-noun compounds. It also assumes that the influence of this variable is independent of the head noun. However, we suggest that both constituents exert an influence and that this influence depends on the pairing of nouns as well as the context. We present an experiment that investigates if the influence of the modifier’s relation frequency is fixed or whether it is affected by the head noun. Our results reveal that modifier relation frequency per se is not an accurate predictor of ease of interpretation: low modifier relation frequency combinations were easily interpreted in cases where the modifier’s general bias was overruled by the semantics of the head noun. As a result, we suggest that models predicting ease of interpretation must take into account the interaction of both constituents. The implications for models of conceptual combination are discussed