# The benefits of ‘deep time thinking’

Richard Fisher

17-21 minutes

(Image credit: Adam Proctor)

Artist Katie Paterson pours a crushed fossil millions of years old (Credit: Adam Proctor)

Extending the mind into million-year timescales can feel daunting, but as Richard Fisher discovered, there are many benefits to be found by embracing a longer view.

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In 1788, three men set off to search a stretch of coast in eastern Scotland, looking for a very special outcrop of rocks. It would reveal that Earth was far, far older than anybody thought.

Leading the party was James Hutton, one of the first geologists. His goal was to show his peers an “unconformity” – two juxtaposing rock layers, separated by a sharp line.

If you stumbled on one, you might not recognise its significance, but it proved that aeons of “deep time” had passed before humans emerged on Earth. There was no other way to explain these features.

Hutton’s unconformity (yellow) at Siccar Point, which he reasoned must have taken millions of years to form (Credit: Adam Proctor)

Hutton’s unconformity (yellow) at Siccar Point, which he reasoned must have taken millions of years to form (Credit: Adam Proctor)

For centuries, the Biblical account of time had been dominant in Europe. By one analysis of the generations in the Old Testament, conducted by an archbishop in 1650, the Earth must have been created in 4004BC.

Hutton, however, would transform that view.

His companions to Siccar Point, east Scotland, in 1788 were astonished. As one of them wrote afterwards: “The mind seemed to grow giddy by looking so far back into the abyss of time. And while we listened with earnestness and admiration to the philosopher who was now unfolding to us the order and series of these wonderful events, we became sensible how much further reason may sometimes go than imagination may venture to follow.”

The insight would be one of geology’s most transformational contributions to human thought, allowing us to “burst the limits of time”, as one eminent scientist later put it. Time, according to Hutton, had “no vestige of a beginning, no prospect of an end”.

Looking down at Hutton’s Unconformity, on an “Anthropocene coast” (Credit: Adam Proctor)

Looking down at Hutton’s Unconformity, on an “Anthropocene coast” (Credit: Adam Proctor)

The discovery of deep time would change how we see the world. Not only did it rewrite the Biblical account of time, it would provide the canvas for the theory of evolution. Later, it would help astronomers to show that the Earth itself was relatively young compared with the age of Universe.

For the past few years, I have been writing and researching about how to take a longer view. To help me understand the mind-expanding scope of deep time, I recently set out to make three films for the BBC about its discovery and implications – starting with a trip to Hutton’s unconformity.

Looking back to the past, how did Hutton’s discovery change the world? How might we make sense of deep time’s daunting scale in the present? And how should we think about the deep future?

Watch all three as a playlist on BBC Reel or further down this page.

In the first of the films, I traced the steps of Hutton and his companions to the unconformity at Siccar Point.

In the 18th Century, the three men used a boat to get there, but I chose to hike there with David Farrier, a professor of literature and the environment at the University of Edinburgh. As the author of the book Footprints, which is about the “future fossils” we are leaving behind in the Anthropocene, he was the ideal companion. Why? As we’d discover, this particular stretch of coastline is now notable for more than its natural features: it also hosts a nuclear power station and a carbon-intensive cement works, whose own legacies will continue long into the future.

Later, I also met musician Karine Polwart, who – during the Covid-19 pandemic – was inspired to record a song about Hutton’s discovery at Siccar Point.

WATCH:

The man who discovered the abyss of time

In the second film, I wanted to explore how we might make sense of the awe-inspiring scale of deep time today – and crucially, not just with the lens of science alone.

When I reflect on how short my own lifespan is within the million-year chronologies of the Earth, it can feel pretty daunting. From the planet’s perspective, our lives are momentary flashes of light on the surface of a lake; briefly bright, but quickly gone. Thinking about deep time can therefore be a sublime experience: astonishing, but tinged with the awareness of your own mortality.

One person who has spent a career thinking about deep time is the artist Katie Paterson. Through her artworks, she makes long-term timescales more accessible, more comprehensible, more human.

In the film, I visited two of her projects: the Future Library in Norway, which contains books that can’t be read until 2114, and Requiem, which tells the story of the Earth and humanity through 34 vials of dust, from pre-solar grains to a crushed tree branch from the site of the Hiroshima atomic bomb.

Paterson’s work helps to make the long view of deep time a little bit easier to comprehend – as well as providing clarity and urgency about the role that our generation is playing within it.

WATCH:

The art of thinking in ‘deep time’

Finally, in the third film, I reflected on our personal, generational connections across long-term time: not just to the past, but the deep future too.

When I daydream about the life that could lie ahead for my daughter Grace, I realise that she stands a pretty good chance of seeing the 22nd Century. Born in 2013, she would be 86 years old when 2100 arrives. If she has grandchildren or great-grandchildren, they might even reach the next century after that.

Through our family ties, we are far closer to seemingly distant dates in time than first appears – and we have a surprising amount in common with one another in terms of our ancestry too. As the film explores, you don’t even need to have children to figure in this deep time narrative, and your actions today will reach far further across time than you might realise.

WATCH:

The 22nd Century people living among us

Making these films, I realised that deep time needn’t be an impersonal, cold concept, and that there are benefits to be found by embracing a million-year view.

The writer John McPhee, who popularised the term in the 1980s, argued – perhaps pessimistically – that human beings may not be capable of grasping the concept of deep time to its full extent. “The human consciousness may have begun to leap and boil some sunny day in the Pleistocene, but the race by and large has retained the essence of its animal sense of time,” he wrote in his influential book Basin and Range. “People think in five generations – two ahead, two behind – with heavy concentration on the one in the middle. Possibly that is tragic, and possibly there is no choice.”

McPhee suggested that the units of years, the common currency of humanity’s temporal understanding, become ever-less useful and tractable once time becomes very big. “Numbers do not seem to work well with regard to deep time. Any number above a couple of thousand years – 50,000, 50 million – will with nearly equal effect awe the imagination to the point of paralysis,” he wrote.

‘Deep time gives me a kind of rootedness’ – Katie Paterson

However, while it is true that million-year chronologies may be beyond our direct sensory faculties, that doesn’t mean we cannot try to extend the mind over thousands, millions or even billions of years. And there could be upsides to doing so: a deep-time view can provide the kind of perspective that we need within the upheaval of the Anthropocene.

As Paterson told me when we met in Edinburgh: “It’s a mind-bending concept thinking about things that happened millions, billions of years into the past. And I can understand that some people might find that pretty difficult. Oddly, I never have. I’ve always just been absolutely delighted by this idea that we’ve got the capacity to know and understand or imagine what’s come before us. I find it really inspiring and eye-opening and moving, and it gives me a kind of rootedness.”

*Richard Fisher is the author of The Long View: Why We Need to Transform How the World Sees Time, and a senior journalist for BBC Future. Twitter: @rifish

The Deep Time films were filmed, edited and produced by Adam Proctor at Fortsunlight.

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The numbers that are too big to imagine

(Image credit: Emmanuel Lafont)

What’s the biggest number you can imagine? (Credit: Emmanuel Lafont)

When you move beyond trillions, there are some extremely mind-bending numbers, says Richard Fisher. Some of them are too large to fit in the mind – or even within the known Universe.

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What’s the biggest number you can think of? When I was a child, it’s the kind of question we’d ask each other in the school playground. Someone would say something hopelessly naïve like “a billion billion billion”, only to be outstripped by a peer who knew about trillions, squillions or kajillions (it didn’t matter if only one of those is real).

Eventually, someone would remember that they knew the winning answer: “infinity!” But the smugness was short-lived. Another kid – with a mathematical mic drop – soon pointed out that they could beat it, with “infinity… plus one”.

Trying to imagine and understand very big numbers, however, is more than just playground game. It’s a task that mathematicians have thought about for centuries. They’ve proposed the existence of numbers that are so enormous that no human being has ever successfully brought them to mind in full, let alone written them down. And as for infinity, it turns out there is more than one of those – and, counterintuitively, some infinities are bigger than others.

Immensities

This article is part of a BBC Future series called Immensities. Through stories from the worlds of science, philosophy, psychology and history, our goal is to see the world with fresh eyes: nature at its grandest, and the human world at its most awe-inspiring.

Let’s start with an obvious point that was lost on my 10-year-old self. There is no specific number you could describe as the biggest, since natural numbers are infinite. You can’t win the playground game.

However, that doesn’t mean that all the big numbers have been thought of, expressed, written down… or even represented by computers.

First let’s climb up the ladder of numbers directly beyond those used in day-to-day life. In news headlines, the biggest numbers – of national debt, for instance – tend to be expressed in the trillions. But there’s a hiererchy of ever-bigger numbers that come afterwards, the names of which rarely get mentioned. It starts with quadrillions, quintillions, sextillions and so on. A quadrillion (the US version) has 15 zeroes, a quintillion has 18, and a sextillion has 21.

Some numbers are so enormous they cannot be conceived of in the mind (Credit: Emmanuel Lafont)

Some numbers are so enormous they cannot be conceived of in the mind (Credit: Emmanuel Lafont)

These numbers are enormous. The human body has around 30 trillion cells – so to get a quadrillion cells in a room, you’d need 34 people. And quintillions only really come into play if you want to talk about, say, how many insects there are on Earth (around 10 quintillion). The number sextillion, meanwhile, is so big that a tower of sextillion people would be 180,000 light years tall – bigger than the diameter of the Milky Way.

You can keep going up to a centillion, which has 303 zeroes in the US version (and beyond, with duocentillion, trecentillion, but these are less standardised). Realistically, only physicists and mathematicians would have much use for a centillion, and even then, only in specialist fields like string theory. If Elon Musk wanted to become a centillionaire, he would have to earn his current wealth every millisecond for the next 1.7 x 10^282 years – a number 283 digits long.

Googols and googol plexes

Another big number, which is not as big as a US centillion, but perhaps better-known, is a googol. This a one followed by 100 zeroes – 10^100, and also happens to have provided the inspiration for a well-known search engine. Google’s founders were drawn to it because it gave a nod to the vast amount of information found online. However, so far the internet isn’t anywhere near that big: to date, the Internet Archive’s Wayback Machine has indexed only 801 billion web pages since the 1990s.

It’s possible to supercharge a googol by making it into a googol plex (the name of Google’s California headquarters.) This number is 10 to the power of a googol – or 10 to the power of 10 to the power of 100.

To get my head around just how big this is, I spoke with the mathematician Joel David Hamkins of the University of Notre Dame in the US, who writes a newsletter about enormous numbers and infinity called Infinitely More.

A googol plex, he explains, is a one followed by a googol number of zeroes. How long would it take you to write that down? Well, you certainly couldn’t do it in your own lifetime, even if you started when you first picked up a pencil as a child.

To get a handle on just how many digits we’re talking about, Hamkins proposes the following thought experiment:

“Suppose that I gave you this printing device: a super-fast printer that would print numbers, and let’s suppose, for example, it could print a million digits every second,” he says. Now imagine it began printing at the beginning of the Universe, 13.8 billion years ago – or 10^18 seconds. “Even if you’re printing a million digits every second, if you let this thing go from the beginning of time, from the Big Bang, you wouldn’t even be close, you would have just the tiniest fraction of a googol plex.”

Counterintuitively. some infinities are larger than others (Credit: Emmanuel Lafont)

Counterintuitively. some infinities are larger than others (Credit: Emmanuel Lafont)

Hamkins also points out something intriguing – there are large numbers smaller than a googol plex that cannot be reduced to a simpler notation or a single word, and therefore are “fundamentally beyond our comprehension”. They’ve never been imagined or expressed.

“The only way to say what those numbers are is to say their digits. But even if you printed a million digits every second, since the beginning of time, you wouldn’t be able to say those numbers,” he says. “So this is an interesting situation, because it means that we have simple descriptions of enormous numbers, but lots of numbers in between are extremely difficult to describe. There are milestone numbers that are simple in terms of their descriptive complexity, but there are these oceans of complexity between them.”

Even if you printed a million digits every second, since the beginning of time, you wouldn’t be able to say those numbers

However, mathematicians have described numbers even bigger than a googol plex. The most famous is Graham’s number.

Conceived of in the 1970s, the mathematician Ronald Graham used it as part of a mathematical proof. He proposed it to solve a problem in a branch of mathematics called Ramsey theory, which deals with how to find order in chaos.

Understanding the maths behind it is a little involved, but the main thing to know is that creating it involves exponentiation to a truly brain-shattering degree. Graham himself explains why in this video for the mathematics YouTube channel Numberphile.

Oh, and you should also know that even if you did try to write it down on paper, there wouldn’t be enough room in the visible Universe to fit it in.

You may also be interested in:

What the way you count reveals about you

The remarkable ways animals understand numbers

The attack that turned a man into a maths genius

What about infinity though? For the average person, infinity seems a straightforward concept – it’s not a number, rather something that goes on forever. Whether the human mind is capable of truly understanding it, however, is another question.

In the 1700s, the writer and philosopher Edmund Burke wrote that “infinity has a tendency to fill the mind with that sort of delightful horror which is the most genuine effect and truest test of the sublime”. For Burke, the concept evoked a mixture of astonishment and fear; pleasure and pain, both at the same time. And there were few times that people would ever encounter it in the world, apart from in the imagination, and even then they could not truly know it.

However, the following century, the logician Georg Cantor took the concept of infinity and made it even more mind-bending. Some infinities, he showed, are bigger than others.

How so? To understand why, consider the numbers as ‘sets’. If you were to compare all natural numbers (1, 2, 3, 4, and so on) in one set, and all the even numbers in another set, then every natural number could in principle be paired with a corresponding even number. This pairing suggests the two sets – both infinite – are the same size. They are ‘countably infinite’.

However, Cantor showed that you can’t do the same with the natural numbers and the ‘real’ numbers – the continuum of numbers with decimal places between 1, 2, 3, 4 (0.123, 0.1234, 0.12345 and so on.)

If you attempted to pair up the numbers within each set, you could always find a real number that does not match up with a natural number. Real numbers are uncountably infinite. Therefore, there must be multiple sizes of infinity.

This is hard to accept, let alone picture, but that’s what happens to the mind when it tries to grapple with mathematical enormity. Such enormous numbers are a great deal more difficult to understand than a 10-year-old me could ever have imagined.

*Richard Fisher is a senior journalist for BBC Future. Twitter: @rifish

The author used ChatGPT to research trusted sources and calculate parts of this story. For the sake of clarity, BBC Future does not use generative AI as a primary source or to replace the journalism needed for our articles.

Update 21 March: The explanation of multiple infinities has been corrected to describe Cantor’s proof about real vs natural numbers.

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