Experiencing the Impossible: The Science of Magic (The MIT Press)

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People rarely think of magic as a way to enhance wellbeing, but such applications do exist and are, in fact, growing rapidly in popularity. Until now, this endeavour has involved a rather disparate group of techniques, but Steve Bagienski and I have recently developed a hierarchical framework to help organise many of these approaches. the definition is comparative (we seek the maximum value), use of multiplication is somewhat arbitrary. It does, however, conveniently constrain the result within bounds [0,1]. In implementation, multiple observations might return the same maximal result in which case selection could be randomised. Experiencing the Impossible is a cogently argued, persuasive and often enthralling account of the pleasures he experienced while researching what he calls “one of the most captivating and enduring forms of entertainment." Bill Blagg’s The Science of Magic is without question the pinnacle of this genre!” – Daniel Hahn, Playhouse Square, Cleveland, OH Created by Bill Blagg, Milwaukee, WI A fully relevant observation (i.e., one that, when concatenated to observations already made, conforms to an optimal plan for one of the goals), decays at the default rate. The less relevant an observation, the lower the decay factor and therefore—through multiplication—the faster its corresponding rate of decay. Practically, to incorporate the notion of forgettability, all observations must be tested for relevance, not only those that may initially be overlooked as a result of selective attention (as at Section 5.3).

The solution to P is a probability distribution which prefers those goals that best satisfy the observations. In seminal work, Ramirez and Geffner (2009) and Ramirez and Geffner (2010) introduced the notion of cost difference as a basis on which to make that distinction, being the difference between the optimal cost of a plan that satisfies observations and the optimal cost of a plan that does not. The power of the formula lies in the fact that both terms can be calculated by a classical planner while one of the key insights is that the lower a goal’s cost difference, the higher its probability (relative to other goals in the distribution).Definition 2. Potential observations consist of a sequence of sets O ⃗ = O 1 , ‥ , O n , where each set O i = { o ∣ occurredattime i } .

The lessons have consequences and their application in the context of goal recognition go a long way towards explaining the persistence of conspiracy theories and fake news, even in the face of contradictory evidence. As we have seen, priming impacts expectation, which we model as prior probability; convincers impact confidence; and the two factors work in tandem. An exaggeratedly confident prediction accentuates the probability of the most probable goal. If, owing to the confidence value ( β in Eq. 8), an observer is sufficiently certain of a particular goal, the probability of that goal approaches 1. At the next time-step, that confident assessment becomes a prior probability. Now the probability of other goals is pushed close to zero with the result that—regardless of implications arising from the most recent observation—they may be overlooked. This matches our understanding from behavioural science and other commentators ( Heuer, 1981) and is precisely the effect noted in ( Masters et al., 2021), where in a fully observable path-planning domain, we find that XGR predicts as most likely a false goal, even after the real but “disbelieved” goal has been achieved. The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding author. Author Contributions Thus, o ⃗ t may represent a different observation sequence at every time-step. Typically, the sequence is first-in-first-out. That is, oldest observations are forgotten first. If an observation is particularly intense, however (i.e., has excessive initial magnitude), it may persist long after more standard observations have been forgotten so that an observation sequence at one time-step may even have different cardinality from that at another. 5.5 The RuseIn summary, the very notion of the “supernatural” was historically short-lived and not the defining feature of premodern notions of witches, demons, or magic—all of which were described as unusual but neither supernatural nor miraculous. So any rejection of the supernatural by modern science would seem to have been unnecessary.