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A friend recently called me with a math question:
“So if we’re measuring the area of a circle, are the units written centimeters squared, or can we just write centimeters?” she asked.
Happy to answer such a straightforward question, I replied “Since you’re talking about area, it has to be centimeters squared. In fact, if it were the volume of a sphere, it would be centimeters cubed, and if it were a four-dimensional sphere it would have to be centimeters to the fourth power.”
“You must be pulling my leg! There’s no such thing as a four dimensional sphere, is there?” She responded incredulously.
“Even though we cannot imagine it in our heads, it works out just fine mathematically for as many dimensions as you want. In fact, there are lots of concepts in mathematics that we cannot wrap our heads around, yet they are quite useful and work out quite well. For example, infinity is a fundamental concept used in calculus, yet none of us has seen infinity or can imagine what infinity is like,” I said.
Without missing a beat, she replied, “So then it’s like God - just because we cannot see or understand something doesn’t make it any less real or useful.”
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