# Tag: Nature

## Power Laws: How Nonlinear Relationships Amplify Results

### “The greatest shortcoming of the human race is our inability to understand the exponential function.”

— Albert Allen Bartlett

## Defining A Power Law

Consider a person who begins weightlifting for the first time.

During their initial sessions, they can lift only a small amount of weight. But as they invest more time, they find that for each training session, their strength increases a surprising amount.

For a while, they make huge improvements. Eventually, however, their progress slows down. At first, they could increase their strength by as much as 10% per session; now it takes months to improve by even 1%. Perhaps they resort to taking performance-enhancing drugs or training more often. Their motivation is sapped and they find themselves getting injured, without any real change in the amount of weight they can lift.

Now, let’s imagine that our frustrated weightlifter decides to take up running instead. Something similar happens. While the first few runs are incredibly difficult, the person’s endurance increases rapidly with the passing of each week, until it levels off and diminishing returns set in again.

Both of these situations are examples of power laws — a relationship between two things in which a change in one thing can lead to a large change in the other, regardless of the initial quantities. In both of our examples, a small investment of time in the beginning of the endeavor leads to a large increase in performance.

Power laws are interesting because they reveal surprising correlations between disparate factors. As a mental model, power laws are versatile, with numerous applications in different fields of knowledge.

If parts of this post look intimidating to non-mathematicians, bear with us. Understanding the math behind power laws is worthwhile in order to grasp their many applications. Invest a little time in reading this and reap the value — which is in itself an example of a power law!

A power law is often represented by an equation with an exponent:

Y=MX^B

Each letter represents a number. Y is a function (the result); X is the variable (the thing you can change); B is the order of scaling (the exponent); and M is a constant (unchanging).

If M is equal to 1, the equation is then Y=X^B. If B=2, the equation becomes Y=X^2 (Y=X squared). If X is 1, Y is also 1. But if X=2, then Y=4; if X=3, then Y=9, and so on. A small change in the value of X leads to a proportionally large change in the value of Y.

B=1 is known as the linear scaling law.

To double a cake recipe, you need twice as much flour. To drive twice as far will take twice as long. (Unless you have kids, in which case you need to factor in bathroom breaks that seemingly have little to do with distance.) Linear relationships, in which twice-as-big requires twice-as-much, are simple and intuitive.

Nonlinear relationships are more complicated. In these cases, you don’t need twice as much of the original value to get twice the increase in some measurable characteristic. For example, an animal that’s twice our size requires only about 75% more food than we do. This means that on a per-unit-of-size basis, larger animals are more energy efficient than smaller ones. As animals get bigger, the energy required to support each unit decreases.

One of the characteristics of a complex system is that the behavior of the system differs from the simple addition of its parts. This characteristic is called emergent behavior. “In many instances,” write Geoffrey West in Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies, “the whole seems to take on a life of its own, almost dissociated from the specific characteristics of its individual building blocks.”

This collective outcome, in which a system manifests significantly different characteristics from those resulting from simply adding up all of the contributions of its individual constituent parts, is called an emergent behavior.

When we set out to understand a complex system, our intuition tells us to break it down into its component pieces. But that’s linear thinking, and it explains why so much of our thinking about complexity falls short. Small changes in a complex system can cause sudden and large changes. Small changes cause cascades among the connected parts, like knocking over the first domino in a long row.

Let’s return to the example of our hypothetical weightlifter-turned-runner. As they put in more time on the road, constraints will naturally arise on their progress.

Recall our exponential equation: Y=MX^B. Try applying it to the runner. (We’re going to simplify running, but stick with it.)

Y is the distance the runner can run before becoming exhausted. That’s what we’re trying to calculate. M, the constant, represents their running ability: some combination of their natural endowment and their training history. (Think of it this way: Olympic champion Usain Bolt has a high M; film director Woody Allen has a low M.)

That leaves us with the final term: X^B. The variable X represents the thing we have control over: in this case, our training mileage. If B, the exponent, is between 0 and 1, then the relationship between X and Y— between training mileage and endurance — becomes progressively less proportional. All it takes is plugging in a few numbers to see the effect.

Let’s set M to 1 for the sake of simplicity. If B=0.5 and X=4, then Y=2. Four miles on the road gives the athlete the ability to run two miles at a clip.

Increase X to 16, and Y increases only to 4. The runner has to put in four times the road mileage to merely double their running endurance.

Here’s the kicker: With both running and weightlifting, as we increase X, we’re likely to see the exponent, B, decline! Quadrupling our training mileage from 16 to 64 miles is unlikely to double our endurance again. It might take a 10x increase in mileage to do that. Eventually, the ratio of training mileage to endurance will become nearly infinite.

We know this state, of course, as diminishing returns: the point where more input yields progressively less output. Not only is the relationship between training mileage and endurance not linear to begin with, but it also gets less linear as we increase our training.

It gets even more interesting. If B=−0.5 and X=4, then Y=0.5. Four miles on the road gets us a half-mile of endurance. If X is increased to 16, Y declines to 0.25. More training, less endurance! This is akin to someone putting in way too much mileage, way too soon: the training is less than useful as injuries pile up.

With negative numbers, the more X increases, the more Y shrinks. This relationship is known as an inverse power law. B=−2, for example, is known as the inverse square law and is an important equation in physics.

The relationship between gravity and distance follows an inverse power law. G is the gravitational constant; it’s the constant in Newton's law of gravitation, relating gravity to the masses and separation of particles, equal to:

6.67 × 10−11 N m2 kg−2

Any force radiating from a single point — including heat, light intensity, and magnetic and electrical forces — follows the inverse square law. At 1m away from a fire, 4 times as much heat is felt as at 2m, and so on.

## Higher Order Power Laws

When B is a positive integer (a whole number larger than zero), there are names for the power laws.

When B is equal to 1, we have a linear relationship, as we discussed above. This is also known as a first-order power law.

Things really get interesting after that.

When B is 2, we have a second-order power law. A great example of this is kinetic energy. Kinetic energy = 1/2 mv^2

When B is 3, we have a third-order power law. An example of this is the power converted from wind into rotational energy.

Power Available = ½ (Air Density)( πr^2)(Windspeed^3)(Power Coefficient)

(There is a natural limit here. Albert Betz concluded in 1919 that wind turbines cannot convert more than 59.3% of the kinetic energy of the wind into mechanical energy. This number is called the Betz Limit and represents the power coefficient above.)[1]

The law of heat radiation is a fourth-order power law. Derived first by the Austrian physicist Josef Stefan in 1879 and separately by Austrian physicist Ludwig Boltzmann, the law works like this: the radiant heat energy emitted from a unit area in one second is equal to the constant of proportionality (the Stefan-Boltzmann constant) times the absolute temperature to the fourth power.[2]

There is only one power law with a variable exponent, and it’s considered to be one of the most powerful forces in the universe. It’s also the most misunderstood. We call it compounding. The formula looks like this:

Future Value = (Present Value)(1+i)^n

where i is the interest rate and n is the number of years.

Unlike in the other equations, the relationship between X and Y is potentially limitless. As long as B is positive, Y will increase as X does.

Non-integer power laws (where B is a fraction, as with our running example above) are also of great use to physicists. Formulas in which B=0.5 are common.

Imagine a car driving at a certain speed. A non-integer power law applies. V is the speed of the car, P is the petrol burnt per second to reach that speed, and A is the air resistance. For the car to go twice as fast, it must use 4 times as much petrol, and to go 3 times as fast, it must use 9 times as much petrol. Air resistance increases as speed increases, and that is why faster cars use such ridiculous amounts of petrol. It might seem logical to think that a car going from 40 miles an hour to 50 miles an hour would use a quarter more fuel. That is incorrect, though, because the relationship between air resistance and speed is itself a power law.

Another instance of a power law is the area of a square. Double the length of two parallel sides and the area quadruples. Do the same for a 3D cube and the area increases by a factor of eight. It doesn’t matter if the length of the square went from 1cm to 2cm, or from 100m to 200m; the area still quadruples. We are all familiar with second-order (or square) power laws. This name comes from squares, since the relationship between length and area reflect the way second-order power laws change a number. Third-order (or cubic) power laws are likewise named due to their relationship to cubes.

## Using Power Laws in Our Lives

Now that we’ve gotten through the complicated part, let’s take a look at how power laws crop up in many fields of knowledge. Most careers involve an understanding of them, even if it might not be so obvious.

### “What's the most powerful force in the universe? Compound interest. It builds on itself. Over time, a small amount of money becomes a large amount of money. Persistence is similar. A little bit improves performance, which encourages greater persistence which improves persistence even more. And on and on it goes.”

— Daniel H. Pink, The Adventures of Johnny Bunko

The Power Behind Compounding

Compounding is one of our most important mental models and is absolutely vital to understand for investing, personal development, learning, and other crucial areas of life.

In economics, we calculate compound interest by using an equation with these variables: P is the original sum of money. P’ is the resulting sum of money, r is the annual interest rate, n is the compounding frequency, and t is the length of time. Using an equation, we can illustrate the power of compounding.

If a person deposits \$1000 in a bank for five years, at a quarterly interest rate of 4%, the equation becomes this:

Future Value = Present Value * ((1 + Quarterly Interest Rate) ^ Number of Quarters)

This formula can be used to calculate how much money will be in the account after five years. The answer is \$2,220.20.

Compound interest is a power law because the relationship between the amount of time a sum of money is left in an account and the amount accumulated at the end is non-linear.

In A Random Walk Down Wall Street, Burton Malkiel gives the example of two brothers, William and James. Beginning at age 20 and stopping at age 40, William invests \$4,000 per year. Meanwhile, James invests the same amount per year between the ages of 40 and 65. By the time William is 65, he has invested less money than his brother, but has allowed it to compound for 25 years. As a result, when both brothers retire, William has 600% more money than James — a gap of \$2 million. One of the smartest financial choices we can make is to start saving as early as possible: by harnessing power laws, we increase the exponent as much as possible.

Compound interest can help us achieve financial freedom and wealth, without the need for a large annual income. Members of the financial independence movement (such as the blogger Mr. Money Mustache) are living examples of how we can apply power laws to our lives.

As far back as the 1800s, Robert G. Ingersoll emphasized the importance of compound interest:

One dollar at compound interest, at twenty-four per cent., for one hundred years, would produce a sum equal to our national debt. Interest eats night and day, and the more it eats the hungrier it grows. The farmer in debt, lying awake at night, can, if he listens, hear it gnaw. If he owes nothing, he can hear his corn grow. Get out of debt as soon as possible. You have supported idle avarice and lazy economy long enough.

Compounding can apply to areas beyond finance — personal development, health, learning, relationships and more. For each area, a small input can lead to a large output, and the results build upon themselves.

Nonlinear Language Learning

When we learn a new language, it’s always a good idea to start by learning the 100 or so most used words.

In all known languages, a small percentage of words make up the majority of usage. This is known as Zipf’s law, after George Kingsley Zipf, who first identified the phenomenon. The most used word in a language may make up as much as 7% of all words used, while the second-most-used word is used half as much, and so on. As few as 135 words can together form half of a language (as used by native speakers).

Why Zipf’s law holds true is unknown, although the concept is logical. Many languages include a large number of specialist terms that are rarely needed (including legal or anatomy terms). A small change in the frequency ranking of a word means a huge change in its usefulness.

Understanding Zipf’s law is a central component of accelerated language learning. Each new word we learn from the most common 100 words will have a huge impact on our ability to communicate. As we learn less-common words, diminishing returns set in. If each word in a language were listed in order of frequency of usage, the further we moved down the list, the less useful a word would be.

Power Laws in Business, Explained by Peter Thiel

Peter Thiel, the founder of PayPal (as well as an early investor in Facebook and Palantir), considers power laws to be a crucial concept for all businesspeople to understand. In his fantastic book, Zero to One, Thiel writes:

Indeed, the single most powerful pattern I have noticed is that successful people find value in unexpected places, and they do this by thinking about business from first principles instead of formulas.

And:

In 1906, economist Vilfredo Pareto discovered what became the “Pareto Principle,” or the 80-20 rule, when he noticed that 20% of the people owned 80% of the land in Italy—a phenomenon that he found just as natural as the fact that 20% of the peapods in his garden produced 80% of the peas. This extraordinarily stark pattern, when a small few radically outstrip all rivals, surrounds us everywhere in the natural and social world. The most destructive earthquakes are many times more powerful than all smaller earthquakes combined. The biggest cities dwarf all mere towns put together. And monopoly businesses capture more value than millions of undifferentiated competitors. Whatever Einstein did or didn’t say, the power law—so named because exponential equations describe severely unequal distributions—is the law of the universe. It defines our surroundings so completely that we usually don’t even see it.

… [I]n venture capital, where investors try to profit from exponential growth in early-stage companies, a few companies attain exponentially greater value than all others. … [W]e don’t live in a normal world; we live under a power law.

The biggest secret in venture capital is that the best investment in a successful fund equals or outperforms the entire rest of the fund combined.

This implies two very strange rules for VCs. First, only invest in companies that have the potential to return the value of the entire fund. … This leads to rule number two: because rule number one is so restrictive, there can’t be any other rules.

…[L]ife is not a portfolio: not for a startup founder, and not for any individual. An entrepreneur cannot “diversify” herself; you cannot run dozens of companies at the same time and then hope that one of them works out well. Less obvious but just as important, an individual cannot diversify his own life by keeping dozens of equally possible careers in ready reserve.

Thiel teaches a class called Startup at Stanford, where he hammers home the value of understanding power laws. In his class, he imparts copious wisdom. From Blake Masters’ notes on Class 7:

Consider a prototypical successful venture fund. A number of investments go to zero over a period of time. Those tend to happen earlier rather than later. The investments that succeed do so on some sort of exponential curve. Sum it over the life of a portfolio and you get a J curve. Early investments fail. You have to pay management fees. But then the exponential growth takes place, at least in theory. Since you start out underwater, the big question is when you make it above the water line. A lot of funds never get there.

To answer that big question you have to ask another: what does the distribution of returns in [a] venture fund look like? The naïve response is just to rank companies from best to worst according to their return in multiple of dollars invested. People tend to group investments into three buckets. The bad companies go to zero. The mediocre ones do maybe 1x, so you don’t lose much or gain much. And then the great companies do maybe 3-10x.

But that model misses the key insight that actual returns are incredibly skewed. The more a VC understands this skew pattern, the better the VC. Bad VCs tend to think the dashed line is flat, i.e. that all companies are created equal, and some just fail, spin wheels, or grow. In reality you get a power law distribution.

Thiel explains how investors can apply the mental model of power laws (more from Masters’ notes on Class 7):

…Given a big power law distribution, you want to be fairly concentrated. … There just aren’t that many businesses that you can have the requisite high degree of conviction about. A better model is to invest in maybe 7 or 8 promising companies from which you think you can get a 10x return. …

Despite being rooted in middle school math, exponential thinking is hard. We live in a world where we normally don’t experience anything exponentially. Our general life experience is pretty linear. We vastly underestimate exponential things.

He also cautions against over-relying on power laws as a strategy (an assertion that should be kept in mind for all mental models). From Masters’ notes:

One shouldn’t be mechanical about this heuristic, or treat it as some immutable investment strategy. But it actually checks out pretty well, so at the very least it compels you to think about power law distribution.

Understanding exponents and power law distributions isn’t just about understanding VC. There are important personal applications too. Many things, such as key life decisions or starting businesses, also result in similar distributions.

Thiel then explains why founders should focus on one key revenue stream, rather than trying to build multiple equal ones:

Even within an individual business, there is probably a sort of power law as to what’s going to drive it. It’s troubling if a startup insists that it’s going to make money in many different ways. The power law distribution on revenues says that one source of revenue will dominate everything else.

For example, if you’re an entrepreneur who opens a coffee shop, you’ll have a lot of ways you can make money. You can sell coffee, cakes, paintings, merchandise, and more. But each of those things will not contribute to your success in an equal way. While there is value in the discovery process, once you’ve found the variable that matters most, you should place more time on that one and less on the others. The importance of finding this variable cannot be overstated.

He also acknowledges that power laws are one of the great secrets of investing success. From Masters’ notes on Class 11:

On one level, the anti-competition, power law, and distribution secrets are all secrets about nature. But they’re also secrets hidden by people. That is crucial to remember. Suppose you’re doing an experiment in a lab. You’re trying to figure out a natural secret. But every night another person comes into the lab and messes with your results. You won’t understand what’s going on if you confine your thinking to the nature side of things. It’s not enough to find an interesting experiment and try to do it. You have to understand the human piece too.

… We know that, per the power law secret, companies are not evenly distributed. The distribution tends to be bimodal; there are some great ones, and then there are a lot of ones that don’t really work at all. But understanding this isn’t enough. There is a big difference between understanding the power law secret in theory and being able to apply it in practice.

The key to all mental models is knowing the facts and being able to use the concept. As George Box said, “all models are false but some are useful.” Once we grasp the basics, the best next step is to start figuring out how to apply it.

The metaphor of an unseen person sabotaging laboratory results is an excellent metaphor for how cognitive biases and shortcuts cloud our judgement.

Natural Power Laws

Anyone who has kept a lot of pets will have noticed the link between an animal’s size and its lifespan. Small animals, like mice and hamsters, tend to live for a year or two. Larger ones, like dogs and cats, can live to 10-20 years, or even older in rare cases. Scaling up even more, some whales can live for 200 years. This comes down to power laws.

Biologists have found clear links between an animal’s size and its metabolism. Kleiber’s law (identified by Max Kleiber) states that an animal’s metabolic rate increases at three-fourths of the power of the animal’s weight (mass). If an average rabbit (2 kg) weighs one hundred times as much as an average mouse (20g), the rabbit’s metabolic rate will be 32 times the mouse’s. In other words, the rabbit’s structure is more efficient. It all comes down to the geometry behind their mass.

Which leads us to another biological power law: Smaller animals require more energy per gram of body weight, meaning that mice eat around half their body weight in dense foods each day. The reason is that, in terms of percentage of mass, larger animals have more structure (bones, etc.) and fewer reserves (fat stores).

Research has illustrated how power laws apply to blood circulation in animals. The end units through which oxygen, water, and nutrients enter cells from the bloodstream are the same size in all animals. Only the number per animal varies. The relationship between the total area of these units and the size of the animal is a third-order power law. The distance blood travels to enter cells and the actual volume of blood are also subject to power laws.

## The Law of Diminishing Returns

As we have seen, a small change in one area can lead to a huge change in another. However, past a certain point, diminishing returns set in and more is worse. Working an hour extra per day might mean more gets done, whereas working three extra hours is likely to lead to less getting done due to exhaustion. Going from a sedentary lifestyle to running two days a week may result in greatly improved health, but stepping up to seven days a week will cause injuries. Overzealousness can turn a positive exponent into a negative exponent. For a busy restaurant, hiring an extra chef will mean that more people can be served, but hiring two new chefs might spoil the proverbial broth.

Perhaps the most underappreciated diminishing return, the one we never want to end up on the wrong side of, is the one between money and happiness.

In David and Goliath, Malcolm Gladwell discusses how diminishing returns relate to family incomes. Most people assume that the more money they make, the happier they and their families will be. This is true — up to a point. An income that’s too low to meet basic needs makes people miserable, leading to far more physical and mental health problems. A person who goes from earning \$30,000 a year to earning \$40,000 is likely to experience a dramatic boost in happiness. However, going from \$100,000 to \$110,000 leads to a negligible change in well-being.

The scholars who research happiness suggest that more money stops making people happier at a family income of around seventy-five thousand dollars a year. After that, what economists call “diminishing marginal returns” sets in. If your family makes seventy-five thousand and your neighbor makes a hundred thousand, that extra twenty-five thousand a year means that your neighbor can drive a nicer car and go out to eat slightly more often. But it doesn’t make your neighbor happier than you, or better equipped to do the thousands of small and large things that make for being a good parent.

###### Footnotes
• 1

http://www.raeng.org.uk/publications/other/23-wind-turbine

• 2

https://www.britannica.com/science/Stefan-Boltzmann-law

## Alexander von Humboldt and the Invention of Nature: Creating a Holistic View of the World Through A Web of Interdisciplinary Knowledge

In his piece in 2014’s Edge collection This Idea Must Die: Scientific Theories That Are Blocking Progress, dinosaur paleontologist Scott Sampson writes that science needs to “subjectify” nature. By “subjectify”, he essentially means to see ourselves connected with nature, and therefore care about it the same way we do the people with whom we are connected.

That's not the current approach. He argues: “One of the most prevalent ideas in science is that nature consists of objects. Of course, the very practice of science is grounded in objectivity. We objectify nature so that we can measure it, test it, and study it, with the ultimate goal of unraveling its secrets. Doing so typically requires reducing natural phenomena to their component parts.”

But this approach is ultimately failing us.

Why? Because much of our unsustainable behavior can be traced to a broken relationship with nature, a perspective that treats the nonhuman world as a realm of mindless, unfeeling objects. Sustainability will almost certainly depend upon developing mutually enhancing relations between humans and nonhuman nature.

This isn't a new plea, though. Over 200 years ago, the famous naturalist Alexander Von Humboldt (1769-1859) was facing the same challenges.

In her compelling book The Invention of Nature: Alexander Von Humboldt’s New World, Andrea Wulf explores Humboldt as the first person to publish works promoting a holistic view of nature, arguing that nature could only be understood in relation to the subjectivity of experiencing it.

Fascinated by scientific instruments, measurements and observations, he was driven by a sense of wonder as well. Of course nature had to be measured and analyzed, but he also believed that a great part of our response to the natural world should be based on the senses and emotions.

Humboldt was a rock star scientist who ignored conventional boundaries in his exploration of nature. Humboldt's desire to know and understand the world led him to investigate discoveries in all scientific disciplines, and to see the interwoven patterns embedded in this knowledge — mental models anyone?

If nature was a web of life, he couldn’t look at it just as a botanist, a geologist or a zoologist. He required information about everything from everywhere.

Humboldt grew up in a world where science was dry, nature mechanical, and man an aloof and separate chronicler of what was before him. Not only did Humboldt have a new vision of what our understanding of nature could be, but he put humans in the middle of it.

Humboldt’s Essay on the Geography of Plants promoted an entirely different understanding of nature. Instead of only looking at an organism, … Humboldt now presented relationships between plants, climate and geography. Plants were grouped into zones and regions rather than taxonomic units. … He gave western science a new lens through which to view the natural world.

Revolutionary for his time, Humboldt rejected the Cartesian ideas of animals as mechanical objects. He also argued passionately against the growing approach in the sciences that put man atop and separate from the rest of the natural world. Promoting a concept of unity in nature, Humboldt saw nature as a “reflection of the whole … an organism in which the parts only worked in relation to each other.”

Furthermore, that “poetry was necessary to comprehend the mysteries of the natural world.”

Wulf paints one of Humboldt’s greatest achievements as his ability and desire to make science available to everyone. No one before him had “combined exact observation with a ‘painterly description of the landscape”.

By contrast, Humboldt took his readers into the crowded streets of Caracas, across the dusty plains of the Llanos and deep into the rainforest along the Orinoco. As he described a continent that few British had ever seen, Humboldt captured their imagination. His words were so evocative, the Edinburgh Review wrote, that ‘you partake in his dangers; you share his fears, his success and his disappointment.'

In a time when travel was precarious, expensive and unavailable to most people, Humboldt brought his experiences to anyone who could read or listen.

On 3 November 1827, … Humboldt began a series of sixty-one lectures at the university. These proved so popular that he added another sixteen at Berlin’s music hall from 6 December. For six months he delivered lectures several days a week. Hundreds of people attended each talk, which Humboldt presented without reading from his notes. It was lively, exhilarating and utterly new. By not charging any entry fee, Humboldt democratized science: his packed audiences ranged from the royal family to coachmen, from students to servants, from scholars to bricklayers – and half of those attending were women. Berlin had never seen anything like it.

The subjectification of nature is about seeing nature, experiencing it. Humboldt was a master of bringing people to worlds they couldn’t visit, allowing them to feel a part of it. In doing so, he wanted to force humanity to see itself in nature. If we were all part of the giant web, then we all had a responsibility to understand it.

When he listed the three ways in which the human species was affecting the climate, he named deforestation, ruthless irrigation and, perhaps most prophetically, the ‘great masses of steam and gas’ produced in the industrial centres. No one but Humboldt had looked at the relationship between humankind and nature like this before.

His final opus, a series of books called Cosmos, was the culmination of everything that Humboldt had learned and discovered.

Cosmos was unlike any previous book about nature. Humboldt took his readers on a journey from outer space to earth, and then from the surface of the planet into its inner core. He discussed comets, the Milky Way and the solar system as well as terrestrial magnetism, volcanoes and the snow line of mountains. He wrote about the migration of the human species, about plants and animals and the microscopic organisms that live in stagnant water or on the weathered surface of rocks. Where others insisted that nature was stripped of its magic as humankind penetrated into its deepest secrets, Humboldt believed exactly the opposite. How could this be, Humboldt asked, in a world in which the coloured rays of an aurora ‘unite in a quivering sea flame’, creating a sight so otherworldly ‘the splendour of which no description can reach’? Knowledge, he said, could never ‘kill the creative force of imagination’ – instead it brought excitement, astonishment and wondrousness.

This is the ultimate subjectivity of nature. Being inspired by its beauty to try and understand how it works. Humboldt had respect for nature, for the wonders it contained, but also as the system in which we ourselves are an inseparable part.

Wulf concludes at the end that Humboldt,

…was one of the last polymaths, and died at a time when scientific disciplines were hardening into tightly fenced and more specialized fields. Consequently his more holistic approach – a scientific method that included art, history, poetry and politics alongside hard data – has fallen out of favour.

Maybe this is where the subjectivity of nature has gone. But we can learn from Humboldt the value of bringing it back.

In a world where we tend to draw a sharp line between the sciences and the arts, between the subjective and the objective, Humboldt’s insight that we can only truly understand nature by using our imagination makes him a visionary.

A little imagination is all it takes.

## The False Allure of a “Natural State” of Man

The heated debate about Sapiens' “natural way of life” is missing the point.
Ever since the Cognitive Revolution, there hasn't been a natural way of life for Sapiens.

— Yuval Noah Harari

### A Natural State of Curiosity

We modern humans have a fascination with trying to figure out our “natural” state. What do we eat — “naturally”? What sort of world are we “meant” to live in? What sort of family dynamic are we “meant” to have? Are we supposed to have sex with only the opposite gender, or is it perfectly “natural” to prefer your own? How much violence is natural and acceptable?

(The line of reasoning is a bit strange once we dig into it. Are modern humans not part of the natural world? Isn’t anything we do basically “natural”? At what point did we divert from “natural” to “unnatural”? We digress…)

One of the central conceits of the “man’s natural state” argument is that if we go back to some point in time, we’ll find it. We’ll finally come across the state of being where man lived totally in harmony with each other and with nature; eating the perfect diet for health, worshipping the correct gods, having sex in the natural and acceptable way. And besides studying religious texts, the tool that’s most frequently employed is the study of ancient, “pre-historic” man and woman. We hope that, by going back far enough, we’ll hit some arbitrary Point of Naturalness. That’s partially the approach used, for example, by the Paleo movement which has become such a popular force in nutrition. We evolved to eat bacon, right?

### What Is Natural?

These types of “meant to be” questions presuppose that we existed in some homogenous state in the past, and that we should be striving to get back to that place; that nature has given us a sort of natural endowment that we are best to stick to. Not so, says Yuval Harari.

The value of a book like Harari’s Sapiens, with its broad sweep of human history, is that we learn that ever since our Cognitive Revolution, the point that what we call history diverges from what we call biology, human society has been consistently molded and remolded; changed to suit the temper of the moment. That’s what makes humanity so unique relative to other intelligent creatures. Culturally, we change rapidly and unpredictably. There are very few absolutes, there are very few arrangements we haven’t tried yet. What’s “natural” depends on which society you’re looking at and at which point in time you’re looking at it.

It stands to reason that the ethnic and cultural variety among ancient hunter-gatherers was equally impressive [as those found in Australia by European settlers], and that the 5 million to 8 million foragers who populated the world on the eve of the Agricultural Revolution were divided into thousands of separate tribes with thousands of different languages and cultures. This, after all, was one of the main legacies of the Cognitive Revolution. Thanks to the appearance of fiction, even people with the same genetic make-up who lived under similar ecological conditions were able to create very different imagined realities, which manifest themselves in different norms and values.

For example, there’s every reason to believe that a forager band that lived 30,000 years ago on the spot where Oxford University stands would have spoken a different language from one living where Cambridge is now situated. One band might have been belligerent and the other peaceful. Perhaps the Cambridge band was communal while the one at Oxford was based on nuclear families. The Cambridgians might have spent long hours carving wooden statues of their guardian spirits whereas the Oxonians may have worshipped through dance. The former perhaps believed in reincarnation, while the latter thought this was nonsense. In one society, homosexual relationships might have been accepted, while in the other they were taboo.

In other words, while anthropological observations of modern foragers can help us understand some of the possibilities available to ancient foragers, the ancient horizon of possibilities was much broader, and much of it is hidden from our view. The heated debates about Homo Sapiens’ “natural way of life” miss the main point. Ever since the Cognitive Revolution, there hasn’t been a natural way of life for Sapiens. There are only cultural choices, from among a bewildering palette of [biological] possibilities.

Take the debate between monogamy and polygamy. Both have certainly been tried before and exist in some form in modern society, with each achieving various levels of success. It’s likely that most modern humans consider monogamy the most “natural” arrangement since it’s the most popular one, but we see the evidence of its failure all the time. Divorces are as common as death-do-us-part marriages, at least in most of Western civilization. We have a host of psychological problems tied to the constant trials of a long term one-to-one relationship. The proponents of polygamy would point to the failures of marriage as being due to the biological prison of monogamy, the unnaturalness of it all.

Wait, no no, say the monogamists. Our biology points the other way: We are meant to live in a tight-knit nuclear family with one spouse. This encourages caring and survival, and strong, unavoidable emotions like jealousy give us evidence that it’s probably right there in our genes. The prevalence of monogamy in modern society must be some evidence that it’s the real contender.

Who’s right? The truth is we don’t really know, and a study of the past is not as revealing as you might think. The Monogamy v. Polygamy debate also points to an even greater problem with our understanding of man in the period before he started writing things down, which is that our knowledge is dwarfed by our lack of knowledge.

### Searching for Keys in the Light

Compared to the many things we do know about our past, there are many times more things we don’t know, and in fact can’t know. Our historical methods have deep limitations:

Unfortunately, there are few certainties regarding the lives of our forager ancestors. The debate between the ‘ancient commune’ and the ‘eternal monogamy’ schools is based on flimsy evidence. We obviously have no written records from the age of foragers, and the archaeological evidence consists mainly of fossilized bones and stone tools. Artifacts made of more perishable materials — such as wood, bamboo, or leather — survive only under unique conditions. The common impression that pre-agricultural humans lived in an age of stone is a misconception based on this archaeological bias. The Stone Age should more accurately be called the Wood Age, because most of the tools used by ancient hunter-gatherers were made of wood.

[…]

Foragers moved house every month, every week, and sometimes even every day, toting whatever they had on their backs. There were no moving companies, wagons, or even pack animals to share the burden. They consequently had to make do with only the most essential possessions. It’s reasonable to presume, then, that the greater part of their mental, religious and emotional lives was conducted without the help of artifacts. An archaeologist working 100,000 years from now could piece together a reasonable picture of Muslim belief and practice from the myriad objects he unearthed in a ruined mosque. But we are largely at a loss in trying to comprehend the beliefs and rituals of ancient hunter-gatherers. It’s much the same dilemma that a future historian would face if he had to depict the social world of twenty-first century teenagers solely on the basis of their surviving snail mail — since no records will remain of their phone conversations, emails, blogs and text messages.

This archaeological bias, as Harari terms it, calls to mind the drunk looking under the streetlight for his keys because “That’s where the light is!” We study what is most study-able. The problem is that this bias leaves behind a whole bunch of interesting questions, a whole lot of interesting stuff that probably occurred.

Take the difference between understanding the diet of the ancient person and understanding how they actually felt about their food, and what that said about who they were:

The basics of the forager economy can be reconstructed with some confidence based on quantifiable and objective factors. For example, we can calculate how many calories per day a person needs in order to survive, how many calories were obtained from a pound of walnuts, and how many walnuts could be gathered from a square mile of forest. With this data, we can make an educated guess about the relative importance of walnuts in their diet.

But did they consider walnuts a delicacy or a humdrum staple? Did they believe that walnut trees were inhabited by spirits? Did they find walnut leaves pretty? If a forager boy wanted to take a forager girl to a romantic spot, did the share of a walnut tree suffice? [Ed: Did the concept of romance mean anything to them?]

That’s the thing: We don’t even really know how they felt about these things. They didn’t leave us any memoirs.

### An Animated View of Religion

Some of the more interesting sets of questions surround religion. One thing we can reliably suppose is that man has been in an essentially constant state of religious belief.

Most scholars suppose that most ancient humans were animists, believing that all things contained a life-force, be it a rock, a tree, a squirrel, or a human. In addition, there were spirits, fairies, angels, and other mystical creatures that play a role in the world. Human beings, in this worldview, are just part of a larger system; there are no Gods puppeteering our outcomes or watching us with a particularly close eye. We’re not the center of the universe.

But even if we can reliably suppose that most forager humans were animists, and it’s up for debate how reliable that is, there were very likely to be hundreds or thousands of varieties within that framework. It’s really the same as the “theistic” view of the world, which has been shared by billions of modern humans in widely varying forms:

The generic rubric ‘theists’ covers Jewish rabbis from eighteenth-century Poland, witch-burning Puritans from seventeenth-century Massachusetts, Aztec priests from fifteenth-century Mexico, Sufi mystics from twelfth-century Iran, tenth-century Viking warriors, second-century Roman legionnaires, and first-century Chinese bureaucrats. Each of these view others’ beliefs and practices as weird and heretical. The differences between the beliefs of groups of ‘animistic’ foragers were probably just as big. Their religious experience may have been turbulent and filled with controversies, reforms, and revolutions.

[…]

We assume they were animists, but that’s not very informative. We don’t know which spirits they prayed to, which festivals they celebrated, or which taboos they observed. Most importantly, we don’t know what stories they told. It’s one of the biggest holes in our understand of human history.

Conquest is another fascinating aspect of history. It’s comparatively easy for us to study Columbus and Pizarro and understand why they sought to explore new worlds, and why their wealthy backers supported the cause. Much of it is recorded and has been analyzed, summarized, and synthesized for our modern study.

But what of the conquests of the vastly longer period of pre-recorded history, what of them? We know they happened: The fossil record tells us that we started out as a species in the African/Asian landmass, bounded by the sea, and clearly, we broke free. Our technology was likely to have been barely up to the task, but we went ahead anyway.

Following the Cognitive Revolution, Sapiens acquired technology, the organizational skills, and perhaps even the vision necessary to break out of Afro-Asia and settled the Outer World. Their first achievement was the colonization of Australia some 45,000 years ago. Experts are hard-pressed to explain this feat. In order to reach Australia, humans had to cross a number of sea channels, some more than 60 miles wide , and upon arrival they had to adapt nearly overnight to a completely new ecosystem.

[…]

The journey of the first humans to Australia is one of the most important events in history, at least as important as Columbus’ journey to America or the Apollo 11 expedition to the moon. It was the first time any human had managed to leave the Afro-Asian ecological system — indeed, the first time any large terrestrial mammal had managed to cross from Afro-Asia to Australia.

Imagine what it must have been like arriving in Australia, with the entirety of human history having taken place on another continent with different animals, weather, plants, and geology. It makes the Moon landing seem kinda tame by comparison.

### The Curtain of Silence

But the even more salient question is why? What would have motivated a band, or many bands of ancient human foragers to take a risky journey across the sea to new land? Were they trying to escape persecution? Were they curious conquerers? Were they trying to prove something? Were they guided by spirits? At current, we can’t know those answers, and thus our understanding of deep history has limits.

Harari calls this The Curtain of Silence.

This curtain of silence shrouds tens of thousands of years of history. These long millennia may well have witnessed wars and revolutions, ecstatic religious movements, profound philosophical theories, incomparable artistic masterpieces. The foragers may have had their all-conquering Napoleons, who ruled empires half the size of Luxembourg; gifted Beethovens who lacked symphony orchestras but brought people to tears with the sound of their bamboo flutes; and charismatic prophets who revealed the words of a local oak tree rather than those of a creator god. But these are all mere guesses. The curtain of silence is so thick that we cannot even be sure such things occurred — let alone describe them in detail.

In the end, though, our guesses make the study of history a fascinating adventure.

Still Interested? Read our previous post on Sapiens, the book itself, or read about some of the biological lessons of history.

## Our Yearning for Immortality: Alan Lightman on one of the most Profound Contradictions of Human Existence

Science does not reveal the meaning of our existence, but it does draw back some of the veils.

***

“Be not deceived,” Epictetus writes in The Discourses, “every animal is attached to nothing so much as to its own interest.” Few things are more in our nature than our yearning for permanence. And yet all evidence argues against us.

This profound human contradiction is what physicist Alan Lightman — the first person to receive dual appointments in sciences and humanities at MIT — explores in one of the essays in The Accidental Universe: The World You Thought You Knew.

## The Accidental Universe

In the foreword to The Accidental Universe, Lightman tells a story of attending a lecture given by the Dalai Lama at the Massachusetts Institute of Technology. Among other things, the Dalai Lama spoke on the Buddhist concept of sunyata, which translates as “emptiness.” More specifically this doctrine means that objects in the physical universe are empty of inherent meaning — objects only receive meaning when we attach it to them with our thoughts and beliefs. This calls into question what is real.

As a scientist, I firmly believe that atoms and molecules are real (even if mostly empty space) and exist independently of our minds. On the other hand, I have witnessed firsthand how distressed I become when I experience anger or jealousy or insult, all emotional states manufactured by my own mind. The mind is certainly its own cosmos.

As Milton wrote in Paradise Lost, “It [the mind] can make a heaven of hell or a hell of heaven.”

In our constant search for meaning in this baffling and temporary existence, trapped as we are within our three pounds of neurons, it is sometimes hard to tell what is real. We often invent what isn’t there. Or ignore what is. We try to impose order, both in our minds and in our conceptions of external reality. We try to connect. We try to find truth. We dream and we hope. And underneath all of these strivings, we are haunted by the suspicion that what we see and understand of the world is only a tiny piece of the whole.

[…]

Science does not reveal the meaning of our existence, but it does draw back some of the veils.

We often think of the world as the totality of physical reality.

The word “universe” comes from the Latin unus, meaning “one,” combined with versus, which is the past participle of vertere, meaning “to turn.” Thus the original and literal meaning of “universe” was “everything turned into one.”

In the first essay “The Accidental Universe,” Lightman argues there is a possibility of multiple universes and multiple space-time continuums. But even if there is only a single universe, “there are many universes within our one universe, some visible and some not.” It all depends on your vantage point.

The challenge arises from explaining what we cannot see in a physical sense but can reason from deductions. We are like a pilot — relying our our incomplete mental instruments to guide us. We must believe what we cannot see and to a large extent we must believe what we cannot prove.

## The Temporary Universe

In, The Temporary Universe, one of the best essays in the collection, Lightman sets out to explore our attachment to youth, immortality, and the familiar, despite their fleeting nature. The essay explores a profound contradiction of human existence — our longing for immortality.

I don’t know why we long so for permanence, why the fleeting nature of things so disturbs. With futility, we cling to the old wallet long after it has fallen apart. We visit and revisit the old neighborhood where we grew up, searching for the remembered grove of trees and the little fence. We clutch our old photographs. In our churches and synagogues and mosques, we pray to the everlasting and eternal. Yet, in every nook and cranny, nature screams at the top of her lungs that nothing lasts, that it is all passing away. All that we see around us, including our own bodies, is shifting and evaporating and one day will be gone. Where are the one billion people who lived and breathed in the year 1800, only two short centuries ago?

[…]

Physicists call it the second law of thermodynamics. It is also called the arrow of time. Oblivious to our human yearnings for permanence, the universe is relentlessly wearing down, falling apart, driving itself toward a condition of maximum disorder. It is a question of probabilities. You start from a situation of improbable order, like a deck of cards all arranged according to number and suit, or like a solar system with several planets orbiting nicely about a central star. Then you drop the deck of cards on the floor over and over again. You let other stars randomly whiz by your solar system, jostling it with their gravity. The cards become jumbled. The planets get picked off and go aimlessly wandering through space. Order has yielded to disorder. Repeated patterns to change. In the end, you cannot defeat the odds. You might beat the house for a while, but the universe has an infinite supply of time and can outlast any player.

We can't live forever. Our lives are controlled by our genes in each cell. The raison d'être for most of these genes is to pass on instructions for how to build.

Some of these genes must be copied thousands of times; others are constantly subjected to random chemical storms and electrically unbalanced atoms, called free radicals, that disrupt other atoms. Disrupted atoms, with their electrons misplaced, cannot properly pull and tug on nearby atoms to form the intended bonds and architectural forms. In short, with time the genes get degraded. They become forks with missing tines. They cannot quite do their job. Muscles, for example. With age, muscles slacken and grow loose, lose mass and strength, can barely support our weight as we toddle across the room. And why must we suffer such indignities? Because our muscles, like all living tissue, must be repaired from time to time due to normal wear and tear. These repairs are made by the mechano growth factor hormone, which in turn is regulated by the IGF1 gene. When that gene inevitably loses some tines … Muscle to flab. Vigor to decrepitude. Dust to dust.

Most of our bodies are in a constant cycle of dying and being rebuilt to postpone the inevitable. The gut is perhaps the most fascinating example. As you can imagine it comes in contact with a lot of nasty stuff that damages tissues.

To stay healthy, the cells that line this organ are constantly being renewed. Cells just below the intestine’s surface divide every twelve to sixteen hours, and the whole intestine is refurbished every few days. I figure that by the time an unsuspecting person reaches the age of forty, the entire lining of her large intestine has been replaced several thousand times. Billions of cells have been shuffled each go-round. That makes trillions of cell divisions and whispered messages in the DNA to pass along to the next fellow in the chain. With such numbers, it would be nothing short of a miracle if no copying errors were made, no messages misheard, no foul-ups and instructions gone awry. Perhaps it would be better just to remain sitting and wait for the end. No, thank you.

Despite the preponderance of evidence against it, our culture strives for immortality and youth. We cling to a past that was but a moment in time in Heraclitus river— photographs, memories of our children, old wallets and shoes. And yet this yearning for youth and immortality, the “elixir of life,” connects us to every civilization that has graced the earth. But it's not only our physical bodies that we want to remain young. We struggle against change — big and small.

Companies dread structural reorganization, even when it may be for the best, and have instituted whole departments and directives devoted to “change management” and the coddling of employees through tempestuous times. Stock markets plunge during periods of flux and uncertainty. “Better the devil you know than the devil you don’t.” Who among us clamors to replace the familiar and comfortable incandescent lightbulbs with the new, odd-looking, “energy-efficient” compact fluorescent lamps and light-emitting diodes? We resist throwing out our worn loafers, our thinning pullover sweaters, our childhood baseball gloves. A plumber friend of mine will not replace his twenty-year-old water pump pliers, even though they have been banged up and worn down over the years. Outdated monarchies are preserved all over the world. In the Catholic Church, the law of priestly celibacy has remained essentially unchanged since the Council of Trent in 1563.

I have a photograph of the coast near Pacifica, California. Due to irreversible erosion, California has been losing its coastline at the rate of eight inches per year. Not much, you say. But it adds up over time. Fifty years ago, a young woman in Pacifica could build her house a safe thirty feet from the edge of the bluff overlooking the ocean, with a beautiful maritime view. Five years went by. Ten years. No cause for concern. The edge of the bluff was still twenty-three feet away. And she loved her house. She couldn’t bear moving. Twenty years. Thirty. Forty. Now the bluff was only three feet away. Still she hoped that somehow, some way, the erosion would cease and she could remain in her home. She hoped that things would stay the same. In actual fact, she hoped for a repeal of the second law of thermodynamics, although she may not have described her desires that way. In the photograph I am looking at, a dozen houses on the coast of Pacifica perch right on the very edge of the cliff, like fragile matchboxes, with their undersides hanging over the precipice. In some, awnings and porches have already slid over the side and into the sea.

One constant over Earth's 4.5-billion-year history is upheaval and change.

The primitive Earth had no oxygen in its atmosphere. Due to its molten interior, our planet was much hotter than it is now, and volcanoes spewed forth in large numbers. Driven by heat flow from the core of the Earth, the terrestrial crust shifted and moved. Huge landmasses splintered and glided about on deep tectonic plates. Then plants and photosynthesis leaked oxygen into the atmosphere. At certain periods, the changing gases in the air caused the planet to cool, ice covered the Earth, entire oceans may have frozen. Today, the Earth continues to change. Something like ten billion tons of carbon are cycled through plants and the atmosphere every few years— first absorbed by plants from the air in the form of carbon dioxide, then converted into sugars by photosynthesis, then released again into soil or air when the plant dies or is eaten. Wait around a hundred million years or so, and carbon atoms are recycled through rocks, soil, and oceans as well as plants.

Shakespeare's Julius Caesar says to Cassius:

“But I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament.”

We can forgive his lack of knowledge on modern astrophysics or the second law of thermodynamics. The North Star, like all stars, including the sun, is slowing dying as they consume fuel. They too will eventually explode or fade into the universe. The only reminders of existence will be cold embers floating in space.

## The Three Signs of Existence

Buddhists have long been aware of the evanescent nature of the world.

Anicca, or impermanence, they call it. In Buddhism, anicca is one of the three signs of existence, the others being dukkha, or suffering, and anatta, or non-selfhood. According to the Mahaparinibbana Sutta, when the Buddha passed away, the king deity Sakka uttered the following: “Impermanent are all component things. They arise and cease, that is their nature: They come into being and pass away.” We should not “attach” to things in this world, say the Buddhists, because all things are temporary and will soon pass away. All suffering, say the Buddhists, arises from attachment.

If only we could detach. “But,” Lightman argues, “even Buddhists believe in something akin to immortality. It is called Nirvana.”

A person reaches Nirvana after he or she has managed to leave behind all attachments and cravings, after countless trials and reincarnations, and finally achieved total enlightenment. The ultimate state of Nirvana is described by the Buddha as amaravati, meaning deathlessness. After a being has attained Nirvana, the reincarnations cease. Indeed, nearly every religion on Earth has celebrated the ideal of immortality. God is immortal. Our souls might be immortal.

Lightman argues that either we are delusional or nature is incomplete. “Either I am being emotional and vain in my wish for eternal life for myself …. or there is some realm of immortality that exists outside nature.”

If the first alternative is right, then I need to have a talk with myself and get over it. After all, there are other things I yearn for that are either not true or not good for my health. The human mind has a famous ability to create its own reality. If the second alternative is right, then it is nature that has been found wanting. Despite all the richness of the physical world— the majestic architecture of atoms, the rhythm of the tides, the luminescence of the galaxies— nature is missing something even more exquisite and grand: some immortal substance, which lies hidden from view. Such exquisite stuff could not be made from matter, because all matter is slave to the second law of thermodynamics. Perhaps this immortal thing that we wish for exists beyond time and space. Perhaps it is God. Perhaps it is what made the universe.

Of these two alternatives, I am inclined to the first. I cannot believe that nature could be so amiss. Although there is much that we do not understand about nature, the possibility that it is hiding a condition or substance so magnificent and utterly unlike everything else seems too preposterous for me to believe. So I am delusional. In my continual cravings for eternal youth and constancy, I am being sentimental. Perhaps with the proper training of my unruly mind and emotions, I could refrain from wanting things that cannot be. Perhaps I could accept the fact that in a few short years, my atoms will be scattered in wind and soil, my mind and thoughts gone, my pleasures and joys vanished, my “I-ness” dissolved in an infinite cavern of nothingness. But I cannot accept that fate even though I believe it to be true. I cannot force my mind to go to that dark place.

“A man can do what he wants,” said Schopenhauer, “but not want what he wants.”

If we are stuck with mortality can we find a beauty in this on its own? Is there something majestic in the brevity of life? Is there a value we can find from its fleeting and temporary duration?

I think of the night-blooming cereus, a plant that looks like a leathery weed most of the year. But for one night each summer its flower opens to reveal silky white petals, which encircle yellow lacelike threads, and another whole flower like a tiny sea anemone within the outer flower. By morning, the flower has shriveled. One night of the year, as delicate and fleeting as a life in the universe.

The Accidental Universe is an amazing read, balancing the laws of nature and first principles with a philosophical exploration of the world around us.

## The Book of Trees: Visualizing Branches of Knowledge

“There certainly have been many new things
in the world of visualization; but unless
you know its history, everything might seem novel.”

— Michael Friendly

***

It’s tempting to consider information visualization a relatively new field that rose in response to the demands of the Internet generation. “But,” argues Manual Lima in The Book of Trees: Visualizing Branches of Knowledge, “as with any domain of knowledge, visualizing is built on a prolonged succession of efforts and events.”

This book is absolutely gorgeous. I stared at it for hours.

While it’s tempting to look at the recent work, it’s critical we understand the long history. Lima’s stunning book helps, covering the fascinating 800-year history of the seemingly simple tree diagram.

Trees are some of the oldest living things in the world. The sequoias in Northern California, for example, can reach a height of nearly 400 feet, with a trunk diameter of 26 feet and live to more than 3,500 years. “These grandiose, mesmerizing lifeforms are a remarkable example of longevity and stability and, ultimately, are the crowning embodiment of the powerful qualities humans have always associated with trees.”

Such an important part of natural life on earth, tree metaphors have become deeply embedded in the English language, as in the “root” of the problem or “branches” of knowledge. In the Renaissance, the philosophers Francis Bacon and Rene Descartes, for example, used tree diagrams to describe dense classification arrangements. As we shall see, trees really became popular as a method of communicating and changing minds with Charles Darwin.

In the introduction Lima writes:

In a time when more than half of the world’s population live in cities, surrounded on a daily basis by asphalt, cement, iron, and glass, it’s hard to conceive of a time when trees were of immense and tangible significance to our existence. But for thousands and thousands of years, trees have provided us with not only shelter, protection, and food, but also seemingly limitless resources for medicine, fire, energy, weaponry, tool building, and construction. It’s only normal that human beings, observing their intricate branching schemas and the seasonal withering and revival of their foliage, would see trees as powerful images of growth, decay, and resurrection. In fact, trees have had such an immense significance to humans that there’s hardly any culture that hasn’t invested them with lofty symbolism and, in many cases, with celestial and religious power. The veneration of trees, known as dendrolatry, is tied to ideas of fertility, immortality, and rebirth and often is expressed by the axis mundi (world axis), world tree, or arbor vitae (tree of life). These motifs, common in mythology and folklore from around the globe, have held cultural and religious significance for social groups throughout history — and indeed still do.

[…]

The omnipresence of these symbols reveals an inherently human connection and fascination with trees that traverse time and space and go well beyond religious devotion. This fascination has seized philosophers, scientists, and artists, who were drawn equally by the tree’s inscrutabilities and its raw, forthright, and resilient beauty. Trees have a remarkably evocative and expressive quality that makes them conducive to all types of depiction. They are easily drawn by children and beginning painters, but they also have been the main subjects of renowned artists throughout the ages.

Our relationship with trees is symbiotic and this helps explain why it permeates our language and thought.

As our knowledge of trees has grown through this and many other scientific breakthroughs, we have realized that they have a much greater responsibility than merely providing direct subsistence for the sheltered ecosystems they support. Trees perform a critical role in moderating ground temperature and preventing soil erosion. Most important, they are known as the lungs of our planet, taking in carbon dioxide from the atmosphere and releasing oxygen. As a consequence, trees and humans are inexorably intertwined on our shared blue planet.

Our primordial, symbiotic relationship with the tree can elucidate why its branched schema has provided not only an important iconographic motif for art and religion, but also an important metaphor for knowledge-classification systems. Throughout human history the tree structure has been used to explain almost every facet of life: from consanguinity ties to cardinal virtues, systems of laws to domains of science, biological associations to database systems. It has been such a successful model for graphically displaying relationships because it pragmatically expresses the materialization of multiplicity (represented by its succession of boughs, branches, twigs, and leaves) out of unity (its central foundational trunk, which is in turn connected to a common root, source, or origin.)

While we can't go back in time it certainly appears like Charles Darwin changed the trajectory of the tree diagram forever when he used it to change minds about one of our most fundamental beliefs.

Darwin’s contribution to biology—and humanity—is of incalculable value. His ideas on evolution and natural selection still bear great significance in genetics, molecular biology, and many other disparate fields. However, his legacy of information mapping has not been highlighted frequently. During the twenty years that led to the 1859 publication of On the Origin of Species by Means of Natural Selection, Darwin considered various notions of how the tree could represent evolutionary relationships among specifics that share a common ancestor. He produced a series of drawings expanding on arboreal themes; the most famous was a rough sketch drawn in the midst of a few jotted notes in 1837. Years later, his idea would eventually materialize in the crucial diagram that he called the “tree of life” (below) and featured in the Origin of Species.

Darwin was cognizant of the significance of the tree figure as a central element in representing his theory. He took eight pages of the chapter “Natural Selection,” where the diagram is featured, to expand in considerable detail on the workings of the tree and its value in understanding the concept of common descent.

A few months before the publication of his book, Darwin wrote his publisher, John Murray: “Enclosed is the Diagram which I wish engraved on Copper on folding out Plate to face latter part of volume. — It is an odd looking affair, but is indispensable to show the nature of the very complex affinities of past & present animals. …”

The illustration was clearly a “crucial manifestation of his thinking,” and of central importance to Darwin’s argument.

As it turned out it was the tree diagram, accompanied by Darwin’s detailed explanations, that truly persuaded a rather reluctant and skeptical audience to accept his groundbreaking ideas.

Coming back to the metaphor, before we go on to explain and show some of the different types of tree diagrams, Lima argues that given the long-lasting nature of the tree and its penetration into our lives as a way to organize, describe, and understand we can use the tree as a prism to better understand our world.

As one of the most ubiquitous and long-lasting visual metaphors, the tree is an extraordinary prism through which we can observe the evolution of human consciousness, ideology, culture, and society. From its entrenched roots in religious exegesis to its contemporary secular digital expressions, the multiplicity of mapped subjects cover almost every significant aspect of life throughout the centuries. But this dominant symbol is not just a remarkable example of human ingenuity in mapping information; it is also the result of a strong human desire for order, balance, hierarchy, structure, and unity. When we look at an early twenty-first-century sunburst diagram, it appears to be a species entirely distinct from a fifteenth-century figurative tree illustration. However, if we trace its lineage back through numerous tweaks, shifts, experiments, failures, and successes, we will soon realize there’s a defined line of descent constantly punctuated by examples of human skill and inventiveness.

## Types of Tree Diagrams

Figurative Trees

Trees have been not only important religious symbols for numerous cultures through the ages, but also significant metaphors for describing and organizing human knowledge. As one of the most ubiquitous visual classification systems, the tree diagram has through time embraced the most realistic and organic traits of its real, biological counterpart, using trunks, branches, and offshoots to represent connections among different entities, normally represented by leaves, fruits, or small shrubberies.

Even though tree diagrams have lost some of their lifelike features over the years, becoming ever more stylized and nonfigurative, many of their associated labels, such as roots, branches, and leaves, are still widely used. From family ties to systems of law, biological species to online discussions, their range of subjects is as expansive as their time span.

Vertical Trees

The transition from realistic trees to more stylized, abstract constructs was a natural progression in the development of hierarchical representations, and a vertical scheme splitting from top or bottom was an obvious structural choice. … Of all visualization models, vertical trees are the ones that retain the strongest resemblance to figurative trees, due to their vertical layout and forking arrangement from a central trunk. In most cases they are inverted trees, with the root at the top, emphasizing the notion of descent and representing a more natural writing pattern from top to bottom. Although today they are largely constrained to small digital screens and displays, vertical trees in the past were often designed in larger formats such as long parchment scrolls and folding charts that could provide a great level of detail.

Horizontal Trees

With the adoption of a more schematic and abstract construct, deprived of realistic arboreal features, a tree diagram could sometimes be rotated along its axis and depicted horizontally, with its ranks arranged most frequently from left to right.

Horizontal trees probably emerged as an alternative to vertical trees to address spatial constraints and layout requirements, but they also provide unique advantages. The nesting arrangement of horizontal trees resembles the grammatical construct of a sentence, echoing a natural reading pattern that anyone can relate to. This alternative scheme was often deployed on facing pages of a manuscript, with the root of the tree at the very center, creating a type of mirroring effect that is still found in many digital and interactive executions. Horizontal trees have proved highly efficient for archetypal models such as classification trees, flow charts, mind maps, dendrograms, and, notably, in the display of files on several software applications and operating systems.

The Book of Trees: Visualizing Branches of Knowledge goes on to explore multi-directional, radial, hyperbolic, rectangular, Voronoi, and circular tree maps as well as sunbursts and icicle trees.

## Rachel Sussman: The Oldest Living Things in the World

Contemporary artist Rachel Sussman has photographed the world's oldest continuously living organisms that are 2,000 years old and older. Braving some of the world's harshest climates spanning from Antarctica to Greenland, the Mojave Desert, and the Australian Outback, she's compiled her photographs and stories of her epic adventures into the beautiful new book The Oldest Living Things in the World. The book includes 124 photographs and 30 essays.

Here are some of the pictures.

Still curious? Sussman gave a 2010 TED talk on the project.

(photos from Colossal)

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