At the start of a new year, a week after a major religious holiday, I wonder whether modern science can support, if not the doctrine of creation, at least the idea that our universe, like our year, had a beginning.

Many cultures have traditions of a universal beginning, but most ancient scientists, like Aristotle, were skeptical. They saw daily and yearly cycles in the heavens and assumed that these processes had always exist. Heavenly bodies move in circles, they thought, and circles have no beginning and no end.

But modern science suggests a beginning of the universe based on two ideas – entropy and infinity. According to scientific understandings of entropy, isolated physical systems tend to change from ordered states to less ordered states. We can scramble eggs, but we can’t unscramble them. After Humpty Dumpty fell off a wall, all the king’s horses and all the king’s men couldn’t put him back together again. (It’s never been explained how the horses were supposed to help.) Hot coffee in a cup cools as it loses its organized heat to its surroundings, which do not reciprocally add heat back to the coffee.

Increased organization is nevertheless common on earth. The elements form molecules and molecules form intricately ordered living organisms. Spiders spin webs and birds build nests. People build houses, bridges, and cars. This is possible because the earth isn’t an isolated system; it receives energy from the sun. The entire universe, by contrast, is an isolated system because it includes all matter and energy. There’s no outside supply, because there’s no outside. So, according to current science, the universe is moving toward chaos.

The law of increasing entropy implies that time has an arrow. It moves in just one direction, from organization to chaos (often with arthritis in between). This arrow of time, combined with what we now know about infinity, implies that the universe must have had a beginning.

“And so on and so on without stop” expresses the basic idea of infinity. The whole integers are infinite because 2 follows 1, 3 follows 2, 4 follows 3 and so on and so on without stop. If there were a highest integer, the series would have a stop and wouldn’t be infinite. It’s infinite because there’s no end to it, a thought that came to me during one of my granddaughters’ dance recitals.

This gives infinity some strange properties. Almost 100 years ago mathematician David Hilbert explained that if a hotel had infinite rooms it could always accommodate additional guests even when fully booked. Suppose that its infinite rooms were all occupied by an infinity of guests. Guest #1 is in room #1, guest #2 is in room #2, and so on without stop. But then suppose that an additional infinity of guests shows up in togas (Roman numeral guests). The new infinity of guests could be accommodated by Hilbert’s hotel by assigning all the even numbered rooms to the Arabic numeral guests, leaving an infinity of odd numbered rooms to the Roman numeral guests. This is why two times infinity equals infinity.

If the universe had no beginning and was therefore infinitely old, there would always be another second (or year or millennium) before any given second (year, millennium, etc.) you could name, just as there is always a negative number lower than any negative number that you can name. In both cases, the series is infinite when counting backwards from minus 1 to minus 2 and so on without stop, or from this minute to the one before to the one before without stop.

But if time has an arrow – if it only moves in one direction, forward – then counting time backwards doesn’t correspond to reality. Counting forward in a universe without a beginning wouldn’t allow time to get to the present. An infinity of seconds (years, millennia, etc.) would have to have been completed before now (or any other particular date you could mention). But completing an infinity is, by definition impossible. It’s inherent in the concept of infinity that there’s always more in an infinite series. So, if the universe had no beginning, we’d never get to the present moment (or any other particular time) any more than we could get to minus 1 by counting all the negative numbers from the lowest to the highest. We can get to minus 1 only if we start counting forward from a finite negative number. Similarly, we can get to the present only if there’s a starting time from which to move forward.

These considerations of entropy and infinity indicate that the universe had a beginning, but they don’t tell us how or why this beginning took place, whether in a Big Bang proposed by astrophysicists or in a divine act of creation as in the Abrahamic religions.

If time has an arrow, then Zeno's paradox would apply, which says that an arrow could never catch up with Achilles, or with even his heel, as long as Achilles is given a head start on it. (Whether Achilles is well heeled is a different question.) Ergo, an infinity of previous moments in time proves that we are not actually now. We have not arrived in the present. We only think we are now, when we are actually not yet, but are delayed in the indefinite (infinite) future. It's a simple matter of logical deduction.