The Great Mental Models Volume 3: Systems and Mathematics
Summary
The book consists of 19 systems and mathematics concepts including 6 supporting ideas that elucidate the mental models necessary to improve one’s learning and thinking. The different concepts from systems and mathematics provide a new way to contour one’s approach to problem-solving.
Table of Contents
Systems
- Feedback Loops
- Equilibrium
- Bottlenecks
- Scale
- Margin of Safety
- Churn
- Algorithms
- Critical Mass
- Emergence
- Irreducibility
- The Law of Diminishing Returns
Mathematics
- Compounding
- Sampling
- Randomness
- Regression to the Mean
- Multiplying by Zero
- Equivalence
- Surface Area
- Global and Local Maxima
Supporting Ideas
- Complex Adaptive Systems
- Chaos Dynamics
- Distributions
- Network Effects
- Pareto Principle
- Order of Magnitude
Breaking It Down
1. Feedback Loops
The technical definition of feedback loops stems from systems theory. A feedback loop is when the outputs (information) of a system affect its own behaviours. Depending on the intricacies of the system, it can be from single or multiple sources.
Feedback can be elucidated as the information communicated in response to an action. Feedback is given consciously and unconsciously on a daily basis.
For example, whenever a friend tells you about how bad their day was and you start to frown, it serves as feedback to your friend that you are not very happy to hear about his/her negative thoughts. Hence, serving as feedback to them not to mention to you about their bad day.
Feedback loops that have quality feedback allow one to understand their behaviour and choices better. Hence, it is important to ensure that our 5 closest people to us give up quality feedback.
Type basic types of feedback loops:
- Balancing (negative) feedback loops: Tend toward an equilibrium
- Thermostat and heating system- the temperature is adjusted to the desired temperature
- Reinforcing (positive) feedback loops: Amplifies a certain process
- Does not counterchange
- They keep change going
- To counterchange, new interventions or conditions have to be injected
Faster feedback = More time to improve
However, it is important to understand that there is both short-term and long-term feedback. For example, eating junk food creates a positive short-term effect of pleasure. However, it creates a negative long-term effect on health issues.
Adam Smith and the Feedback Loop of Reactions
Adam Smith is a well-known economist, especially for his book “The Wealth of Nations”. He also wrote a book (the first he wrote) that was more philosophy based called “The Theory of Moral Sentiments” where he described how there are invisible forces that guide us. For example, how the approval and disapproval of others influence our behaviour.
Human nature itself is self-centric (selfish) which can be seen in how we accentuate the harm that was done to us much stronger than the harm that is widespread in the world. Despite our inherent self-centric human nature, the majority are cooperative and kind due to reciprocity. When one does something selfish, it causes others to have a disapproving reaction to it. However, when someone does something selfless, it gains the approval of others.
The concept itself of reciprocity and how the approval and disapproval of others influence our behaviour explains how it creates a feedback loop that encourages good behaviour while discouraging bad behaviour.
Everyday feedback loops
How does one incentivise desired behaviours while discouraging negative behaviours? It requires one to have a system that has a checked reinforcing feedback loop that is both sustainable and achievable.
4 aspects of social systems through feedback loops
- Creating the right future incentives
- Minimizing choices or actions that create a negative feedback loop in the long term. For example, paying off kidnappers incentivises them to repeat the action. Another example is making all music free from copyright. This will reduce the incentive for people to create music and push music to the next stage.
- Influencing behaviour at the margins
- Thinking about the margins is to look at problems not in totality but rather in incremental terms. A little more of this leads to a little less of that.
- Dealing with information cascades
- Can be seen in crowds forming around street performers and queues forming for a certain restaurant. People draw unconscious inferences from what they see others are doing and do the same, leading to a reinforcing feedback loop creating a stronger impression.
- Building trust
- It can be seen on roads where there is trust between drivers that they will abide by rules created by society – green light means go and a red light means stop.
- The Prisoner’s Dilemma, it shows how our decision making is influenced by our previous experiences. Hence, the choice of creating a positive feedback loop by cooperating and showing a willingness to trust should be used in one’s life.
- The fewer people cooperate, the less incentive there is for future cooperation
- The prevention is to impose rules that discourage defection from cooperation and trust
Kadinsky’s Iterations
It shows how the experience of trying gives one the experience of what is good and what has to be worked on. Incorporating the process of paying attention to feedback and implementing it allows one to improve over the long term.
Wassily Kandinsky’s famous work “Painting with White Borders” was not a try one hit piece of work. He used feedback to make small changes to many copies of the sketch. Each sketch he did from the previous one had 1 or 2 different changes made from the previous. By the 21st picture, it created Kandinsky’s famous work painting with white borders. Each sketch he did serve as a base of information on what he had to work on.
2. Equilibrium
Equilibrium is reaching a state of stability.
Two types of equilibrium:
- Static equilibrium: State that is consistent and unchanging
- Dynamic equilibrium: State where it fluctuates around a certain range
Homeostasis and Equilibrium
Homeostasis shows how changes in one’s environmental conditions cause changes in one’s internal conditions. For example, thermoregulation and blood glucose regulation espouse the wonders of homeostasis.
Homeostasis does not need to return the body to its previous state but rather to a state where it “feels good” under new conditions. Hence, the silver lining here is defining for oneself what “feels good”.
Exploiting assumptions
To overcome a plateau, it is essential to think about what an opponent expects or considers the norm. Followed by rethinking what the equilibrium is in one’s field.
When it comes to business, magic tricks, persuasion and more, there are many conventional assumptions and expectations that are unconsciously established. Hence, one can exploit the assumptions to work around – causing radical results to be achieved.
Complexity of equilibrium
The project Biosphere 2 is to create mini earth in an attempt to create livable conditions out of the earth. After being sealed in the biosphere for two years, the 8 scientists faced problems with low oxygen levels which required fresh oxygen to be brought in externally. The experiment proved the complexities of maintaining life in a sealed environment.
3. Bottlenecks
A bottleneck is the slowest component of a system.
Bottleneck elucidates how limiting factor(s) can both help or hurt one/
It is pivotal to understand how solving one bottleneck may create another bottleneck. The challenge is finding a way to optimize the system itself while limiting the effects of its bottleneck.
Liebig’s law of the minimum
The idea of a plant’s growth is limited by the nutrient that is least available – constricting yield due to resource limitation.
Trans-Siberian Railway
It delineates how it is necessary to anticipate the consequences of how one deals with a certain bottleneck.
The Trans-Siberian Railway (TSR) was the longest railway spanning the entirety of Russia from St. Petersburg in the West, close to Finland, to Vladivostok on the Pacific Ocean just East of North Korea.
The challenging terrain, weather, labour and transportation created insurmountable woes when it came to building the railway.
The shortage of labour was solved by incentivising the workers with money. However, it creates incentives to keep the shortage going so that the money keeps coming as well. It delineates how throwing money into a problem without understanding its root cause is unlikely to yield good results.
From the example of the TSR, it is important to identify and plan how one should manage the bottlenecks so that the consequences that might ensue are solved immediately.
One can attempt in simulating conditions that one is likely to face and try to find the potential bottlenecks before time.
Bottleneck and Innovation
Bottleneck helps us as it forces us to think out of the box. When a limiting factor emerges, one is forced to try radically different practices and methods to solve it. An example is a war being a catalyst of innovation in order to have access to necessary materials which were unobtainable. An example is the creation of nylon to replace silk. In the 1930s, the US obtained most of its silk from Japan and was at risk of losing its supply due to rising tensions between both countries. The creation of nylon which was the first synthetic fibre found in swimwear, fishing nets and more are a testimony to its utility. It is light strong and waterproof making it a good replacement for silk.
During the war, nylon replaced silk as a key material in creating parachutes and tents.
Another example is the creation of Ameripol to replace rubber. Ameripol was the creation to remove the need to have natural resources to create rubber. Rubber was necessary for war as it is found in almost every item and device used in fighting. Rubber was a key material in the tires used for vehicles especially.
Bottlenecks force one out of their comfort zone and unleash their creativity to reach a point of a solution.
4. Scale
The concept of scale provides insights into how size might impact one’s systemic choices as the effects of a micro-scale might not represent the effects of a macro scale.
Higher scale systems = Higher complexity
This equation holds true due to more connections and complexities as scale increases.
If you do not look at things on a large scale, it will be difficult to master strategyMiyamoto Musashi
For example, when a company is in its startup stage, it is easy for information to flow due to lesser connections and complexities – reducing the need for a PR and HR department. However, when the company scales up, the intricacies of information become more complex. Hence, more work and energy have to be put in place to ensure that information flows smoothly.
With growth, resilience can be increased by ensuring that there is a clear measure of independence between different parts of a system. If the different systems are dependent on each other, it will create potential bottlenecks as not all parts of a system will progress together linearly.
Economies of Scale
As scale increases, the marginal cost decreases. Similarly, as income per capita increases, the overall demand tends to increase. As good as economies of scale is, there is a point where it breaks even.
Long-lived Japanese companies (Shinise)
In Japan, there are many companies that have been around for a very long time. One of the reasons why they have been around for a very long time is the nature of the way they scale. They tend to be small and run by a family and their extended family. They trade within a district and have a loyal customer base. Coupled with a strong internal philosophy, it guides the company during changing times. With the company being small, it is easier for them to pivot as compared to big companies.
An example is the most long-lived Japanese company, Kongo Gumi. It is a construction company specialising in high-quality Buddhist temples operating from 78 AD to 2006. During World War II when the demand for Buddhist temples was low, the company pivoted to making coffins.
When companies become bigger ins scale, the systems themselves become bigger making them less flexible.
Being the Right Size
Size plays a part especially biologically – affecting the body compositions of different animals.
As mentioned by Geoffrey West who wrote the book Scale, “Scaling up from the small to the large is often accompanied by an evolution from simplicity to complexity while maintaining basic elements or building blocks of the system unchanged or conserved”.
5. Margin of Safety
The margin of safety is the meaningful gap between what a system is capable of handling and what is required. It is a buffer between safety and danger.
Cost of margin of safety
Even though margin of safety brings about its ostensible advantages, it comes with costs.
The first form of cost is the cost of having that margin of safety. The a fine line between having efficiency as compared having a margin of safety. The question will lie in the risk and reward balance.
The second form is the heuristics that come with a margin of safety especially when human nature is in play. For example, when drivers have seat belts, safe brakes and other forms of extra safety features, it might not decrease the overall risk of accidents. This is due to the complacency bred from the extra safety provided. Hence, it is important to consider different heuristics and human nature involved.
Business: Margin of safety
The margin of safety could mean wasting resources and potentially becoming less competitive. If a company’s pursuit for efficiency leads to no margin of safety, it is as good as viewing the world as a perfect world with no changes. The margin of safety for businesses should provide them with no necessary protection from economic downturns and issues.
Minimum effective dose
Minimum effective dose is the pursuit of balance between a substance being medicine and poison.
Having too much of a substance can be harmful while a tiny dose can provide beneficial effects. The minimum effective dose is to calculate the lowest possible amount of a medication/substance to provide meaningful benefits for an average patient. This is followed by calculating the upper limits of it (maximum tolerated dose).
Learning as a margin of safety
The margin of safety in learning comes in the form of learning more so that one has fewer blind spots. This is held true as a learning provides one with more knowledge to adapt to changing situations and be better aware of potential problems/blind spots.
Ego impedes the use of a margin of safety
Ego tends to cause one to learn just enough to solve current and immediate problems. However, it is usually insufficient in solving future problems – leading to no margin in safety in what one knows.
Ego also tends to lead one to leverage on their natural strengths. It is commonly said as early successes can lead to one’s downfall. When one leverages on their natural strengths, it reduces the need for preparation. In situations where one is unable to leverage on their natural strengths, one might be unaccustomed to the rigour of preparation. Therefore, the only way to be ready is to foremost build as vast a repertoire of knowledge in anticipation of the possibilities one might face. It is followed by cultivating the ability to know what is generally relevant and useful now and in the future.
Learning margin of safety from Jacques Jaujard
The motto “To lead is to anticipate” suits Jacques Jaujard, director of the French National Museums during World War II perfectly. He protected and safeguarded many cultural treasures through his application of the margin of safety.
Before the war, many did not believe that the Nazis would target Paris and its cultural treasures. However, Jacques Jaujard believe that there was a possibility of this occurring. Jacques was aware of the importance of cultural treasures in war. Other than cultural significance, they are vulnerable as the country’s enemy will try to seize them for profit. Hence, he went out of his way to hide and relocate all the cultural treasures to different locations in the country side.
His experience, it elucidates how a greater margin of safety should be incorporated for higher-risk situations.
In a nutshell
In the modern world, specialisation has been the cornerstone for success. However, having broad competence increases the likelihood of being saved from the randomness of life. Efficiency is great for small tasks with small consequences. However, for big tasks with big consequences, the margin of safety becomes essential.
The margin of safety delineates how one’s pursuit of efficiency should not cause one to be vulnerable to changes.
6. Churn
Churn is the necessary ongoing replenishment of materials to keep a system maintained/going.
Churn can be observed everywhere from one’s skin cells being constantly replaced, trees dying followed by new trees growing, changing parts of a car, old furniture breaking leading one to buy new furniture and more.
Churn allows one to see how the system changes and learn how to work with it.
Business: Churn
Churn for businesses refers to losing a customer through a lost subscription or a change in customer behaviour. The rate of the churn affects how businesses conduct themselves. The rate of churn allows companies to evaluate what the cost of customer acquisition should be.
Churn can also be applied to employees in terms of how long they usually stay on the job and the costs of hiring and training.
When the rate of churn is high in systems, replacing the necessary components will lead to incremental costs.
7. Algorithms
Algorithms are a clear set of rules that produces instructions on what to do – allowing one to achieve a standard outcome. Conceptually, they provide the essential inputs and variables to achieve the desired output with the non-essential variables removed.
Algorithms remove the tedious aspect of going through certain processes to achieve a set outcome. It provides the skeletal and essential “recipe” to achieve set outcomes.
It allows one to automate the entire process instead of having to go through the mental rigour of achieving the same set outcome every single time.
A definition provided by Yuval Noah Hariri is “An algorithm is a methodical set of steps that can be used to make calculations, resolve problems, and reach decisions. An algorithm isn’t a particular calculation, but the method followed when making the calculation.
Three defining characteristics of algorithms
1. Substrate neutrality: “The power of the procedure is due to its logical structure, not the causal powers of the materials used in the instantiation.” It does not matter whether the recipe is seen digitally or on a physical copy. It does not matter what the “base” (substrate) is, but more of the method/process used is the same.
2. Underlying mindlessness: “Each constituent step, and the transition between steps, is utterly simple.” For a method/recipe to be an algorithm, it must provide the exact/key details where one can walk through each process step by step without any interpretation error or misunderstanding. Essentially it can be a simple copy and paste – removing/reducing the mental work initially required.
3. Guaranteed results: “Whatever it is that an algorithm does, it always does it if it is executed without a misstep. An algorithm is a foolproof recipe.” Using a good algorithm, the food/dessert made will always taste the same every time.
An example is the book by Peter T. Leeson “The Invisible Hook: The Hidden Economics of Pirates”. He shared how pirates are like constitutions with set rules to guide their behaviour and goals. In his book, he mentioned how every detail that went to creating the ship’s articles (rules/policies) needed to align and value-add to their profit. What sets the pirates apart is they had no consideration of the ramifications of their actions on others. They went for whatever articles helped with their profits (bottom lines).
For example, the crew was unallowed to gamble and drink onboard. Gambling creates negative consequences such as conflicts and reduced cooperation. While drinking onboard could disrupt the rest of the others and hamper their performance the subsequent day. Furthermore, they set clear rules on how the crew is awarded and punished.
Blackbeard is a popular and famous pirate for leading probably less than 700 crewmates. A Chinese pirate named Ching Shih is an example of how articles allowed her to lead approximately 70,000 – 80,000 pirates and up to 200 ships. She married the pirate Zheng Yi and after his passing, he led the crew herself. Ching Shih ensured that the rules set in place are stringently followed. She shows how algorithms (rules) ensure cohesion within a system.
For a system to create its intended outcome, the inputs have to be aligned and in the same direction – increasing the likelihood of a predictable outcome.
Bayer, German pharmaceutical company: Finding quality inputs
In the 1920s, Bayer started trying to create the world’s first broad-spectrum antibiotic through the use of algorithmic thinking.
After World War 1, a bacterial infection such as Streptococcus (Strep) was an incurable infection. Exposure to contaminated tools and instruments could lead to bacterial infection that was unstoppable once it entered the body. Hence, Bayer went on to find a cure for bacterial infections in the body.
Heinrich Horlein who was then in charge of pharmaceutical research for Bayer lacked scale and was too dependent on individual scientists reaching their own breakthroughs. Hence, he created an industrial system (algorithm) to identify antibacterial compounds and hired many to filter through each antibacterial candidate using the same algorithmic-like process.
The algorithmic-like process had a similar testing and evaluation process to see if the antibacterial compound was safe for humans. Hence, after creating countless new antibacterial compounds, it went through the entire process of testing and evaluation. The chemical was given in three different ways – intravenously, subcutaneously, and by mouth.
Intravenously: into or by means of a vein or veins
Subcutaneously: applied under the skin
In 1932, the methodology worked. Sulfur was attached to an azo compound creating Chemical K1-195 where no toxicity was found after recovering from bacterial infection.
The example of Bayer’s algorithmic-like approach delineates the future process incorporated and followed by other drugmakers – allowing many other useful antibiotics being creating through the same system/model.
Supporting Idea 1: Complex Adaptive Systems
Complex systems: Systems in which the entities follow fixed rules
Complex adaptive systems: Systems in which the entities adapt
Complex adaptive systems are harder to manage and work with as their individual components cannot be understood modularly due to the unpredictable, nonlinear way it responds.
The first step to understanding and working with complex adaptive systems is understanding how one cannot expect them to be governed by predictable rules nor understand the macro through the micro. Hence, it is vital to embrace its unpredictable and nonlinear nature.
To learn from it, it requires one to have humility and think like a scientist. One must not mistake correlation for causation and be open to learning more about the system and accepting change.
8. Critical Mass
Critical mass is the final unit of input before it leads to disproportionate impact. An example is how heated water is at critical mass when it is hot enough to change from liquid state to gaseous state. Another example given by Shane Parrish on how critical mass applies to businesses is how the critical mass for businesses is when when they make enough money to no longer require external investment or they arrive at a point where financial growth of a company becomes self-perpetuating.
An example of leveraging on critical mass is on how to influence the minds and perceptions of others. The effort of changing the minds and perceptions is high. However, the effort can be further reduced by changing of the minds of opinion leaders that will catalyze change.
Hence, critical mass provides insights into the amount of a certain input needed for a system to change its state.
9. Emergence
Emergence is when systems as a whole functions in a whole that one cannot predict by looking at their different parts.
Shane Parrish shares how the mental model of emergence elucidates the new capabilities are often produced from seemingly innocuous elements.
It is vital to understand that individuals cannot understand systems with granular properties cannot be reduced to their individual components.
Emergence enables one to understand that sometimes systems exhibit capabilities that are beyond the additive properties of their components.
Emergence enumerates the importance of learning new skills, interacting with new people. It is through new experiences and knowledge that allows one to create unexpected possibilities.
Supporting Idea: Chaos Dynamics
Chaos Dynamics is also popularly known as the butterfly effect which states how challenging it is to predict future behavior of chaotic systems as it requires perfect understanding of the initial conditions. It elucidates how a small difference can cost huge changes.
10. Irreducibility
The concept of irreducibility is best understood by what Albert Einstein said.
It can be scarcely be denied that the supreme goal of all theory is 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.Albert Einstein
Irreducibility challenges individuals to think things through to their most basic components. Thinking about the minimum amount of time, components and structure required to maintain the overall qualities. A good example is how to use the least amount of words and complexity to bring a point across. It is being able to use simplicity to convey a message but not to a point where simplicity conveys no meaning at all.
Typography
Typography is striking a delicate balance between creativity and comprehensibility.
Gall’s law
According to Gall’s law, complex systems all started from simple systems that invariably evolved into complex systems through incremental changes. Gall’s law informs us the detriments of trying to build complex systems from scratch. Instead try to figure out the simple systems in order to change it into a complex one.
Irreducibility shed light on the need to remove the non essentials. The focus should be on knowing the minimum elements. Followed by exploring and changing from there.
11. Law of diminishing returns
The law of diminishing returns enumerates how past a certain point, diminishing returns will kick in.
Essentially, it explains how increasing input will lead to lesser outputs. An example will be a number of workers running a factory. The more people hired at the start will lead to higher and faster production. However, past a certain point, it will cause production to be lower and slower due to a plethora of reasons.
Diminishing returns and societal collapse
It explains as societies grow and develop, they become more complex and require more and more energy to maintain its current state. An important issue is that individuals find the cost of being part of the society supersedes the benefits of it. Thus, it makes a case for society to return to simpler levels of organization rather than high level of complexities.
Supporting Idea: Distributions
Distributions provides the contours on what to expect from a certain data set. It allows one to make predictions about the probability, frequency and the possibility of future events.
Four characteristics that determines the type of distribution
- Is the data made up of discrete values or is it continuous
- Are the data points symmetric or asymmetric?
- Are there upper and lower limits on the data?
- What is the likelihood of observing extreme values
Normal distribution
- Majority of values cluster around the midpoint with a few falling on either side
Power law distribution
- The values in a power law distribution cluster at low or high values
- An example is wealth gap where most individuals cluster around a small range of values at one end of the curve.
Geometric distribution
- Intution as to when a particular sucess might happen
Binomial distribution
- How long it will take a to get a particular numbers of successes
Poisson distribution
- An idea of the distribution of rate events in a large population
Memoryless distribution
- Makes one feel better when you have to wait a while for the next bus
12. Compounding
Play iterated games. All the returns in life, whether in wealth, relationships, or knowledge, come from compound interest.”Naval Ravikant
Shane Parrish encourages readers to be more deliberate about identifying how their past experiences can improve their chances of success in the future.
He also shares the importance of compounding relationships through networking. Networking enables individuals to have their current networks have their own networks to strengthen each other’s networks. The more interesting and influential, the stronger the network becomes.
Supporting Idea: Network effects
Network effects happen when the utility of a product or service increases in value as more people adopt it.
It has a reinforcing feedback loop whereby the new value created attracts new users who in turn create more value and the cycle repeats.
13. Sampling
Sampling allows one to provide a relative measure of the entire population. It is important to note that according to the law of large numbers, the larger the sample size, the more the result obtained will be closer to the true value.
Generally, the more measurements included, the more accurate the result is.
When it comes to sampling, it is essential to provide a broad diversity and ensure it is unbiased. This increases the accuracy and value of the measurement.
Insurance
Insurance uses the notion of reducing uncertainty by spreading the cost of adverse events among groups of people, companies and other entities. Just as for insurance, a larger sample size tends to increase the accuracy of the expected number of payouts per year. It is through this probability that insurance companies know how much they should charge those that are insured.
14. Randomness
Randomness is useful for generating ideas and creativity. This can be done by reading more, travelling more, asking questions, looking for original documents and engaging one’s senses to gain more knowledge of what one is writing about.
Randomness provides new connections by introducing one or more new elements.
It is vital to distinguish the difference between pseudorandomness and true randomness. True randomness detaches from causal factors – resulting in no one being able to predict the outcome.
Supporting Idea: Pareto principle
In 1906, Italian polymath Vilfredo Pareto came out with the Pareto principle after researching on wealth distribution and observing peas. He noticed how 20% of the population held 80% of the wealth while 20% of the plants produced 80% of the peas. He came out with the principle stating how 80% of output is determined by 20% of the input. While the remaining 20% of output is determined by 80% of the input.
It is important to understand that the Pareto principle is a rule of thumb rather than a universal law. The useful aspect of the principle is it helps individuals to notice how only 20% of a product’s features are used by 80% of the users. Hence, it is important to make sure that 20% of features are well-built.
15. Regression to the mean
Regression to the mean is how data that has outliers will tend to be followed by data close to it. The concept shed light on how despite achieving success, one’s regular skills and knowledge will reflect the outcome of it.
A counter against the regression to the mean is to view their track record rather than their peak performance.
16. Multiplying by zero
This mental model encourages readers to look for the zero in a system as it causes an existential threat to the system as a whole. The concept of any number multiplied by zero equals zero elucidates how if a certain part of a system is at zero will lead to its failure.
An example is how a competent and organized team can be brought down by one unmotivated person who incessantly complains. Another example of how zero for a restaurant is its food. If its food is bad while everything else is exemplary, it will still not have to return customers.
Finding and transforming our zeros
When it comes to zeros, it is important to ruminate on what our personal zeros are that will negate all the other good and strengths in ourselves. It is through identifying where we can start working on the zero.
17. Equivalence
Equivalence enables us to see that there is more than one route to success. It is vital to understand how things may differ in their details, they might have the same underlying principles and concepts.
Supporting Idea: Order of magnitude
Order of magnitude is to express large or small numbers in a compact fashion. The book shares about the Richter scale that is used to understand orders of magnitude through seismic events
18. Surface Area
Surface area as a concept allows us to think about one’s exposure to new ideas. Large surface area comes with more significant risks while shrinking surface areas have lower risks. Another application of surface area as a concept applies to creativity. One can further generate ideas and expand creativity is increasing exposure to new disciplines which provides more diversity.
An example given in the book is the Tube map design seen in many railways. The original design came from Harry Beck that made it for the London Underground. The map places stations side by side instead of by geological distances. The beauty of the tube map stems from the overall surface area of London being significantly reduced to a few main points of information for a single purpose. The tube map elucidates how when it comes to communication, it is useful to consider reducing surface area to remove details that can increase complexity.
19. Global and local maxima
Maxima is the largest value while the minima are the lowest value. The concept revolves around how one’s maxima may be the local maxima but not that global maxima.
Many tend to be stuck at a local maximum. In order to reach new heights, it necessitates change. It requires individuals to go through troughs in order to reach new peaks.
Optimization
Optimization allows one to know how and when to optimize and when to avoid overoptimization.