Tag: Galileo

Thought Experiment: How Einstein Solved Difficult Problems

“We live not only in a world of thoughts, but also in a world of things.
Words without experience are meaningless.”
— Vladimir Nabokov

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The Basics

“All truly wise thoughts have been thought already thousands of times; but to make them truly ours, we must think them over again honestly, until they take root in our personal experience.”
— Johann Wolfgang von Goethe

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Imagine a small town with a hard working barber. The barber shaves everyone in the town who does not shave themselves. He does not shave anyone who shaves themselves. So, who shaves the barber?

The ‘impossible barber’ is one classic example of a thought experiment – a means of exploring a concept, hypothesis or idea through extensive thought. When finding empirical evidence is impossible, we turn to thought experiments to unspool complex concepts.

In the case of the impossible barber, setting up an experiment to figure out who shaves him would not be feasible or even desirable. After all, the barber cannot exist. Thought experiments are usually rhetorical. No particular answer can or should be found.

The purpose is to encourage speculation, logical thinking and to change paradigms. Thought experiments push us outside our comfort zone by forcing us to confront questions we cannot answer with ease. They reveal that we do not know everything and some things cannot be known.

In a paper entitled Thought Experimentation of Presocratic Philosophy, Nicholas Rescher writes:

Homo sapiens is an amphibian who can live and function in two very different realms- the domain of actual facts which we can investigate in observational inquiry, and the domain of the imaginative projection which we can explore in thought through reasoning…A thought experiment is an attempt to draw instruction from a process of hypothetical reasoning that proceeding by eliciting the consequences of a hypothesis which, for anything that one actually knows to the contrary, may be false. It consists in reasoning from a supposition that is not accepted as true- perhaps even known to be false but is assumed provisionally in the interests of making a point or resolving a conclusion.

As we know from the narrative fallacy, complex information is best digested in the form of narratives and analogies. Many thought experiments make use of this fact to make them more accessible. Even those who are not knowledgeable about a particular field can build an understanding through thought experiments. The aim is to condense first principles into a form which can be understood through analysis and reflection. Some incorporate empirical evidence, looking at it from an alternative perspective.

The benefit of thought experiments (as opposed to aimless rumination) is their structure. In an organized manner, thought experiments allow us to challenge intellectual norms, move beyond the boundaries of ingrained facts, comprehend history, make logical decisions, foster innovative ideas, and widen our sphere of reference.

Despite being improbable or impractical, thought experiments should be possible, in theory.

The History of Thought Experiments

Thought experiments have a rich and complex history, stretching back to the ancient Greeks and Romans. As a mental model, they have enriched many of our greatest intellectual advances, from philosophy to quantum mechanics.

An early example of a thought experiment is Zeno’s narrative of Achilles and the tortoise, dating to around 430 BC. Zeno’s thought experiments aimed to deduce first principles through the elimination of untrue concepts.

In one instance, the Greek philosopher used it to ‘prove’ motion is an illusion. Known as the dichotomy paradox, it involves Achilles racing a tortoise. Out of generosity, Achilles gives the tortoise a 100m head start. Once Achilles begins running, he soon catches up on the head start. However, by that point, the tortoise has moved another 10m. By the time he catches up again, the tortoise will have moved further. Zeno claimed Achilles could never win the race as the distance between the pair would constantly increase.

In the 17th century, Galileo further developed the concept by using thought experiments to affirm his theories. One example is his thought experiment involving two balls (one heavy, one light) which are dropped from the Leaning Tower of Pisa. Prior philosophers had theorized the heavy ball would land first. Galileo claimed this was untrue, as mass does not influence acceleration. We will look at Galileo’s thought experiments in more detail later on in this post.

In 1814, Pierre Laplace explored determinism through ‘Laplace’s demon.’ This is a theoretical ‘demon’ which has an acute awareness of the location and movement of every single particle in existence. Would Laplace’s demon know the future? If the answer is yes, the universe must be linear and deterministic. If no, the universe is nonlinear and free will exists.

In 1897, the German term ‘Gedankenexperiment’ passed into English and a cohesive picture of how thought experiments are used worldwide began to form.

Albert Einstein used thought experiments for so of his most important discoveries. The most famous of this thought experiments was on a beam of light, which was made into a brilliant children's book. What would happen if you could catch up to a beam of light as it moved he asked himself? The answers lead him down a different path toward time, which lead to the special theory of relativity.

In On Thought Experiments, 19th-century Philosopher and physicist Ernst Mach writes that curiosity is an inherent human quality. We see this in babies, as they test the world around them and learn the principle of cause and effect. With time, our exploration of the world becomes more and more in depth. We reach a point where we can no longer experiment through our hands alone. At that point, we move into the realm of thought experiments.

Thought experiments are a structured manifestation of our natural curiosity about the world.

Mach writes:

Our own ideas are more easily and readily at our disposal than physical facts. We experiment with thought, so as to say, at little expense. This it shouldn’t surprise us that, oftentime, the thought experiment precedes the physical experiment and prepares the way for it… A thought experiment is also a necessary precondition for a physical experiment. Every inventor and every experimenter must have in his mind the detailed order before he actualizes it. Even if Stephenson knew the train, the rails and the steam engine from experience, he must have, nonetheless, have preconceived in his thoughts the combination of a train on wheels, driven by a steam engine, before he could have proceeded to the realization. No less did Galileo have to envisage, in his imagination, the arrangements for the investigation of gravity, before these were actualized. Even the beginner learns in experimenting than as insufficient preliminary estimate, or nonobservance of sources of error has for him no less tragic comic results than the proverbial ‘look before you leap’ does in practical life.

Mach compares thought experiments to the plans and images we form in our minds before commencing an endeavor. We all do this — rehearsing a conversation before having it, planning a piece of work before starting it, figuring out every detail of a meal before cooking it. Mach views this as an integral part of our ability to engage in complex tasks and to innovate creatively.

According to Mach, the results of some thought experiments can be so certain that it is unnecessary to physically perform it. Regardless of the accuracy of the result, the desired purpose has been achieved.

We will look at some key examples of thought experiments throughout this post, which will show why Mach’s words are so important. He adds:

It can be seen that the basic method of the thought experiment is just like that of a physical experiment, namely, the method of variation. By varying the circumstances (continuously, if possible) the range of validity of an idea (expectation) related to these circumstances is increased.

Although some people view thought experiments as pseudo-science, Mach saw them as valid and important for experimentation.

Types of Thought Experiment

“Can't you give me brains?” asked the Scarecrow.

“You do not need them. You are learning something every day. A baby has brains, but it does not know much. Experience is the only thing that brings knowledge, and the longer you are on earth the more experience you are sure to get.”
― L. Frank Baum, The Wonderful Wizard of Oz

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Several key types of thought experiment have been identified:

  • Prefactual – Involving potential future outcomes. E.g. ‘What will X cause to happen?’
  • Counterfactual – Contradicting known facts. E.g. ‘If Y happened instead of X, what would be the outcome?’
  • Semi-factual – Contemplating how a different past could have lead to the same present. E.g. ‘If Y had happened instead of X, would the outcome be the same?’
  • Prediction– Theorising future outcomes based on existing data. Predictions may involve mental or computational models. E.g. ‘If X continues to happen, what will the outcome be in one year?’
  • Hindcasting– Running a prediction in reverse to see if it forecasts an event which has already happened. E.g. ‘X happened, could Y have predicted it?’
  • Retrodiction– Moving backwards from an event to discover the root cause. Retrodiction is often used for problem solving and prevention purposes. E.g. ‘What caused X? How can we prevent it from happening again?’
  • Backcasting – Considering a specific future outcome, then working forwards from the present to deduce its causes. E.g. ‘If X happens in one year, what would have caused it?’

Thought Experiments in Philosophy

“With our limited senses and consciousness, we only glimpse a small portion of reality. Furthermore, everything in the universe is in a state of constant flux. Simple words and thoughts cannot capture this flux or complexity. The only solution for an enlightened person is to let the mind absorb itself in what it experiences, without having to form a judgment on what it all means. The mind must be able to feel doubt and uncertainty for as long as possible. As it remains in this state and probes deeply into the mysteries of the universe, ideas will come that are more dimensional and real than if we had jumped to conclusions and formed judgments early on.”

― Robert Greene, Mastery

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Thoughts experiments have been an integral part of philosophy since ancient times. This is in part due to philosophical hypotheses often being subjective and impossible to prove through empirical evidence.

Philosophers use thought experiments to convey theories in an accessible manner. With the aim of illustrating a particular concept (such as free will or mortality), philosophers explore imagined scenarios. The goal is not to uncover a ‘correct’ answer, but to spark new ideas.

An early example of a philosophical thought experiment is Plato’s Allegory of the Cave, which centers around a dialogue between Socrates and Glaucon (Plato’s brother.)

A group of people are born and live within a dark cave. Having spent their entire lives seeing nothing but shadows on the wall, they lack a conception of the world outside. Knowing nothing different, they do not even wish to leave the cave. At some point, they are lead outside and see a world consisting of much more than shadows.

“The frog in the well knows nothing of the mighty ocean.”

— Japanese Proverb

Plato used this to illustrate the incomplete view of reality most us have. Only by learning philosophy, Plato claimed, can we see more than shadows.

Upon leaving the cave, the people realize the outside world is far more interesting and fulfilling. If a solitary person left, they would want to others to do the same. However, if they return to the cave, their old life will seem unsatisfactory. This discomfort would become misplaced, leading them to resent the outside world. Plato used this to convey his (almost compulsively) deep appreciation for the power of educating ourselves. To take up the mantle of your own education and begin seeking to understand the world is the first step on the way out of the cave.

Moving from caves to insects, let’s take a look at a fascinating thought experiment from 20th-century philosopher Ludwig Wittgenstein. Imagine

Imagine a world where each person has a beetle in a box. In this world, the only time anyone can see a beetle is when they look in their own box. As a consequence, the conception of a beetle each individual has is based on their own. It could be that everyone has something different, or that the boxes are empty, or even that the contents are amorphous.

Wittgenstein uses the ‘Beetle in a Box’ thought experiment to convey his work on the subjective nature of pain. We can each only know what pain is to us, and we cannot feel another person’s agony. If people in the hypothetical world were to have a discussion on the topic of beetles, each would only be able to share their individual perspective. The conversation would have little purpose because each person can only convey what they see as a beetle. In the same way, it is useless for us to describe our pain using analogies (‘it feels like a red hot poker is stabbing me in the back’) or scales (‘the pain is 7/10.’)

Thought Experiments in Science

Although empirical evidence is usually necessary for science, thought experiments may be used to develop a hypothesis or to prepare for experimentation. Some hypotheses cannot be tested (e.g string theory) – at least, not given our current capabilities.

Theoretical scientists may turn to thought experiments to develop a provisional answer, often informed by Occam’s razor.

Nicholas Rescher writes:

In natural science, thought experiments are common. Think, for example, of Einstein’s pondering the question of what the world would look like if one were to travel along a ray of light. Think too of physicists’ assumption of a frictionlessly rolling body or the economists’ assumption of a perfectly efficient market in the interests of establishing the laws of descent or the principles of exchange, respectively…Ernst Mach [mentioned in the introduction] made the sound point that any sensibly designed real experiment should be preceded by a thought experiment that anticipates at any rate the possibility of its outcome.

In a paper entitled Thought Experiments in Scientific Reasoning, Andrew D. Irvine explains that thought experiments are a key part of science. They are in the same realm as physical experiments. Thought experiments require all assumptions to be supported by empirical evidence. The context must be believable, and it must provide useful answers to complex questions. A thought experiment must have the potential to be falsified.

Irvine writes:

Just as a physical experiment often has repercussions for its background theory in terms of confirmation, falsification or the like, so too will a thought experiment. Of course, the parallel is not exact; thought experiments…no do not include actual interventions within the physical environment.

In  Do All Rational Folks Think As We Do? Barbara D. Massey writes:

Often critique of thought experiments demands the fleshing out or concretizing of descriptions so that what would happen in a given situation becomes less a matter of guesswork or pontification. In thought experiments we tend to elaborate descriptions with the latest scientific models in mind…The thought experiment seems to be a close relative of the scientist’s laboratory experiment with the vital difference that observations may be made from perspectives which are in reality impossible, for example, from the perspective of moving at the speed of light…The thought experiment seems to discover facts about how things work within the laboratory of the mind.

One key example of a scientific thought experiment is Schrodinger’s cat.

Developed in 1935 by Edwin Schrodinger, Schrodinger's cat seeks to illustrate the counterintuitive nature of quantum mechanics in a more understandable manner.

Although difficult to present in a simplified manner, the idea is that of a cat which is neither alive nor dead, encased within a box. Inside the box is a Geiger counter and a small quantity of decaying radioactive material. The amount of radioactive material is small, and over a period time, it is equally probable it will decay or not. If it does decay, a tube of acid will smash and poison the cat. Without opening the box, it is impossible to know if the cat is alive or not.

Let's ignore the ethical implications and the fact that, if this were performed, the angry meowing of the cat would be a clue. Like most thought experiments, the details are arbitrary – it is irrelevant what animal it is, what kills it, or the time frame.

Schrodinger’s point was that quantum mechanics are indeterminate. When does a quantum system switch from one state to a different one? Can the cat be both alive and dead, and is that conditional on it being observed? What about the cat’s own observation of itself?

In Search of Schrodinger’s Cat, John Gribbin writes:

Nothing is real unless it is observed…there is no underlying reality to the world. “Reality,” in the everyday sense, is not a good way to think about the behavior of the fundamental particles that make up the universe; yet at the same time those particles seem to be inseparably connected into some invisible whole, each aware of what happens to the others.

Schrodinger himself wrote in Nature and The Greeks:

We do not belong to this material world that science constructs for us. We are not in it; we are outside. We are only spectators. The reason why we believe that we are in it that we belong to the picture, is that our bodies are in the picture. Our bodies belong to it. Not only my own body, but those of my friends, also of my dog and cat and horse, and of all the other people and animals. And this is my only means of communicating with them.

Another important early example of a scientific thought experiment is Galileo’s Leaning Tower of Pisa Experiment.

Galileo sought to disprove the prevailing belief that gravity is influenced by the mass of an object. Since the time of Aristotle, people had assumed that a 10g object would fall at 1/10th the speed of a 100g object. Oddly, no one is recorded as having tested this.

According to Galileo’s early biography (written in 1654), he dropped two objects from the Leaning Tower of Pisa to disprove the gravitational mass relation hypothesis. Both landed at the same time, ushering in a new understanding of gravity. It is unknown if Galileo performed the experiment itself, so it is regarded as a thought experiment, not a physical one. Galileo reached his conclusion through the use of other thought experiments.

Biologists use thought experiments, often of the counterfactual variety. In particular, evolutionary biologists question why organisms exist as they do today. For example, why are sheep not green? As surreal as the question is, it is a valid one. A green sheep would be better camouflaged from predators. Another thought experiment involves asking: why don’t organisms (aside from certain bacteria) have wheels? Again, the question is surreal but is still a serious one. We know from our vehicles that wheels are more efficient for moving at speed than legs, so why do they not naturally exist beyond the microscopic level?

Psychology and Ethics — The Trolley Problem

Picture the scene. You are a lone passerby in a street where a tram is running along a track. The driver has lost control of it. If the tram continues along its current path, the five passengers will die in the ensuing crash. You notice a switch which would allow the tram to move to a different track, where a man is standing. The collision would kill him but would save the five passengers. Do you press the switch?

This thought experiment has been discussed in various forms since the early 1900s. Psychologists and ethicists have discussed the trolley problem at length, often using it in research. It raises many questions, such as:

  • Is a casual observer required to intervene?
  • Is there a measurable value to human life? I.e. is one life less valuable than five?
  • How would the situation differ if the observer were required to actively push a man onto the tracks rather than pressing the switch?
  • What if the man being pushed were a ‘villain’? Or a loved one of the observer? How would this change the ethical implications?
  • Can an observer make this choice without the consent of the people involved?

Research has shown most people are far more willing to press a switch than to push someone onto the tracks. This changes if the man is a ‘villain’- people are then far more willing to push him. Likewise, they are reluctant if the person being pushed is a loved one. In

In Incognito: The Secret Lives of The Brain, David Eagleman writes that our brains have a distinctly different response to the idea of pushing someone and the idea of pushing a switch. When confronted with a switch, brain scans show that our rational thinking areas are activated. Changing pushing a switch to pushing a person and our emotional areas activate. Eagleman summarizes that:

People register emotionally when they have to push someone; when they only have to tip a lever, their brain behaves like Star Trek’s Mr. Spock.

The trolley problem is theoretical, but it does have real world implications. For example, the majority of people who eat meat would not be content to kill the animal themselves- they are happy to press the switch but not to push the man. Even those who do not consume meat tend to ignore the fact they are indirectly contributing to the deaths of animals due to production quotas, which mean the meat they would have eaten ends up getting wasted. They feel morally superior as they are not actively pushing anyone onto the tracks, yet are still like an observer who does not intervene in anyway. As we move towards autonomous vehicles, there may be real life instances of similar situations. Vehicles may be required to make utilitarian choices – such as swerving into a ditch and killing the driver to avoid a group of children.

Although psychology and ethics are separate fields, they often make use of the same thought experiments.

The Infinite Monkey Theorem and Mathematics

“Ford!” he said, “there's an infinite number of monkeys outside who want to talk to us about this script for Hamlet they've worked out.”

― Douglas Adams, The Hitchhiker's Guide to the Galaxy

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The infinite monkey theorem is a mathematical thought experiment. The premise is that infinite monkeys with typewriters will, eventually, type the complete works of Shakespeare. Some versions involve infinite monkeys or a single work. Mathematicians use the monkey(s) as a representation of a device which produces letters at random.

In Fooled By Randomness, Nassim Taleb writes:

If one puts an infinite number of monkeys in front of (strongly built) typewriters, and lets them clap away, there is a certainty that one of them will come out with an exact version of the ‘Iliad.' Upon examination, this may be less interesting a concept than it appears at first: Such probability is ridiculously low. But let us carry the reasoning one step beyond. Now that we have found that hero among monkeys, would any reader invest his life's savings on a bet that the monkey would write the ‘Odyssey' next?

The infinite monkey theorem is intended to illustrate the idea that any issue can be solved through enough random input, in the manner a drunk person arriving home will eventually manage to fit their key in the lock even if they do it without much finesse. It also represents the nature of probability and the idea that any scenario is workable, given enough time and resources.

To learn more about thought experiments, consider reading The Pig That Wants to Be Eaten, The Infinite Tortoise or The Laboratory of the Mind.

Galilean Relativity and the Invasion of Scotland

A few centuries ago, when Galileo (1564-1642) was trying to make a couple of points about how our world really works, one of the arguments that frequently came up in response to his ‘the earth orbits the sun’ theory was “if the earth is moving through space, how come I don’t notice?”

Not that I have much to begin with, but I don’t feel the wind constantly in my hair, I don’t get orbit-induced motion sickness, so why, Galileo, don’t I notice this movement as the earth is spinning around over 100,000 km per hour?

His answer is known as Galilean Relativity and it contains principles that have broad application in life.

Understanding Galilean Relativity allows you to consider your perspective in relation to results. Are you really achieving what you think you are?

First, an explanation of the theory.

Imagine you are on a ship that has reached constant velocity (meaning without a change in speed or direction). You are below decks and there are no portholes. You drop a ball from your raised hand to the floor. To you, it looks as if the ball is dropping straight down, thereby confirming gravity is at work. You are able to perceive this vertical shift as the ball changed its location by about three feet.

Now imagine you are a fish (with special x-ray vision) and you are watching this ship go past. You see the scientist inside, dropping a ball. You register the vertical change in the position of the ball. But you are also able to see a horizontal change. As the ball was pulled down by gravity it also shifted its position east by about 20 feet. The ship moved through the water and therefore so did the ball. The scientist on board, with no external point of reference, was not able to perceive this horizontal shift.

This analogy helped Galileo explain why we don’t notice the earth moving — because we’re at the same constant velocity, moving with our planet.

It can also show us the limits of our perception. And how we must be open to other perspectives if we truly want to understand the results of our actions. Despite feeling that we’ve got all the information, if we’re on the ship, the fish in the ocean has more he can share.

History offers an illuminating example of this principle at work.

In the early fourteenth century, two English kings (Edwards I and II) were repeatedly in conflict with Scotland over Scottish independence.

Nationalism wasn’t as prevalent as an identity characteristic as it is today. Lands came and went with war, marriage, and papal edicts, and the royal echelons of Europe spent a lot of time trying to acquire and hold on to land, as that is where their money ultimately came from.

There were a lot of factors that led Edward I, King of England, to decide that Scotland should be his. It has to do with how William the Conqueror divided things up in the area in 1066, the constant struggle by the English for the strategic upper hand against France, and more generally, the fact that the King of England was at the head of a feudal system that, “by enlarging a class of professional soldiers who owed military service in payment for land, it enabled it,” says William Rosen in his book The Third Horseman: Climate Change and the Great Famine of the 14th Century.

Edward I wanted to rule Scotland. The Scots weren’t interested. He invaded half a dozen times and succeeded only in giving birth to a separate Scottish identity. His desire for Scotland became his Galilean ship. He couldn’t see beyond that desire to understand how his actions were actually fundamentally undermining his goals.

History regards Edward I as a decent king. Strategic in battle, a good administrator, and so one can assume that what he generally wanted was to rule over a prosperous and powerful country. In his mind then it may have been a very simple equation – since prosperity in the middle ages was tied up with land, then to have more of it must be good. And Scotland was in a convenient location, as opposed to, say, Mongolia.

What Edward I did not see was that the repeated invasion of Scotland was undermining the very prosperity and power he was hoping to augment. It was costing tons of money, money that had to be raised from the nobility that supported his monarchy, which in turn had to be raised via the peasants from the land. People were getting sick of watching their taxes go up in flames on the Scottish border. And, as Rosen claims, “A king’s authority depends utterly on the loyalty and faith of his people.” Lose your popular support and you lose everything.

When Edward I died, his son, Edward II, inherited his father’s quest to own Scotland. He too repeatedly invaded with no lasting success. And he had it even worse. The beginning of his reign coincided with a major famine that decimated the population. This was followed by diseases that swept through the agricultural animal populations. So there was less money to support war.

But Edward II kept taxing and invading Scotland anyway, indifferent to the plight of his people. This contributed to widespread disgust with his reign and eventually led to his being disposed of, and likely murdered, in favor of his son. A cautionary tale on what happens when you lose the loyalty of the people you are meant to be leading!

This all begs the question, was Scotland really such a great prize to justify the repeated attempts to conquer it?

The answer is no. As Rosen writes, “the conquest of medieval Scotland was, by any rational economic calculus, a poor bargain for both of England’s King Edwards, who together spent more than the entire value of the country in one failed expedition after another.”

They certainly did not see this.

It is important to know that in Galilean relativity, neither the perspective of the scientist on the ship nor the fish in the ocean is incorrect. Both perspectives are true for those doing the observing. Because the scientist has no external frame of reference, he is not mistaken when he says that the ball moved only vertically, and not horizontally.

You aren’t always going to be able to adjust for Galilean relativity. Given the roles, expectations, and mythology surrounding kings, both Edwards were acting according to the viewpoint they had.

So discussing the attempted conquest of Scotland by both Kings is not about revealing that their assumptions were incorrect. From their perspective acquiring land was always a good thing. But by failing to consider other perspectives they didn’t achieve their intended results – control of Scotland – and, more importantly, were unable to appreciate the results they were affecting. More land cannot come at the expense of support for your leadership.

It is likely that at least one advisor might have said to the Edwards, ‘hey, maybe you should spend some more money on preventing the starvation of the population that pays you taxes and take a break on this Scottish thing’. This is where understanding Galilean relativity is useful – you won’t shoot the messenger.

You will know that sometimes you are on the ship, and the limitations this entails, and so be open when the fish shares his perspective with you.

Charlie Munger: 5 Simple Notions that Help Solve Problems

In 1996, Charlie Munger gave a talk titled “Practical Thought about Practical Thought where he explained the success of Coca-Cola using the simplest, most fundamental academic models he could find. Ideas from the physical world, from biology, and from psychology and business.

Munger starts the speech by outlining five simple notions that help him quickly solve problems. His approach, combined with learning how to think, is very much worth downloading into your own brain and using as a recipe. While the wording Munger uses to describe his approach is different, it's very similar to the approach used by Elon Musk, Richard Feynman, and others.

1. Simplify

… it is usually best to simplify problems by deciding big “no-brainer” questions first.

2. Numerical Fluency

[this] helpful notion mimics Galileo's conclusion that scientific reality is often revealed only by math, as if math was the language of God. Galileo's attitude also works well in messy practical life. Without numerical fluency, in the part of life most of us inhabit, you are like a one-legged man in an ass-kicking contest.

3. Invert

Inverting the problem won’t always solve it, but it will help you avoid trouble. Call it the avoiding stupidity filter.

… it is not enough to think problems through forward. You must also think in reverse, much like the rustic who wanted to know where he was going to die so that he'd never go there. Indeed, many problems can't be solved forward. And that is why the great algebraist, Carl Jacobi, so often said: “invert, always invert.” And why Pythagoras thought in reverse to prove that the square root of two was an irrational number.

4. Study The Basics

You need to understand the big nuggets of wisdom in the three buckets of useful knowledge. You can think of the basics as a mental models approach.

Munger believes in using these regularly and in combination:

… the best and most practical wisdom is elementary academic wisdom. But there is one extremely important qualification: you must think in a multidisciplinary manner. You must routinely use all the easy-to-learn concepts from the freshman course in every basic subject. Where elementary ideas will serve, your problem solving must not be limited, as academia and many business bureaucracies are limited, by extreme balkanization into disciplines and subdisciplines, with strong taboos against any venture outside assigned territory. …

If, in your thinking, you rely on others, often through purchase of professional advice, whenever outside a small territory of your own, you will suffer much calamity.

This happens in part because professional advisors are often undone, not by their conscious malfeasance rather by troubles found in their subconscious bias.

His cognition will often be impaired, for your purposes, by financial incentives different from yours. And he will also suffer from the psychological defect caught by the proverb: to a man with a hammer, every problem looks like a nail.”

5. Lollapalooza Effects

And you need to watch out for when really big ideas combine.

… really big effects, lollapalooza effects, will often come only from large combinations of factors. For instance, tuberculosis was tamed, at least for a long time, only by routine combined use in each case of three different drugs. And other lollapalooza effects, like the flight of an airplane, follow a similar pattern.

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Still Curious?  See how Munger applies these in this essay. Learn more about the wit and wisdom of Charlie Munger by picking up a copy of Poor Charlie's Almanack and Damn Right!: Behind the Scenes with Berkshire Hathaway billionaire Charlie Munger.