My experience with the concept of infinity has been limited,
to say the least. It has been confined to the number of days until Christmas
(It will NEVER get here, were my thoughts as a child) to the doodling’s of the
infinity symbol on the cover of my high school binder (for some reason it was
cool back in 1975) to the declarations of love by my children when they were
young (“I love you to the moon and back, infinity times!!”) When pushed to
further contemplate the reality of infinity, my mind is bound by its finite
nature. I cannot conceive a line that has no beginning nor end.
It was with this bewilderment that I read Chapter 1 of Dr.
Kent A. Beesey’s book “To Infinity and Beyond.” I anticipated with great
excitement the prospect that, finally, this mysterious and unfathomable concept
would have its secrets revealed to me and I would understand infinity. Oh, the
things I could do with this knowledge…. well, I can’t really think of anything
but I’m sure understanding infinity would make me the life of the next ward
party as I explained it to all within the sound of my voice.
Imagine then, my dismay when I read these words “The
collection of all subsets of a set is called its power set. Informally, to
obtain a power set we look for all combinations of objects from a given set.
For example, the power set of {1, 2, 3} is {Ø, {1}, {2}, {3}, {1, 2}, {1, 3},
{2, 3}, {1, 2, 3}}, where Ø represents the empty set. If the idea of a power
set intrigues you, then I encourage you to take (or audit) an introductory
course in set theory. In that course we prove that the cardinality of the power
set is always greater than the cardinality of the original set.” What??? I feel
pretty comfortable in saying that the idea of a power set does not intrigue me,
so we can set aside any notions of an introductory course in set theory.
While Dr. Beesey attempts to explain infinity in the simplest
of terms, I was pretty much lost from the beginning. I did, however, understand
and could relate to the example of the number of seats in the Marriott Center
and the number of individuals wanting to attend an event there. It is easy to
see how if the sets P (people) and S (seats) match up, they have the same
cardinality. I see that every Sunday when my family comes to dinner: I have 8
chairs and 13 people who want to sit at the table to eat. The cardinality of Set P is definitely more
than the cardinality of Set S. It also means that Set C (my couch) will get
dirty as the result of Set G (My Grandchildren) spilling Set D (their dinner)
on it. Or maybe I am confusing the concept.
Dr. Beesey sums up my feelings in this statement: “The
mathematically minded should be overcome by cerebral exhaustion” although I
would amend it to say “The mathematically challenged will definitely get a
headache.” While this exercise did little to expand my understanding of infinity,
it did prompt me to ponder the limits of the human mind and the infinite power
of God. As I considered the vastness of the universe and the concept of infinity
and eternal life, I was humbled and awed at the great gift of this life
experience. That we even have minds so equipped that we can wrestle with these
concepts is proof of God’s existence to me.
But just to make sure that I put my knowledge of infinity to
good use, when my husband walked by I grabbed him and said “Hey, I love you to
the moon and back, infinity times!”
