This post is about the 3rd (and, so far, the last) volume about the Great Mental Models by Shane Parrish, so following The Great Mental Models – General Thinking Concepts and The Great Mental Models, vol. 2 – Physics, Chemistry and Biology.

As an engineer, I actually expected more, but then I remembered that these models are for everyone with no prior knowledge (at least, no more than the average knowledge you should acquire during high school). Without any unnecessary words, here’s the “recap” coming from my notes and, as always, after recommending you to buy the books, that are also wonderfully made talking about the book as an object, with high-quality paper (while reading, I felt a sensation I almost forgot, the one you may recall from turning the pages of the good big books you touched when you were much younger), I remember that all the words you’ll find hereafter between parenthesis are MY thoughts/considerations, not the the author’s thinking.

0. Intro

• “How much you know in the broad sense determines wjat you understand of the new things you learn”, Hilde Ostby and Ylva Ostby
• “The more moving parts you have in something, the more possibilities there are”, Adam Frank
• (for more, see “Range” by Epstein)
• “Systems thinking is a discipline for seeing wholes. It is a framework for seeing interrelationships rather than things, for seeing pattern of change rather than static snapshots”, Peter Senge

1. Systems

“In spite of what you majored in, or what the textbooks say, or what you think you’re an expert at, follow a system wherever it leads. It will be sure to lead across traditional disciplinary lines”, Donella Meadows

1.1 Feedback loops

• Think of feedback as info communicated in response to an action.
• We provide and receive feedback everyday
  • Sometimes formal, sometimes unconsciously e.g. with body language
  • In complex systems, feedback is rarely immediate
    • This delay may complicate establish causes and effects
    • (and it’s also harder to commit for long-term results)
    • The faster you get accurate feedback, the more quickly you can iterate to improve
      • (For more, read “SuperForecasting”, “Atomic Habits“, “Dopamine nation” and others)
• Most common in human behavior is the feedback when incentives are involved
• A valuable skill is learning to communicate feedback in a precise and easy way
• In “The theory of moral sentiments”, Adam Smith found that humans are basically selfish, so to foster cooperation, societies developed way like reproval reactions if someone do something good, approval otherwise – so: a feedback on our actions
  • (You can read much more in “Loneliness” by Cacioppo)
• 4 aspects of social systems in feedback:
  1. Creating the right future incentives: Future incentives are crucial for shaping behavior over time. In a social system, establishing the right incentives means designing rewards or penalties that align individual goals with the collective goals of the organization or society. This involves understanding what motivates people and structuring incentives that encourage desirable behaviors while discouraging undesirable ones. For example, a company might offer bonuses for employees who innovate, thereby fostering a culture of creativity and problem-solving.
  2. Influencing behavior at the margins: This refers to the subtle shifts in behavior that occur at the edge of decision-making processes. Small changes in policy, environment, or circumstances can significantly influence how individuals make decisions. Influencing behavior at the margins doesn’t involve drastic changes; rather, it focuses on nudging behavior in desired directions through slight adjustments. For instance, slightly lowering the price of healthier food options in a cafeteria can nudge people towards making healthier eating choices without requiring them to dramatically alter their behaviors.
  3. Dealing with information cascades: Information cascades occur when people make decisions based on the observed actions of others rather than their own private information or intuition. This can lead to rapid widespread behaviors that aren’t necessarily grounded in rational decision-making. To manage information cascades, it is important to ensure that accurate and transparent information is available to prevent the spread of misinformation and to encourage decisions based on sound data. For example, during a public health crisis, clear and consistent communication from trusted sources can prevent panic and encourage appropriate responses.
  4. Building trust: Trust is foundational to any functioning social system. Building trust involves consistent and reliable actions that reinforce the belief that others will perform as expected. High-trust environments encourage cooperation, reduce the cost of transactions (as less verification is needed), and facilitate more robust feedback loops, as people feel safe sharing honest feedback. Building trust can involve transparent processes, accountability mechanisms, and a culture that values ethical behavior and integrity. For example, a company that openly shares its decision-making processes and involves employees in dialogue will likely build stronger trust than one that operates in secrecy.
     • See also the prisoner dilemma, where is found that often iterative repetition of experiment can lead to cooperative behavior

1.2 Equilibrium

• When a system is too far from equilibrium, it will likely fall apart
• A system is in equilibrium when it’s in a stable state
  • (Actually there different forms of equilibrium)
• In a family or any group with limited resources, to maintain equilibrium, adjustment is needed
  • e.g.: if one child wants to take music lesson, need to spend less on food, to remain in a certain range of money flow
• In a body, homeostasis is responsible to keep everything normal in a certain range
  • (see allostatic regulations/range)
• Information is crucial to maintain equilibrium, as well as understanding that we often deal with uncertainty
  • This is also true when doctors talk with patient, anyway doctors need to actively support patient in making decision, since they have in theory much more knowledge on medicine
    • (for more, see “The Paradox of Choice” and Decisive” and others)
  • Shared Decision Making
• Important knowing and testing assumptions
  • This was particularly true during the first phases of space explorations, to understand how a body can better survive outside earth
• Proactively look for what can happen after a “move”, if a do X, it may happen Y so I’ll need to adjust this way
  • (see also robotics and AI, plus all the control systems like ICS/SCADA)

1.3 Bottlenecks

• All systems have parts slower (or weaker) than others, called bottlenecks, since that is the part where flow become slower compare to other sections
• Nobody want bottlenecks (unless needed), that’s why they delegate
  • (for more, read “Buy Back Your Time” and many others on delegation and time)
• As a corollary, you can’t get rid of bottlenecks, since once you remove the first one, another part will be the bottleneck
  • Sometimes, only way to get rid is re-design the whole system
    • (in engineering, beware of legacy, can be ICT or physical roads/constructions)
• Most known bottlenecks are resources like manpower and materials during a construction
  • (but also obstacles like ancient vases if you want to build a 3rd line in Rome subway or extend one of the first two)
  • (beware of critical path in Gantt and any PM tool)
• Bottlenecks inspire innovation, to overcome limits
  • (like crisis, they can push for optimizing or re-thinking)

1.4 Scale

• We can scale up or down a system
  • Sometimes better stay small
  • Remember that scaling is often non-linear
    • e.g.: in baking, you can’t just double all the ingredients, since for example doubling the yeast can lead to faster fermentation, compared to same ratio in smaller scale
  • Greater size often means more connections and interactions, growing not linear and leading to bottlenecks
    • (see for example ICT system, but also urban structures and social ones)
• There’s a big difference from network of family-run companies and big industries
  • Economy at scale is different, pros and cons
• Not always going on scale of being part of biggest companies is better
  • See a lot of Japanese examples, like Kongo Gumi or Tsuen Tea
• (see also Roman empire or empires in general, scaling up / expanding is something absolutely non-linear)
• Also in evolution, scaling up or down is something questioned by Haldane in 1926 book “On being the right size”, where he made hypothesis on why some animals are just that big or small, including their body parts
• There are many factors involved in scaling up, for example one of the biggest innovations for factories to grow was the artificial light, a game changer that enabled work also during the night, also providing new ways to live the night.
  • Building distribution of electricity and gas was crucial to increase coverage of light and so to develop this new system at scale
• Remember that connecting and grow change the (eco)system as a whole
• (not always “bigger is better”, sometimes also the exposure to failure increase (see constructions but also big companies), so find the right size)

1.5 Margin of safety

• A margin of safety is needed to expect the unexpected and so to manage variations, to respond to inputs also in nonlinear ways.
• It’s like a buffer between safety and danger
  • Engineers design stuff with extra-buffer for safety
    • More robust systems able to deal with much more load than the one allowed
    • Backup/redundancy
    • The higher the stakes, the higher the margin of safety
      • One thing is breaking a pen at school, another one is breaking a critical component of a bridge
  • Be aware that margin of safety can lead to more sense of being safe
    • e.g.: drivers with seat belt fasted are more likely to drive with less care, so putting more at risk pedestrians since the driver feel safer in case of accident
  • At the opposite, too much margin of safety can lead to waste of resource
    • (just as an example: over-dimensioning an ICT carrier to prevent even one minute down if it’s not critical line can be a huge waste)
• Anticipate the worst
  • (like engineers, look at the worst case scenario, but in a reasonable way, see Taleb on black swans)

1.6 Churn

• A system may require stocks, more than just the active parts used
• Make sure you replenish both stocks and the part to maintain them
• It’s valid for cells in the body, trees in the forest, employees turnover at work, etc.
• When dealing with customers, be aware that retention of 90% compared to competitors’ 95% can lead to a big difference over time
• You can use churn to innovate
  • (see the concept of Ship of Theseus, changing parts time by time and becoming something completely new)
  • (see also the concept of Kaizen, but applied when parts change and replacing old ones with new different/better)

1.7 Algorithms

• Algorithms turn inputs to outputs
• Once you identify steps to solve a certain kind of problem, you don’t have to start again from scratch
  • (this is the basic concept behind SOPs, modularity, etc.)
• It’s not a calculation, but the method used when making a calculation
  • (this is determinism, different from probabilistic, e.g. AI)
• Dennett identified 3 characteristics for an algorithm:
  • 1. Substrate neutrality, ignoring layers below or above
  • 2. Underlying mindlessness, almost everyone can follow them one step at time
  • 3. Guaranteed results, if you follow the recipe with same input and conditions, you’ll almost surely obtain same output
• Even some pirates established rules to cooperate each others and pursuing/achieving their results
  • Even including rules to follow in case a captain decide to abuse power
• In several business and activities, there are huge benefits in implementing and using (and, depending on intellectual property and need to know and confidentiality, sharing) algorithms, to automate and replicate procedures.
  • (see standard, commercial procedures like in airlines, etc.)
• Remember that, in complex systems, you can’t just copy-paste parts of algorithms
  • “No gluing together of partial studies of a complex nonlinear system can give a good idea of the behavior of the whole”, Murray Gell-Mann

1.8 Critical mass

• A system becomes critical when it’s on the verge of changing from one state to another
  • Once a system reaches a certain threshold, it only needs a tiny nudge to change it
    • (it’s observed in fires, transistors, Hook law, etc., sometimes non-reversible)
    • See for example boiling water, when 1°C makes the difference between liquid and gas
  • In society, an example is shifting in Overton window
• Common examples in society are about movements and protests
  • (read more in “The Tipping Point”)
  • (it applies also for “popular” people with their followers, with politics, religions, etc.)
• In nuclear physics, critical mass refers to the minimum amount of fissile material needed to start a self-sustaining reaction
• You can see it like a peak of a hill, where you require a lot of effort to put a big ball on the top, but once you’re over the hill, the ball will fall other side alone and fast
  • (the point is in understanding “The dip”: when to stick to climbing and when is better quitting)
  • (sometimes, it’s like bamboo that seems not growing, but then suddenly growing overnight, but they acquired energy day by day before hitting a certain threshold, same is for any apparent sudden growing)
• Interaction is paramount
• Even if environment alone doesn’t make the change, modifying environment can help in reaching or not the critical mass, or faster or slower

1.9 Emergence

• Emergence is when a system as a whole function in ways we can’t predict by looking at their part.
  • As Aristotle put: “The whole system is over and above its parts, and not just the sum of them all”
• “You look at where you’re going and where you are and it never makes much sense, but then you look back at where you’ve been and a pattern seems to emerge. And if you project forward from that pattern, then sometimes you can come up with something”, Robert Pirsig in “Zen and the Art of Motorcycle Maintenance”, 1974
• Grouping people may lead to unexpected results
  • (note: for good or bad)
  • Example was “The mothers of the Plaza de Mayo” in Argentina, grouping to search for the “desaparesidos”, at the same becoming visible and so making it difficult for the government to explicitly capturing them.
• Emergence is not strictly related to complexity
  • Some complex systems don’t show different behaviors when scaling up, while some simple systems can explode in unpredictable behavior when growing
• One of the cause of our cultural evolution and tech progress compared to chimps is that our babies are exposed, since very young age, to many individuals to learn
  • Boyd and Richerson, Henrich and others studied the power of cultural learning
    • Henrich said that innovation doesn’t take a genius or a village, it takes a big network of freely interacting minds
    • (see also the collective knowledge and other similar concepts)
• The more we expose and connect to people, ideas and skills, the more we can build something bigger and different
• See also the butterfly effect
  • (but also serendipity)

1.10 Irreducibility

• According to Einstein, one of the biggest effort in theories is trying to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience
• Irreducibility is strictly related to the first principles thinking
  • (see The Great Mental Models – General Thinking Concepts)
• Sometimes, a system work in an intended way within certain limits
  • (this is well known compared with the Newtonian physics, but also in distributed parameters in electromagnetism)
• According to Gall’s law, something started simple like a single-cell bacteria can evolve to big mammals, completely different and that probably nobody predicted, same is for cities, big inventions like airplane coming from what once was idea of a bicycle
• Like in Plato’s idea of forms, the goal is to find the barely minimum elements to be able to identify the object
  • (like in ML/AI, maybe we can be content enough to cluster the majority of cases, with a good confusion matrix, depending on how many FP and FN we can accept)
  • (see Child Development when a child develop a schema and different models to classify an animal, than test assumptions and change with bayesian updates or completely destroy and rebuild a model)
• In communications, irreducibility is crucial to create impact in short and immediate messages, like “Loose lips might sink ships” during wartime
  • Importance of symbols
    • (there’s a world here, if you read Umberto Eco and many others)
• Lot of example in typography, in advertisement, in design, in conceptual art, and so on
• Master the minimum elements
  • (also minimalism, less is more, clean trait, focus on the core/basis, etc.)

1.11 The law of diminishing returns

• Also related to non-linearity in systems, this is the phenomenon observed when you want to lose weight, at first you lose certain kg, but with same effort over time you start losing less and less
  • Same is when you hire workers, the growth of result is not linear
  • (it tends to be asymptotic)
  • (see also in learning curve and mastering, like in “The First 20 Hours” compared to the 10K hours to master and many other things)
• Diminishing returns of homework
• Diminishing returns of mass incarceration
  • Durkheim suggested that probably is impossible to conceive a society without crime, that a certain amount of criminals will always be present, due to human nature, as long as people are divergent from main opinions and the legal/correct way to act/behave.
    • “New opinions are always suspected, and usually opposed, without any other reason but because they are not already common”, John Locke
• Same it apply to some economical patterns, that’s why Warren Buffett said “what the wise do in the beginning, fools do in the end”
  • (see all the people investing in crypto when it was mainstream, so too late)
• Same is true when something has success like movies and songs and all the others start trying to replicate the success, the last ones will fail in a annoying and saturated market

2. Mathematics

• “What is mathematics? It is only a systematic effort of solving puzzles posed by nature”

2.1 Distributions

• Many phenomena roughly follow the normal distribution, more or less concentrated toward the mean value, but it’s not the only distribution to describe things.
  • Important to notice that complex datasets rarely follow precisely these curves
• You can test your data toward a distribution to see how accurate is it, but keep in mind that future point may not follow the distribution

2.2 Compounding

• Compounding follows a power law, something so “magical” that it’s said that Einstein described it as “the eight wonder of the world”.
  • Naval Ravikant said that iterated games in life, in wealth, in relationships, in knowledge, may pay returns in compound interest.
• Depending on usage, can quickly build or destroy something.
• Across populations, it seems that Jews were the first ones to understand the power of committing to learn, so they sent their children 6-7 y.o. to schools, understanding the value of compound interest in education
  • Learning to read lead to learning to write and so to keep books about tracing money in commerce and many activities
• (as also pointed out by Carl Sagan in “The Demon-Haunted World”, investing in education can lead to progress, and also the opposite is sadly true in US now)
• Reinvesting experience
  • Not everyone with a degree win a Nobel prize, often the difference is in perseverance and reinvesting knowledge
  • We sometimes stop reinvesting interest because we stop challenging ourselves: 20 years of living become the same year repeated 20 times.
• Starting career / graduating during recession can lead to disadvantage compared to other generations, but with some effort it’s possible to overcome the situation
  • One of the way is through networking: each person you know may lead to additional people
  • (like the old saying: “your net-work is your net-worth”)
• (see in general the known rule that +1% for 365 days will end up with 1.01^365 = 37)
• A special socio-economic case: basic income in a way and death taxes in the opposite, as ways to reduce disparity from rich and poor, in first case giving money to cumulate (but it won’t work in the majority of cases, due to lack of education) and the second one to erode accumulated wealth in generations, both cases in theory according with compounding effect

2.3 Network effects

• Network effect is the reinforcing feedback observed when more people buy a product or service or do something, attracting more users.
  • Ultimately, it will produce a winner-takes-all market
    • (ending up in a kind of monopoly de facto)
• One of the most enabling factor is technology
  • (at scale, see models before)
• It won’t grow to an indefinite point: more users only build more value up to a certain point
  • e.g.: more people using a train is good to lower the price, but after a certain point it becomes slower and more dangerous
  • same is for online communities, when in a small forum users post with high standards, but then it becomes popular and attract worse users
    • (plus enshittifcation)

2.4 Sampling

• “Numbers are intellectual witnesses that belong only to mankind”, Honoré de Balzac
• When we want info about a population, we search for a sample that represent the whole, we use sample to tell us about the world
  • (for much more, read books like “How to lie with statistics” and similar ones)
• Small samples may fail greatly to include significative outliers
  • They have limits, but however better than single anecdotes
• Small samples can be useful when combined in meta-analysis
  • However, there are certain rules, depending on the context, to define the minimum sample and how to take it
• George Gallup, one of the fathers of the opinion poll, said that you can decide if a pot of soup needs more seasoning by tasting a single spoonful – provided you’ve stirred it well first.
• Insurance and other companies heavily rely on data, but there’s a limit: they can sample only a fraction of all possibilities, so they can’t have all the accurate historical data, that’s why they can’t model/predict all the terrorism or natural risks
  • (of course, much more on “Antifragile” by Taleb, on Nile’s observed levels and many other examples)
• We often have huge biases in sample, like explained in the authors of “The weirdest people in the world?”, where they noted that lot of behavioral scientists publish studies often centered on WEIRD people (Western, Educated, Industrialized, Rich and Democratic).
  • (similar issues observed in medicine)
  • In “Invisible women”, Caroline Criado Perez found that if you make a study in certain societies or sectors, for example people using metro in Azerbaijan, it’s really likely to end with nonsense conclusions like telling it’s safe using a metro for a woman there, when basically there are no women in these metro.
• (read “Weapons of Math Destruction” for much more)

2.5 Randomness

• This is a hard model to use, since humans are not so able to comprehend true randomness, we’re build to find patterns, to have illusion to predict things
  • Even worse, once we claim having found a pattern or correlation, it’s hard to accept there’s not
• Switching to the past, a major bias is the hindsight one, when we tend to look everything in the past as logic and clearly correlated and inevitable
• Same it applies to serendipity and creating process
  • The most honest authors are the ones that admit that inspiration exists, that you can’t just “force” ideas to follow a certain structure, sometimes rest and changing completely is needed
  • (Don’t trust too much who tell you there’s a structured and secure way to create masterpieces)
  • Smiley wrote about the creative process for fictions authors, telling that there are very few universal points in common, sometimes they just add some random elements and see if they work somehow
  • Great novels aren’t a formula
• Be aware that randomness is different from pseudorandomness, that is something not random but that we can fail to recognize
• Odds in sequences of numbers…
  • (see “How not to be wrong”, there are a lot of counter-intuitive logic at first, but then explained by math)

2.6 Pareto Principle

• The well known 80-20 rule
  • (there’s not to much to say about it, specially with examples: if you really never heard about it, you can just read the Wikipedia page, it’s something too basic that I refuse to write about)

2.7 Regression to the mean

• When we have success, we may come back to the “normality” and it seems we are not great as before, but probably we just fail to recognize that we’re in the regression to the mean
• Identified by Francis Galton, this phenomenon is well known as well
  • (see “The art of thinking clearly” bias n. 19, “The Demon-Haunted World”, “How to lie with statistics” and so on, with the usual examples in sport, investment, etc.)
• When luck is a factor, instead of trying to replicate an unusual success or giving up after an exceptional failure, we can instead try to find the mean and build from there

2.8 Multiplying by zero

• “Multiplication by zero destroys information. This means there cannot be a reverse process. Some activities are so destructive they cannot be undone”, Paul Lockhart
• A zero in a system has the power to revert everything happened before.
  • If you prepare everything for a fancy restaurant, but the last part, that is actually food, is bad, there’s no great value in everything before.
• They can be physical systems or big companies or governments, if everything is perfect but a crucial part fail completely, that can be marketing research for a company or R&D or anything, the whole system fails.
• Zeroes don’t hide: you can easily spot them in a process
  • (see also bottlenecks model)
• Zeroes can be transformed
  • Think of an intelligent person with stuttering: they know what to say, but just have the last part of the comm process that try to zeroing (or bottlenecking) all the chain.
    • Lot of famous people discovered that they don’t stutter when for example they act or sing, so transforming the zero in the last part of the process into something else: it will not “cure” the zero, but find another way
  • Try to transform zeroes at least in ones
    • So not nulling the whole result

2.9 Equivalence

• Things don’t have to be equal: we can do different things to achieve same result!
  • Different input and different processes
  • (this is a key point in rational people that don’t want all the people to be equal despite genre, race, religion, etc., but having equal opportunities to achieve same result)
• According to Donald Brown, different cultures have same fundamentals, but are not equals, so they come to similar results, but running on different paths
  • Various math systems developed independently in Egypt, Rome, China, India, …
    • Same is for some discoveries and inventions
    • That’s why in some cases the first one to really discover/invent something will not receive the credits, that will go to another one that came to same results in another part of the world, later and maybe independently
• We can appreciate the richness of the solution space, appreciating also the effort others take to come to similar results from different input and path, and sharing/exchanging experience and PoV

2.10 Order of magnitude

• It’s not easy for our brain to deal with different order of magnitude
  • We move from talking about microbiology to talk about planets
• Comparisons help, like saying that a certain planet is big X times something we deal with, in everyday life
• We need comparison in effects too, that’s why Richter scale was invented: from 0 to 10, it compares earthquakes to their effects

2.11 Surface area

• Surface area is the amount of something that is in contact with, or able to react to, the outside world
• Increasing that area con be good or bad
• Large areas could mean, for example, more space to protect
  • (this is true for security systems, countries, etc.)
  • If a project depends on too many teams, it’s more likely to have issues
• Some communities for example are strong due to the fact that they reduce / don’t expand their surface area – pros and cons, since for example they are closed and don’t interact and don’t innovate
  • e.g.: old style circus doing same things over and over across generations of families vs. Cirque du Soleil

2.12 Global and local maxima

• You can have one global maximum but several local maxima
• “We may need to temporarily worsen our solution if we want to continue searching for improvement”, Brian Christian and Tom Griffiths
• Same it applies on the opposite if you’re working in reverse to dim something
• Elements of great bands like Queen reached their local maximum before creating something new for the global maximum
• Sometimes, it’s more powerful to make the big changes before we try to optimize the details.

Make a good use of these models!