Mental Model #8: Look for Equilibrium Points. This mental model is about noticing trends in progress. When you first start something, you go from zero to one - that's an infinite rate of progress. Then you go from one to two, two to three, and so on, and the rate of progress slows, and the returns start diminishing. Somewhere around there is an equilibrium point that truly represents what the average mean will be. Don't make the mistake of not waiting for it.

Mental Model #9: Wait for the Regression to the Mean. This is the final mental model about seeing the whole picture in terms of information. A change without a reason for the change is not really a change; it's just a deviation. As such, it doesn't represent what will continue to happen in the future. A regression to the mean is when things settle back down and resume what they were doing before - this is representative of reality.

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Peter Hollins is a bestselling author, human psychology researcher, and a dedicated student of the human condition.

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MM #8: Look for Equilibrium Points

Use to find real patterns in data and not be fooled.

The second piece of the general mental model of visiting a city in all seasons, or simply seeing the whole picture, has to do with what are known as diminishing returns.

This is an economic principle that describes how an increase in resources doesn't always correspond to an increase in the outcome you want. In plain terms, this means that where you might be ecstatic to eat one donut, the amount of joy you feel will drastically decrease as you get to donut number ten. There is no linear relationship between input and output.

What we get back from our efforts is a decrease of what we were seeking; there is a natural rate of decay for where the more resources we put into something, the less we get out of it. Sometimes it is even an inverse relationship (the more resource, the less output).

The mistake we often make is to base our assumptions, predictions, projections, or information in general on the assumption that input will always correspond with output. We must look past shiny beginnings that are misrepresentative and wait for equilibrium, because that's what we should draw conclusions from. While there isn't necessarily a predictable rate that diminishing returns follows, the existence of it is predictable in general. If you don't account for it, you are being myopic and not seeing the world for what it is.

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If you are learning how to play a new instrument, you will make leaps and bounds at the beginning because it is all new. It's easy to go from not knowing how a piano works to playing "Twinkle Twinkle Little Star," and yet that represents a mathematically infinite amount of improvement. However, this progress will rapidly slow down, and you will have to put in increasing amounts of effort to keep improving. How will you fare when you must constantly struggle? That's the equilibrium where your true rate of improvement lies.

The law of diminishing returns encourages us to look for equilibrium points to accurately assess and learn information. Just like with black swan events, you can't base your judgments off outliers or skewed information.

But equilibrium points also apply to how much effort we should expend toward an outcome.

More often than not, when we decide to put more "input" into our work, something else tends to get lost. If you try reading 900 words a minute, you will lose comprehension and understanding, which is far more valuable to the overall task of reading. If you try learning the piano too intensely, you will burn out and start hating it. If you try to study for nine hours straight, chances are you won't remember much. Not recognizing the law of diminishing returns will usually hurt you.

So this mental model has two uses: first, to more accurately analyze information about others; second, to know where your own equilibrium points are and when you should rethink how much effort you are putting in for the number of results you are getting.

This doesn't mean that your efforts are worthless - in general, if you don't work toward something, you won't get anything at all. But by the same token, working harder and harder toward something doesn't mean your rewards will increase in proportion to your efforts.

For the answer, we're going to have to go all the way back to Mother Goose: be like Goldilocks and find a zone of satisfaction.

In the off chance that you need a refresher, Goldilocks was the fabled girl who went into the home of three bears while they were out and about and started sampling all their food and furnishings. She found the father bear's chair "too hard," the mother bear's chair as "too soft," and the baby bears chair to be "just right." Other variations have Goldilocks being picky about the size of the bowls and the taste of the food.

If you can overlook the fact that Goldilocks seemed to think there's nothing wrong with breaking and entering into a wild animal's home, the moral of the story is that there is a certain zone of satisfaction where your input and effort provide an acceptable amount of satisfaction or outcome. If you expend too many resources and effort, you move out of the zone - too little outcome. If you expend too little, you move out of the zone - too little outcome. If you expect too much or too few results, you also move out of the zone.

Seeing the world clearly requires having a clear understanding of cause and effect.

MM #9: Wait for the Regression to the Mean

Use to find real patterns in data and not be fooled. (Yes, again)

As mentioned in the discussion of black swan events, sometimes we mistake an "extreme" or extraordinary event for something we need to plan around, but more often than not the event is just an "outlier" that doesn't really signify how things are. Even if a big event or happening shakes up our immediate surroundings, it shouldn't be automatically used to assume a "new reality." More likely than not, the black swan event won't (or at least shouldn't) have a total, utter change to your daily experience or beliefs.

Related to that is the idea of "regression to the mean." For those of you (like myself) for whom math isn't exactly second nature, the "mean" essentially represents something akin to an "average": a sort of midpoint that indicates a sort of normalcy, a kind of "typical" value. In our definition, "the mean" means the usual or most common status of a given situation.

For example, consider a week of family meals. Probably at least five times every week the family eats at home. On the weekend or on special occasions, the family might go to a restaurant and have a more expensive meal that they don't have to cook. That's an outlier, though. Usually, they'll eat at home, and that's "the mean."

Maybe one week they'll go to a really expensive restaurant. Perhaps they'll go on a cruise for a week and eat every single meal in a luxury ocean liner. But that's not something they can sustain every single day. Eventually they're going to get back to their usual routine of eating at home without too many bells and whistles. That's their usual practice - the mean - and at some point, they're going to "regress" and settle back into it.

Take the common example of how obsessive and optimistic a couple is when they first get together. This is known as the honeymoon period, and it is imbued with new relationship energy. But it would be a mistake to assume that this rate of love and obsession is truly representative of the relationship. There will soon be a regression to a normal and sustainable rate of love - the real rate of love that can be expected. That's when you know if a relationship is more than a cocktail of hormones.

If you are a basketball player and you have a long history of making shots at a 40% rate, that's your mean. If you start making shots at a 50% rate, it doesn't mean that you're suddenly a better player, because eventually, you will just regress back to the mean. Outliers that appear to be patterns or deviations can fool us.

Regression to the mean happens with every aspect of our lives. If you start dating someone new, your apartment is going to be clean and your hygiene will probably be immaculate. And yet, this doesn't represent a true change in behavior on your side. As the relationship grows longer and more comfortable, you will regress to the mean in your cleanliness and hygiene. If there was no basis for a change in the first place, eventually things will simply get back to normal.

A slightly more scientific explanation of regression to the mean, as originally conceived by British statistician Sir Francis Galton, is that in any sequence of events that are affected by different conditions or variables - such as environment, emotions, and plain old luck - extraordinary events are usually followed by more ordinary, typical ones. So when an aberrant, deviant, or untypical event happens, it's much more likely that it won't happen again in a patterned way. Rather, the pattern that's much more probable to return is "the usual."

This mental model encourages you to simply wait and see. If something extreme occurs, wait to see the recovery. If something unexpected or unpredicted happens, wait to see the aftermath. If something appears to be trending, wait to see what happens after it stops trending (for example, the seeming rise of bellbottom pants every couple of decades).

Remember, without an actual basis for a change or extreme event, the mean will always do what Arnold Schwarzenegger uttered in the Terminator, "I'll be back."

Let the entire cycle play out and assess all of the information you'll encounter during that time. Don't make any sudden moves or change of plan after the occurrence of the big, abnormal event. By being patient and waiting for events to return to their normal state, you'll get a much better sense of how the situation has been changed. Statistically speaking, it will probably not be that much at all.

Visiting a city in all four seasons may be difficult, time-consuming, and tedious, but these three mental models are just the beginning of how to properly collect information and be unswayed by seductive yet incorrect perspectives. "Black swan" events, equilibrium points, and regressions to the mean all obscured our thoughts because they are more emotional than realistic.

An essential aspect of seeing the whole picture is to understand when things are and are not connected or related. We have a tendency to fabricate a cause and effect relationship where there is none.

There are clear psychological reasons for this. Uncertainty scares people. At least some of the time, we want to know what's going to happen in the near and distant future. When we can't figure it out with hard evidence or data, we use our instincts, gut feelings or "hunches."

Sometimes it's true those hunches are on the money and can save a lot of trouble. But more often than not, those hunches don't amount to real information and tend to be a waste of our analytical resources. Even the ones that turn out to be correct are more similar to a stopped clock being correct twice a day by default. Everyone has their lucky guesses.

If we have this tendency, we might as well try to ensure that it is as accurate and clear as possible. While there's no surefire way to accurately predict everything that's going to happen in the future, there are several mental models we can use to establish the likelihood of certain events happening - or, more helpfully, prepare us for whatever results emerge. They don't allow us to predict the future, but they do encourage us to analyze the chain of events and incorporate probabilistic thinking into our daily lives.

These models rely on objectivity and logic instead of subjective emotions and intuition. They also help us understand when our analyses of certain situations and correlated events are working, or whether we're making associations and links between events that really don't have any relation to each other. The goal with these models is to evaluate and plan for the future in a more precise and practical way.