To formalise this, we build on the notion of a rationality measure (RM) from ( Masters and Sardina, 2019b). The documented purpose of the RM is to evaluate an agent’s future expected degree of rationality, given their past behaviour. Here, we use it to evaluate and compare the apparent rationality of the observation sequences that would result from adding each of multiple potential observations (each o ∈ O t) to the recalled observation sequence ( o ⃗ t − 1) assembled so far. That is, given what we know, which potential observation provides the most rational continuation towards any one of the known possible goals.

How the scientific study of magic reveals intriguing—and often unsettling—insights into the mysteries of the human mind.

OPINION article

MIT Press Direct is a distinctive collection of influential MIT Press books curated for scholars and libraries worldwide. Paraphrased, Newtonian physics required the supernatural to explain why gravity doesn’t collapse everything together. Subbotsky, E., Hysted, C. & Jones, N. (2010). Watching films with magical content facilitates creativity in children. Perceptual and Motor Skills, 111(1), 261–277. As before, the lower the cost difference with respect to a path between anchors, the higher the probability that they are the goal. 5 Lessons From Magic

Finally, on a philosophical level, a key issue is the problem of demarcation. It is harder to demarcate the boundaries of magic and science than is popularly supposed. There is no single scientific method that all the sciences share. Knowledge is produced differently in different scientific disciplines. Attempts to define science in terms of falsifiability have been unsuccessful. Part of the meaning of science comes from its putative opposition to magic. But this opposition cannot be fully maintained. Every attempt to define science to include astronomy but exclude astrology turns out to either leave out a well-recognized science or include a denigrated pseudoscience. Popular statements often treat science as a unitary agent. But there is not one science, nor one scientific consensus. MIT Press began publishing journals in 1970 with the first volumes of Linguistic Inquiry and the Journal of Interdisciplinary History. Today we publish over 30 titles in the arts and humanities, social sciences, and science and technology. What do we see when we watch a magician pull a rabbit out of a hat or read a person's mind? We are captivated by an illusion; we applaud the fact that we have been fooled. Why do we enjoy experiencing what seems clearly impossible, or at least beyond our powers of explanation? In Experiencing the Impossible, Gustav Kuhn examines the psychological processes that underpin our experience of magic. Kuhn, a psychologist and a magician, reveals the intriguing—and often unsettling—insights into the human mind that the scientific study of magic provides. For if there be innate gravity, it is impossible now for the matter of the earth and all the planets and stars to fly up from them, and become evenly spread throughout all the heavens, without a supernatural power, and certainly that which can never be hereafter without a supernatural power, could never be heretofore without the same powers. This event is recounted in the Malleus Maleficarum (The Hammer of Witches), a 1486 text so infamous that it has been described “ the most significant ‘witchhunting’ guide published in early modern Europe” and as “ without question the most important and sinister work on demonology ever written.” While its influence has probably been exaggerated, it contains a number of striking anecdotes (and a whole lot of misogyny). But from a contemporary vantage, one of the most remarkable things about the text is that it principally denied that witchcraft was supernatural or miraculous. According to the text:to perceive them could be quite as difficult as to count with the naked eye the grains of sand on the seashore. Sometime in the 15 th century, a group of university students got together in the town of Oberdorf in Bavaria to do what students have done the world over: drink beer. After they had been at it for a while, they decided that whoever fetched the next round wouldn’t have to pay for it. One student went to get beer, but on opening the door, he saw an unusually dark fog and he refused to go out. Then, a foolhardy member of the group boasted, “Even if the Devil was present, I shall fetch the drinks.” To their consternation, those in attendance all saw the man borne aloft into the air, shouting as he was carried out the door by an invisible demon in the direction of further libations. Lesson 9. The Disappearing Coin. The magician takes a coin in his right hand, then passes it to his left hand. In case we might suspect that he did not really pass the coin, he shows us that his right hand is empty. But then he reveals that his left hand is empty too! The ruse is a plausible, but untrue, reason, or action conveying a reason, for concealing the true purpose for doing something” which “makes it possible for the magician to do an unnatural thing naturally” ( Fitzkee, 1945). The actions involved in a ruse may receive attention at the time they take place (everyone saw the magician handle the cardboard sleeve around the bullets, the container of pens, the wine glass, the plate) but what he did with each prop seemed to have a valid purpose at the time and is likely to be forgotten once that purpose is complete. What is surprising here is that spectators, who are in a hyper-vigilant mode when watching a magic performance, are so willing to disregard and forget incidental events. This is to do with the way memories are stored and retrieved. Whereas once it was thought our memories were laid down almost like video recordings ( Chabris and Simons, 2009), available to “replay” under hypnosis, for example; we now believe that each time we recall a memory we reconstruct it from mental representations that are highly abstracted and edited down according to perceived relevance ( Loftus and Palmer, 1996). Part of the problem is that the supernatural itself is a red herring. In a broad historical overview, the “supernatural” (Latin supranaturalis) was an inadvertent product of the twelfth century recovery of Aristotle, which had caused the merger of two notions of “nature” (φύσις and naturalis). The problem became how to understand miracles. If miracles were “natural” then that would imply that they weren’t very special. But if miracles were “against nature” ( contra naturum), then it would seem that God was unnatural or in violation of divine laws.

To decide which of multiple potential observations is most likely to be attended, encoded, and available for future recall, we must put together both the top-down and bottom-up aspects of selective attention exposed in Lessons 3 and 2. That is, we propose to rely on both magnitude and relevance. While much of the science behind magic has been understood only relatively recently, magicians have been exploiting it for a lot longer. Areas covered include our perception of reality, which a magician exploits whilst performing; how our eyes deceive us; illusions and how they work; and the many ways to elicit mind control. Even Michael Faraday, the godfather of modern scientific thought, carried out ground-breaking studies on people’s consciousness during séances. Faraday concluded that the key to the apparent magic observed during the classic table turning phenomenon was simply down to the participants’ involuntary movements. Here at last my own beliefs in science, rather than taking away from the magic, increased my appreciation of it in a way I had never experienced before. Magic, which has exploited such aspects of the visual for centuries, offers us a framework to explore perception in an intriguing way, and the potential for understanding our perceptual system by investigating how magic exploits its blindness and gaps is enormous. In a goal recognition system designed to mirror human belief, confidence should increase when predictions are confirmed.

A memory-constrained agent (such as a human) cannot remember everything. Even if we initially give our full attention to a situation, we may nevertheless forget or misremember the details. Furthermore, as magicians know, this forgetfulness is almost certain to occur if our attention is overloaded and/or we are encouraged to reconstruct our memories from “alternative facts”. Observe that o ⃗ t − 1 ⋅ o in the denominator of Eq. 5 represents the observations available so far (i.e., at time-step t− 1) to which each newly available observation o ∈ O t is appended. Recall also that s t−1 is the first remembered observation—or effective starting point—at time-step t. Our findings have important implications for the way we process and think about information in our daily lives. We are continually exposed to false information, and it is often difficult to distinguish between real and fake news. Our results carry the rather worrying implication that even false ideas that we know to be impossible could affect our reasoning capacity and prevent us from discovering the truth. To be capable of reflecting the likely beliefs of a human agent, a robust goal recognition system should support the possibility that observable events may go unnoticed.