Infinity

The idea of infinity is something that nobody can fully comprehend.  The idea of “forever” is something thrown around by Hallmark, TV commercials, and stupid love letters but is rarely used for anything other than gross exaggeration.  How to understand such an amazing concept as infinity?

The English word “infinity” is derived from the Latin term “Infinitas,” which can be translated as “the state of being without finish.”  The Greek term, “apeiros,” means “endless.”  Can we ever really understand that? 

Mathematically, the idea of infinity is still hard to grasp.  For every number “n,” there exists a number “n+1.”  For every number “n” there also exists a number “n-1.”  Forever.  Always.  The set of all Real Numbers (1,2,3,4,…) is infinite and the set of all Integers (…,-3,-2,-1,0,1,2,3,…) goes from negative to positive infinity.  John Green, in The Fault in Our Stars, "There are infinite numbers between 0 and 1.  There's .1 and .12 and .112 and an infinite collection of others.  Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million."  Can you imagine that?  There’s ALWAYS a bigger value and ALWAYS a smaller number, no matter how high or low of a numeral you choose!  Try to wrap your head around that.

There’s something called “Menger’s Sponge,” introduced by Karl Meger,that was designed to be a sort of 3-dimensional model of infinity.  Take a cube, and divide each side into nine equal squares.  Remove the middle square.  Take the remaining 8 squares on each side of the cube, divide each square into nine equal squares, and remove the middle square.  This would theoretically go on for an infinite number of squares, never ending.

Theoretically, this is a perfect example of infinity, you could always take out more, always remove another square.  In reality however, consider a block of concrete.  You can cut out the middle squares and repeat maybe… 10 times.  After that, though, the block would be in danger of cracking or falling apart.  There is a limit to the practical application of Menger’s Sponge in that, in reality, no structure would be stable after a certain amount of mass had been removed.

Biblically, we know that God has no beginning and no end.  This can be related to a mathematical statement that there are infinitely many numbers, positive and negative: you can accept it as truth, but no one can fully grasp the sheer magnitude of such a set.  Human ability to understand infinity is like a practical understanding of Menger’s Sponge.  We’ll never be able to understand God’s infinite nature, infinite grace, and infinite abilities beyond a certain extent as our mind simply cannot comprehend the concept of infinity. 

Does this mean that we stop trying to learn about God or stop trying to understand His greatness?  No, of course not!  What it does mean, however, is that we can appreciate Him all the more.  If we can appreciate a philanthropist for doing a good thing that we can understand, how much more can we appreciate and be amazed by the works of One who is so great and awesome that we literally are incapable of understanding the magnitude of His grace?