In Newcomb’s paradox you can choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to accurately deduce your choice, and uses that deduction to fill the two boxes. The way they do this guarantees that you made the wrong choice. Newcomb’s paradox is that game theory’s expected utility and dominance principles appear to provide conflicting recommendations for what (...) you should choose. Here we show that the conflicting recommendations assume different probabilistic structures relating your choice and the algorithm’s prediction. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the probabilistic structure relating the problem’s random variables is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcomb’s paradox, the focus of much previous work, is irrelevant. We end by showing that Newcomb’s paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its ‘prediction’ after you make your choice rather than before. (shrink)

Humans, like other primates, are intensely social creatures. One of the major functions of our brains must be to enable us to be as skilful in social interactions as we are in our interactions with the physical world. Furthermore, any differences between human brains and those of our nearest relatives, the great apes, are likely to be linked to our unique achievements in social interaction and communication rather than our motor or perceptual skills. Unique to humans is the ability to (...) mentalise, that is to perceive and communicate mental states, such as beliefs and desires. A key problem facing science is to uncover the biological mechanisms underlying our ability to read other minds and to show how these mechanisms evolved. To solve this problem we need to do experiments in which people interact with one another rather than behaving in isolation. Such experiments are now being conducted in increasing numbers and many of the leading exponents of such experiments have contributed to this volume. 'The Neuroscience of Social Interactions' will be an important step in uncovering the biological mechanisms underlying social interactions - undoubtedly one of the major programmes for neuroscience in the 21st century. (shrink)

There are four types of information an agent can have concerning the state of the universe: information acquired via observation, via control, via prediction, or via retrodiction, i.e., memory. Each of these four types of information appear to rely on a different kind of physical device. However it turns out that there is some mathematical structure that is common to those four types of devices. Any device that possesses that structure is known as an “inference device”. Here I review some (...) of the properties of IDs, including their relation with Turing machines, and quantum mechanics. I also review the bounds on the joint information about the physical universe that can be held by any set of IDs. These bounds constrain the possible mathematical structure of any universe that contains agents with information concerning that universe in which they are embedded. (shrink)

The important recent book by Schurz ( 2019 ) appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where there is a uniform prior—they prove that there are “as many priors” (loosely speaking) for which any induction algorithm _A_ out-generalizes some induction algorithm _B_ as vice-versa. Importantly though, in addition to the NFL theorems, there are many _free lunch_ theorems. (...) In particular, the NFL theorems can only be used to compare the expected performance of an induction algorithm _A_, considered in isolation, with the expected performance of an induction algorithm _B_, considered in isolation. There is a rich set of free lunches which instead concern the statistical _correlations_ among the generalization errors of induction algorithms. As I describe, the meta-induction algorithms that Schurz advocates as a “solution to Hume’s problem” are simply examples of such a free lunch based on correlations among the generalization errors of induction algorithms. I end by pointing out that the prior that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference. (shrink)