INFINITY. It is a concept that defies imagination. We have a hard-enough time trying to wrap our minds around things that are merely extremely big: our solar system, our galaxy, the observable universe. But those scales are nothing compared with the infinite. Just thinking about it can make you queasy.
But we cannot avoid it. Mathematics as we know it is riddled with infinities. The number line stretches to eternity and beyond, and is infinitely divisible: countless more numbers lurk between any two others. The number of digits in a constant like pi is limitless. Whether geometry, trigonometry or calculus, the mathematical manipulations we use to make sense of the world are built on the idea that some things never end.
Trouble is, once unleashed these infinities are wild, unruly beasts. They blow up the equations with which physicists attempt to explain nature's fundamentals. They obstruct a unified view of ...
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