Similarity, I submit, is insidious.
~ Nelson Goodman (1972, 437)
An American monkey, after getting drunk on brandy, would never touch it again, and thus is much wiser than most men.
~ Charles Darwin (quote found here)
Similarity is a seductive but slippery concept. It is seductive because we need the notion of similarity so we can group objects together and differentiate among them. Birds are similar to one another and they are different from reptiles. Similarity affords generalization. Many of the robin’s attributes generalize to the eagle, and few generalize to the turtle. In the social world, similarity breeds liking. We like those who are similar to us more than we like those who are not (assuming that we like ourselves).
Similarity judgments can be deceptively simple. They seem to emerge effortlessly from the brain-mind’s perceptual work. Making the judgments themselves is often easier than understanding how we make them. When I was a student at the University of Bielefeld, Germany, I learned the statistical technique of multidimensional scaling by judging the similarity of pairs of beers. My friends and I would drink two sips of different unlabeled beers and judge their similarity on a 9-point scale. Ignoring the progressive contamination of the data by creeping inebriation, we fed the data into the MDS program and found a 2-dimensional solution. Once we saw where the various types of beer lay on the plane, we labeled the axes ‘bitterness’ and ‘alcoholic content.’ The first axis scaled the pilsners and the ales, whereas the second axis scaled the bock and the light versions. This was before the era of flavored boutique beers.
Similarity judgments feel easy because we tend to focus on one or two attributes or dimensions at a time, forgetting that there are innumerable other attributes or dimensions on which two objects could be compared. We also tend to forget that two objects could easily appear more or less similar once a third object is introduced. A penguin looks more similar to a robin when a turtle appears on the scene, whereas it looks less similar when a sparrow appears.
A perception or a judgment of similarity inescapably depends on context. When we ask how similar objects A and B are to each other with regard to attribute C, we may want to ask what other attributes we could consider and what other objects might provide a frame of reference.
In science and folklore, the human being’s (hereafter: man) place in nature is a perennial concern. Traditionalists with a debt to theology tend to look for evidence supporting man’s uniqueness, whereas biologists tend to look for shared attributes. The former group – let’s call them the exceptionalists – would be happy if they found an attribute that is incontrovertibly unique to man. There are many candidates: language and culture are good examples, and so is the ability to drink beer and smoke a cigarette at the same time. The latter group – let’s call them the commonalists – greet these proposals as a challenge. They perform experiments to show that some nonhuman animal species – typically a primate – can do what the exceptionalists think only man can do, or that they have an attribute formerly considered the dominion of man. This kind of research narrows the dissimilarity gap between man and monkey – until, that is, exceptionalists propose new unique attributes. Setting aside the context effects created by third species (such as turtles), let us now ask what a research result from the Santos lab does to judgments of man-monkey similarity in a multi-attribute world. Likewise, let us ask what the discovery of a uniquely human attribute might do.
How similar are man and monkey? The main challenge to finding an answer to this question is to gather an adequate pool of attributes. We could begin by listing all the attributes man and monkey share [a], then list all those that only man has [b], and finally list those that only monkey has [c]. The list of attributes that neither has [d] remains empty – for now. As an index of similarity, we compute the phi coefficient, which is defined as (ad – bc)/√((a+c)(b+d)(a+b)(c+d)). We already see that phi will be negative because d = 0, as long as neither b or c is zero. If we exclude attributes that neither man nor monkey has, we can only find evidence for dissimilarity. For example, if a = b = c = 1, phi = -.5. If we set [a] to 1,000, thereby emphasizing the huge overlap in man’s and monkey’s attribute, phi = -.000999; still negative.
Let us then include positive values for [d] (attributes absent in man and monkey). If a = b = c = d = 1, then phi = 0. This, I believe, is the wrong null hypothesis. Once you admit jointly absent attributes, you realize that their potential number is far greater than any number for present attributes. Suppose the number of attributes man has is finite and that you are able to list them all. Assume the same for monkey. Now, when building the list of attributes that neither man nor monkey has, you realize that you don’t know where to stop. The potential number of jointly absent attributes might be infinite. To make the task tractable, assume that you make a list of attributes for each mammalian species, and cull all the attributes that neither man nor monkey has from this list. My hunch is that the result is d > a. If this is not convincing, make a list for each species of animal, plant, and mineral. Now you see the point: [d] becomes huge. As [d] increases, so does phi, with the surprising result that the similarity between man and monkey (or any two creatures or things) mostly depends on how many jointly absent attributes are being considered.
But the fragility (or indeterminacy) of phi as an index of similarity is not the main point of this post. The main point is to explore the bias introduced by the anthropocentric approach to the study of similarity. Both, exceptionalists and commonalists, begin with attributes that man has and seek to show that monkey has them too (to refute exceptionalism) or seek to show that monkey does not have them (to refute commonalism). Neither group spends much time looking for attributes that monkey has and man does not (of course, other researchers who are not invested in the man-monkey similarity debate are concerned with those attributes, among others).
To appreciate the difference between the two research strategies, begin with a data set consisting of a = b = c = 1 and d = 7; phi = .375. Now add one observation to [a] (and subtract one from [d]) because you have conducted a successful Santos-like study. Now, phi = .52. Conversely, begin with the same data set and add one observation to [b] (and subtract one from [d]) because you found an attribute that man has and monkey does not. Now phi = .23. As you can see, the increase in assessed similarity after adding a shared attribute is about as large as the decrease obtained from adding a uniquely human attribute. If you grant, however, that the number of jointly absent attributes can be large, an asymmetry emerges. If a = b = c = 1 and d = 97; phi = .49. The addition of a jointly present attribute results in phi = .66, whereas the addition of a unique human attribute results in phi = .39. The change in phi is about twice as large after adding a shared attribute than after adding a uniquely human attribute. This asymmetry does not become more pronounced if the number of jointly absent attributes is increased further. For d = 1,000, the results are about the same.
The upshot of this back-of-the-envelope analysis is that the commonalists have an easier time than the exceptionalists for two reasons. First, when commonalists succeed in showing that monkey can do what man does, the statistical impact on overall measures of similarity is greater than when exceptionalists claim that monkey can not do what man does. Second, commonalists can search broadly. All they need to do is find one species of animal that has an attribute formerly thought to be unique to man. In contrast, the exceptionalists’ case rests on the failure of all animal species to display a behavior or performance. Absence of evidence, as they say, is not evidence of absence. Having to argue from ignorance weakens one’s case.
Meanwhile, how similar are you to your partner, your kid, your pet, the Dalai Lama, or Jack the Ripper? Sure, there are shared and unique attributes, but what the PHI?
In the Protagoras, Plato has Protagoras say to Socrates: "There is always some point of view in which everything is like every other thing; white is in a certain way like black, and hard is like soft, and the most extreme opposites have some qualities in common [and so] all things are like one another; and yet things which are alike in some particular ought not to be called alike, not things which are unlike in some particular, however slight, unlike." Of course, Socrates goes on to prove that this is an incoherent position.
Goodman, N. (1972). Seven strictures on similarity. In N. Goodman (Ed.), Problems and projects (pp. 437-447). New York: Bobbs- Merrill.
Lakshminarayanan, V. R., Chen, M. K, & Santos, L. R. (in press). The evolution of decision-making under risk: Framing effects in monkey risk preferences. Journal of Experimental Social Psychology,