Earth as a hard drive

What is the Earth's information storage capacity, and how full is it? The answer teaches us surprising things about how the level of order in the universe increases/Cesar A. Hidalgo

in brief

If we define information as an order and then calculate the amount of information our planet can hold, we find that the Earth's hard drive is mostly empty, despite billions of years of life and thousands of years of human cultural activity.
This mental exercise teaches us a lot about the formation of order in the universe. Although the universe is hostile to order, because its total entropy is always increasing, information increases over time.
Humans have a part in the growth of information on Earth, but we are still very limited in our ability to create order.

Seth Lloyd, a professor of quantum computing at the Massachusetts Institute of Technology (MIT), published in 2002 a formula that makes it possible to estimate the number of bits that the universe can contain. The word "bit" describes a basic unit of information that represents an answer to a "yes" or "no" question. A computer stores bits in transistors, but a bit can also be encoded in the physical state of a particle, for example the spin of an electron. The Lloyd formula uses the physics of information to gauge the rate at which physical systems are able to process information and store it. The estimate is calculated based on Planck's constant (an incredibly small quantity that is the basis of quantum mechanics), the speed of light and the age of the universe. Lloyd deduced that the universe could contain an enormous number of bits: 10 to the 90th power, or trillion trillion trillion trillion trillion trillion trillion megabits.

Lloyd developed his formula because his work on quantum computers, which use single atoms to encode information and perform calculations, led him to think of the universe in terms of bits held in atoms. He conducted a thought experiment when he asked himself: "What is the largest computer that will ever be built?" And the answer: a computer that will use every atom in the universe. A computer that can store 10 to the power of 90 bits.

But the beautiful thing about Lloyd's formula is its ability to be used to estimate the information capacity of any physical system, not necessarily the entire universe. Recently, I was inspired by Lloyd's formula while researching the computational capacity of economic economies and human societies. Lloyd's formula almost does not include the complexity inherent in our economies, but it allows us a rough estimate of the capacity of systems for storing information and processing it. We will therefore think of the Earth as a hard drive. According to Lloyd's formula, our planet is capable of storing 10 to the 56-bit power, a trillion trillion trillion trillion gigabit, approximately. But is this planetary hard drive mostly empty or almost full?

To answer this question, we turn to the studies of Martin Hilbert and Priscilla Lopez. In 2011, when Hilbert was working at the University of Southern California and López at the University of Catalonia in Spain, they published an estimate of the amount of cultural information stored in texts, images and films found in the world. They estimated that by 2007 humans had accumulated 2 to the 10th power of 21 bits, or two trillion gigabits. But there is much more information on our planet than is contained in the products of culture. Information is also embodied in objects that humans have designed and built, such as our cars and shoes, and in biological systems, such as ribosomes, mitochondria and DNA. Indeed, it turns out that most of the information that the earth contains will be stored in the biological mass. According to Lloyd's formula, I estimate that the Earth actually contains about 10 to the 44-bit power. The number may seem large, but it is a tiny fraction of its information capacity. If humans continue to create 10 to the 21 bits every year, it will still take a trillion times longer than the age of the universe to fill our planetary hard drive.

What these calculations teach us is that although the Earth has a tremendous capacity to store information, order is still a rare commodity. This insight, in turn, teaches us a lot about the way the earth creates information and processes it and the obstacles that may limit the growth of the order in the future.

The Computational Universe

The first thing that the emptiness of information on our planet reveals is that information is difficult to grow: it is difficult to produce it, it is difficult to maintain it and it is challenging to combine it into new configurations. This difficulty fits well with observations from the past and can be explained by the hostility that the universe shows towards the appearance of an order. According to the second law of thermodynamics the universe has a natural tendency towards the medium, a tendency which eliminates order. Heat energy flows from a hot place to a cold place, music fades and disappears as it passes through the air and the swirls in your upside-down coffee quickly dissipate into milky clouds. This transition from order to disorder is known as an increase in entropy.

And yet, there are loopholes in this trend that allow pockets of order to appear. Think of a biological cell, the human body or an economy built by humans. These systems are highly organized and defeat the physical increase in entropy, albeit only locally. Information-rich systems can exist only if they "emit" entropy at their edges, only if they pay for their high level of organization through heat dissipation. As the Nobel laureate chemist Ilya Prigozhin wisely put it: "Entropy is the price of organization."

There are three tricks in our universe that allow order to appear or be preserved. The first, and perhaps the most familiar, is related to the flow of energy. Imagine a bathtub full of water: water molecules splash from each other in all directions randomly until you remove the stopper. As soon as the water starts racing towards the drainage point, and the kinetic energy of the liquid increases, a vortex appears. Within this vortex, order is fulfilled: each molecule in the vortex has a speed similar to that of its neighbors, both in the magnitude of the speed and in its direction. This correspondence is the primordial source of macroscopic information. To understand the durability of information, and not just its formation, we need the second trick: the existence of solid materials. Solid objects, like DNA, preserve order for a long time. Without them the information would be too fluid to last, connect and grow.
But in order to explain the emergence of more complex forms of order (such as the information inherent in a city or economy) or the formation of order that led to the existence of life and societies on Earth, we need the third trick: the ability of matter to calculate. A tree, for example, is a computer that knows which direction to grow its roots and on it. Trees know when to turn certain genes on or off to fight parasites, when to shrivel and when to singe leaves and how to harvest carbon dioxide from the air through photosynthesis. As computers, trees give birth to order in the macroscopic structure of their branches and the microscopic structure of their cells. Most of the time we don't see trees as computers, but in fact the trees contribute to the growth of information on our planet precisely because they make calculations.

A cohesive imagination

We can learn another, more surprising thing from thinking of our planet as a hard drive: despite the forces arrayed against the emergence of order, information gradually grows. The Earth's hard drive is more full today than it was yesterday or a billion years ago. In part, it is fuller because life has appeared on it: the biological mass contains a great deal of information. But the growth of order in the world also results from the production of cultural information.

To understand why, we will examine the difference between apples that grow on the trees and between the "apples", i.e. the Apple iPhones, which some of us carry in their pockets to check email messages. For our purposes, we are only interested in the origin of the physical order inherent in any object. The first apple embodies an order that existed in the world before humans appeared in it. Apples existed before they had a name, price or market. The iPhone is different because it is an object that first existed in someone's mind, and only then in the real world. This is a solid piece of order that first appeared as something imaginary. As we will see later, objects of this type are unique.

Biological species that are able to imagine objects and then create them have advantages over other animals. The real, yet imaginary objects that are common in our economy empower us because they give us access to the skills and practical uses of the knowledge embedded in other people's nervous systems. Most people use toothpaste every day, but they don't know how to produce sodium fluoride, the active ingredient in toothpaste. However, the lack of this knowledge does not prevent them from enjoying the practical uses arising from the understanding required to produce sodium fluoride. People make practical use of the knowledge of others through products, which are, in effect, solid pieces of imagination. Products empower us and markets make us not only richer, but also smarter.

The problem is that it's hard to create products. This often requires the cooperation of many people. To contribute to the growth of information, people must create networks among themselves capable of calculating products. We need networks because the computational capacity of systems, as well as their information storage capacity, has a limit. Biological cells are limited computers that transcend their limitations through multicellularity. Humans also have limitations, and we transcend our finite computational capacities through social and professional networks. Economic farms are decentralized computers that operate using the hardware known to us as social networks. Ultimately, it is the re-incarnation of computation, fitting humans into economic economies, that allows complex forms of information to grow, but it also makes it challenging.

Growth limits

The last thing this thought experiment teaches us is that the ability of human networks to generate information is a very limited ability. Forget everything you've heard about big data: from a cosmic perspective, we create an incredibly small amount of information (even if during this production we use enough energy to release the carbon dioxide that warms our planet).

Our ability to create information is limited in part because our ability to create networks of humans is limited by historical, organizational, or technological constraints. Language barriers, for example, fragment our global society and make it difficult for people born in distant parts of the world to connect. Technological forces may help lower these obstacles. The development of flights and long-distance means of communication lowered the price of long-distance connections. This allows us to weave very global networks that increase our information processing capacity. However, these technologies are not a panacea. Our ability to process information together may be greater than it was in previous decades, but it is still small.

How, then, will the growth of information on Earth develop in the coming centuries? According to the optimistic view, the forces of technological globalization and the fall of narrow social institutions, such as patriotism and religion, will help erode the historical differences that continue to spread hatred between people of different backgrounds of language, ethnicity, religion and nationality. And at the same time, the technological changes will bring an era of hyper-connectivity. Electronics, which will evolve from portable devices to wearable devices to implanted devices, will yield new forms of mediated social interactions.

For thousands of years, our biological species' ability to produce information has been fueled by our ability to embed that information in the environment, whether through assembling stone axes or writing epic poetry. This talent provided us with the upgrade and coordination needed to increase our computational capacity. We are now in the midst of a new revolution that may change this dynamic and increase its power even more. In the current millennium, man and machine will unite through devices that will merge the biological computers that reside between our ears with the digital machines that have emerged from our curious minds. The hyper-connected society that will result from this will present our species with some of the most difficult moral challenges in human history. We may lose some aspects of our humanity that some consider essential: for example, we may escape death. But this merger, between our bodies and the information processing machines born from our imaginations, may be the only way to increase information even more. We were born from information, and now, information is born from us at an increasing rate.