On Mental Models

the lattice of the mind

And back in the spring of 1720, Sir Isaac Newton owned shares in the South Sea Company, the hottest stock in England. Sensing that the market was getting out of hand, the great physicist muttered that he “could calculate the motions of the heavenly bodies, but not the madness of the people.” Newton dumped his South Sea shares, pocketing a 100% profit totaling £7,000. But just months later, swept up in the wild enthusiasm of the market, Newton jumped back in at a much higher price—and lost £20,000 (or more than $3 million in today’s money). For the rest of his life, he forbade anyone to speak the words “South Sea” in his presence. - Benjamin Graham

Obtaining worldly wisdom is the aim for many as it supersedes mere knowledge. Knowledge is the accumulation of facts and data that one has learned about or experienced. It’s being aware of something, and having information. Knowledge is about facts and ideas that one acquires through study, research, investigation, observation, or experience. Whereas wisdom is the ability to discern and judge which aspects of that knowledge are true, right, lasting, and applicable to one’s life. It’s the ability to apply that knowledge to the greater scheme of life. It’s also deeper; knowing the meaning or reason; about knowing why something is, and what it means to life. Knowledge is passive, wisdom is active.

Lattice

Combining key ideas from all disciplines and then developing a latticework in one’s head to hang all mental models on is what improves ones odds of being successful. Mental models are what one uses when making large and small decisions. It’s what one uses to establish base rates, priors, etc. It’s the framework in which all action relies. Chances of good decisions improve when many, disparate models yield the same conclusion. Some might argue that this is what intelligence is, the ability for one to recognize, construct, implement patterns and data in a way to increase survival.

One should educate oneself and then constantly train to see problems by seeing/thinking differently. For example, learn big ideas so well that they are always known. Mathematics, physics, biology, sociology, and human psychology are some of these big ideas that one should understand.

The key is finding linkages and connecting one idea to another (lattice). Connectionism – we learn by analogy, more connections leads to more intelligence. There are a massive number of connections more efficient than raw speed (small world networks are everywhere). Two keys to innovative thinking – understand basic disciplines we draw knowledge from and be aware of the benefits and uses of metaphors. Be concise, memorable, and colorful when depicting thoughts, actions, and ideas. More importantly translate ideas into models – stimulating understanding and new ideas.

The wise man does at once what the fool does finally. - Machiavelli

Mathematics

Bayes’ Theorem is the constant updating of initial beliefs with new information leading to new and improved beliefs. It’s the rational individuals most frequently used tool. Bayes’ theorem/rule is widely used within the intelligence community. In the Bayesian (or epistemological) interpretation, probability measures a “degree of belief.” Bayes’ theorem then links the degree of belief in a proposition before and after accounting for evidence. For example, suppose it is believed with 50% certainty that a coin is twice as likely to land heads then tails. If the coin is flipped a number of times and the outcomes observed, that degree of belief may rise, fall or remain the same depending on the results.

Decision Tree Theory. Patterns in a Random Forrest… A decision tree is the most powerful and popular tool for classification and prediction. A Decision tree is a flowchart-like tree structure, where each internal node denotes a test on an attribute, each branch represents an outcome of the test, and each leaf node (terminal node) holds a class label. 

Probability theory is a branch of mathematics that investigates the probabilities associated with a random phenomenon. A random phenomenon can have several outcomes. Probability theory describes the chance of occurrence of a particular outcome by using certain formal concepts.

Probability theory makes use of some fundamentals such as sample space, probability distributions, random variables, etc. to find the likelihood of occurrence of an event. Suppose the probability of obtaining a number 4 on rolling a fair dice needs to be established. The number of favorable outcomes is 1. The possible outcomes of the dice are {1, 2, 3, 4, 5, 6}. This implies that there are a total of 6 outcomes. Thus, the probability of obtaining 4 on a dice roll, using probability theory, can be computed as 1 / 6 = 0.167.

The Kelly criterion, Kelly strategy, Kelly formula, or Kelly bet is a formula for bet sizing that leads almost surely to higher wealth compared to any other strategy in the long run (i.e. the limit as the number of bets goes to infinity).Simply, its how to size bets. 2p – 1 = x (p = probability of winning). To compensate people not having an infinite bankroll or time horizon, halve (or take some fraction) of the Kelly Criterion. Never fail to take variation into account – trends of system vs. trends in system (individual winners even during sideways overall market). Never fail to take into account regression to the mean.

The Kelly bet size is found by maximizing the expected logarithm of wealth which is equivalent to maximizing the expected geometric growth rate.

Kelly fraction betting. For payoff equal to 1, the formula is as follows:

%K = 2p-1 and if p = 0.55 then %K = 0.1 or 10% of available equity.

There is also a numerical algorithm for the fractional Kelly strategies and for the optimal solution under no leverage and no short selling constraints

You can at least know more than anyone else. You may not be able to predict price changes but you can start to see patterns. - Mandelbrot

Physics

There are three pillars of physics - Quantum, Gravity, and Thermodynamics. These pillars have been erected by Newton, Einstein, Feynman, Bohr, Doric, Maxwell, and Boltzmann.

The Quantum: Critical mass - in the sub-atomic realm governed by the rules of quantum mechanics, a process called fission provides the fundamental source of energy for both atom bombs and nuclear reactors. What separates these two vastly different results -- one violent, the other controlled -- is the concept of critical mass, an imaginary dividing line that determines whether a nuclear reaction is slow and prolonged or rapid and short-lived. The likelihood of fissions and chain reactions depends partly on the mass of the radioactive material involved. At a point called critical mass, the chain reactions are largely self-sustaining but not increasing. Each radioactive element has a specific critical mass for a sphere of the substance; for example, the critical mass of uranium-235 is 56 kg, whereas only 11 kg of plutonium-239 is required. Scientists who maintain stockpiles of radioactive materials store them in such a way that these quantities never occur in the same general vicinity; otherwise, they may produce violent bursts of lethal radiation.

Space bending: Thanks to Einstein, we know that our three-dimensional space is warped and curved. And in curved space, normal ideas of geometry and straight lines break down, creating a chance to explore an unfamiliar landscape governed by new rules. But studying how physics plays out in a curved space is challenging: Just like in real estate, location is everything. General relativity and quantum mechanics are the two most successful conceptual breakthroughs of modern physics, but Einstein’s description of gravity as a curvature in space-time doesn’t easily mesh with a universe made up of quantum wave-functions. In flat space, the shortest distance between two points is a straight line, and parallel lines will never intersect—no matter how long they are. In a curved space, these basics of geometry no longer hold true. The mathematical definitions of flat and curved are similar to the day to day meaning when applied to two dimensions. One can get a feel for the basics of curved spaces by imagining—or actually playing around with—pieces of paper or maps.

Loop quantum gravity: states that particles loop together in the quantum realm to become space, the loops are space itself, thus it cannot be measured. electrons leaps, quarks, electrons, neutrinos, higs bosons are the particles of the universe, (Feynman). The word "loop" appears in the name because the theory's foundation is based on a rewriting of Einstein's general relativity in terms of lines (instead of points as it's usually done). It doesn't change any of the physics but makes some calculations easier, especially when it comes to quantizing space-time. What does it mean to quantize space-time? It means there's a fundamental unit, a discrete chunk, of space-timey-ness that sits at some imperceptibly small scale. If one were to zoom in to this screen, the smooth curves and clean edges of the letters would be revealed as a vast number of little squares — pixels. In much the same way, if one were to zoom in to space-time, one would see that time doesn't advance into the future continuously but in quick little tick-tick-ticks of a discrete clock. When one moves, it wouldn't be a smooth motion; it would just consist of stuttering steps from one space-time pixel to another.

Thermodynamics: Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In particular, it describes how thermal energy is converted to and from other forms of energy and how thermal energy affects matter. Heat or its move to cold is one of the only ways to quantify time, as time itself does not exist. Time is merely a comparison to distance. Path of least resistance: particles want to take the easiest route(why would video game makers render things that are not viewable?) energy is path-independent.

The laws of thermodynamics gives a clear insight about energy, entropy, and thermal equilibrium of any system.

• The first law of thermodynamics, which is also known as the Law of Conservation of Energy, states that energy can neither be created nor be destroyed, it can only be transferred from one form to another.

• The second law of thermodynamics says that the entropy of any isolated system always increases.

• The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.

• The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

A poet once said, 'The whole universe is in a glass of wine.' We will probably never know in what sense he meant it, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflection in the glass; and our imagination adds atoms. The glass is a distillation of the earth's rocks, and in its composition we see the secrets of the universe's age, and the evolution of stars. What strange array of chemicals are in the wine?

How did they come to be? There are the ferments, the enzymes, the substrates, and the products. There in wine is found the great generalization; all life is fermentation. Nobody can discover the chemistry of wine without discovering, as did Louis Pasteur, the cause of much disease. How vivid is the claret, pressing its existence into the consciousness that watches it! If our small minds, for some convenience, divide this glass of wine, this universe, into parts -- physics, biology, geology, astronomy, psychology, and so on -- remember that nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let it give us one more final pleasure; drink it and forget it all! - Richard P. Feynman

Chemistry

Chemistry is involved in everything we do. Chemistry is the study of matter, defined as anything that has mass and takes up space, and the changes that matter can undergo when it is subject to different environments and conditions. 

The country which is in advance of the rest of the world in chemistry will also be foremost in wealth and in general prosperity. - William Ramsay

It’s not the poison it’s the dose. Everything is toxic at some concentration. The only thing we can explain perfectly with math is the hydrogen atom. Everything else is an approximation, but as computer memory becomes cheaper, our approximations get better. Some approximations are so good nowadays that they have predictive power.  Really small things don’t behave like anything else. This is the main challenge in understanding the universe. It’s the basis of a field of chemistry and physics called “quantum dynamics.”  Ex. If one throws a rubber ball at an impenetrable wall in the normal world, it’ll bounce back. If the world behaved like it does at the really small level, there would be an 18% chance that ball passes through to the other side. 

Chemistry seeks to understand not only the properties of matter, like the mass or composition of a chemical element, but also how and why matter undergoes certain changes — whether something transformed because it combined with another substance, froze because it was left for two weeks in a freezer, or changed colors because it was exposed to too much sunlight.

Chemistry is traditionally divided into five major subdisciplines: organic chemistry, biochemistry, inorganic chemistry, analytical chemistry, and physical chemistry. The types of problems studied in each subdiscipline are different, and the skills needed to be a practicing chemist in each discipline are different. At the heart of each, however, is a fundamental desire to understand the Universe on a molecular level.

Organic Chemistry

Organic chemistry is the study of carbon and its compounds, particularly carbon in combination with hydrogen, oxygen, nitrogen and often the halogens. There are three major topics of interest to the average organic chemist: Synthesis, whereby the chemist tries to come up with methods to prepare specific compounds of interest, such as novel drug candidates; Mechanism, which is the study of the detailed flow of electrons within and between molecules, leading to a particular outcome for a reaction; Spectroscopy, wherein the chemist studies the interaction of a material with electromagnetic radiation of various wavelengths in order to determine its properties, and ultimately its structure.

Physical Chemistry

The field of chemistry is diverse. At any one time around the world, people called chemists are making new molecules, ensuring compliance with environmental laws, probing the secrets of stars and the origins of life, and teaching computers to predict the behavior of matter. The reason all these pursuits can be called chemistry is two fold. First, all chemists have an interest in molecules, the basic building blocks of everything. Second, all chemical pursuits share a set of common underlying principles. These are the principles of quantum mechanics, thermodynamics, kinetics, and statistical mechanics. These principles unify our understanding of the natural world and make diverse phenomena part of the same whole. These unifying principles are the subject of physical chemistry.

Inorganic Chemistry

Organic chemistry has often been defined as the chemistry of the living, and inorganic chemistry defined as nonliving chemistry. Those broad generalizations have provided limitless areas for investigation, but are not entirely accurate.

Inorganic chemistry arose from the arts and sciences of dealing with minerals and ores. Such questions as how to convert naturally occurring substances such as flint or chert into tools or how to convert metal ores (many of them metal oxides, carbonates or sulfides) into free metals were investigated during the middle Pleistocene age.

Modern inorganic chemistry has grown to encompass such areas as new high-temperature superconductors, metal cluster catalysis and metalloenzyme processes. No single definition can possibly portray the many, varied aspects of inorganic chemistry which leads to endless possibilities for learning.

Biochemistry

Biochemistry is the study of the chemistry of living systems. In a very real sense, biochemistry involves the use of principles of general chemistry, organic chemistry, inorganic chemistry, analytical chemistry, and physical chemistry applied to the understanding of biological systems. We examine how living organisms function at the molecular level by looking at the basic molecular structures, systems, reactions, and other chemical and physical processes which occur with those systems. But in order to understand a living system, we must then examine how those molecules, systems, and processes are inextricably interrelated in a complex web of interactions. To do this, we study the structures of the various classes of biomolecules (such as proteins, carbohydrates, lipids, and nucleic acids), how their activity is affected by their structures, and how they interact with one another in an incredibly complex and dynamic array of metabolic processes which transfer, store, and release energy to meet the needs of the organism.

The chemists are a strange class of mortals, impelled by an almost insane impulse to seek their pleasures amid smoke and vapor, soot and flame, poisons and poverty; yet among all these evils I seem to live so sweetly that may I die if I were to change places with the Persian king. - Johann Becher

Biology

Biology, also referred to as the biological sciences, is the study of living organisms utilizing the scientific method.

A simple model for personal wealth, namely geometric Brownian motion (GBM).

I like to call this the equation of life. Why? Because life can be (and has been) defined as the thing that self-reproduces, and that’s what the equation describes. A quantity X that produces more of itself in a noisy way. It describes what happens to the biomass of an embryo in its early stages of development, or to the population of some species growing in a rich environment.

Biology examines the structure, function, growth, origin, evolution, and distribution of living things. It classifies and describes organisms, their functions, how species come into existence, and the interactions they have with each other and with the natural environment. There are four unifying principles form the foundation of modern biology: cell theory, evolution, genetics and homeostasis.

A central organizing concept in biology is that life changes and develops through evolution and that all lifeforms known have a common origin. Charles Darwin established evolution as a viable theory by articulating its driving force, natural selection (Alfred Russel Wallace is recognized as the co-discoverer of this concept). Darwin theorized that species and breeds developed through the processes of natural selection as well as by artificial selection or selective breeding.

Genetic drift was embraced as an additional mechanism of evolutionary development in the modern synthesis of the theory. Biological form and function is created from and is passed on to the next generation by genes, which are the primary units of inheritance. Physiological adaption to an organism's environment cannot be coded into its genes and cannot be inherited by its offspring.

The fundamental essence of individuality, and the units in which individuality ought to be measured, is information. You’re dealing with an individual if you’re dealing with “the same thing” between today and tomorrow, and where that sameness isn’t just passive inertia, but is actively propagated. Individuals maximally propagate information from their past to their future. This propagation is measurable, at least in theory. Therefore, individuality ought to also be measurable. Biology is hardware, culture is software.

Philosophy

Philosophy forces one to think and can’t be transferred intact from one mind to another. Philosophy is simply the love of wisdom. One needs a philosophy and one needs to write it down and revisit it.

Don’t explain your philosophy. Embody it. - Epictetus

There are three main branches of philosophy:

• Metaphysics – ideas independent of space and time (God, afterlife)

• Aesthetics / ethics (deontology) / politics three main branches

• Epistemology – study of the nature/limits of knowledge; thinking about thinking

Metaphysics is:

• Socrates: Admitting Ignorance

• Aristotle: Theory of Everything

• Epictetus: Accepting Necessity

• Descartes: Radical Doubt

• Kierkegaard: Preparing to Leap

• Wittgenstein: Freeing fly from bottle

• Heidegger: Self-Concealing of Being

• Hadot: A Way of Life

Ethics is:

• Homer: The field to which stray horses return

• Heraclitus: Character

• Aristotle: Prologue to Politics

• Epictetus: Control

• Kant: A Universal Imperative

• Nietzsche: Ressentiment

• Marx: Distraction from the Revolution

• Mill: Optimizing Good Outcomes

• Williams: Mostly luck

Epistemology is:

• Plato: Reason, Appetite, Pride

• Aristotle: A Creature of Habit

• Epictetus: Free

• Plotinus: A Splinter of Divine Light

• Luther: A Saboteur

• Kant: A Content Creator

• Nietzsche: Revenge of the Nerds

• Freud: A Crime Scene

• Fanon: Internalized Oppression

• Dawkins: A Meme Dealer

It’s regularly said that Plato is the godfather of secular philosophy because he trusted the powers of human reason. What’s overlooked is that Plato often remarks on the failure of human rationality, arguing that it’s not human minds that are reliably rational, but divine minds. We humans can, on occasion, mirror such true intelligence. We can hope to track its paths; but only as a shadow tracks its body.

Aristotle, writing on first principles, said: In every systematic inquiry (methodos) where there are first principles, or causes, or elements, knowledge and science result from acquiring knowledge of these; for we think we know something just in case we acquire knowledge of the primary causes, the primary first principles, all the way to the elements.

Later he connected the idea to knowledge, defining first principles as “the first basis from which a thing is known.” The search for first principles is not unique to philosophy. All great thinkers do it. The coach reasons from first principles. The rules of football are the first principles: they govern what you can and can’t do. Everything is possible as long as it’s not against the rules. The play stealer works off what’s already been done. Sure, maybe he adds a tweak here or there, but by and large he’s just copying something that someone else created.

The difference between reasoning by first principles and reasoning by analogy is like the difference between being a chef and being a cook. If the cook lost the recipe, he’d be screwed. The chef, on the other hand, understands the flavor profiles and combinations at such a fundamental level that he doesn’t even use a recipe. He has real knowledge as opposed to know-how.

One should develop rigorous, cohesive epistemological routines. Doing so allows one to understand that disorder is simply order misunderstood. A strong philosophical foundation is the foundation that one stands upon to see the patterns of reality.

Sociology

One should study how individuals function in society. The ultimate goal being to more accurately predict group behavior. The relationship between individual investor and stock market is a profound puzzle. The market is an amalgamation of human thinking and action represented in price. All human interactions and systems are complex and adaptive – one can’t separate the parts from the whole. Human behavior constantly changes as agents update actions based on information and therefore the system adapts.

Self-organization and self-reinforcement is a phenomena found in physics, biology, economics, etc. Emergence – larger entities arise out of interactions of simpler, smaller entities and have characteristics that the smaller entities do not exhibit. Crowds can be collectively intelligent if they are diverse and independent. Smart and dumb agents (people) lead to better outcomes than a group of just smart people.

Information cascades, which leads to diversity. Breakdowns happen when people make decisions based on others rather than private information and this leads to an inefficient system. This is group think, rather than one thinking for oneself. The decision making is outsourced to the crowd. This can also happen with small groups with a dominant leader. The thinking is outsourced to the leader, thus the individuals in the group think and do as the leader dictates.

Failure to explain caused by failure to describe – Mandelbrot 

Self-organized criticality – the market is one example where instability is inherent, unpredictable and small fluctuations lead to big changes. The volatility in the market is also what leads to creative destruction and eventual growth. Only the strong survive. Different meta-models of reality (quant vs. fundamentally oriented) leads to instability. Ie one agent views the market in one way and bets on the viability of the view while a competing agent places a bet based on a different view of the market. Complex adaptive, self-organization leads to emergence which leads to instability, unpredictability, criticality. All elements are what make systems beautiful and dynamic. It is sclerosis that leads to death.

Psychology

Key aspects of psychology that one should understand to better approach life and markets are: anchoring, framing, overreaction, overconfidence, mental accounting, loss aversion key biases.

Equity risk premium is puzzling – people hold bonds because of loss aversion and mental accounting. Loss aversion makes people short-term focused. Longer investor holds an asset, the more attractive it becomes IF not evaluated frequently – advises checking prices only once per year!

Information overload can lead to illusion of knowledge. Don’t be a Walter Mitty investor – feed during difficult times! Decisions we make based on skill lead to higher risk taking and lead to higher probabilities of successful outcomes. Luck is always a factor, but one with skill and experience increases ones odds of luck looking favorably upon them.

Mental models are imprecise ways of modeling reality but very helpful and simplify life. Mistakes – believe models equiprobable, focus on  few or one, ignore what is not easily seen. Innate pattern seeking leads to magical thinking and superstitions by people trying to explain the unexplainable. In this case, beliefs precede reasoning, beliefs dictate what one sees. This is why people listen to forecasters – doing so quells anxiety. People hate to live with anxiety/uncertainty even if they rationally know how misguided it is.

One can reduce noise via accurate communication of information, which makes for better rational decisions. Correction device – get information from first-hand sources and then do ones best to remove prejudices and biases

Economics

There exists a bridge between physics, economics and the stock market. Equilibrium – state of balance between two opposing forces, powers or influences. Static vs. dynamic. Rational actions lead to stock market equilibrium – where the shadow price (intrinsic value) = stock price.

Some argue the market is complex adaptive system – a network of many individual agents all acting in parallel and interacting with one another. The critical variable that makes a system both complex and adaptive is the idea that agents in the system accumulate experience by interacting with other agents and then change themselves to adapt to a changing environment. The market is reflexive, memetic, and randomly iterating. Thus, the system is actually irrational, organic, not efficient.

Evolution and natural selection are akin to the law of economic selection. After crashes, the market and the economy are best understood from a biological perspective as an equilibrium could not account for them. Struggle between species and individuals of same species is what leads to natural selection and evolution.

Joseph Schumpter – economics is essentially an evolutionary process of continuous and creative destruction. Innovation, a visionary and action-oriented entrepreneur and access to credit are all necessary. Innovation leads to periods of punctuated equilibria – creative destruction.

4 distinct features of economy:

1. Dispersed interaction – what happens in the economy is determined by the interactions of a great number of individual agents all acting in parallel

2. No global controller

3. Continual adaptation (co-evolution)

4. Out of equilibrium dynamics – constant change leads to a system constantly out of equilibrium

   1. Evolution takes place sin stock market via economic selection and capital allocation

   2. Living systems make themselves up as they go along

   3. Efficiency and evolutionary / behavioral not necessarily exclusive – times of less emotions leads to more efficient market

Literature

Read selectively but analytically. Always evaluate its worth in the larger picture and then either reject or incorporate what one learns into mental models – the importance of reflection. This improves understanding (over fact collecting) and critical thinking. Critical mindsets evaluate the facts and separate facts from opinion. Reading fiction is important because it helps one learn from others’ experiences.

Detectives best practices

1. Develop a skeptic’s mindset; don’t automatically accept conventional wisdom

2. Conduct a thorough investigation

3. Begin an investigation with an objective and unemotional viewpoint

4. Pay attention to the tiniest details

5. Remain open-minded to new, even contrary, information

6. Apply a process of logical reasoning to all you learn

7. Become a student of psychology

8. Have faith in your intuition

9. Seek alternative explanations and redescriptions

Decision Making

Intuition is helpful when a situation is reliable enough to be predictable and when one can learn regularities through prolonged practice (mostly linear systems). Intuition is nothing more than recognition – an increased store of knowledge and connections leads to improved intuition.

It is not enough to think about difficult problems one way. One needs to think about them forwards and backward. Inversion often forces one to uncover hidden beliefs about the problem one is trying to solve. “Indeed,” says Munger, “many problems can’t be solved forward.”

How one thinks is more important than what one thinks. Humans are cognitive misers and stop thinking the minute they’re satisfied with an answer. Building blocks from many disciplines used to form mental models must be dynamic and updated with new information. The inability to do so will leave one at a disadvantage in a complex adaptive environment that is constantly changing and progressing.