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For thousands of years, belief in the beginning of creation was solely an affirmation within the numinous arena of faith. Even as late as the 18th-century Enlightenment, the famous skeptic David Hume could argue that cosmology was outside the realm of science and that the question of the origin of the universe could never be empirically decided. Yet, many philosophers and scientists before and after Hume would disagree, viewing the beginning of the universe as a logical necessity, a clear scientific conclusion, or even the result of mathematical proof.
The Logical Contradiction of an Eternal Cosmos
The Late Roman philosopher, mathematician, scientist, and theologian, John Philoponus, logically demonstrated that in an eternal cosmos, an infinite number of moments must have been traversed. Yet, if infinity has actually been traversed, then it is not truly infinity (because infinity is a limit that can never be reached). Aristotle had rejected the idea of an infinite series of causes as a logical contradiction, but he also held that the world was eternally old. Philoponus showed that Aristotle was guilty of a logical contradiction and then used this paradox of infinity to prove the world had to have a beginning. Moreover, Philoponus argued logically that this cosmic beginning was ex nihilo (“out of nothing”)—precisely what he believed was being described in the Genesis narrative.
Johannes Kepler’s Scientific Paradox of a Dark Sky
The astronomer Johannes Kepler developed a scientific argument for the beginning of the cosmos that was aided by his empirical reflections on the nature of stars. Going back to an argument from the dark sky that was initially put forward by Philoponus more than a thousand years earlier, Kepler pointed out that an infinitely old Universe uniformly populated by stars would have an infinite number of stars. Consequently, the night sky of an infinite universe would be completely bright. Why, then, is the night sky mostly dark? Kepler’s answer was that our universe is not infinite, but finite, because it had a beginning in time.
Entropy and Lord Kelvin’s Irreversible Arrow of Time
Three centuries after Kepler, the Victorian scientist William Thomson, known as Lord Kelvin, developed a more detailed resolution to the Dark Sky paradox by showing that the stars have been shining for only a limited amount of time and that universal darkness existed before the birth of stars.1 Proposing a new understanding of the universe that focused on what Kelvin called “energy,” Thomson argued that the cosmos was fundamentally historical and evolving, being governed by the dual principles of the conservation of energy and the dissipation (or transformation) of energy.
His new science of thermodynamics also introduced the idea of an irreversible arrow of cosmic time, where entropy—or cosmic disorder—would continually increase over time until all cosmic energetic processes would eventually come to an end. However, since entropy could not have been increasing forever, Kelvin’s second law of thermodynamics entailed that the cosmos ultimately had a beginning in time.
The Beginning and the Big Bang
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The physicist Albert Einstein provided a crucial clue that would help elucidate the mystery of cosmic beginnings when he published his theory of General Relativity in 1915. Realizing that Einstein’s equations could be interpreted to predict a non-static and non-eternal universe, in 1927, physicist Georges Lemaître published the original version of what later became known as the Hubble Law, regarding the relation of the velocities and the distances of “red-shifted” galaxies that are moving away from us.
In the same year, Lemaître proposed a theory of an expanding universe with a beginning to space-time. Projecting the expansion of the cosmos back in time, Lemaître concluded that an initial “creation-like” event must have occurred where and when the fabric of time and space came into existence, a point that he called the “primeval atom.”2
Then, in 1929, astronomer Edwin Hubble found that every single distant galaxy he observed was moving away from us at a very high speed. This meant that if the motion of the galaxies was traced backward in time, they would all merge together at some moment in the past, pointing precisely to the type of cosmos that Lemaître predicted—a dynamically evolving universe with an explosive beginning in time. While Lemaître preferred to call this initial point of creation the “primeval atom,” a popular cosmologist who rejected Lemaître’s hypothesis, Fred Hoyle, coined the phrase “Big Bang” for the theory, and the term stuck.
According to physicist Stephen Hawking, the discovery of the Big Bang, “finally brought the question of the beginning of the universe into the realm of science.”3 As mathematical physicists John Barrow and Frank Tipler explain, “at this singularity,” known as the Big Bang, “space and time came into existence” and “literally nothing existed before the singularity.”4 Physicists Hawking and George Ellis thus conclude that “the results we have obtained support the idea that the universe began a finite time ago. However, the actual point of creation, the singularity, is outside the scope of presently known laws of physics.”5
A Mathematical Proof of Finite Time
While the cosmic veil of the breakdown of matter, energy, and space-time preceding the first moment of the Big Bang may forever preclude cosmologists from glimpsing the actual physical beginning of the universe, a theorem developed in the early 21st century by mathematical physicists Arvind Borde, Alan Guth, and Alexander Vilenkin—known as the BGV Theorem—has shown that the universe must have nevertheless had a beginning. According to Vilenkin, the BGV Theorem demonstrates that if a universe is (on average) everywhere expanding, then its material history cannot be extended into the infinite past.
This theorem provides a mathematical proof that any universe undergoing, on average, cosmic expansion throughout its history cannot be infinite in the past, meaning it must have had a past space-time boundary and, therefore, a beginning. Moreover, the BGV Theorem holds regardless of the specific physical model of the early universe and applies even to oscillating universes, inflationary universes, and the multiverse. Mathematically speaking, then, a past-eternal universe is impossible. As Vilenkin reflects: “With the [BGV] proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape; they have to face the problem of a cosmic beginning.”6
Edward Robert Harrison, Darkness At Night: A Riddle of the Universe, (Harvard University Press, 1989) 159.
Georges. Lemaître, Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extragalactiques, G. Lemaître, Annales de la Société scientifique de Bruxelles, Série A, 47, 49-59 (1927); Georges Lemaître, “The beginning of the world from the point of view of quantum theory,” Nature, CXXVII (3210), (1931a), 706.
Stephen Hawking, A Brief History of Time: From the Big Bang to Black Holes, (Bantam Books, 1990), 8.
John Barrow and Frank Tipler, The Anthropic Cosmological Principle, (Oxford University Press, 1988), 442
Stephen Hawking and George Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, 2023), 364
Alexander Vilenkin, Many Worlds In One: The Search for Other Universes ( Hill and Wang, 2007), 176.
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