Translated from “El universo Babel”, published in the Spanish review Acontecimento, nb 139, 2021.
How big is the universe?
A long-standing question that has received various answers over the centuries. Curiously, it seems that the numbers have been steadily increasing until today. Let’s go for a short walk through this matter. A short walk since many have studied the subject over the last millennia. An exhaustive review would be a book or a PhD thesis.
In the cosmology of the ancient Hebrews, our world lies beneath a dome. By identifying the most remote places mentioned in the book of Genesis, we can get an idea of the size of this vault, since it would be a hemisphere placed on the ground. From the mythical Tarshish in the west, which some place near Gibraltar, to the Kingdom of Sheba in the southeast, probably around our Yemen, we end up with a dome of at least 6,000 kilometers in diameter. According to the Pesachim of the Babylonian Talmud (about 4th century), “the size of the world is six thousand parasangs” (Pesachim 94a), that is, about 30,000 km.
Light, which circles the Earth 7 times in 1 second, takes between 0.02 and 0.1 seconds to cross this universe.
To the joy, or despair, of the students of the last 2 millennia and more, the Greeks invented  geometry, trigonometry, and a couple of other “y’s”. After a series of clever measurements, they managed to measure the diameter of the Earth and the distance to the Moon or to the Sun. As for the diameter of the Earth, 12,800 km, Eratosthenes got it right . As for the distance to the Moon, about 380,000 km, Hipparchus of Nicaea also got it right. As for the distance to the Sun, Hipparchus himself gave 16 million km, falling short of the actual 150 million.
What was the size of their universe? From Aristotle to Copernicus, it was thought that the cosmos surrounded the Earth in concentric spheres. The Sun did not occupy the last sphere but the fourth. Before the last sphere, that of the “prime mover”, the penultimate sphere was that of the “fixed stars”. How far away were they? According to Al-Farghani, a Persian astronomer of the 9th century, they were located at about 20,000 Earth radii, that is, 128 million km. Ptolemy came to the same conclusion.
Light, which circles the Earth 7 times in 1 second, takes 15 minutes to cross this universe.
Centuries go by, and so do the measurements. In the 17th century, Johannes Kepler estimated the distance to the “fixed stars” at 60,000,000 Earth radii, or 384 billion km.
Light takes 15 days to cross this universe .
Centuries go by, and so do the measurements. In 1838 Friedrich Bessel succeeded in measuring the distance to a distant star. The model of “fixed stars” on a penultimate sphere was already abandoned. This time the answer does not come in light minutes, nor in light days. It comes in light years. 10.5, to be precise.
Light takes at least 21 years (2×10.5) to cross the Bessel universe.
Centuries and measurements pass. Our galaxy, the Milky Way, has been known for millennia. One just has to look up on a summer night to admire this marvel. But for centuries, people didn’t know that this whitish trail that obliterates the night sky was actually the sum of countless stars. This ensemble came to play the role of the “universe”. In 1920, it was supposed to be about 30,000 light-years large .
Light takes at least 30,000 years to traverse the 1920 universe.
Let’s take a momentary step back… to move forward. In the 10th century, Abd Al-Rahman Al Sufi, another Persian astronomer, describes in his “Book of Fixed Stars” (the title rings a bell, isn’t it?) what we now call the Andromeda galaxy. For Al Sufi, as for everyone until 1920, Andromeda was not another galaxy like ours. It was “something”, a “nebula” , inside our Milky Way. Then some started to suspect it was outside. It took until 1920 for this “Great Debate” to be settled: Are nebulae like Andromeda inside or outside our galaxy? Answer: outside. It was like realizing that New York is not a western suburb of Madrid, but another immense city on the other side of the Atlantic. Suddenly, the scale expands again. How far is Andromeda? 2.5 million light years. The famous Edwin Hubble played a role in this story.
Light takes at least 2.5 million years to cross the 1920 universe.
Twentieth-century observations continued to expand the universe. They showed that there’s more than one galaxy out there. There are billions of billions. Today, the diameter of the observable universe is estimated at nearly 100 billion light-years. It has 2 trillion galaxies. Each with billions of stars.
Are we there yet? Not sure. There may be even more.
Einstein taught us that space is just another physical object that can be stretched or compressed. Until Einstein, space was the unchanging stage in the theater of the universe. With Einstein, space becomes another actor in the play. In fact, observations over the last 100 years have shown that our universe is expanding. Really. It went through the famous Big Bang some 13 or 14 billion years ago and since then, it is expanding. Now, according to speculative theories, any point in our universe could begin to “inflate”, giving birth to another Big Bang from which another universe would expand, like a bubble growing from the surface of another. And the process would never stop. Each universe in turn would give birth to other universes, which would give birth to other universes, and so on.
Of course, that seems far-fetched. However, from planet Neptune to antimatter, through a dozen of elementary particles like the famous “Higgs boson”, it happened so many times in the history of science that something predicted by a theory ended up being found in the real world, that we’d better delay the mockery .
If these speculations are true. If this “multiverse” really exists, then our universe of 100 billion light years minimum, is just one more. One more among millions of millions or even maybe an infinite number of universes.
0.02 light seconds, 15 light minutes, 15 light days, 21 light years, 30,000 light years, 2.5 million light years, 100 billion light years, multiverse… Our perception of reality has not stopped growing. In a little more than 20 centuries, it went from about 10-10 to 1011 light years!
Could it be that we live in something like Jorge Luis Borges’ The Library of Babel ? In Borges’ novel, we could imagine that “the men of the Library” first thought that their library occupied what they had in sight. Then, as they explored it, they realized it was much larger than they thought. They even suspected that it might be infinitely large. In fact, the infinite potentials of our universe and those of the library of Babel have received a common attention by some physicists.
It seems “common sense” is not well adapted to assess reality. I don’t think wise men like Aristotle would have ever suspected that their universe was so small compared to the real one. But the most amazing thing of all is that maybe in a certain sense, Borges’ The Library of Babel really exists.
Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A, Tycho Brahe to Newton, R. Taton, C. Wilson, Michael Hoskin, Cambridge University Press, 2003.
Elementary Cosmology: From Aristotle’s universe to the Big Bang and beyond, James Kolata, Institute of Physics Publishing, 2020.
 Or, discovered ? Fascinating debate. In this regard, I recommend the excellent Conversations on Mind, Matter, and Mathematics, by Jean-Pierre Changeux and Alain Connes.
 By the way, that the people of the Middle Ages thought the earth was flat is what we now call a Fake News. They knew very well that it was round. On the origin of this Fake News, see Inventing the Flat Earth by Jeffrey Burton Russell, or the recent PhD thesis of my friend Pablo de Felipe at the University of Bristol, Flattening the Medieval Earth. The Early Modern Origins of the “Flat Error”.
 The invention of the telescope is not unrelated to this sudden increase in measured distances.
 See the April 26, 1920 debate between Harlow Shapley y Heber Curtis, The Scale of the Universe, Bulletin of the National Research Council, Vol. 2, Part 3, May, 1921, Number 11, pp 171-217.
 Scientific synonym for “I have no idea what it is”.
 See the Wikipedia page on Timeline of particle discoveries.