The Rigor of Angels: Borges, Heisenberg, Kant, and the Ultimate Nature of Reality

by William Egginton

For if the fundamental insight of quantum mechanics is that one must choose to measure position or momentum first, and what one chooses affects what one will come up with when one measures the next value, this necessarily leads to a fundamental limit on the amount of information we can have about the world. As we drill down into the most basic presumption of Newton’s classical world—namely, that knowing everything about a particle’s position and momentum and the forces acting on it means knowing its past and future—we run into an impenetrable barrier. Perfect precision in our knowledge of the one creates radical indeterminacy in our knowledge of the other.

We quickly see that the strangeness sprang from what we expected to see, rather than from what we in fact observe.

Ultimately, to judge the guilt or rectitude of another’s choices is not to know the secrets of that person’s heart; it is to consider what I would have done, what I should have done, had I been in that person’s shoes. Indeed, to judge another person is to raise for oneself the question of the path not taken. It is to imagine another life and compare it with one’s own. It is nothing more, and nothing less, than the existential burden of one who is free to choose, and to regret those choices. As he sat down to write his obituary, Samuel Goudsmit couldn’t know how Werner Heisenberg judged his own life and choices, but in the end he seemed to realize that such knowledge was not his goal. The absolution he gave wasn’t for Heisenberg. It was for himself.

One can imagine knowing the world perfectly, but only at the cost of being what one knows; or one can imagine being identical with the world, but only at the cost of knowing it. Like what Heisenberg’s most famous principle revealed about momentum and place, we can’t have both.