What characterizes a useful model?
If a model agrees with reality, it is most likely true. One idea from biology that agrees with reality is that "people on average act out of self-interest." But not the idea that "people's personalities can be evaluated by using the Rorschach ink-blot test." It can't predict people's personalities. Ask: What is the underlying big idea? Do I understand its application in practical life? Does it help me understand the world? How does it work? Why does it work? Under what conditions does it work? How reliable is it? What are its limitations? How does it relate to other models?
Charles Munger gives an example of a useful idea from chemistry - autocatalysis:
If you get a certain kind of process going in chemistry, it speeds up on its own. So you get this marvelous boost in what you're trying to do that runs on and on. Now, the laws of physics are such that it doesn't run on forever. But it runs on for a goodly while. So you get a huge boost. You accomplish A- and, all of a sudden, you're getting A+ B + C for awhile.
He continues telling us how this idea can be applied:
Disney is an amazing example of autocatalysis ... They had all those movies in the can. They owned the copyright. And just as Coke could prosper when refrigeration came, when the videocassette was invented, Disney didn't have to invent anything or do anything except take the thing out of the can and stick it on the cassette.
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Which models are most reliable? Charles Munger answers:
The models that come from hard science and engineering are the most reliable models on this Earth. And engineering quality control - at least the guts of it that matters to you and me and people who are not professional engineers - is very much based on the elementary mathematics of Fermat and Pascal: It costs so much and you get so much less likelihood of it breaking if you spend this much ...
And, of course, the engineering idea of a backup system is a very powerful idea. The engineering idea ofbreakpoints- that's avery powerful model, too. The notion of a critical mass - that comes out of physics - is a very powerful model.
A valuable model produces meaningful explanations and predictions oflikely future consequences where the cost of being wrong is high.
A model should be easy to use. If it is complicated, we don't use it.
It is useful on a nearly daily basis. If it is not used, we forget it. And what use is knowledge if we don't use it?
Considering many ideas help us achieve a holistic view
Those who love wisdom must be inquirers into many things indeed.
Heraclitus
What can help us see the big picture? How can we consider many aspects of an issue? Use knowledge and insights from many disciplines. Most problems need to be studied from a variety of perspectives. Charles Munger says, "In most messy human problems, you have to be able to use all the big ideas and not just a few of them."
The world is multidisciplinary. Physics doesn't explain everything; neither does biology or economics. For example, in a business it is useful to know how scale changes behavior, how systems may break, how supply influences prices, and how incentives cause behavior.
Since no single discipline has all the answers, we need to understand and use the big ideas from all the important disciplines - mathematics, physics, chemistry, engineering, biology, psychology, and rank and use them in order of their reliability. Charles Munger illustrates the importance of this:
Suppose you want to be good at declarer play in contract bridge. Well, you know the contract - you know what you have to achieve. And you can count up the sure winners you have by laying down your high cards and your invincible trumps.
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But if you're a trick or two short, how are you going to get the other needed tricks? Well, there are only six or so different, standard methods: You've got long-suit establishment. You've got finesses. You've got throw-in plays. You've got cross-ruffs. You've got squeezes. And you've got various ways of misleading the defense into making errors. So it's a very limited number of models. But if you only know one or two of those models, then you're going to be a horse's patoot in declarer play...
If you don't have the full repertoire, I guarantee you that you'll overutilize the limited
repertoire you have - including use of models that are inappropriate just because they're available to you in the limited stock you have in mind.
Suppose we have a problem and ask: What can explain this? How can we achieve this? How can we then use different ideas? Charles Munger tells us how to do it:
Have a full kit of tools... go through them in your mind checklist-sryle... you can never make any explanation that can be made in a more fundamental way in any other way than the most fundamental way. And you always take with full attribution to the most fundamental ideas that you are required to use. When you're using physics, you say you're using physics. When you're using biology, you say you're using biology.
We also need to understand how different ideas interact and combine. Charles Munger says:
You get lollapalooza effects when two, three or four forces are all operating in the same direction. And, frequently, you don't get simple addition. It's often like a critical mass in physics where you get a nuclear explosion if you get to a certain point of mass - and you don't get anything much worth seeing if you don't reach the mass.
Sometimes the forces just add like ordinary quantities and sometimes they combine on a break-point or critical-mass basis... More commonly, the forces coming out of... models are conflicting to some extent. And you get huge, miserable trade-offs ... So you [must] have the models and you [must] see the relatedness and the effects from the relatedness.
The British mathematician and philosopher Alfred North Whitehead said: "The problem of education is to make the pupil see the wood by means of the trees." We need to consider many aspects of an issue and synthesize and integrate them. We need to understand how it all fits together to form a coherent whole. The term synthesis comes from classical Greek and means literally "to put together." Below are some examples of how this can be used in problem-solving.
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We can combine ideas within a discipline. We saw in Part Two how psychological tendencies can combine and give Lollapalooza effects.
We can try to find connections between ideas or derive new ideas from these connections. The modern evolutionary synthesis was a unification of several ideas within biology.
We can combine ideas from different disciplines. The ideas of scaling from mathematics, systems and constraints from physics, and competitive advantage from microeconomics often explain how business value is created or destroyed.
We can try to see relationships between phenomena, and try to find one principle that can explain them all. The British physicist James Clark Maxwell combined in one model the laws of electricity and magnetism with the laws of behavior of light. This single model explained optical, electrical and magnetic phenomena.
We can find similarities or functional equivalents within or between disciplines. The functional equivalent of viscosity from chemistry is stickiness in economics.
How can we learn an idea so it sticks in our memory?
Samuel Johnson said: "He is a benefactor of mankind who contracts the great rules of life into short sentences, that may be easily impressed on the memory, and so recur habitually to the mind."
Richard Feynman answered the following question in one of his physics lectures:
If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made ofatoms - little particles that move around in perpetual motion, attracting each other when they area little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if jus
t a little imagination and thinking are applied.
We can use the Feynman "one sentence explanation" when dealing with big ideas. "What sentence contains the most information in the fewest words?" An example of a one-sentence idea from psychology is: "We get what we reward for." A sentence from physics is: "Energy is neither created nor destroyed - only changed from one form into another."
Another way to understand a model is to give it a "hook." Associate the model with a dramatic real-life story, analogy, individual, or picture. For example to
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remember social proof, we can think about the Genovese homicide in New York City (see Part Two).
A Chinese proverb says, "I forget what I hear; I remember what I see; I know what I do." Since the best way to learn something is by doing it, we must apply models routinely to different situations. Like any skill, this takes both practice and discipline.
Search for explanations
What happens and why does it happen?
One way of forcing us to learn models to better deal with reality is to open our eyes and look at the things we see around us and ask "why" things are happening (or why things are not happening). Take some simple examples as "why do apples fall downward?" or "why do we fall down when we slip?" or "why don't we fall off the earth?" The English mathematician and physicist Sir Isaac Newton's law of gravitation can explain this.
Newton's 1st law tells us that an object in motion tends to continue in motion at a steady speed in a straight line, and an object at rest tends to stay at rest, unless the object is acted upon by an outside force.
This means that there are only 3 ways to change an object: an object at rest can start to move, an object in motion at a steady speed can go up or down in speed, and an object in motion in a straight line can change direction. And what is needed to change an object's motion? A force.
All change in motion happens in response to the action of force(s). By forces, we mean a push or a pull that acts on an object. When we open a door or throw a baseball, we are using forces (muscular effort). Almost everything we do involves forces.
Newton's 2nd law tells us that force is the product of mass and acceleration. Acceleration is any change in speed and/or direction. It depends on the mass (measures an object power to resist change in its state of motion) of an object and the magnitude and direction of the force acting on it. The more force we use at a given mass, the greater the acceleration. But the more mass, the more an object resists acceleration. For example, the more force we use to throw a baseball, the greater the acceleration of the ball. If we increase mass, we have to add more force to produce the same rate of acceleration.
Newton's 3rd law is that forces work in pairs. One object exerts a force on a second object, but the second object also exerts a force equal and opposite in direction to the force acting on it - the first object. As Newton said in Philosophiae Natura/is Principia Mathematica: "If you press a stone with your
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finger, the finger is also pressed by the stone." If we throw a baseball, the ball also "throws" us or pushes back on our hand with the same force.
Now we come to the force of gravity. Influenced by Johannes Kepler's work on planetary motion and Galileo Galilei's work on freely falling objects, Newton found out that there was a force that attracts two objects to each other. Two factors influence the degree of attraction. Mass and distance. The greater the mass of two objects or the closer the distance between them, the greater the attraction between them. This also means that the greater the distance between the objects, the weaker the force of gravity. If we for example double the distance, the force is as fourth as strong.
Mathematically we can state the force of attraction or gravitation as equal to the mass of one object multiplied with the mass of the other object divided by the square of the distance between the objects. All this is multiplied with a constant (a number that doesn't change in value)-g (9.8 meters per second each second or 9.8m/s2 ). We can call g, the acceleration of gravity near the surface of the Earth.
It is the force ofgravity that makes an apple fall toward the Earth.
The Earth attracts the apple with a force that is proportional to its mass and inversely proportional to the square of the distance between them. But Newton's third law says that the apple also exerts an equal and opposite force on the Earth. The force of attraction on the apple by the Earth is the same as the force of attraction on the Earth by the apple. So even if it looks to us like the apple falls to the Earth, both the Earth and apple fall toward each other. The force is the same but as we see from Newton's second law, not the acceleration. Their masses differ. The Earth's mass is so large compared to the apple that we see the apple "falling." Apples fall, starting at rest, to the Earth since they have less mass than the Earth, meaning they accelerate (change speed) more toward the Earth than the Earth does toward the apple. The Earth's great mass also explains why we fall toward the Earth when we slip.
The same force draws the Moon to the Earth. But what keeps the Moon in orbit around the Earth instead of crashing into the Earth?
Newton knew that there must be some force pulling the Moon toward the Earth. Otherwise according to the 1st law the Moon would continue in motion in a straight line at a steady speed instead of its more elliptical motion. Some force must continuously pull the Moon out of its straight-line motion and change its direction. And since the Moon's orbit is circular, this force must originate from the center of the Earth. Why? Newton knew that a centripetal force (any force
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directed toward a fixed center) controls objects going in a circle around a fixed point.
That force is gravity. It changes the Moons acceleration by continually changing its direction toward the center of the Earth causing the Moon to curve into circular motion. As the Moon moves horizontally in a direction tangent (the straight line that touches a curve) to the Earth, at each point along its path, gravity pulls it inward toward the center of the Earth and the result is a Moon in circular orbit.
The Moon's speed is great enough to ensure that its falling distance matches the Earth's curvature. The Moon remains at the same distance above Earth since the Earth curves at the same rate as the Moon "falls." By the time the Moon has fallen a certain distance toward Earth, it has moved sideways about the same distance. If its speed were much lower, the pull of gravity would gradually force the Moon
closer to the Earth until they crash into each other. If its speed where much higher,
the Moon would escape the force of gravity and move away from us.
The Moon doesn't accelerate as much as the apple, because of its distance to Earth (the force of gravity is weaker). The Moon in its orbit is about sixty times as far away from the Earth's center as the apple is.
Newton's law of gravitation isn't enough to describe the motion of objects whose speed is near the speed oflight. Why? According to Albert Einstein's theory of relativity, the mass of an object is not a constant. It increases as its speed approaches the speed oflight. Newton's theories and the theory of relativity also differ when gravitational fields are much larger than those found on Earth. Under most conditions, though, Newton's laws and his theory of gravitation are adequate.
The relative influence of gravity varies with size and scale.
Why does falling.from a high tree not harm an insect?
In Two New Sciences, Galileo Galilei wrote: "Who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height or a cat from a height of eight or ten cubits will suffer no injury?"
Imagine if a mouse, a horse and a human were to be thrown out of an airplane from 1,000 yards. What happens? The biologist J.B.S. Haldane said in On Being the Right Size (reprinted in The World of Mathematics): "You can drop a mouse
down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a h
orse splashes."
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Physical forces act on animals differently. Gravity has a more powerful effect on bigger things, than on smaller things. Gravity is a major influence on us, but is of minor significance to smaller animals. Since human surface area is so small, gravitational forces act upon our weight. But gravity is negligible to very small animals with high surface area to volume ratios. The dominant force is then surface force. Haldane says: "Divide an animal's length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force [of gravity]."
"Weight affects speed when air resistance is present.
On smaller scales, gravity becomes less and less important compared with air resistance. Throw a mouse off the plane and it floats down as frictional forces acting on its surface overcome the influence of gravity.
A falling object falls faster and faster, until the force of air drag acting in the opposite direction (arising from air resistance) equals its weight. Air drag depends on the surface area (the amount of air the falling object must plow through as it falls) and the speed of the falling object. Since a mouse has so much surface area compared to its small weight, it doesn't have to fall very fast before the upward acting air drag builds up to its downward-acting weight. The net force on the mouse is then zero and the mouse stops accelerating.
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