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Identity Crisis

Brian Hayes

One and the Same

We seldom notice it, but words such as "equal," "identical" and "the same" conceal a deep ambiguity. Consider this pair of sentences:

On Friday Alex and Baxter wore the same necktie.
On Friday Alex and Baxter had the same teacher.

These two instances of "the same" are not at all the same. Unless Alex and Baxter were yoked together at the neck on Friday, they wore two ties; but they had only one teacher. In the first case two things are alike enough to be considered indistinguishable, and in the second case there is just one thing, which is necessarily the same as itself. The two concepts are so thoroughly entangled that it's hard to find words to speak about them. Where confusion is likely I shall emphasize the distinction with the terms "separate but equal" and "selfsame."

When there's some uncertainty about whether two things are alike or are really just one thing, the usual strategy is to examine them (it?) more closely. If you study the two neckties long enough, you're sure to find some difference between them. Even identical twins are never truly identical; when you get to know them better, you learn that one has a tattoo, and the other can't swim. (If all else fails, you can ask them; they know who they are.)

The strategy of looking harder until you spot a difference doesn't work as well inside the computer, where everything is a pattern of bits, and separate patterns really can be equal. Bits have no blemishes or dents or distinguishing features.

Another way to decide between the two kinds of sameness is through the rule of physics (or metaphysics) that a single object cannot be in two places at the same time, and two objects cannot occupy the same space at the same time. Thus all you have to do is bring Alex and Baxter together in the same room and check their neckwear.

The computational equivalent of this idea states that two objects are in fact the selfsame object only if they have the same address in memory. Thus two copies of an object can be distinguished, even though they correspond bit-for-bit, because they have different addresses. This is a practical method in widespread use, and yet it has certain unsatisfactory aspects. In the first place it assumes that the computer's memory is organized into an array of unique addresses, which is certainly the usual practice but is not the only possibility. Second, letting identity hinge on location means that an object cannot move without changing into something else. This idea that where you live is who you are contradicts everyday experience. It is also a fiction in modern computer systems, where data are constantly shuffled about by mechanisms such as virtual memory, caches and the storage-management technique called garbage collection; to maintain the continuity of identity, all of these schemes have to fool programs into thinking that objects don't move—a source of subtle bugs.

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