What XAI can learn from Penn & Teller
How magicians deliver explanations and what that means for Explainable AI
TK Insert Jimmy Ichihana picture here
Penn & Teller: Fool Us is an American television show. The hosts - Penn Jillette and Teller (hereafter P&T) - are renowned magicians who have performed together for several decades. On the show, magicians from all over the world are invited to perform a magic trick for P&T. If neither host can explain how the trick was done to the satisfaction of the magicians, the magicians have successfully fooled P&T. Over the first six seasons, 298 magicians have attempted to fool P&T with 77 foolers, yielding a successful explanation rate of 74.16%.
TK Pullquote here: By dissecting how P&T explain magic tricks, we can develop some intuition about architecting Explainable AI (XAI) systems.
Beyond amazing magic tricks, this show is about generating conversational explanations in an adversarial setting. By dissecting how P&T explain magic tricks, we can develop some intuition about architecting Explainable AI (XAI) systems.
The most important aspect of each episode is the explanation of the trick itself. It would be a simple matter for P&T to explain the trick in plain language, but this would violate an unwritten rule in the magic community, which largely believes in keeping the mechanics of magic tricks hidden from public view. Although this is not a view that P&T completely subscribe to, they explain the trick coded in magic jargon as opposed to plain language. In this way, P&T can demonstrate that they have deciphered the key principles of how the trick was done without giving away its mechanics to the public.
There are four typical structures of explanations.
- Type 1: You did not fool us. Here is how you did the trick (presented in magic jargon).
- Type 2: We are uncertain. This is how we think you did it. If you agree with our reasoning, you did not fool us.
- Type 3: You partially fooled us. There is a part of the trick that we were not able to decipher.
- Type 4: You completely fooled us. We have no idea how the trick was done.
A Type 3 or 4 explanation results in a fooling.
Four tricks: a glimpse of an ontology of magic
This is the fun part of the article (wherein you are allowed to watch TV for science). I selected four performances which are amazing magic tricks in their own right but differ markedly in their explanations.
Given the setting of the show, magicians don’t simply perform well-known tricks but strive to create elements of novelty. In some cases they perform several tricks with a theatrical element connecting them. Each section below represents an instance of one type of explanation.
Exact Cuts: Jimmy Ichihana (Season 6, Episode 6)
Jimmy Ichihana, who came back to the show for the second time to perform close-up card magic, does two different card routines that involve cutting a deck of cards exactly  by color, suit, or number at very high speed. Given the speed at which he presents the effects, some parts of the trick fooled Penn and other parts fooled Teller, but between them they were able to decipher the trick completely and give a Type 1 explanation.
TK: Add video embed https://www.youtube.com/watch?v=lWJz1NMT638
We can make two observations from this performance.
Replaying the input: Given the rate at which Ichihana was handling the cards and producing effects, it is unlikely that either of P&T were able to decompose the act in real-time and likely had to replay the act mentally to figure out how the trick was done. In magic, the performer has complete control of how the trick proceeds, and can sometimes have multiple paths to the effect, so P&T often need to replay the trick mentally to decipher it. They have no way of deciphering it on the fly because they don’t know what to pay attention to - the whole point of magic tricks is to misdirect viewers and control their attention.
Two is better than one: This is a case where having both P&T try to explain the trick was better than having either one of them alone. The deliberative process after viewing a trick includes generating, evaluating, and discarding or selecting the most viable explanation of the trick. Consider, as a logical extrapolation of this observation, the limiting case of P&T being replaced by every magician who ever lived. In this case the probability of successful fooling is vanishingly small.
Film to life: Rokas Bernatonis (Season 3, Episode 6)
We now look at a Type 2 explanation. Rokas Bernatonis performs  a trick that combines two well known tricks called Card to Wallet and Film to Life. P&T correctly identify the two tricks and then tell Bernatonis in code that they think the combined trick has certain elements and ask Bernatonis if they are wrong. He says they are correct and therefore not fooled.
- Explanations must quantify uncertainty: In this case, the explanation of the trick included uncertainty, and this was explicitly mentioned.
Composition: Eric Mead (Season 4, Episode 10)
Eric Mead  fooled P&T with a close-up coin magic trick that involved sleight of hand. It is worth watching the trick to see how wonderfully it is orchestrated. It felt like there was nothing superfluous in his routine.
At the outset, Mead states that the trick he is about to perform is a variant of a Cylinder and Coins trick invented by John Ramsay. It is not clear if this concession is simply part of the "verbal misdirection, which may or many not have already begun" intended to force P&T into a mental frame. The look of pure delight on P&T’s faces throughout the routine is ample evidence of the mastery demonstrated by Mead. Two salient points emerge from the dialogue and subsequent explanations
Historical knowledge and evolution of tricks: Magic has a very long history and it is reported that Teller possesses encyclopedic knowledge of magic history. A successful explanation requires recognizing that a specific trick is being performed and knowing whether it has any variants or introduces novelty beyond the original trick. During the performance, Eric Mead indicates this novelty by claiming that "I’m certain that there are a couple of beats along the way that are puzzling or mystifying to them." It would be a lot easier to fool P&T if they did not possess this wealth of historical knowledge and a sense for how it evolves over time. This drift in historical knowledge (aka training data) is important to capture in XAI systems.
Mutual common knowledge: Both Mead and P&T have some knowledge of each other’s magic repertoire. Mead notes that the trick they are about to see has been performed by P&T "on this very stage". Similarly, P&T note that "we know you and we know this trick". This is similar to common knowledge in the game theoretic sense. XAI systems will need a way to capture common knowledge of the domain.
Nothing to go on: Harry Keaton (Season 6, Episode 3)
In this trick, Harry Keaton  asks the emcee of the show, Alyson Hannigan, to feel objects hidden inside a minimal rectangular box. When she discloses what she thinks she is feeling, Keaton uncovers the box to reveal a completely different object. For instance, she says she feels a sponge, and Keaton reveals a small rock.
P&T had never seen anything like it before - "... we got no way to figure out anything because you invented the damn thing. ..." Clearly this is a Type 4 explanation. Further research shows Keaton’s trick has a lineage starting in 1954, P&T were likely unaware of the existence of the effect, and didn’t hazard any guesses at explaining it. What can we learn from this explanation?
- Complete novelty defies explanation in conventional terms: Whether the novelty is actual or merely perceived because the trick is completely outside the P&T’s experience, it is impossible to explain the mechanics of the trick. For an XAI system an appropriate capability to have in this situation is to be able to recognize that a novel out-of-distribution sample has been encountered and decline to offer explanation.
The enire premise of Fool Us is for P&T to explain what they think is going on in their visual and auditory fields as the performers actively try to fool them. P&T's explanations are both domain-specific and audience-specific. In order to be relevant, explanations must take the expertise of the recipient into account. Designers of XAI systems need to recognize this important requirement.
Explanations on the show are consistent with the literature on explanations from the social sciences. See Miller for example. P&T’s explanations are conversational and hew closely to the Gricean maxims of relevance, quality, and quantity. They, however, consciously violate the fourth maxim of avoiding obscurity of expression and ambiguity to protect the secrets of magic.
Finally, we note that there are two distinct stages of explanation on the show. The first is to diagnose how the trick was done and the second is to convey an explanation of that cause in conversational terms to the performing magician.
Taken together, these observations of explanations in adversarial settings suggest a generic architecture for Explainable AI Systems. A forthcoming paper will present one candidate architecture.