The Great Mental Models Volume 3: Systems and Mathematics

by Rhiannon Beaubien

Network effects occur when the utility of a product or service increases as more people use it. More users mean more value for all users. An obvious example is the telephone. If you own one but none of your friends do, it’s not much use. But with each additional friend who gets one, the utility increases.

Users become reluctant to switch to an alternative because of the advantages created by network effects. Once network effects take hold, a product or service will continue to grow in popularity even without additional marketing.

companies put a lot of effort into attracting early users in the hopes of reaching the critical mass requisite for network effects to take hold. Often, it is a matter of luck.

Network effects don’t just occur for technology. We can apply the concept to any situation where the value of something increases the more people use it.

Stores of value like gold are subject to network effects. The more people hold them as a long-term store of value, the more stable their prices become and the more appealing they are to future investors.

Understanding the influence and importance of sampling is a fundamental key to understanding the world better. The mental model of sampling is a first principle for a number of concepts in mathematics, especially in statistics.

Seeing as we often use statistics to gain a picture of reality, taking sampling into account will broaden your knowledge of other areas involving measurement, such as psychology. It will also help you think about risk and reward while delineating luck from skill.

Numbers are intellectual witnesses that belong only to mankind...

When we want to get information about a population (meaning a set of alike people, things, or events), we usually need to look at a samp...

We use samples to tell us about the world. The exception is a census, which aims to include everyone, not just a sample.

Sample size refers to the number of people, things, or events we look at from a population. It can have an enormous influence on the results we get.

One area where sampling is especially salient is in scientific studies of people, in which case the sample size is the number of participants.

We’re all the more inclined to respect anecdotes if they confirm what we already believe. An anecdote is a sample size of one, and we should collect more data points if possible. The exception is when one result indicates something is possible. The first person to survive a heart transplant was more than an anecdote.

Traveling, living in a big city, or otherwise finding a way to meet more diverse people may make you more tolerant. Exposing yourself to a broader range of ideas through interdisciplinary, far-reaching reading may make you more open-minded. Learning more about the history of your industry and accumulating more experience may make you more risk aware as you learn about rarer yet more extreme possibilities.

In looking through any dictionary, it’s easy to find words that have multiple meanings. Does dove refer to a bird or the past action of jumping into a pool? To capture the entire history and use of a language, the first dictionaries must consider hundreds of thousands of data points. The OED, although not the first English dictionary, was the first to accomplish the feat of a thorough cataloguing of the English language.

The insights you get from a large number of data points are only going to be as good as the range of possibilities they cover.

They go on to demonstrate that the people in WEIRD societies are outliers in many ways; therefore, we probably shouldn’t be using studies based entirely on the behavior of WEIRD subjects as representative of the entire human population.

If we want to say something meaningful about human nature, then our data set ought to contain information from a sample of humans that represent the diversity found on the planet.

Data needs to be collected in order to be analyzed, so you need to ask yourself if you have the right mechanisms to collect the data that will give you the fullest picture possible—or at least enough to make a good decision with the potential for good outcomes.

Therefore, making rules and changes based on data needs to look hard at the data being used.

“If you aren’t aware of how those biases operate, if you aren’t collecting data and taking a little time to produce evidence-based processes, you will continue to blindly perpetuate old injustices.”

“We need to be less cavalier in addressing questions of human nature on the basis of data drawn from this particularly thin, and rather unusual, slice of humanity.”

You will reduce your chances of a good outcome if the data you collect is not representational of the people affected by the decisions you make. Yes, large sample sizes are better than small sample sizes for decision-making, but it’s critical to remember that not all data sets are created equal.

Conclusion What this model teaches us is that sample size is often an invisible component of what we think we know about the world. In most situations, increasing our sample size gives us valuable information that lets us see our situation in a new light. But to have representative samples takes work. Using this model means taking the time to explore what isn’t obvious and being aware of how easy it is to corrupt our samples with bias.

Randomness can be a hard model to use because humans aren’t great at comprehending true randomness. When we look at the world, we tend to see order.

We notice patterns and sequences, like thinking the world is out to get us because a few bad things happened in a row. Yet our sense of predictability and order is an illusion. Much of what we encounter day to day is random; we just don’t perceive that. Using randomness as a model means being willing to accept that it exists and looking for situations where it can help us.

The dictionary definition of randomness is “proceeding, made, or occurring without definite aim, reason, or pattern.”1 It is the opposite of predictability and order...

[T]he human mind is built to identify for each event a definite cause and can, therefore, have a hard time accepting the influence of unrelated or random factors. » Leonard Mlodinow2

It’s hard to accept that much of what happens in our lives is chance, not ordained in any way. It’s like the world throws random dots at us, and humans are constantly trying to draw lines between them, even if none exist. Randomness thus forces us to confront our lack of control over outcomes in many situations.

The history of ideas is a history of gradually discarding the assumption that it’s all about us. » Paul Graham3

When we open a history book, we see structured narratives. Events have a beginning, a middle, and an end. It only seems this way in retrospect. Not only are past events random, so is the information we have about them.

Randomness is a fundamental part of the universe, and embracing it instead of trying to fit order where it doesn’t belong can help us do two things: be less predictable and be more creative.

Making use of chance can be a deliberate and effective part of approaching the hardest sets of problems. » Brian Christian and Tom Griffiths8

A question authors always seem to be asked in an interview is, “Where do you get your ideas?” More than a few have gone on record stating how much they hate this question. Why? Because it implies there is an idea bank, or a creativity app, or some defined source authors can access. When they are faced with a blank page, they can purchase or otherwise pull out an idea from this source, and away they go.

The reality is far messier. Ideas come from everywhere with great inconsistency. What is inspiring to one author one day may not inspire them the next time they are looking for an idea. And a particular source of inspiration is unlikely to work for another author in exactly the same way. When one’s creativity feels blocked or when interesting ideas seem inaccessible, the introduction of randomness can come to the rescue.

She makes it clear that although ideas definitely come from somewhere, an author can never know precisely where that might be. And so randomness—in this case understood as unpredictability—is a very useful tool when trying to create.

The writing process for fiction is far from formulaic. Sometimes you start with the whole plot in your head, and sometimes you don’t. Sometimes you plan out every chapter before you start writing, and sometimes your characters unexpectedly steer your story in a different direction.

Sometimes you have enough ideas to give you momentum to reach the end, and sometimes you get stuck halfway through. Smiley recalls how she dealt with a challenging time writing a story: “Rather than planning and working out in advance, as I had done with m...

Writing a work of fiction is not a linear process. As Smiley describes in one experience: “One day I waited for inspiration, got some, went off in a completely new direction, then had second thoughts the next day and tried something new.”11 Often an author will have to try a variety of options for a particular scene in order to determine the best way forward.

When you begin a novel, where you start is often not where you end up. You may have certain ideas going into it, but your research demonstrates you’ve made some erroneous assumptions, and you have to change your plot or your setting. Or a character turns out to be more interesting than you imagined, and they end up carving out a bigger role for themselves.

Which brings up another important point with regard to the value of randomness in novel writing: authors are by no means universal themselves. The experiences, desires, assumptions, and goals of those telling the stories are just as varied as the stories themselves.

“Defoe’s nonconformist religious training gave him a sense of sympathetic connection with subjects not previously given serious literary treatment—prostitutes, servants, criminals, working men and women, courtesans, adventurers of all stripes.”13 And Defoe is but one example. We can imagine that all novelists draw on their own lives for inspiration, and their particular backgrounds determine what they see in the world around them.

Even with an interesting story developing in the brain, with plot points and characters pushing to get out and onto the page, sometimes authors get stuck. Instead of waiting to get unstuck as if by magic, the better solution is to add an element of randomness and see where it takes you.

If you are bored with your subject, it is fatal to try to think your way out of it.”14 Instead you must experience your way out of it. If you are stuck, it means that everything you currently think cannot help you.

You must get out into the world and experience the serendipity of stumbling into new things. One of these new things will help you continue your story, and you have no way of knowing in advance which thing it will be. So get out there and see what you run into.

“As you aim for perfection, don’t forget that there is no perfect novel, that because every novel is built out of specifics, every novel offers some pleasures but does not offer some others, and while you can try to achieve as many pleasures as possible, some cancel out others.”15 A particular novel cannot be all things to all people.

One can neither master creativity nor be creative all the time. When you are stuck while pursuing the nebulous task of trying to achieve creative output, introducing an element or two of randomness can help you make new connections to move past the block you are pushing against.

Pseudorandomness is the appearance of randomness due to our inability to predict or detect a pattern although there are underlying causal influences.

True randomness is different. It is still coupled with probability distributions but is completely detached from any causal factor, meaning there’s no explanation that we could apply to even approximately guess a more or less likely outcome for the next trial.

Our tendency to create a narrative to order and organize the world makes us predictable. We are also highly suggestible, remembering the most recent things we were exposed to. Thus humans often behave ...