COMPUTING SCIENCE
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.
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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