Pons Asinorum

By Joel Marks

Published in Philosophy Now, no. 35, p. 48, March/April 2002

Three travelers seek lodging for the night. They come upon a pension that charges 10 euros per person. It turns out that there is only one room available, but they don't mind sharing; so they pay the clerk 30 euros. When the proprietor returns, however, she decides that the guests should be given a discount for having to bunch up, so she summons the bellhop and hands him 5 euros to refund to them. Not being a completely honest fellow, the bellhop pockets two euros; this conveniently leaves one euro to be returned to each guest. Therefore each guest has now paid nine euros, for a total of 27 euros. But 27 plus the two in the bellhop's pocket = 29. What happened to the thirtieth euro?

When I first heard this puzzle, I was bedazzled. It seemed so simple; yet no matter how I turned it over in my mind, I could not come up with a solution. I even entertained the hypothesis that I must be dreaming, or under the influence of Descartes' evil daemon, "who has directed his entire effort to misleading me, [for] how do I know that I am not deceived every time I add two and three or count the sides of a square or perform an even simpler operation, if such can be imagined?" (Meditation One).

Soon, however, I came up with this surprising conclusion: There is no thirtieth euro! The travelers ended up paying 27 euros. The proprietor had 25, and the bellhop kept two. THAT'S IT. And yet ... I still could not shake from my head the notion that there was a missing euro. So it occurred to me that the puzzle could be conceived as a kind of illusion -- a calculative illusion, we might call it. An analogy can be drawn to a visual illusion, like the bent-stick-in-water, which is not really bent, but, even when one is fully knowledgeable of its straight shape, continues to APPEAR bent at the waterline (due to the refraction of light). Just so, I now knew there was no thirtieth euro, but I couldn't dispel the mental impression that there was.

Finally I was able to dispel even the illusion. This came about precisely because of its refractoriness. I could not rid my mind of that thirtieth euro; there had to be a way to account for it. And so there is: For at the end, the proprietor has 25 euros, the bellhop two, and the guests three. VOILA: 30 euros! So NOW the puzzle became: Why had there seemed to be a puzzle in the first place? Indeed, for some of my more logically adept friends and colleagues, there had been no puzzle about the 30th euro, and they were only puzzled about what was puzzling me. I can still experience a kind of Gestalt switching (as when viewing the picture of a vase and two facial profiles) between my puzzlement and my lack thereof. What makes for the difference?

The answer I have come up with is that this "puzzle" arises from a simple "mental mishearing": Where the situation at the end is that the guests have PAID 27 euros, one might inattentively "hear" this as their now POSSESSING 27 euros. Then indeed there would be a mystery (for the bellhop only possesses two, so where's the thirtieth?). But in fact at the end the guests only retain three euros of the original 30.

I have therefore passed through three stages: (1) puzzlement (indeed, astonishment), (2) knowledge, but with remaining unease or residual illusion, and (3) "total enlightenment" or "wisdom," with no puzzle or illusion extant (and even understanding why there had been puzzlement in the first place). The progression is instructive: From time to time life throws us for a loop, and, indeed, PHILOSOPHY is in the very business of questioning fundamental assumptions. But sometimes, as with the three lodgers puzzle, we eventually discover a way to buttress our original conception of things; Wittgenstein considered philosophy itself to be one big faux-puzzle maker, which it was his calling to foil. However, the history of thought -- not to mention, the narratives of our individual lives -- is surely rife with cases of a new conception's replacing the old after some initial shock, such as the discoveries of pi, the stellar nature of the Milky Way, the absence of an ethereal medium, radioactivity, the expansion of the universe, the incompleteness of arithmetic, and so many others. So the truly philosophical task may be to discern which are the real and which the ersatz puzzles.

Which, for example, is the Anthropic Cosmological Principle? It seems that the various physical constants of our universe are exquisitely fine-tuned for the coming into being of ... us! The odds of this having come about by chance are said to be infinitesimal; ergo, we have empirical evidence of some (vast) intelligence and purposiveness (God?) pre-existing the universe. Is this a genuine problem for the secular mind?

Apparently NOT. Here is a homely analogy. Suppose you hit a golf ball into the air and it comes down in a dark forest. Well, no mystery there: Where it came down is where it came down. If we want to explain why it landed where it did, we would naturally look to physical laws and conditions. Now change the point of view: Pick a particular point hidden in the deep woods and challenge somebody to strike that precise location with the ball. We would expect only a Tiger Woods to attempt the feat, but even he would probably find it impossible.

Just so, the "fine-tuning" of nature that resulted in us may seem unlikely to the point of impossibility (SANS an act of intentional design or creation), but the refutation of this "mystery" is that we are just "looking at things through the wrong end of the telescope": We pose the "problem" from the vantage of the end‑point, whereas causality works from the beginning, and then, whatever happens, happens. Thus, the "problem" needs no solution because it is not really a problem.

Yet there are others who see a deeper riddle posed by the constants of nature, and who consequently disparage the formulation above as the "WEAK Anthropic Principle," or "WAP." Is there a Strong Anthropic Principle constituting a real puzzle? (Or would one just be a SAP to think so?) You will have to consider that for yourself outside the confines of this column.

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Joel Marks is Professor Emeritus of Philosophy at the University of New Haven in West Haven, Connecticut, U.S.A. He would like to thank Bill DeMayo and Julie Chenell for prompting reflection on the present topics.