Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity

Fantastic numbers and where to find them: a cosmic quest from zero to infinity

Antonio Padilla is a theoretical physicist and cosmologist at the University of Nottingham. He was chairman of UK Cosmology for over a decade and is known for his frequent appearances on the popular YouTube channel, Numerophile.

Below, Antonio shares 5 key insights from his new book, Fantastic numbers and where to find them: a cosmic quest from zero to infinity. Listen to the audio version – read by Antonio himself – in the Next Big Idea app.

1. 0.0000000000000001

It’s a small number, and small numbers betray something unexpected. For example, I am a very bad singer. I’m definitely not supposed to win The X Factor Where american idol. You could say that the probability of me winning is a very small number.

The Higgs boson is also unexpected, so it too has a small number. You may have heard of the Higgs boson. It made headlines after its discovery at CERN’s Particle Physics Laboratory in 2012. Particle physicists were running around excitedly then. The Higgs was said to be the final piece of the particle puzzle, helping to explain the origin of mass in our universe.

What no one ever tells you is that we particle physicists were also a little ashamed. Our best microscopic theories told us that the Higgs boson was able to transform into other fundamental particles. All that shape-shifting is expected to weigh so heavily on the Higgs that it would weigh up to a few micrograms, roughly the same as a fairy fly, a tiny wasp that happens to be the smallest insect in the world.

“The Higgs was said to be the final piece of the particle puzzle, helping to explain the origin of mass in our universe.”

The thing is, fundamental particles don’t tend to weigh as much as insects. Although the Higgs theoretically should weigh as much as fairy, it does not. It is 0.0000000000000001 times lighter and no one understands why. We’ve tried to explain what’s happening in many ways: by considering extra dimensions, fancy super symmetries where we double the number of particles in nature, and we’ve even tried to split the Higgs into tiny little pieces. In vain, because experiments at CERN have not yet found any evidence to explain the Higgs boson. The mystery remains.


The Higgs was unexpected, but it’s not as unexpected as our universe. Our universe is described by a very small number: 10(-120). It’s less than a part in a googol.

The universe is expanding, which means that the space between galaxies is getting bigger, not because the galaxies are moving apart from each other, but because space itself is getting bigger. This expansion is accelerating. Something is pushing the universe, making it grow at an ever faster rate.

Most physicists believe it is driven by the energy of empty space. That’s what we call vacuum energy– the energy left behind when you empty the universe of all stars, planets, humans and little green men, so that only the void remains. You might think that something so empty can’t carry any energy, but that’s not true. Quantum mechanics tells us that the vacuum is a vibrant place, a bubbling broth of virtual particles that appear and disappear. These particles weigh down the vacuum in the same way that they weigh down the Higgs. They give the vacuum an energy that can push the universe.

The problem is that he wants to push too hard. When you do the math, you realize that the vacuum must have a lot of energy. In fact, the energy is so great that it should have obliterated the universe from birth, but it didn’t happen. The universe has grown big and old. This is because the true vacuum energy is much lower than we expected. To retrieve the amount of cosmic acceleration we see through our telescopes, we need the vacuum energy to be 10(-120) times smaller than our theoretical prediction.

It sucks, doesn’t it? I’ve spent most of my career thinking about this problem. The universe had to know from the beginning that it would grow big and old. He must have had some degree of precognition.

3. A googolplex.

Maybe you have heard of a googol? It’s a 1 followed by a hundred zeros. Well, a googolplex is bigger: it’s a follow-up to a googolplex! To fully appreciate its size, consider a Googolplician universe. It is a universe that is a googolplex in meters, inches, or some other Earth-like unit.

“In a googolplician universe, your lookalike is over there, probably reading Book Bites.”

In a googolplician universe, you will find something remarkable: doppelgängers. Exact copies of me, you and everyone you know. I’m not just talking about look-alikes, but replicas, down to quantum DNA: same nose, same hair, same thoughts.

It all has to do with the number of different ways to fit together a human-sized volume of space. There is much less than a googolplex to do it. The reason has something to do with black hole physics. Anyway, one of these assemblages is for me, one for you, one for the empty space, etc. As you move through the Googoplician universe, seeing repetition is inevitable. There just aren’t enough arrangements available for it to be different every time.

In a googolplician universe, your doppelganger is there, probably reading Book Bites.

4. Graham’s number.

Think of a very large number and try to imagine it. Are you still here? If so, I’m pretty sure you didn’t think of Graham’s number, because if you did, you’d be dead.

Graham’s number is large. In fact, for a long time it was said to be the largest number ever to appear in a mathematical proof. Graham’s number isn’t just as big as a trillion, or even a googolplex. It’s a real leviathan. If you tried to imagine its decimal representation written out in full, digit by digit, your head would crumble into a black hole. This is a condition known as black hole head death and there is no known cure.

This happens because there is an insane amount of information in Graham’s number, and the information weighs. What if we tricked Justin Bieber by making him think of Graham’s Number? As the numbers of Graham’s number entered his brain, he gained mass. Eventually, there are so many that his brain starts to heat up and wants to explode. Assuming he can avoid this, what next? More numbers, more information, more weight. Eventually, he reaches a point where the only object capable of storing that much weight in a space the size of his head is a black hole.

“The hope is that one day we can understand what is really going on at the center of a black hole, and maybe, just perhapsat the time of creation.

Head-sized black holes are super dangerous. The problem is that the black hole’s surface is very close to the dreaded singularity lurking inside. This is where space and time become infinitely torn and twisted and the gravitational field becomes infinitely strong. If a Black Hole Bieber were accosted by a fan, the tides of gravity on its black hole head would tear the fan to shreds. Graham’s Number would be bad news for anyone obsessed with Justin Bieber.

5. Infinite.

Black Hole Biebers may sound fanciful, but black holes are unmistakably real, and within them lies the singularity – the place where spacetime touches infinity, where the gravitational field spirals out of control. This is where the physical world seems to be breaking down and our equations no longer make sense. You don’t just find singularities inside black holes. You also find them in the Big Bang, when you trace the universe back to the beginning of time.

To conquer these infinities, we need a quantum theory of gravity – a way of thinking about the strongest gravitational fields and how they interact with all the material world at the smallest of scales. We need a theory of everything.

That is, a theory where the building blocks of nature are not particles, but strings. Tiny little strings, wriggling and vibrating, constituting each of us, and space-time itself. These strings are expected to eliminate gravity infinities, and the hope is that one day we can use them to understand what’s really going on at the center of a black hole, and maybe, just perhaps, at the time of creation. At the genesis.

Thanks to the symphony of strings, we may one day know the thought of God.

To listen to the audio version read by author Antonio Padilla, download the Next Big Idea app today:

Hear key information in the next big idea app

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