Find Out How To Combine Building Blocks Of Knowledge And Come Up With Great Ideas

A great idea or invention is usually a combination of other different ideas or inventions. Things don’t happen in a vacuum and as the old saying goes, you stand upon the shoulders of giants.

One of the greatest skills that you can have is to be able to combine ideas from different sources. And this is something that expert-generalists, or Renaissance Men, excel at. Their greatest assets are their combinatorial and associative skills.

However, how do you develop and cultivate these types of skills?

Step 1: Collect pieces of information

The first thing you need to do is to know the information and have it available. So the first step is the collection phase.

This has been described in different ways, as collecting pieces of a puzzle or different building blocks. If you want to glue together a picture out of a puzzle or build a house, you need to have the pieces ready in order to do that.

Each piece of knowledge is a like a building block, you can use it in different ways and combine it with other building blocks. The combinations are endless and every resulting structure can look different, even if you use the same building blocks (or it can look the same, up to you really).

How do you go about collecting these building blocks? One thing is by reading a lot. That’s why I wrote a short article on the reading habits of guys like Warren Buffett or Charlie Munger. It is kind of obvious, but a lot of people don’t do it.

Another way is to collect different experiences, like Steve Jobs says. Go to different places, expose yourself to different ideas, try different things. All of this will enrich you, and give you some building blocks which you can use later.

Once you have a good selection of building blocks (information) ready, you can go on to creating a few useful mental models to guide you. These are basically representations of real, or imaginary situations or things that you create in your head.

Scottish psychologist Kenneth Craik proposed the idea (although similar ideas were proposed earlier by others as well) that the mind works by constructing small-scale models of reality in order to reason and to offer explanations for events. Modern research so far seems to prove this assertion.

You can actively use these workings of your brain by building a latticework of mental models, something that comes from Charlie Munger, one of the greatest financial investors of all time.

From all the studying he does, Munger selects a handful of big ideas and stores them for later. These can come from things like physics, chemistry, economics, humanities, or any other type of discipline. As long as you think it will be useful later.

To quote Charlie Munger:

You have to learn all the big ideas in the key disciplines in a way that they’re in a mental latticework in your head and you automatically use them for the rest of your life. If you do that, I solemnly promise you that one day you’ll be walking down the street and you’ll look to your right and left and you’ll think “my heavenly days, I’m now one of the few competent people in my whole age cohort.” If you don’t do it, many of the brightest of you will live in the middle ranks or in the shallows.

The sources of mental models can come from anywhere. When you are reading books or collecting experiences, try to summarize some of the big lessons that you get out of them. These can then serve as your own personal mental models.

Step 2: Things start clicking automatically

You might not believe me, but collecting the information is the most important step. By collecting more and more information, things will start clicking automatically. Trust me! 🙂

You might have had the experience of you not understanding a problem, trying to go at it through different ways and failing. Then you forgot about the problem, but were walking one day and suddenly things clicked.

This is often called the “Eureka” moment, just like Archimedes had his “Eureka” moment when he was entering the bathtub.

Maria Popova, in an article for “Smithsonian Magazine” writes:

There is a curious cultural disconnect between our mythology of spontaneous ideation – the Eureka! moment, the stroke of genius, the proverbial light bulb – and how “new” ideas actually take shape, amalgamated into existence by the combinatorial nature of creativity. To create is to combine existing bits of insight, knowledge, ideas, and memories into new material and new interpretations of the world, to connect the seemingly dissociated, to see patterns where others see chaos.

These sudden flashes of the lightbulb are quite common. This doesn’t mean that something appears out of nothing. The building blocks of your idea are already there in the brain. It is that your brain is just playing around with them subconsciously.
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Combinatorial Knowledge Is The Key To Many Innovations – Find Out How To Apply It

In 2007, Steve Jobs got on stage to reveal a device which would go on to revolutionize the way we work in the world today. The device in question is the iPhone and it ushered in the era of the smartphone.

Ever the showman, Jobs gave a riveting speech. There is one part that really stands out and describes the essence of what the iPhone is.

An iPod, a phone, an internet mobile communicator. An iPod, a phone, an internet mobile communicator. An iPod, a phone, an internet mobile communicator. Do you get it? These are not three separated devices. This is one device, and we are calling it iPhone.

He mentioned three things: an iPod, a phone, and an internet mobile communicator. All of these things existed on the market when the iPhone came out. However each one was its own device.

What did Jobs and Apple do? They combined them and put them on one device!

This is what combinatorial knowledge is all about. You take different already existing pieces and combine them together to make something new. This something new can be another piece of knowledge, or a new device or anything else.

It is very, very hard to be truly original and come up with something totally new, something that has never existed before and which truly changes our understanding of the world. For the most part, to do that, you truly need to dedicate a lot of time to your field. This is what Albert Einstein did with his theory of relativity.

However, if you dig deeper, you will notice that even Einstein used some previously discovered knowledge, which served as inputs. He then combined it with his own things. James Hutton, when coming up with his theories on geology, also combined different strands of knowledge that were floating around in his time.

Combinations of knowledge from different sources is the key to new knowledge. It is also the key to new revolutionary devices like the iPhone.

An article in “Wired” magazine describes how Jobs came up with the idea:

In 2002, shortly after the first iPod was released, Jobs started thinking about developing a phone. He saw millions of Americans lugging separate phones, BlackBerrys, and — now — MP3 players; naturally, consumers would prefer just one device. He also saw a future in which cell phones and mobile email devices would amass ever more features, eventually challenging the iPod’s dominance as a music player. To protect his new product line, Jobs knew he would eventually need to venture into the wireless world.

The article goes on to list some of the challenges that such a product would have to overcome:

If the idea was obvious, so were the obstacles. Data networks were sluggish and not ready for a full-blown handheld Internet device. An iPhone would require Apple to create a completely new operating system; the iPod’s OS wasn’t sophisticated enough to manage complicated networking or graphics, and even a scaled-down version of OS X would be too much for a cell phone chip to handle. Apple would be facing strong competition, too: In 2003, consumers had flocked to the Palm Treo 600, which merged a phone, PDA, and BlackBerry into one slick package. That proved there was demand for a so-called convergence device, but it also raised the bar for Apple’s engineers.

These challenges lay in vastly different fields, not only with the technology, but also the way the wireless industry was structured and the business models. In order to make the iPhone a success, all these things would have to be pulled together.

Compare this description of what Steve Jobs (and his Apple team) did, and what Johannes Guttenberg did when coming up with his printing press. A passage in Samuel Arbesman’s “The Half-life of Facts” describes the process:

It turns out that the printing press is far from simple. The technological innovations that Gutenberg developed were much more than the modification of a wine press and the addition of the idea of movable type. Gutenberg combined and extended a whole host of technologies and innovations from an astonishing number of areas, and that is what made his work so powerful.

He used metallurgical developments to create metal type that not only had a consistent look (Gutenberg insisted on this), but type that could be easily cast, allowing whole pages to be printed simply at once. He used chemical innovations to create a better ink than had ever been used before in printing.

Gutenberg even exploited the concept of the division of labor by employing a large team of workers, many of whom were illiterate, to churn out books at a rate never before seen in history. And he even employed elegant error-checking mechanisms to ensure that the type was always set properly: There was a straight line on one side of each piece of type so that the workers could see at a glance whether any letters had been set upside down.

Only by having the combined knowledge of all of these technologies does the printing press become possible and cost-effective.

Just like Steve Jobs had to combine different elements when coming up with the iPhone, Johannes Guttenberg had to do something similar when he came up with the printing press. If you look at other types of inventions that revolutionized our world, you will most likely see a similar process at play.
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What Is The Secret Behind Warren Buffet’s Success? It’s Quite Simple Actually!

Warren Buffett is one of the richest men on the planet and in the investment world he is seen as one of the best investors of all time. His decisions have made him billions many times over.

However what is his secret? What does he do that gives him that mental edge?

It’s actually quite simple. He reads a lot!

One time he was asked what the secret to success is. This is his reply:

Read 500 pages like this every day. That’s how knowledge works. It builds up, like compound interest. All of you can do it, but I guarantee not many of you will do it.

That’s it. This is what gives him the combinatorial mental powers that he has. The more he reads, the more information he has, the more things he can combine.

It also makes him less impulsive and more rational. To quote him again:

I read and think. So I do more reading and thinking, and make less impulse decisions than most people in business. I do it because I like this kind of life.

His investment partner, Charlie Munger, also reads a lot. From all the information he reads, he creates a select amount of mental models, which he then uses to guide him when making investment decisions, as well as many other decisions in life.

For him, reading a lot (and a variety of books) is fundamental:

In my whole life, I have known no wise people (over a broad subject matter area) who didn’t read all the time – none, zero.

If you look at many of the successful people of today, the expert-generalists that have created the iconic enterprises of the past decades, they share this exact same trait with Buffett and Munger. They read a lot.

When he was young and beginning his investing career, Buffett would read between 600 and 1000 pages a day! He still spends about 80% of his day reading.

I already mentioned that Elon Musk also reads like 2 books a day. Bill Gates reads 50 books a year. In the old days, guys like Thomas Jefferson or Benjamin Franklin would also spend their days reading a variety of books.

As Benjamin Franklin said:

An investment in knowledge always pays the best interest.

The elite thinkers spend much of their time sucking up as much knowledge as they can.

What does the average person do? This:

There is a book by Tom Corley called “Rich Habits: The Daily Success Habits of Rich Individuals”, where the author mentions some very interesting findings.

There was a study done that surveyed the reading habits of different people. The results were quite telling.

Rich people (those with an annual income of over 160 000 Dollars) read primarily for self-improvement. Poor people (annual income of 35 000 Dollars or less) read for entertainment.

To quote him:

The rich are voracious readers on how to improve themselves. They’re reading self-improvement books, biographies, books about successful people, things like that.

You see what I am getting at? If you want to be successful, you need to start reading a lot. You might not become a multi-billionaire like Warren Buffett, but you will definitely have a leg up on the average dude on the street.
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Return Of The Renaissance Man: The Future Belongs To Expert Generalists

He’s back!

No, I am not talking about the Terminator, although with the recent advances in AI and robotics, he could be here as well. I am talking about the almost forgotten, and nowdays often maligned, jack of all trades, the polymath, the Renaissance Man.

Now he is referred to as an expert-generalist. Just like the 20th century belonged to the specialist, the 21st century seems to belong to the person who can pull on different strands of knowledge from a wide variety of disciplines.

Elon Musk, Steve Jobs, Charlie Munger, all of these guys have one thing in common: their strength comes not in being good at one thing, but in knowing a lot of different things. They are the expert-generalists, the modern Renaissance Men who have gone on to become the icons of our modern age.

The advantage of expert-generalists is that they can bring in new perspectives from a variety of fields, unhindered by the often narrow viewpoint of a specialist.

A specialist can get bogged down in the little nitty-gritty details of their field, forgetting to see the whole picture. A great danger, one that they often fall for, is functional fixedness.

This is because they were taught to do something in a certain way and over the years they have become great at doing things that way. On the negative side this can put blinders on them and result in tunnel vision.

They are great at innovating within their paradigm, but this can also make them a bit stiff when it comes to paradigm change. All kinds of little cognitive biases can prevent them from seeing the forest for the trees.

If you look at the great innovators of our age, most of them were able to combine the knowledge of different fields and come up with something new. They have the ability to not only think in analogies, but also to be great first principles thinkers.

Henry Ford was able to go back to first principles and change the way that cars were manufactured by applying an analogy of conveyor belts from a different discipline.

Tomas Bata was able to revolutionize the way shoes were made and make his company one of the first true global companies, not only because he had a good understanding of making shoes, but also because he had a deep knowledge of other things, such as the psychology of people.

If you go back to Charlie Munger and his investment strategy, you will see that the secret of his success is the fact that he has a wide variety of mental models from different fields that he can call upon when needed.

The idea of an expert-generalist is as old as humanity, but the term itself was coined by Orit Ganiesh, who is the CEO of Bain Consulting. Her definition of it is:

Someone who has the ability and curiosity to master and collect expertise in many different disciplines, industries, skills, capabilities, countries, and topics. He or she can then, without necessarily even realizing it, but often by design: Draw on that palette of diverse knowledge to recognize patterns and connect the dots across multiple areas. Drill deep to focus and perfect the thinking.

The role of an expert-generalist is not in the trenches, doing the routine work, but instead high on top, doing the strategic thinking and making crucial decisions. This is where their expertise is needed.

Now that I have convinced you of the value of expert-generalists, one question arises: What you need to do to become one?

Well, that’s the whole point of this blog, to give you the tools that you need in order to become an expert-generalist and be able to smash through any obstacle in your way.
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Paradigm Shifts, Creative Destruction And How You Change The World

Most people pass their entire life doing things the same way, never considering that it is not the only way of working. Yet sometimes things change and the old ways don’t work anymore. That’s when you need to step up in order to survive.

Aesop’s Fables have been told to kids for thousands of years to teach them moral lessons and help them navigate in a complicated world. One such fable is that of “The Crow and the Pitcher”.

The allegory starts off with a crow flying around on a hot, dusty day. The crow is exhausted from thirst, but keeps on circling in the sky, eyes alert, but struggling to find anything to drink.

Finally, he spots a pitcher. Excited, he descends down to it, only to discover that it contains very little water.

He puts his beak into the pitcher, hoping to be able to reach at the water, but can’t. He tries pushing it over, but it doesn’t fall. He attempts all kinds of different ways to get at the water, but no success.

Then an idea pops into his head. He collects stones nearby and stacks them next to the pitcher.

Picking them up with his beak, he starts dropping these stones into the pitcher, one by one. Slowly, but surely the water level starts rising and gets a little higher with each stone thrown in.

Finally, he puts in the last few stones, and the water level in the pitcher rises high enough for him to put his beak into it and drink.

There are several moral lessons to be learned from this little story. Hard work, persistence and ingenuity are all things that ancient commentators saw as the things you were supposed to take out of it.

The little crow failed several times, but got back up and tried in a different way, persisting where others would have given up. He was also smart in noticing how the world works around him and applying that to solve the problem. The crow had a goal and didn’t stop until he achieved it.

One moral stands above the rest though: necessity is the mother of invention.

Old ways of doing things didn’t work any more. The crow tried all the traditional ways of getting at the water, but not one of them worked.

In order to survive, he needed to start thinking outside the box.

As a result of that little incident, the crow experienced an internal paradigm shift. However this was not only a change in how he views the world, but a change in how he works in the world.

He realized that he didn’t need to rely only on his own body to do things, but that he could use other objects lying around to help him perform different jobs better.

The crow became a tool user.

The story is not far from the truth, in fact modern crows have been studied and have exhibited similar problem-solving and tool-using techniques.

Once you learn that you don’t need to rely on what nature gave you in order to do your daily activities, but instead can pick up different objects in your vicinity and use them to help you, it’s a huge revelation and it completely changes the way you live.

You expend less energy, and need less resources to do daily things. You can also do new things, things you have never been able to do before.

It opens up a world of possibilities. Possibilities that had been closed to you before.

Chimpanzees and other primates have also been seen using tools in the wild. Different groups use different tools and techniques, which means that it is not an instinctual behavior, but instead a learned one.

It has been observed how when one individual discovers a new technique to do a certain activity, the technique spreads to many of the other individuals in the community. This new way of doing things completely changes their lives.

They experience a paradigm shift.

Technological Revolutions and Paradigm Shifts

When our ancestors picked up tools for the first time, they also experienced the first technological revolution.
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Paradigm Shifts, Scientific Revolutions And How You See The World

People are conditioned to see a certain way, believing it is the only way to look at things and don’t even consider the possibility of a different explanation for what they are seeing.

Plato illustrated how this works in in his work “The Republic” using an imaginary dialogue between Socrates and his pupil, Glaucon. This dialogue is called “The Allegory of the Cave”.

Imagine being a prisoner chained inside of a cave. You have been in this situation since you were born, and your chains prevent you from moving, so that even your head is in a fixed position.

There are others chained in the cave with you, but since you cannot move your head, you cannot see them directly. You can only see the wall in front of you.

Behind your back is a fire that is burning bright and between that fire and your back is a raised walkway and a wall. Hidden behind this wall are the puppet masters, who often hold up puppets above their heads.

The shadows of these puppets are projected on the walls of the cave, and so the only thing that you can see are these shadows.

Of course as a chained and immobile prisoner, you do not know this. You think that these shadows are real. They are your reality.

Since you have nothing to do, you would be bored often and to pass the time start playing games with the other prisoners.

You and the others would start trying to guess which shadow would appear on the wall next. Sometimes, some of the prisoners would predict (guess) correctly and all the other guys would praise them and think that they are so smart for being able to do this.

Imagine then, that one day somehow your chains get lose and you manage to free yourself. Now you are able to turn around, and even flee the cave.

The moment you turn your head for the first time, you would probably get a big shock. Your eyes would be hurt by the bright fire and things would be hazy.

You would see a big disconnect between what you thought was real and what was starting to emerge in front of you. You would probably not believe your eyes and instead turn back around to look at what was familiar to you, the shadows.

Then, as you are getting back to your reality, someone takes you and drags you out of the cave, outside into the real world. The sun is shining, the wind is blowing and the green of nature is all around you.

You would be angry at the guy who dragged you out and start feeling a lot of pain. Not being accustomed to light, the sun would temporarily blind you and cause you even more pain.

However, slowly, your eyes would start getting accustomed to the light. First you would only see hazy shadows everywhere, but little by little, the images would start getting clearer.

For the first time, you are able to see real people all around you. You realize how wrong you were about reality when you were in the cave, and start reasoning about all this in your head.

Armed with all this knowledge, you now want to return to the cave and free your fellow prisoners, not just physically, but also intellectually.

You go back to the cave, but as you enter, your eyes are now not used to seeing in such darkness and you are temporarily blinded again.

You try to explain to your fellow prisoners what you saw outside, but they don’t believe you, think that you are mad, and at last try to kill you. They feel much more comfortable in their version of reality, than in the real world.

The prisoners were living their entire lives believing in a certain way and thinking that what they see is what the world is really like. They came up with explanations of how this works and held them as truth.

They interpreted what they saw with their eyes and heard with their ears in one way and did not accept the view that it could be otherwise. They were focused on this one reality and way of seeing things, that they could not comprehend that there could be another way of seeing the world.

Have a look at the picture below. What do you see?

Have a look again. What do you see?

Is it a duck? Or a rabbit?

Most people at first only see only one of these things. They either see a duck or a rabbit. Which one of these was it for you?

Now go back to the picture. Can you see the other image? If you saw a duck, can you see the rabbit or vice versa?

Most people after a while, can refocus and reframe their thinking and see the other image. After a point, some can even see both images basically at the same time.

Yet at the beginning, they only saw one and not the other! It’s all a matter of perception.

Paradigm shifts

This type of reframe is what is called a paradigm shift.
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What IKEA Can Teach You About Making Money

In an interview for “Popular Science” magazine, Nick Offerman, the guy who plays Ron Swanson on the series “Parks and Recreation”, talked about his love for building things with his own hands.

He is a guy who has enough money to buy whatever he wants, but he still keeps a small woodworking studio on the side and using traditional techniques (they won’t even use a cutter jig to cut their dovetail joints!), builds all kinds of stuff out of wood.

To quote Offerman:

Keeping whatever calluses I can on my hands is an important part of my personality.

If you think about it, you are probably not that different yourself and neither are the people you know. You (or many of your friends) still probably keep that crude “bird” you cut out of wood in 6th grade during your “I want to be an expert craftsman” phase or that model airplane you spent months building, almost giving up at certain points, but always returning again to glue one more piece.

I remember how proud I was when I finished a crappy Tic Tac Toe game in my QBasic class back in high school. It only had some basic functionalities, shitty graphics, and wasn’t very exciting, but the important thing was that I had programmed it myself and it worked!

It’s a psychological effect. People feel much more proud of something that they had built themselves, than of something that they bought off the shelf. There is a sense of accomplishment that fuels self-esteem.

The Ikea Effect

IKEA is a billion-dollar furniture company that has stores around the world. It sells furniture that you have to assemble yourself, and that is the secret of its success.

A study that came out in 2011, examined what it calls the “IKEA effect”.

The psychologists behind this study had people assemble IKEA boxes, fold origami and build Lego sets. What they found out was that at the end, after successfully finishing their products, these same people valued them as highly or even more so than the same products created by experts.

Basically, people had a preference for building things with their own hands, over getting everything done for them. And this is exactly the business model that IKEA has employed right from the beginning.

The psychology behind this is related to a cognitive bias called the endowment effect. Things that you own (and things that you create yourself) have a much bigger emotional value for you than ones you don’t:

“In one experiment a social psychologist found that people were more reluctant to give up a lottery ticket they had chosen themselves, than one selected at random for them. They wanted four times as much money for selling the chosen ones compared to what they wanted for the randomly selected ticket. But in random drawings it doesn’t make any difference if we choose a ticket or are assigned one. The probability of winning is the same. The lesson is, if you want to sell lottery tickets, let people choose their own numbers instead of randomly drawing them.” Peter Bevelin “Seeking Wisdom”

This is also why people often get attached to their houses or cars and have a sense of loss when they have to move out or give them away.

The lesson here is if you involve others in the making of a final product, whether that product is a project, a model airplane, or a piece of furniture, they will value the final product much more than if they were not involved at all.
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What Is Your Brain?

Four thousand years ago in Ancient Egypt, if you were of higher status and died, you would have ended up getting mummified. The Ancient Egyptians believed that if your body was preserved after death in this world, then a comfortable life in the afterlife would be assured for your soul.

There was a special process that was applied when mummifying a body. The body was embalmed in chemicals and then wrapped up in several layers of cloth. However before the wrapping, the internal organs were taken out and put in jars.

The stomach, the liver, the lungs, and the intestines were all removed and placed in canopic jars made of either wood, stone or porcelain and sometimes topped with the head of a god. The heart stayed in, because the Egyptians believed that it would be weighted (and thereby judged) against the feather of the goddess of truth, morality and justice, Maat.

To remove the brain, a long, sharp object was first put through the nostril. It would break through into the brain and then liquefy it. The liquefied brain would then ooze out through the nostril. What would they do with it?

Once it came out, they would collect it and… throw it away! The Ancient Egyptians did this because they believed that it was of no importance for the human being. For them, it was the heart that was the center of all action.

For the Ancients, the brain just seemed to be some sort of a squishy substance with no real purpose, apart from filling up the head.
egyptbrain1
That view began to change when Galen (remember the former physician of the gladiators?), one of the most well-known doctors of Antiquity, did a demonstration where he silenced a squealing pig by isolating a nerve that tied the larynx to the brain. In this way he proved that the brain was the organ controlling the actions of living things.

Galen was not the first ancient to speculate on the nature of the brain and its role in the body (for example Hippocrates did too), but he was the first one that we know of that traced out the different nerves and muscles and connected them to the brain, and also who gave practical proofs (such as the pig experiment) of how this works.

However, among many people this view still didn’t catch on and most still kept on considering the heart as the primary seat of human actions until the Renaissance proved once and for all the central role of the brain in the body.

The role of the brain

The brain is the primary organ in the nervous system and controls the behavior of living beings. It is the most complex organ in the body. The basic structure of the human brain bears many similarities to that of other animals, but there are also some important differences. These differences are what give humans the power to reason.

There are numerous basic roles that the brain performs in the body:

  • handles all your physical movement (balance, walking, standing)
  • regulates internal processes (such as breathing, body temperature)
  • controls your actions (whether through instinct or reason)

This happens when signals from the outside (collected through sight, smell, touch, taste, hearing) are passed into the brain, which then interprets them and acts based on this interpretation. Most of this happens subconsciously.

For example this is how the signals that are captured by your hearing are transported to and then interpreted by the brain:

hearing_mechanics_cropped

How does the brain perform its functions?
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Elon Musk Problem Solving: Applications Of First Principles Thinking

The first principles approach for problem solving that Elon Musk uses is an awesome way to find unconventional solutions to all kinds of problems. However this type of thinking does not come naturally to most people.

There are numerous mental barriers that prevent people from thinking in first principles. These barriers can be overcome with certain techniques, such as the generic parts technique and also by asking lots of questions. The hardest part of this entire process, though, is the application.

How can you take this knowledge and these techniques and apply them in practice? How can you make first principles thinking a part of your life?

In Part 2, we learned how to think in first principles. In this part, we will learn how to use that thinking in order to solve real-life problems. Here we go from theory to application.

Concrete examples from history

Eureka! Eureka!” These legendary words were shouted by Archimedes, the Ancient Greek inventor, as he ran naked through the streets of Syracuse. This word can be roughly translated as “I have found it!” and since that time has become a synonym of discovery.

archimedes_cigar_box

Archimedes was a really clever guy and discovered a lot of cool and practical stuff, but his legend was solidified by this one famous incident. The story that precedes this is the perfect example of using first principles thinking to come up with solutions to problems (and it even includes discovering some first principles themselves!).

King Hiero II of Syracuse wanted a golden crown to be made and assigned the work to a local goldsmith. When the goldsmith came back with the finished product, King Hiero suspected that the crown was not all gold and instead that the goldsmith had sneaked in some silver. However how to prove this little hunch?

Luckily, the King had Archimedes loitering around his city and so assigned the problem to him. Archimedes had to determine whether the crown was pure gold or it also included silver, without damaging it. This was almost an impossible problem and no one else in the kingdom had been able to come up with a solution.

This problem was initially also hard for Archimedes himself. He kept pondering it in his mind, but just couldn’t get around to figuring out a method to solve this little conundrum.

That’s where the story gets interesting. Archimedes was a cleanly fellow and one day was getting ready for his bath. He filled up the bath almost to the top with water, stripped down and then got in. As soon as he got into the bath, the water overflowed and spilled over the edge.

Archimedes noticed that as he got into the bath, the level of the water rose. This is what sparked the lighting bolt of discovery. He had discovered a first principle!

He summarized this principle in one of his works “On Floating Bodies”:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

This is the first principle that Archimedes needed in order to solve the problem. If he submerged the crown in water, the crown would displace an amount of water equal to its volume. Archimedes could then use this fact to test whether the crown contained silver. If it did, then the crown would be less dense.

There is some discussion on the exact method that he used, but no matter the exact steps, it is a great example of coming up with first principles and then using them to solve a problem.

And yes, the goldsmith was a sneaky, dishonest dude and Archimedes proved it.
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