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Tag Archives: History

Are Great Men and Women a Product of Circumstance?

Few books have ever struck us as much as Will Durant's 100-page masterpiece The Lessons of History, a collection of essays which sum up the lifelong thoughts of a brilliant historian.

We recently dug up an interview with Durant and his wife Ariel — co-authors of the 11-volume masterpiece The Story of Civilization — and sent it to the members of the Farnam Street Learning Community. While the interview is full of wisdom in its entirety, we picked one interesting excerpt to share with you: Durant's thoughts on the “Great Man” (and certainly, Great Woman) theory of history.

Has history been Theirs to dictate? Durant has a very interesting answer, one that's hard to ignore once you think about it:

Interviewer: Haven’t certain individuals, the genius, great man, or hero, as Carlisle believed, been the prime determinants of human history?

Will Durant: There are many cases, I think, in which individual characters have had very significant results upon history. But basically, I think Carlisle was wrong. That the hero is a product of a situation rather than the result being a product of the hero. It is demand that brings out the exceptional qualities of man. What would Lenin have been if he had remained in, what was it, Geneva? He would have a little…. But he faced tremendous demands upon him, and something in him responded. I think those given us would have brought out capacity in many different types of people. They wouldn’t have to be geniuses to begin with.

Interviewer: Then what is the function or role of heroes?

Will Durant: They form the function of meeting a situation whose demands are always all his potential abilities.

Interviewer: What do you think is the important thing for us, in studying the course of history, to know about character? What is the role of character in history?

Will Durant: I suppose the role of character is for the individual to rise to a situation. If it were not for the situation, we would never have heard of him. So that you might say that character is the product of an exceptional demand by the situation upon human ability. I think the ability of the average man could be doubled if it were demanded, if the situation demanded. So, I think Lenin was made by the situation. Of course he brought ideas, and he had to abandon almost all those ideas. For example, he went back to private enterprise for a while.

One way we might corroborate Durant's thoughts on Lenin is to ask another simple question: Which U.S. Presidents are considered the most admired?

Students of history have three easy answers pop in (and polls corroborate): George Washington – the first U.S. President and a Founding Father; Abraham Lincoln – the man who held the Union together; and finally Franklin Delano Roosevelt – unless the U.S. amends its Constitution, the longest serving U.S. President now and forever.

All great men, certainly. All three of which rose to the occasion. But what do they share?

They were the ones holding office at the time of (or in the case of Washington, immediately upon winning) the three major wars impacting American history: The American Revolution, the American Civil War, and World War II. 

It raises an interesting question: Would these men be remembered and held in the same esteem if they hadn't been handed such situations? The answer pops in pretty quickly: Probably not. Their heroism was partly a product of their character and partly a product of their situation.

And thus Durant gives us a very interesting model to bring to reality: Greatness is in many of us, but only if we rise, with practical expediency, to the demands of life. Greatness arises only when tested.

For the rest of Durant's interview, and a lot of other cool stuff, check out the Learning Community.

The 16 Best Books of 2016

Rewarding reads on love, life, knowledge, history, the future, and tools for thinking. Out of all the books I read this year, here is a list of what I found most worth reading in 2016.

1. The Psychology of Man’s Possible Evolution
These lectures, which were originally called Six Psychological Lectures, were first privately printed in the 1940s. Of the first run of 150 copies, none were sold. The essays were published once again after Ouspensky’s death, and unlike last time became a hit. While the book is about psychology, it’s different than what we think of as psychology — “for thousands of years psychology existed under the name philosophy.” Consider this a study in what man may become — by working simultaneously on knowledge and inner unity.

2. The Island of Knowledge: The Limits of Science and the Search for Meaning
Imagine the sum of our knowledge as an Island in a vast and endless ocean. This is the Island of Knowledge. The coastline represents the boundary between the known and unknown. As we grow our understanding of the world, the Island grows and with it so does the shores of our ignorance. “We strive toward knowledge, always more knowledge,” Gleiser writes, “but must understand that we are, and will remain, surrounded by mystery.” The book is a fascinating and wide-ranging tour through scientific history. (Dig Deeper into this amazing read here.)

3. When Breath Becomes Air
It’s been a while since I’ve cried reading a book. This beautifully written memoir, by a young neurosurgeon diagnosed with terminal cancer, attempts to answer the question What makes a life worth living? If you read this and you’re not feeling something you’re probably a robot.

4. The Sovereign Individual: Mastering the Transition to the Information Age
The book, which argues “the information revolution will destroy the monopoly power of the nation-state as surely as the Gunpowder Revolution destroyed the Church’s monopoly,” is making the rounds in Silicon Valley and being passed around like candy. Even if its forecasts are controversial, the book is a good read and it’s full of interesting and detailed arguments. I have underlines on nearly every page. “Information societies,” the authors write, “promise to dramatically reduce the returns to violence … When the payoff for organizing violence at a large scale tumbles, the payoff from violence at a smaller scale is likely to jump. Violence will become more random and localized.” The Sovereign Individual, who, for the first time “can educate and motivate himself,” will be “almost entirely free to invest their own work and realize the full benefits of their own productivity.” An unleashing of human potential which will, the authors argue, shift the greatest source of wealth to ideas rather than physical capital — “anyone who thinks clearly will potentially be rich.” Interestingly, in this potential transition, the effects are “likely to be centered among those of the middle talent in currently rich countries. They particularly may come to feel that information technology poses a threat to their way of life.” The book predicts the death of politics, “weakened by the challenge from technology, the state will treat increasingly autonomous individuals, its former citizens, with the same range of ruthlessness and diplomacy it has heretofore displayed in its dealings with other governments.” As technology reshapes the world, it also “antiquates laws, reshapes morals, and alters preconceptions. This book explains how.”

5. To Kill a Mockingbird
I know, I know. Hear me out. Someone I respect mentioned that he thought Atticus Finch was the perfect blend of human characteristics. Tough and skilled, yet humble and understanding. He’s frequently rated as a “most admired” hero in fiction, yet he’s a lawyer competing with Jedis, Detectives, Spies, and Superheroes. Isn’t that kind of interesting? Since it had been at least 15 years since I’d read TKM, I wanted to go back and remember what made Atticus so admired. His courage, his humility, his understanding of people. I forgot just how perceptive Finch was when it came to what we’d call “group social dynamics” — he forgives the individual members of the mob that show up to hurt Tom Robinson simply because he understands that mob psychology is capable of overwhelming otherwise good people. How many of us would be able to do that? Atticus Finch is certainly a fictional, and perhaps “unattainably” moral hero. But I will point out that not only do real life “Finch’s” exist, but that even if we don’t “arrive” at a Finchian level of heroic integrity and calm temperament, it’s certainly a goal worth pursuing. Wise words from the book Rules for a Knight sums it up best: “To head north, a knight may use the North Star to guide him, but he will not arrive at the North Star. A knight’s duty is to proceed in that direction.” (Here are some of the lessons I took away from the book.)

6. Lee Kuan Yew: The Grand Master’s Insights on China, the United States, and the World
If you’re not familiar with Lee Kuan Yew, he’s the “Father of Modern Singapore,” the man who took a small, poor island just north of the equator in Southeast Asia with GDP per capita of ~$500 in 1965 and turned it into a modern powerhouse with GDP per capita of over $70,000 as of 2014, with some of the lowest rates of corruption and highest rates of economic freedom in the world. Finding out how he did it is worth anyone’s time. This book is a short introduction to his style of thinking: A series of excerpts of his thoughts on modern China, the modern U.S., Islamic Terrorism, economics, and a few other things. It’s a wonderful little collection. (We’ve actually posted about it before.) Consider this an appetizer (a delicious one) for the main course: From Third World to First, Yew’s full account of the rise of Singapore. (Dig deeper here.)

7. An Illustrated Book of Bad Arguments
Perfect summer reading for adults and kids alike. One friend of mine has created a family game where they all try to spot the reasoning flaws of others. The person with the most points at the end of the week gets to pick where they go for dinner. I have a suspicion his kids will turn out to be politicians or lawyers.

8. Intuition Pumps and Other Tools for Thinking
Dan Dennett is one of the most well known cognitive scientists on the planet . This book is a collection of 77 short essays on different “thinking tools,” basically thought experiments Dennett uses to slice through tough problems, including some tools for thinking about computing, thinking about meaning, and thinking about consciousness. Like Richard Feynman’s great books, this one acts as a window into a brilliant mind and how it handles interesting and difficult problems. If you only walk away with a few new mental tools, it’s well worth the time spent. (You can learn a lot more about Dennett here, here, and here.)

9. The Seven Sins of Memory (How the Mind Forgets and Remembers)
I found this in the bibliography of Judith Rich Harris’ No Two Alike. Schacter is a psychology professor at Harvard who runs the Schacter Memory Lab. The book explores the seven “issues” we tend to find with regard to our memory: Absent-mindedness, transience, blocking, misattribution, suggestibility, bias, and persistence. The fallibility of memory is so fascinating: We rely on it so heavily and trust it so deeply, yet as Schacter shows, it’s extremely faulty. It’s not just about forgetting where you left your keys. Modern criminologists know that eyewitness testimony is deeply flawed. Some of our deepest and most hard-won memories — the things we know are true — are frequently wrong or distorted. Learning to calibrate our confidence in our own memory is not at all easy. Very interesting topic to explore. (We did a three part series on this book. Introduction and parts One, Two, and Three).

10. Talk Lean: Shorter Meetings. Quicker Results. Better Relations
This book is full of useful tips on listening better, being candid and courteous, and learning what derails meetings, conversations, and relationships with people at work. Don’t worry. It’s not about leaving things unsaid that might be displeasing for other people. In fact, leaving things unsaid is often more detrimental to the relationship than airing them out. Rather, it’s about finding a way to say them so people will hear them and not feel defensive. If you want to get right to the point and not alienate people, this book will help you. I know because this is something, personally, I struggle with at times.

11. The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
I recently had a fascinating multi-hour dinner with the author, Pedro Domingos, on where knowledge comes from. Historically, at least, the answer has been evolution, experience, and culture. Now, however, there is a new source of knowledge: Machine learning. The book offers an accessible overview of the different ways of machine learning and the search for a master, unifying, theory. The book also covers how machine learning works and gives Pedro’s thoughts on where we’re headed. (Dig deeper in this podcast.)

12. Why Don’t We Learn from History?
This is a short (~120pp) book by the military historian and strategist B.H. Liddell Hart, a man who not only wrote military history but surely influenced it, especially in Germany in the World War period. He wrote this short synthesis at the end of his life and didn’t have a chance to finish it, but the result is still fascinating. Hart takes a “negative” view of history; in other words, What went wrong? How can we avoid it? The result of that study, as he writes in the introduction, is that “History teaches us personal philosophy.” Those who learn vicariously as well as directly have a big leg up. Something to take to heart. I plan to read more of his works.

13. A Powerful Mind: The Self-Education of George Washington
What a great book idea by Adrienne Harrison. There are a zillion biographies of GW out there, with Chernow's getting a lot of praise recently. But Harrison narrows in on Washington’s self-didactic nature. Why did he read so much? How did he educate himself? Any self-motivated learner is probably going to enjoy this.

14. Sapiens: A Brief History of Humankind
One of the best books I’ve come across in a long time. Sapiens is a work of “Big History” — in the style of Jared Diamond’s Guns, Germs, and Steel — that seeks to understand humanity in a deep way. Many of Professor Harari’s solutions will be uncomfortable for some to read, there is no attempt at political correctness, but his diagnosis of human history is undeniably interesting and at least partially correct. He draws on many fields to arrive at his conclusions; a grand method of synthesis that will be familiar to long-time Farnam Street readers. The book is almost impossible to summarize given the multitude of ideas presented. But then again, most great books are. (Dig deeper into this amazing read here, here, and here.)

15. Becoming Wise: An Inquiry into the Mystery and Art of Living — A refreshing signal in world of noise that should be read and immediately re-read. There is so much goodness in here that scarcely will you find more than a page or two in my copy without a mark, bent page, or highlight. The entire book offers texture to thoughts you knew you had but didn't know how to express.

16. The Happiness Trap: How to Stop Struggling and Start Living
The way most of us search for and attempt to hold onto fleeting moments of happiness ends up ensuring that we’re miserable. A great practical book on developing mindfulness, which is so important in many aspects of your life, including satisfaction. Might be the best self-help book I’ve read.



Frozen Accidents: Why the Future Is So Unpredictable

“Each of us human beings, for example, is the product of an enormously long
sequence of accidents,
any of which could have turned out differently.”
— Murray Gell-Mann


What parts of reality are the product of an accident? The physicist Murray Gell-Mann thought the answer was “just about everything.” And to Gell-Mann, understanding this idea was the the key to understanding how complex systems work.

Gell-Mann believed two things caused what we see in the world:

  1. A set of fundamental laws
  2. Random “accidents” — the little blips that could have gone either way, and had they, would have produced a very different kind of world.

Gell-Mann pulled the second part from Francis Crick, co-discoverer of the human genetic code, who argued that the code itself may well have been an “accident” of physical history rather than a uniquely necessary arrangement.

These accidents become “frozen” in time, and have a great effect on all subsequent developments; complex life itself is an example of something that did happen a certain way but probably could have happened other ways — we know this from looking at the physics.

This idea of fundamental laws plus accidents, and the non-linear second order effects they produce, became the science of complexity and chaos theory. Gell-Mann discussed the fascinating idea further in a 1996 essay on Edge:

Each of us human beings, for example, is the product of an enormously long sequence of accidents, any of which could have turned out differently. Think of the fluctuations that produced our galaxy, the accidents that led to the formation of the solar system, including the condensation of dust and gas that produced Earth, the accidents that helped to determine the particular way that life began to evolve on Earth, and the accidents that contributed to the evolution of particular species with particular characteristics, including the special features of the human species. Each of us individuals has genes that result from a long sequence of accidental mutations and chance matings, as well as natural selection.

Now, most single accidents make very little difference to the future, but others may have widespread ramifications, many diverse consequences all traceable to one chance event that could have turned out differently. Those we call frozen accidents.

These “frozen accidents” occur at every nested level of the world: As Gell-Mann points out, they are an outcome in physics (the physical laws we observe may be accidents of history); in biology (our genetic code is largely a byproduct of “advantageous accidents” as discussed by Crick); and in human history, as we'll discuss. In other words, the phenomenon hits all three buckets of knowledge.

Gell-Mann gives a great example of how this plays out on the human scale:

For instance, Henry VIII became king of England because his older brother Arthur died. From the accident of that death flowed all the coins, all the charters, all the other records, all the history books mentioning Henry VIII; all the different events of his reign, including the manner of separation of the Church of England from the Roman Catholic Church; and of course the whole succession of subsequent monarchs of England and of Great Britain, to say nothing of the antics of Charles and Diana. The accumulation of frozen accidents is what gives the world its effective complexity.

The most important idea here is that the frozen accidents of history have a nonlinear effect on everything that comes after. The complexity we see comes from simple rules and many, many “bounces” that could have gone in any direction. Once they go a certain way, there is no return.

This principle is illustrated wonderfully in the book The Origin of Wealth by Eric Beinhocker. The first example comes from 19th century history:

In the late 1800s, “Buffalo Bill” Cody created a show called Buffalo Bill's Wild West Show, which toured the United States, putting on exhibitions of gun fighting, horsemanship, and other cowboy skills. One of the show's most popular acts was a woman named Phoebe Moses, nicknamed Annie Oakley. Annie was reputed to have been able to shoot the head off of a running quail by age twelve, and in Buffalo Bill's show, she put on a demonstration of marksmanship that included shooting flames off candles, and corks out of bottles. For her grand finale, Annie would announce that she would shoot the end off a lit cigarette held in a man's mouth, and ask for a brave volunteer from the audience. Since no one was ever courageous enough to come forward, Annie hid her husband, Frank, in the audience. He would “volunteer,” and they would complete the trick together. In 1880, when the Wild West Show was touring Europe, a young crown prince (and later, kaiser), Wilhelm, was in the audience. When the grand finale came, much to Annie's surprise, the macho crown prince stood up and volunteered. The future German kaiser strode into the ring, placed the cigarette in his mouth, and stood ready. Annie, who had been up late the night before in the local beer garden, was unnerved by this unexpected development. She lined the cigarette up in her sights, squeezed…and hit it right on the target.

Many people have speculated that if at that moment, there had been a slight tremor in Annie's hand, then World War I might never have happened. If World War I had not happened, 8.5 million soldiers and 13 million civilian lives would have been saved. Furthermore, if Annie's hand had trembled and World War I had not happened, Hitler would not have risen from the ashes of a defeated Germany, and Lenin would not have overthrown a demoralized Russian government. The entire course of twentieth-century history might have been changed by the merest quiver of a hand at a critical moment. Yet, at the time, there was no way anyone could have known the momentous nature of the event.

This isn't to say that other big events, many bad, would not have precipitated in the 20th century. Almost certainly there would have been wars and upheavals.

But the actual course of history was in some part determined by small chance event which had no seeming importance when it happened. The impact of Wilhelm being alive rather than dead was totally non-linear. (A small non-event had a massively disproportionate effect on what happened later.)

This is why predicting the future, even with immense computing power, is an impossible task. The chaotic effects of randomness, with small inputs having disproportionate and massive effects, makes prediction a very difficult task. That's why we must appreciate the role of randomness in the world and seek to protect against it.

Another great illustration from The Origin of Wealth is a famous story in the world of technology:

[In 1980] IBM approached a small company with forty employees in Bellevue, Washington. The company, called Microsoft, was run by a Harvard dropout named bill Gates and his friend Paul Allen. IBM wanted to talk to the small company about creating a version of the programming language BASIC for the new PC. At their meeting, IBM asked Gates for his advice on what operating systems (OS) the new machine should run. Gates suggested that IBM talk to Gary Kildall of Digital Research, whose CP/M operating system had become the standard in the hobbyist world of microcomputers. But Kildall was suspicious of the blue suits from IBM and when IBM tried to meet him, he went hot-air ballooning, leaving his wife and lawyer to talk to the bewildered executives, along with instructions not to sign even a confidentiality agreement. The frustrated IBM executives returned to Gates and asked if he would be interested in the OS project. Despite never having written an OS, Gates said yes. He then turned around and license a product appropriately named Quick and Dirty Operating System, or Q-DOS, from a small company called Seattle Computer Products for $50,000, modified it, and then relicensed it to IBM as PC-DOS. As IBM and Microsoft were going through the final language for the agreement, Gates asked for a small change. He wanted to retain the rights to sell his DOS on non-IBM machines in a version called MS-DOS. Gates was giving the company a good price, and IBM was more interested in PC hardware than software sales, so it agreed. The contract was signed on August 12, 1981. The rest, as they say, is history. Today, Microsoft is a company worth $270 billion while IBM is worth $140 billion.

At any point in that story, business history could have gone a much different way: Kildall could have avoided hot-air ballooning, IBM could have refused Gates' offer, Microsoft could have not gotten the license for QDOS. Yet this little episode resulted in massive wealth for Gates and a long period of trouble for IBM.

Predicting the outcomes of a complex system must clear a pretty major hurdle: The prediction must be robust to non-linear “accidents” with a chain of unforeseen causation. In some situations this is doable: We can confidently rule out that Microsoft will not go broke in the next 12 months; the chain of events needed to take it under quickly is so low as to be negligible, no matter how you compute it. (Even IBM made it through the above scenario, although not unscathed.)

But as history rolls on and more “accidents” accumulate year by year, a “Fog of the Future” rolls in to obscure our view. In order to operate in such a world, we must learn that predicting is inferior to building systems that don't require prediction, as Mother Nature does. And if we must predict, must confine our predictions to areas with few variables that lie in our circle of competence, and understand the consequences if we're wrong.

If this topic is interesting to you, try exploring the rest of the Origin of Wealth, which discusses complexity in the economic realm in great (but readable) detail; also check out the rest of Murray Gell-Mann's essay on Edge. Gell-Mann also wrote a book on the topic called The Quark and the Jaguar which is worth checking out. The best writer on randomness and robustness in the face of an uncertain future, is of course Nassim Taleb, whom we have written about many times.

Jared Diamond: How to Get Rich

We're constantly asked for examples of the “multiple mental models” approach in practice. Our standard response includes great books like Garrett Hardin's Filters Against Folly and Will Durant's The Lessons of History.

One of the well-known examples of this brand of thinking is Guns, Germs, and Steel, a book that opened thousands of eyes to the power of leaping across the walls of history, sociology, biology, geography and other fields to truly understand the world. (If you haven't read it yet, why are you still here? Go order it and read it!)

Jared Diamond, the book's author, is a great master of synthesis across many fields — works like The Third Chimpanzee and Collapse show great critical thinking prowess, even if you don't come to 100% agreement with him.

Lesser known than Guns, Germs, and Steel is a follow-up talk Diamond gave entitled How to Get Rich:

… probably most lectures one hears at the museum are on fascinating but impractical subjects: namely, they don't help you to get rich. This evening I plan to redress the balance and talk about the natural history of becoming rich.

The talk is a great, and short, introduction to “multiple mental models” thinking. Diamond, of course, does not literally answer the question of How to Get Rich. He's smart enough to know that this is charlatan territory if answered too literally. (Three steps to surefire wealth!)

But he does effectively answer an interesting part of the equation of getting rich: What conditions do we need to set up maximal productivity, learning, and cooperation among our groups? 

Diamond answers his question through the same use of inter-disciplinary synthesis his readers would be familiar with: As you read it, you'll see models from biology, military history, business/economics, and geography.

His answer has two main parts: Optimal group size/fragmentation, and optimal exposure to outside competition:

So what this suggests is that we can extract from human history a couple of principles. First, the principle that really isolated groups are at a disadvantage, because most groups get most of their ideas and innovations from the outside. Second, I also derive the principle of intermediate fragmentation: you don't want excessive unity and you don't want excessive fragmentation; instead, you want your human society or business to be broken up into a number of groups which compete with each other but which also maintain relatively free communication with each other. And those I see as the overall principles of how to organize a business and get rich.

Those are wonderful lessons, and you should read the piece to see how he arrives at them. But there's another important reason we bring the talk to your attention, one of methodology.

Diamond's talk offers us a powerful principle for our efforts to understand the world: Look for and study natural experiments, the more controlled, the better.

I propose to try to learn from human history. Human history over the last 13,000 years comprises tens of thousands of different experiments. Each human society represents a different natural experiment in organizing human groups. Human societies have been organized very differently, and the outcomes have been very different. Some societies have been much more productive and innovative than others. What can we learn from these natural experiments of history that will help us all get rich? I propose to go over two batches of natural experiments that will give you insights into how to get rich.

This wonderfully useful approach, reminiscent of Peter Kaufman's idea about the Three Buckets of Knowledge, is one we see used effectively all the time.

Judith Rich Harris used the naturally controlled experiment of identical twins separated at birth to solve the problem of human personality development. Michael Abrashoff had a naturally controlled experiment in leadership principles when he had to turn around the USS Benfold without hiring or firing, or changing ships or missions, or offering any financial incentive to his cadets. Ken Iverson had a naturally controlled experiment in business principles by succeeding dramatically in a business with massive headwinds and no tailwinds.

And so if we follow in the steps of Diamond, Peter Kaufman, Judith Rich Harris, Ken Iverson, and Michael Abrashoff, we might find natural experiments that help illuminate the solutions to our problems in unusual ways. As Diamond says in his talk, the world has already tried thousands of things: All we have to do is study them and then align with the way the world works.

Alex Bellos: Every Number Tells a Story

“We depend on numbers to make sense of the world,
and have done so ever since we started to count.”

— Alex Bellos

From The Grapes of Math By Alex Borros
From The Grapes of Math By Alex Bellos


The earliest symbols used for numbers go back to about 5000 years ago Sumer (modern day Iraq). They didn't really look far for names. Ges, the word for one, also meant man. Min, the word for two, also meant women. At first numbers served a practical purpose, mostly things like counting sheep and determining taxes.

“Yet numbers also revealed abstract patterns,” writes Alex Bellos in his fascinating book The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life, which, he continues, “made them objects of deep contemplation. Perhaps the earliest mathematical discovery was that numbers come in two types, even and odd: those that can be halved cleanly, such as 2, 4 and 6, and those that cannot, such as 1, 3 and 5.

Pythagoras and Number Gender

Pythagoras, the Greek teacher, who lived in the sixth century BC and is most famous for his theorem about triangles, agreed with the Sumerians on number gender. He believed that odd numbers were masculine and even ones were feminine. This is where it gets interesting … why did he think that? It was, he believed, a resistance to splitting in two that embodied strength. The ability to be divisible by two, in his eyes was a weakness. He believed odd numbers were master over even. Christianity agrees with the gender theory, God created Adam first and Eve second. The latter being the sin.

Large Numbers

Numbers originally accounted for practical and countable things, such as sheep and teeth. Things get interesting as quantities increase, because we don't use numbers in the same way.

We approximate using a “round number” as a place mark. It is easier and more convenient. When I say, for example, that there were a hundred people at the market, I don’t mean that there were exactly one hundred people there. … Big numbers are understood approximately, small ones precisely, and these two systems interact uneasily. It is clearly nonsensical to say that next year the universe will be “13.7 billion and one” years old. It will remain 13.7 billion years old for the rest of our lives.

Round numbers usually end in zero.

The word round is used because a round number represents the completion of a full counting cycle, not because zero is a circle. There are ten digits in our number system, so any combination of cycles will always be divisible by ten. Because we are so used to using round numbers for big numbers, when we encounter a big number that is nonround— say, 754,156,293— it feels discrepant.

Manoj Thomas, a psychologist at Cornell University, argues that we are uneasy with large, non-round numbers, which causes us to see them as smaller than they are and carries with it practical implications when, say, selling a house. “We tend to think that small numbers are more precise,” he says, “so when we see a big number that is precise we instinctively assume it is less than it is.” If he's right the result is that you will pay more for expensive and non-round prices. Indeed his experiments seem to agree. In one, respondents viewed pictures of several houses and sales prices, some were round and some were larger and non-round (e.g., $490,000 and $492,332). On average subjects judged the precise one to be lower. As Bellos concludes on large numbers, “if you want to make money, don't end the price with a zero.”

Number Influence When Shopping

One of the ways to make a number seem more precise is by subtracting 1.

When we read a number, we are more influenced by the leftmost digit than by the rightmost, since that is the order in which we read, and process, them. The number 799 feels significantly less than 800 because we see the former as 7-something and the latter as 8-something, whereas 798 feels pretty much like 799. Since the nineteenth century, shopkeepers have taken advantage of this trick by choosing prices ending in a 9, to give the impression that a product is cheaper than it is. Surveys show that anything between a third and two-thirds of all retail prices now end in a 9.

Of course we think that other people fall for this and surely not us, but that is not the case. Studies like this continue to be replicated over and over. Dropping the price one cent, say from $8 to $7.99 influences decisions dramatically.

Not only are prices ending in 9 harder to recall for price comparisons, we've also been conditioned to believe they are discounted and cheap. The practical implications of this are that if you're a high-end brand or selling an exclusive service, you want to avoid bargain aspect. You don't want a therapist who charges $99.99, any more than you want a high-end restaurant to list menu prices ending in $.99.

In fact, most of the time, it's best to avoid the $ all together. Our response to this stimulus is pain.

The “$” reminds us of the pain of paying. Another clever menu strategy is to show the prices immediately after the description of each dish, rather than listing them in a column, since listing prices facilitates price comparison. You want to encourage diners to order what they want, whatever the price, rather than reminding them which dish is most expensive.

These are not the only nor most subtle ways that numbers influence us. The display of absurdly expensive items first creates an artificial benchmark. The real estate agent, who shows you a house way above your price range first, is really setting an artificial benchmark.

The $100,000 car in the showroom and the $10,000 pair of shoes in the shop window are there not because the manager thinks they will sell, but as decoys to make the also-expensive $50,000 car and $5,000 shoes look cheap. Supermarkets use similar strategies. We are surprisingly susceptible to number cues when it comes to making decisions, and not just when shopping.

We can all be swayed by irrelevant random numbers, which is why it's important to use a two-step framework when making decisions.

Numbers and Time

Time has always been counted.

We carved notches on sticks and daubed splotches on rocks to mark the passing of days. Our first calendars were tied to astronomical phenomena, such as the new moon, which meant that the number of days in each calendar cycle varied, in the case of the new moon between 29 and 30 days, since the exact length of a lunar cycle is 29.53 days. In the middle of the first millennium BCE, however, the Jews introduced a new system. They decreed that the Sabbath come every seven days ad infinitum, irrespective of planetary positions. The continuous seven-day cycle was a significant step forward for humanity. It emancipated us from consistent compliance with Nature, placing numerical regularity at the heart of religious practice and social organization, and since then the seven-day week has become the world’s longest-running uninterrupted calendrical tradition.

Why seven days in the week?

Seven was already the most mystical of numbers by the time the Jews declared that God took six days to make the world, and rested the day after. Earlier peoples had also used seven-day periods in their calendars, although never repeated in an endless loop. The most commonly accepted explanation for the predominance of seven in religious contexts is that the ancients observed seven planets in the sky: the Sun, the Moon, Venus, Mercury, Mars, Jupiter and Saturn. Indeed, the names Saturday, Sunday and Monday come from the planets, although the association of planets with days dates from Hellenic times, centuries after the seven-day week had been introduced.

The Egyptians used the human head to represent 7, which offers “another possible reason for the number’s symbolic importance.”

There are seven orifices in the head: the ears, eyes, nostrils and mouth. Human physiology provides other explanations too. Six days might be the optimal length of time to work before you need a day’s rest, or seven might be the most appropriate number for our working memory: the number of things the average person can hold in his or her head simultaneously is seven, plus or minus two.

Bellos isn't convinced. He thinks seven is special, not for the reasons mentioned above, but rather because of arithmetic.

Seven is unique among the first ten numbers because it is the only number that cannot be multiplied or divided within the group. When 1, 2, 3, 4 and 5 are doubled the answer is less than or equal to ten. The numbers 6, 8 and 10 can be halved and 9 is divisible by three. Of the numbers we can count on our fingers, only 7 stands alone: it neither produces nor is produced. Of course the number feels special. It is!

Favorite Numbers and Number Personalities

When people are asked to think of a digit off the top of their head, they are most likely to think of 7. When choosing a number below 20, the most probable response is 17. We'll come back to that in a second. But for now let's talk about the meaning of numbers.

Numbers express quantities and we express qualities to them. Here are the results from a simple survey that paints a “coherent picture of number personalities.

From The Grapes of Math by Alex Borros
From The Grapes of Math by Alex Bellos


Interestingly, Bellos writes, “the association of one with male characteristics, and two with female ones, also remains deeply ingrained.”

When asked to pick favorite numbers, we follow clear patterns, as shown below in a heat map, in which the numbers from 1 to 100 are represented by squares. Bellos explains:

(The top row of each grid contains the numbers 1 to 10, the second row the numbers 11 to 20, and so on.) The numbers marked with black squares represent those that are “most liked” (the top twenty in the rankings), the white squares are the “least liked” (the bottom twenty) and the squares in shades of gray are the numbers ranked in between.

From the Grapes of Math by Alex Bellos
From the Grapes of Math by Alex Bellos

The heat map shows conspicuous patches of order. Black squares are mostly positioned at the top of the grid, showing on average that low numbers are liked best. The left-sloping diagonal through the center reveals that two-digit numbers where both digits are the same are also attractive. We like patterns. Most strikingly, however, four white columns display the unpopularity of numbers ending in 1, 3, 7 and 9.

Numbers are a part of our lives. We see them everywhere. They influence us, they guide us, and they help us solve problems. And yet, as The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life shows us, their history and patterns can also be a source of wonder.

Eric Hoffer and the Creation of Fanatical Mass Movements

What is the nature of a true mass movement? In 1951, the American philosopher Eric Hoffer attempted to answer this, and published his first and most well-known work: The True Believer: Thoughts on the Nature of Mass Movements.

The True Believer became a hit because it was released on the heels of World War II and at the outset of the US/Soviet Cold War, and hoped to explain the nature of the “mass movements” that created widespread devastation: Nazism, Fascism, and Stalinism among them. Most people were still hungry for answers. (Heck, many people all over the world were still hungry, period.)

Hoffer took the analysis a bit further. What did all mass movements seem to have in common? He didn't stop with modern political movements, but thought also about religious movements, reformations, and nationalist movements throughout history, featuring heavy commentary on Christianity and Islam in particular.

The book is a series of loosely connected cogitations on the nature of fanatically organized mass movements, the kind that can lead to mass murder and starvation as in the cases above, but that have also led to movements we generally look fondly upon like the Catholic Reformation, the American Revolution, and the Indian Independence Movement.

Like any good book, it's impossible to summarize without losing a tremendous amount of understanding. But Hoffer does offer a loose framework for how mass movements start and move into completion, and his insights here are worth studying, for they give us a great window into humanity and history. This will be a longer one, but it's worth the ride.

The Intellectual Underpinning of Revolution

Hoffer makes it clear that the nature of a true mass movement is one of unified struggle. It comes at a time of disillusionment with the state of affairs. It's not necessarily and not even usually desperation, though: People who can barely feed themselves do not tend to revolt, for they do not have the time, interest, or energy. Revolt tends to happen in a society of intellectual discourse and, counter-intuitively, a certain amount of freedom.

But when conditions are right and people are sufficiently whipped into a fervor, a mass movement can arise among a frustrated group. Hoffer outlines the basic definition of a mass movement by emphasizing the call for self-sacrifice as a central element:

The vigor of a mass movement stems from the propensity of its followers for united action and self-sacrifice. When we ascribe the success of a movement to its faith, doctrine, propaganda, leadership, ruthlessness and so on, we are but referring to instruments of unification and the means used to inculcate a readiness for self-sacrifice. It is perhaps impossible to understand the nature of mass movements unless it is recognized that their chief preoccupation is to foster, perfect and perpetuate a facility for united action and self-sacrifice. To know the processes by which such a facility is engendered is to grasp the inner logic of most of the characteristic attitudes and practices of an active mass movement.

With few exceptions, any group or organization which tries, for one reason or another, to create and maintain compact unity and a constant readiness for self-sacrifice usually manifests the peculiarities—both noble and base—of a mass movement. On the other hand, a mass movement is bound to lose much which distinguishes it from other types of organization when it relaxes its collective compactness and begins to countenance self-interest as a legitimate motive of activity. In times of peace and prosperity, a democratic nation is an institutionalized association of more or less free individuals. On the other hand, in time of crisis, when the nation’s existence is threatened, and it tries to reinforce its unity and generate in its people a readiness for self-sacrifice, it almost always assumes in some degree the character of a mass movement. The same is true of religious and revolutionary organizations: whether or not they develop into mass movements depends less on the doctrine they preach and the program they project than on the degree of their preoccupation with unity and the readiness for self- degree of their preoccupation with unity and the readiness for self-sacrifice.

The essential nature, then, of a fanatical mass movement is one where a group of loyal followers can be made to believe, or simply nudged into indulging a prior belief that their own life is less important than a greater cause. A willingness to lose their own identity for the “greater good,” however defined, seems a necessary element.

In order for this to happen, a population must obviously be given something to believe — a cause strong enough to subsume them. And in order to do that, the cause must be all-encompassing. The reason Hoffer titles the book True Believer is that a strong mass movement only works when it purports to provide a solution that can be turned to for all the essential answers: The Bible, the Qur'an, Liberty, Freedom, Communism, Equality, Lebensraum, the State, the Nation…all-encompassing narratives which would become the central dogma of a mass movement, to be enacted and upheld by force. (These narratives would become a central element of Yuval Harari's wonderful book Sapiens about 50 years later. He called them the human myths.)

The process is kicked off by a radical intellectual, or what Hoffer calls a Man of Words.

The Man of Words

As Hoffer describes it, the process begins with a thinker or a group of thinkers with a strong set of ideas that offer a solution to a proposed societal problem. Karl Marx. Jesus Christ. Thomas Paine. Martin Luther. The German philosophers. The French philosophers.

These intellectuals “prepare the ground” for the movements to come, by providing the central dogmas of the revolution which begin to get the populace on board by giving them an alternative to the present. A new future. And without these forceful new ideas, the momentum will eventually die.

Generally, this only works in a society where the intellectuals are not already part of the establishment: There has to be a certain disaffected nature to their work. If they don't hate the powers that be, why bother inciting Revolution — intentionally or not? Hoffer makes the point that in societies where the intellectuals are the ruling class, or participate heavily in the ruling class, there's not much of a tendency towards a true mass movement.

In one passage, he describes the outline of this beginning period:

The men of letters of eighteenth-century France are the most familiar example of intellectuals pioneering a mass movement. A somewhat similar pattern may be detected in the periods preceding the rise of most movements. The ground for the Reformation was prepared by the men who satirized and denounced the clergy in popular pamphlets, and by men of letters like Johann Reuchlin, who fought and discredited the Roman curia. The rapid spread of Christianity in the Roman world was partly due to the fact that the pagan cults it sought to supplant were already thoroughly discredited. The discrediting was done, before and after the birth of Christianity, by the Greek philosophers who were bored with the puerility of the cults and denounced and ridiculed them in schools and city streets.

Christianity made little headway against Judaism because the Jewish religion had the ardent allegiance of the Jewish men of words. The rabbis and their disciples enjoyed an exalted status in Jewish life of that day, where the school and the book supplanted the temple and the fatherland. In any social order where the reign of men of words is so supreme, no opposition can develop within and no foreign mass movement can gain a foothold. The mass movements of modern time, whether socialist or nationalist, were invariably pioneered by poets, writers, historians, scholars, philosophers and the like. The connection between intellectual theoreticians and revolutionary movements needs no emphasis.

But it is equally true that all nationalist movements— from the cult of la patrie in revolutionary France to the latest nationalist rising in Indonesia—were conceived not by men of action but by fault-finding intellectuals. The generals, industrialists, landowners and businessmen who are considered pillars of patriotism are latecomers who join the movement after it has become a going concern. The most strenuous part of the early phase of every nationalist movement consists in convincing and winning over these future pillars of patriotism. The Czech historian Palacky said that if the ceiling of a room in which he and a handful of friends were dining one night had collapsed, there would have been no Czech nationalist movement.

Such handfuls of impractical men of words were at the beginning of all nationalist movements. German intellectuals were the originators of German nationalism, just as Jewish intellectuals were the originators of Zionism. It is the deep-seated craving of the man of words for an exalted status which makes him oversensitive to any humiliation imposed on the class or community (racial, lingual or religious) to which he belongs however loosely. It was Napoleon’s humiliation of the Germans, particularly the Prussians, which drove Fichte and the German intellectuals to call on the German masses to unite into a mighty nation which would dominate Europe. Theodore Herzl and the Jewish intellectuals were driven to Zionism by the humiliations heaped upon millions of Jews in Russia, and by the calumnies to which the Jews in the rest of continental Europe were subjected toward the end of the nineteenth century. To a degree the nationalist movement which forced the British rulers out of India had its inception in the humiliation of a scrawny and bespectacled Indian man of words in South Africa

Of course, the Man of Words is simply an intellectual forbear. Although it has happened, it's rare that he or she is the actual leader of the movement. As Hoffer points out, Christ was not a Christian and Marx was not a Marxist. The movements came as a result of their anti-establishment thought-work, but there's a crucial difference between the Man of Words and the Fanatic which will begin catalyzing the movement: the Man of Words may be a lot more intellectually flexible than the true believers who follow in their footsteps:

The genuine man of words himself can get along without faith in absolutes. He values the search for truth as much as truth itself. He delights in the clash of thought and in the give-and-take of controversy. If he formulates a philosophy and a doctrine, they are more an exhibition of brilliance and an exercise in dialectics than a program of action and the tenets of a faith. His vanity, it is true, often prompts him to defend his speculations with savagery and even venom; but his appeal is usually to reason and not to faith. The fanatics and the faith-hungry masses, however, are likely to invest such speculations with the certitude of holy writ, and make them the fountainhead of a new faith. Jesus was not a Christian, nor was Marx a Marxist.


The reason for the tragic fate which almost always overtakes the intellectual midwives of a mass movement is that, no matter how much they preach and glorify the united effort, they remain essentially individualists. They believe in the possibility of individual happiness and the validity of individual opinion and initiative. But once a movement gets rolling, power falls into the hands of those who have neither faith in, nor respect for, the individual. And the reason they prevail is not so much that their disregard of the individual gives them a capacity for ruthlessness, but that their attitude is in full accord with the ruling passion of the masses.

The next steps, the corralling of the people, is often carried out by a Fanatic.

Fanatics of a Revolution

When the moment is ripe, only the fanatic can hatch a genuine mass movement. Without him the disaffection engendered by militant men of words remains undirected and can vent itself only in pointless and easily suppressed disorders. Without him the initiated reforms, even when drastic, leave the old way of life unchanged, and any change in government usually amounts to no more than a transfer of power from one set of men of action to another. Without him there can perhaps be no new beginning.

This may be a bit of historical curve-fitting, but Hoffer thinks that a frustrated creative intellectual makes a pretty good Fanatic, and points to specific examples of where that held — Hitler, Robespierre and Lenin among them. Whether or not that is true matters less than the fact that the Fanatic is responsible for galvanizing the movement and pushing it to a point of no return.

But the Fanatic is not really a good leader or manager in a long-term sense, simply because of the nature of their fanaticism: They believe too strongly in their dogmas, and their intellectual blindness pushes them to blunder. Hitler and Mussolini would be excellent examples. Their fanaticism got them a long way, but ultimately it sowed the seeds of its own destruction.

If it is to be a sustainable movement, then the Men of Action, as Hoffer names them, will have to do the hard work.

Men of Action: Holding Down the Fort

Hoffer continues by describing the final phase of the beginning of a Movement: Leadership by a practical actor with less devotion to pure fanaticism and a healthier dose of order (ideally):

The chief preoccupation of a man of action when he takes over an “arrived” movement is to fix and perpetuate its unity and readiness for self-sacrifice. His ideal is a compact, invincible whole that functions automatically. To achieve this he cannot rely on enthusiasm, for enthusiasm is ephemeral. Persuasion, too, is unpredictable. He inclines, therefore, to rely mainly on drill and coercion. He finds the assertion that all men are cowards less debatable than that all men are fools, and, in the words of Sir John Maynard, inclines to found the new order on the “necks of the people rather than in their hearts.” The genuine man of action is not a man of faith but a man of law.

Still, he cannot help being awed by the tremendous achievements of faith and spontaneity in the early days of the movement when a mighty instrument of power was conjured out of the void. The memory of it is still extremely vivid. He takes, therefore, great care to preserve in the new institutions an impressive façade of faith, and maintains an incessant vow of fervent propaganda, though he relies mainly on the persuasiveness of force. His orders are worded in pious vocabulary, and the old formulas and slogans are continually on his lips. The symbols of faith are carried high and given reverence. The men of words and the fanatics of the early period are canonized.

Though the steel fingers of coercion make themselves felt everywhere and great emphasis is placed on mechanical drill, the pious phrases and the fervent propaganda give to coercion a semblance of persuasion, and to habit a semblance of spontaneity. No effort is spared to present the new order as the glorious consummation of the hopes and struggles of the early days.

It is, of course, true that the categories often overlap. Joseph Stalin was both a practical leader and a man of deep fanaticism, as was Hitler. The leaders of the American Revolution certainly carried both traits, as did Gandhi in leading the Indian Independence. The balance between the fanaticism necessary to catalyze real change and the practical sense needed to sustain a cohesive movement probably affords some measure of success or failure as time goes on. (Nazism collapsed, at least partially, due to fanaticism outstripping reality.)

From there, the new movement, no longer a minority but the dominant power, must find a way to stabilize, and it often does this by patching together a structure from many other institutions:

Stalin’s Russia was a patchwork of bolshevism, czarism, nationalism, pan-Slavism, dictatorship and borrowings from Hitler, and monopolistic capitalism. Hitler’s Third Reich was a conglomerate of nationalism, racialism, Prussianism, dictatorship and borrowings from fascism, bolshevism, Shintoism, Catholicism and the ancient Hebrews. Christianity, too, when after the conflicts and dissensions of the first few centuries it crystallized into an authoritarian church, was a patchwork of old and new and of borrowings from friend and foe. It patterned its hierarchy after the bureaucracy of the Roman Empire, adopted portions of the antique ritual, developed the institution of an absolute leader and used every means to absorb all existent elements of life and power.


Thus we have an outline for the True Believer style mass social movement: It starts by creating an ideology, a set of dogmas around which a fanatical leader or group can create a following. From there, it must find a way to sustain itself as reality creeps in on ideology — structure is introduced or the whole thing will collapse. In almost all cases, there is tremendous violence, although in certain (rare) circumstances, it can be bloodless. Even the rise of religions or nations that promote peace came with tremendous bloodshed.

In the end, mass movements likely take many forms, but Hoffer gives us as good a framework as any to start thinking about the way they are constructed.

Still Interested? Check out the whole book, it's a very interesting read.