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Identity Crisis

Brian Hayes

Always the Same

A big advantage of the serial-number approach to identity is that things stay the same even as they change. Identity doesn't depend on location or on any combination of attributes. Two bank accounts might have exactly the same balance, but they are different accounts because they have different account numbers. Within a single account the balance is likely to vary from day to day, but it remains the selfsame account.

This interplay of constancy and change is certainly a familiar feature of human life. My friend Dennis Flanagan has written that the molecules in most of the tissues of the human body have a residence half-life of less than two weeks. Clearly, then, I'm not the man I used to be—and yet I am. Indeed, it is when this process of continual molecular replacement ceases that "I" vanish.

In the semantics of programs, the unique identity of objects matters only when things can change. In a programming system without assignment operators or other ways of modifying existing values, the distinction between separate-but-equal things and the selfsame thing is of no consequence. If an object can never change after it is created, then the outcome of a computation will never depend on whether the program uses the original object or an exact copy.

Figure 2. Why do all electrons look alike?Click to Enlarge Image

For certain abstract kinds of objects, the whole concept of individual identity seems beside the point. In the equation 2x – 2 = x + 2, should we think of the three 2's as being three separate-but-equal entities, or are they three expressions of a single archetype of 2-ness? It doesn't seem to matter. There is no way of telling one 2 from another. The same can be said of other abstractions, such as alphabetic characters or geometric points.

Even some elements of the physical world share this indifference to individuality. Electrons and other elementary particles seem to be utterly featureless; unlike snowflakes, no two are different. All electrons have exactly the same mass and electric charge, and they carry no serial numbers. They are a faceless multitude. No matter how long and hard we stare, there is no way to tell them apart. They are all separate but equal.

Or else maybe they are all the selfsame electron. In 1948 John Archibald Wheeler, in a telephone conversation with his student Richard Feynman, proposed the delightful hypothesis that there is just one electron in the universe. The single particle shuttles forward and backward in time, weaving a fabulously tangled "world line." At each point where the particle's world line crosses the spacetime plane that we perceive as "now," it appears to us as an electron if it is moving forward in time and as a positron if it is going backward. The sum of all these appearances constructs the material universe. And that's why all electrons have the same mass and charge: because they are all the same electron, always equal to itself.

© Brian Hayes

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