The Infinite and our Place in the Universe

HS #41 2018.12.13

The Infinite and Our Place in the Universe

Let’s listen to Immanuel Kant on one of his evening walks about Konigsberg:

 “Two things fill the mind with wonder and awe the more steadily I reflect upon them: the starry heavens above me and the moral law within me. The starry heavens begin at the place I occupy in the external world of sense.  The moral law begins at my invisible self, my personality, which has true infinity. 

The former annihilates my importance as an “animal” which must give back to the planet (a mere speck in the universe) the matter from which it came. The latter, on the contrary, infinitely raises my worth as that of an “intelligence” independent of animality with a final destination not restricted by the boundaries of this life, but reaching into the infinite.”

Three thousand years ago, a shepherd boy destined to become the King of Israel gazed into the night sky, took his lute and composed something quite similar: “When I look at thy heavens, the work of thy fingers, what is man that thou art mindful of him? Yet Thou hast made him a little less than God.“

Theologian, astrophysicist and WTS emeritus professor, Chris Kaiser, with the benefit of modern scientific knowledge, still asked the same,  “Scientific theories will always leave us with the perplexing question of the relationship between humanity and nature, history and cosmology. Which is the real drama? Is it the evolution of the universe, with the rise of life on earth and the history of humanity a mere curiosity, a freak sideshow doomed to extinction and oblivion? Or is the story of humanity the real drama with the vast panorama of the universe merely a background?”

Why do we humans ponder our place in the universe?  Is it because, as the writer of Ecclesiastes said, “He has put eternity into man’s mind“?  Why did Kant keep referring to the infinite?  What does the infinite have to do with our understanding of ourselves?

Thirty years ago, as a new professor at Hope College, I wrote a paper: “Infinity and the Absolute: Insights into our World, Our Faith and Ourselves.” I began, “The more I ponder the infinite, the more I question my ability to know, because I become increasingly aware of the limitations of my own mind. On the other hand, contemplating the infinite and endeavoring to understand its connection to the world outside of me and the faith within me, serves me by clarifying my position in the scheme of things. Thus in grappling with the infinite, the mind is at once humbled by the inability to fully understand, while enriched by the very attempt to understand.”

David Hilbert, perhaps the greatest mathematician of the twentieth century, observed, “The Infinite. No other question has ever moved so profoundly the spirit of man, no other idea has so fruitfully stimulated his intellect.” 

For thousands of years, mathematicians and philosophers wrestled with the meaning of the infinite. For some it was a pejorative term, others associated it with the divine. Then Georg Cantor singlehandedly ripped the curtain from top to bottom revealing the infinite’s inner sanctum. 

Cantor successfully defined the infinite. Essentially, an infinite collection is one in which after removing some, there are still as many as before. John Newton, the author of “Amazing Grace”, captured the idea exactly: “When we’ve been there ten thousand years . . . we’ve no less days to sing God’s praise than when we first begun.”

Cantor also proved that there are different sizes of infinity - - in fact there are an infinite number of sizes.  But he was humbled by it as well. Cantor could not answer a vexing question: Are the sizes of infinity discrete (like the numbers 1, 2, 3) or are they all bunched together (like the possible distances along a ruler). Cantor, obsessed with this question and taunted by mathematicians who rejected his ideas, died in an insane asylum. 

But Hilbert recognized the significance of his findings. In 1900, Hilbert, the key-note speaker at the International Congress of Mathematicians, listed 23 problems for mathematicians to solve in the next century. Cantor’s problem was number one.  The answer, in 1963, shocked everyone.  It was totally unexpected. 

No wonder Cantor associated this unknowable, otherworldly infinite with the divine, envisioning the different sizes of infinity as angels leading to the very throne of the inscrutable Absolute Infinite. The Infinite: humbling, mysterious, and surprising – almost as surprising as an infant lying in a manger.