A simple explanation of how differential gears work and why they are necessary.
Tag: Richard Feynman
“The world is much more interesting than any one discipline.”
— Edward Tufte
NPR’s Science Friday talks with data scientist Edward Tufte on everything from Steve Jobs’ considerations of cognitive load to Picaso’s art.
Tufte also offered some insights into human nature.
If you’re told what to look for, you can’t see anything else. …
I think there’s a lot of premature labeling. Now, the situation in teaching is different. You’re trying to point out where people should see. But analytical seeing, I believe you should try to stay in the sheer optical experience as long as possible.
Once you have an idea, or somebody tells you something to look for, that’s about all you can see. I had this experience recently: A dear friend of ours has been diagnosed with Alzheimer’s, and I hadn’t seen her for about six months. And when she came and visited, I couldn’t see her anymore. I was always looking now for symptoms, how the dementia was manifesting itself. And I know about how words control scenes. I couldn’t see her through any other lens but the possible symptoms. And that one word, that one piece of knowledge, and I was self-aware of it, totally corrupted every time I looked at her.
|Still curious? Tufte’s Envisioning Information, written in 1990, still remains a must-read. Learn more about Tufte’s Feynman diagrams.|
In this clip from a documentary film shot in Yorkshire in 1973, physicist and philosopher Richard Feynman (1918-1988) talks with Fred Hoyle, an accomplished astronomer from the United Kingdom.
Feynman poses the question: “What, today, do we not consider part of physics, which may ultimately be part of physics?”
His answer (which should be cued up here at the 7:10 mark) is the initial conditions of the universe, as well as the possibility that the physical laws themselves, evolve with time.
As he explains, there was a time when we considered the properties of substances to be chemistry, but as the quantum mechanical understanding of the atom evolved, we came to discover that this was actually all a part of physics.
In physics, our acceptance of the way things are (i.e. given conditions) without wondering why they’re like that is akin to playing chess without asking where the pieces should be placed before the game even starts.
It’s as though we’re doing a chess game and we’re working on the rules but we’re not worrying about how the pieces are supposed to be set up on the board in the first place. We tell ourselves, that’s not our business, that’s the business of cosmology and how the universe came to be. It’s interesting that in many other sciences, there’s a historical question. Like geology, we ask “How did the earth evolve into its present condition?” In biology, it’s “How did the various species evolve to get to be the way they are?” But the one field that has not admitted any evolutionary question is physics. “Here are the laws!” we say. We don’t even think about how they got that way. We think, well it’s been that way forever, it’s always been that way. It’s always been the same laws. And we try to explain the universe that way. So it might turn out that they’re not the same all the time, and that there is a historical, evolutionary question.
This fascinating conversation between two great minds continues in the follow-up video. Listen on to hear Feynman explain why he’s afraid to speculate about things.
“He (Richard Feynman) was always searching for patterns, for connections, for a new way of looking at something, but I suspect his motivation was not so much to understand the world as it was to find new ideas to explain. The act of discovery was not complete for him until he had taught it to someone else.”— Daniel Hillis
- Simplify the problem down to an “essential puzzle.” Here’s how Danny Hillis explained Feynman’s use of simplicity: “He always started by asking very basic questions like, ‘What is the simplest example?’ or ‘How can you tell if the answer is right?’ He asked questions until he reduced the problem to some essential puzzle that he thought he would be able to solve. Then he would set to work.”
- Continually master new techniques and then apply them to your library of unsolved puzzles to see if they help. As mathematician Gian Carlo-Rota explained when describing Feynman’s use of this strategy: “Every once in a while there will be a hit, and people will say: ‘How did he do it? He must be a genius!’”
There are four simple steps to the Feynman Technique, which I’ll explain below:
- Choose a Concept
- Teach it to a Toddler
- Identify Gaps and Go Back to The Source Material
- Review and Simplify (optional)
If you’re not learning you’re standing still. So what’s the best way to learn new subjects and identify gaps in our existing knowledge?
Two Types of Knowledge
There are two types of knowledge and most of us focus on the wrong one. The first type of knowledge focuses on knowing the name of something. The second focuses on knowing something. These are not the same thing. The famous Nobel winning physicist Richard Feynman understood the difference between knowing something and knowing the name of something and it’s one of the most important reasons for his success. In fact, he created a formula for learning that ensured he understood something better than everyone else.
It’s called the Feynman Technique and it will help you learn anything faster and with greater understanding. Best of all, it’s incredibly easy to implement.
“The person who says he knows what he thinks but cannot express it usually does not know what he thinks.”
— Mortimer Adler
There are four steps to the Feynman Technique.
Step 1: Teach it to a child
Take out a blank sheet of paper and write the subject you want to learn at the top. Write out what you know about the subject as if you were teaching it to a child. Not your smart adult friend but rather an 8-year-old who has just enough vocabulary and attention span to understand basic concepts and relationships.
A lot of people tend to use complicated vocabulary and jargon to mask when they don’t understand something. The problem is we only fool ourselves because we don’t know that we don’t understand. In addition, using jargon conceals our misunderstanding from those around us.
When you write out an idea from start to finish in simple language that a child can understand (tip: use only the most common words), you force yourself to understand the concept at a deeper level and simplify relationships and connections between ideas. If you struggle, you have a clear understanding of where you have some gaps. That tension is good –it heralds an opportunity to learn.
Step 2: Review
In step one, you will inevitably encounter gaps in your knowledge where you’re forgetting something important, are not able to explain it, or simply have trouble connecting an important concept.
This is invaluable feedback because you’ve discovered the edge of your knowledge. Competence is knowing the limit of your abilities, and you’ve just identified one!
This is where the learning starts. Now you know where you got stuck, go back to the source material and re-learn it until you can explain it in basic terms.
Identifying the boundaries of your understanding also limits the mistakes you’re liable to make and increases your chance of success when applying knowledge.
Step 3: Organize and Simplify
Now you have a set of hand-crafted notes. Review them to make sure you didn’t mistakenly borrow any of the jargon from the source material. Organize them into a simple story that flows.
Read them out loud. If the explanation isn’t simple or sounds confusing that’s a good indication that your understanding in that area still needs some work.
Step 4 (optional): Transmit
If you really want to be sure of your understanding, run it past someone (ideally who knows little of the subject –or find that 8-year-old!). The ultimate test of your knowledge is your capacity to convey it to another.
Not only is this a wonderful recipe for learning but it’s also a window into a different way of thinking that allows you to tear ideas apart and reconstruct them from the ground up. (Elon Musk calls this thinking from first principles.) This leads to a much deeper understanding of the ideas and concepts. Importantly, approaching problems in this way allows you to understand when others don’t know what they are talking about.
Feynman’s approach intuitively believes that intelligence is a process of growth, which dovetails nicely with the work of Carol Dweck, who beautifully describes the difference between a fixed and growth mindset.
“But the problem, you see, when you ask why something happens, how does a person answer why something happens?”
— Richard Feynman
In this beautiful video Richard Feynman on the nature of why questions and how they help us understand the world.
Interviewer: If you get hold of two magnets, and you push them, you can feel this pushing between them. Turn them around the other way, and they slam together. Now, what is it, the feeling between those two magnets?
Feynman: What do you mean, “What’s the feeling between the two magnets?”
Interviewer: There’s something there, isn’t there? The sensation is that there’s something there when you push these two magnets together.
Feynman: Listen to my question. What is the meaning when you say that there’s a feeling? Of course, you feel it. Now, what do you want to know?
Interviewer: What I want to know is what’s going on between these two bits of metal?
Feynman: They repel each other.
Interviewer: What does that mean, or why are they doing that, or how are they doing that? I think that’s a perfectly reasonable question.
Feynman: Of course, it’s an excellent question. But the problem, you see, when you ask why something happens, how does a person answer why something happens? For example, Aunt Minnie is in the hospital. Why? Because she went out, slipped on the ice, and broke her hip. That satisfies people. It satisfies, but it wouldn’t satisfy someone who came from another planet and knew nothing about why when you break your hip do you go to the hospital. How do you get to the hospital when the hip is broken? Well, because her husband, seeing that her hip was broken, called the hospital up and sent somebody to get her. All that is understood by people. And when you explain a why, you have to be in some framework that you allow something to be true. Otherwise, you’re perpetually asking why. Why did the husband call up the hospital? Because the husband is interested in his wife’s welfare. Not always, some husbands aren’t interested in their wives’ welfare when they’re drunk, and they’re angry.
And you begin to get a very interesting understanding of the world and all its complications. If you try to follow anything up, you go deeper and deeper in various directions. For example, if you go, “Why did she slip on the ice?” Well, ice is slippery. Everybody knows that, no problem. But you ask why is ice slippery? That’s kinda curious. Ice is extremely slippery. It’s very interesting. You say, how does it work? You could either say, “I’m satisfied that you’ve answered me. Ice is slippery; that explains it,” or you could go on and say, “Why is ice slippery?” and then you’re involved with something, because there aren’t many things as slippery as ice. It’s not very hard to get greasy stuff, but that’s sort of wet and slimy. But a solid that’s so slippery? Because it is, in the case of ice, when you stand on it (they say) momentarily the pressure melts the ice a little bit so you get a sort of instantaneous water surface on which you’re slipping. Why on ice and not on other things? Because water expands when it freezes, so the pressure tries to undo the expansion and melts it. It’s capable of melting, but other substances get cracked when they’re freezing, and when you push them they’re satisfied to be solid.
Why does water expand when it freezes and other substances don’t? I’m not answering your question, but I’m telling you how difficult the why question is. You have to know what it is that you’re permitted to understand and allow to be understood and known, and what it is you’re not. You’ll notice, in this example, that the more I ask why, the deeper a thing is, the more interesting it gets. We could even go further and say, “Why did she fall down when she slipped?” It has to do with gravity, involves all the planets and everything else. Nevermind! It goes on and on. And when you’re asked, for example, why two magnets repel, there are many different levels. It depends on whether you’re a student of physics, or an ordinary person who doesn’t know anything. If you’re somebody who doesn’t know anything at all about it, all I can say is the magnetic force makes them repel, and that you’re feeling that force.
You say, “That’s very strange, because I don’t feel a kind of force like that in other circumstances.” When you turn them the other way, they attract. There’s a very analogous force, electrical force, which is the same kind of a question, that’s also very weird. But you’re not at all disturbed by the fact that when you put your hand on a chair, it pushes you back. But we found out by looking at it that that’s the same force, as a matter of fact (an electrical force, not magnetic exactly, in that case). But it’s the same electric repulsions that are involved in keeping your finger away from the chair because it’s electrical forces in minor and microscopic details. There’s other forces involved, connected to electrical forces. It turns out that the magnetic and electrical force with which I wish to explain this repulsion in the first place is what ultimately is the deeper thing that we have to start with to explain many other things that everybody would just accept. You know you can’t put your hand through the chair; that’s taken for granted. But that you can’t put your hand through the chair, when looked at more closely, why, involves the same repulsive forces that appear in magnets. The situation you then have to explain is why, in magnets, it goes over a bigger distance than ordinarily. There it has to do with the fact that in iron all the electrons are spinning in the same direction, they all get lined up, and they magnify the effect of the force ’til it’s large enough, at a distance, that you can feel it. But it’s a force which is present all the time and very common and is a basic force of almost – I mean, I could go a little further back if I went more technical – but on an early level I’ve just got to tell you that’s going to be one of the things you’ll just have to take as an element of the world: the existence of magnetic repulsion, or electrical attraction, magnetic attraction.
I can’t explain that attraction in terms of anything else that’s familiar to you. For example, if we said the magnets attract like rubber bands, I would be cheating you. Because they’re not connected by rubber bands. I’d soon be in trouble. And secondly, if you were curious enough, you’d ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I’m trying to use the rubber bands to explain. So I have cheated very badly, you see. So I am not going to be able to give you an answer to why magnets attract each other except to tell you that they do. And to tell you that that’s one of the elements in the world – there are electrical forces, magnetic forces, gravitational forces, and others, and those are some of the parts. If you were a student, I could go further. I could tell you that the magnetic forces are related to the electrical forces very intimately, that the relationship between the gravity forces and electrical forces remains unknown, and so on. But I really can’t do a good job, any job, of explaining magnetic force in terms of something else you’re more familiar with, because I don’t understand it in terms of anything else that you’re more familiar with.