Infinity

The never-ending debate

The size and structure of the universe has been a pressing question for humankind since the very first human being to look up at the sky and ask why? How is it possible that the laws of physics allow the creation of something out of nothing? How is the universe expanding, and through what medium? Some believe that human beings are inherently lacking in the intelligence to comprehend the configuration of the universe and how it has been continuously changing for the last fourteen billion years; others believe we are on the brink of figuring it out. 

The concept of infinity, specifically when referring to infinite space, is immeasurable, as the definition of infinity itself states. However, Merriam-Webster’s second definition of the word is “an indefinitely great number or amount,” and the most common definition of number is a sum of units (where the sum is, in theory, calculable). The concept of infinity has always been extremely puzzling and difficult to grasp, and if infinity truly exists as it is defined, there will never be a way for humans to measure it. Should we be using the term in modern astronomy if we don’t truly understand it?  

Think of it this way—at any discrete time on earth (assuming everything on earth is held constant for that instant), there is a finite number of grains of sand. Of course, that number of grains would be impossible for a human to count in their lifetime and would be so incredibly large that humankind would likely not even have the phrasing to describe it. However, that “incalculably” large number is, theoretically, definite and fixed. The universe as we know it today is, of course, incomprehensibly large and continuously expanding, but at any one moment in time, its size is bound. Most astronomers agree that it is improper to say the universe is expanding infinitely when no one knows the potential bounds of the universe. Can humans understand the true meaning of “infinity” with our currently limited knowledge of the universe? The answer to this astronomical enigma lies at the frontiers of modern astronomy.  

American philosopher William Lane Craig gives a three-point argument against the infinite, influenced by Byzantine philosopher Philoponus:  

1) An actual infinite cannot exist  

2) A beginningless temporal series of events is an actual infinite 

3) Therefore, a beginningless temporal series of events cannot exist

This theory argues that since there has been a finite amount of time since the Big Bang (approximately 13.8 billion years), there was a definite beginning to the universe. As stated in point two, if “a beginningless temporal series of events is an actual infinite,” a temporal series of events with a beginning must be finite. As of right now, humans have not defined a “beginningless” event; so, the concept of infinity is void following Craig’s theory. 

However, questioning the abstraction of infinity in terms of astronomy brings about the question of infinity in terms of mathematics: is there a number at the end of the number line? If so, what happens when you add 1 to it? Additionally, there is said to be an infinite amount of non-integer numbers; that is, between 0 and 1 lies 0.1, 0.01, 0.001, etc. The prior example of disproving infinity using grains of sand does not quite apply here, as there truly seems to be an incalculable amount of decimal numbers between any two integers; the debate of infinity in mathematics versus infinity in astronomy may just have to be resolved as two diverging abstractions. 

Complicating the argument of finite space was Edwin Hubble’s discovery of the expansion of the universe in 1929. Hubble plotted the redshift of distant galaxies (signifying their movement away from Earth) against their relative distance from Earth, which proved that the universe was expanding; at the time, this largely discredited the idea among cosmologists that there existed a limit for the expansion of the universe. Many thought the idea of a finite universe to be as implausible as the idea of having a brick wall at its edge. As an infinite space grows, it remains infinite; thus, Hubble’s discovery introduced to the 20th century the idea of a truly limitless universe. 

Additionally, according to British astrophysicist Joseph Silk, experts “feel closest to” the flat model of universe expansion. This model states that the universe would “expand forever, but the expansion rate would slow to zero after an infinite amount of time”. The current accelerating expansion of the universe (as proven by the Supernova Cosmology Project and the High-Z Supernova Search Team) provides yet another paradox: if the expansion of the universe is speeding up right now, at what point will that expansion begin to slow, and why? 

Humans have a tendency to characterize curiosity about the universe as “existentialism”; however, questioning the meaning of life, the nature of the universe, and the origin of ourselves is quite possibly the deepest instinct someone can have. Some are frightened about how vast the unknown is, and some are exhilarated by it. My favourite part of astronomy has always been that there is really no right or wrong; I can theorize as accurately about the size of the universe as the brightest astrophysicist in the world today can—that is to say, humankind really knows nothing about the universe we live in. Then again, the next scientific revolution could be right around the corner; as for me, I’m on the edge of my seat waiting for it.