Rambow’s Rules for Life

Shortly after my son was born, I began drafting a letter to him — something I hoped he would remember me by long after I was gone that would also help him live the best life possible. The letter included many of the most important lessons I’ve learned in life — advice on how to be happy, healthy, and successful. My hope was that it would help him avoid many of the mistakes I made. For anyone who might be interested, here is the advice. I’ve divided it into three parts: (1) keys to success, (2) keys to happiness, and (3) miscellaneous advice.

KEYS TO SUCCESS

1. BE INDUSTRIOUS. Let your natural, default state be one in which you are always creating or learning something of value. If you’re always productive, success will be almost automatic, and you’ll never regret how you spent your time. Build things. Write. Learn new skills or languages. Keep a list of things you want to accomplish, and make sure you’re always chipping away at it. Don’t waste any time, because time is the most precious thing you have. This doesn’t mean that you should be a workaholic; quality time with friends and family is vital as well. Relaxation and recreation, in moderation, are not a waste of time; in fact, they can help replenish your well of creativity and make you even more productive — and creative pursuits are a big part of what makes life meaningful.
   
2. CULTIVATE USEFUL SKILLS. Skills give you freedom and power. If you’re good at coding, you have the freedom and power to create new software. If you speak a foreign language, you have the freedom and power to live and succeed in a different country and to make friends with people you otherwise wouldn’t even be able to communicate with. Look around and think about what skills you’d like to have. What skills are employers looking for? What skills match your interests, talents, and affinities? What skills will give you the freedom and power to get a good job and earn a good wage? What skills will give you the freedom and power to do the things in life that you really want to do? It’s not just about work; there are plenty of skills apart from work that make life more enjoyable and fulfilling.
   
3. BUILD PERSONAL CONNECTIONS. Cultivate and maintain lifelong friendships and business relationships. Always be engaged in your community — at work, at school, in your neighborhood — and make positive contributions while also building useful connections. Help others, and don’t hesitate to seek their help as well. It’s not about using people; it’s about being part of something bigger than yourself — a community that benefits everyone. Make sure the relationships are genuine; care about the people in your network, and learn to speak their love languages. Good relationships will help you not just to be more successful, but to be happier as well — because companionship is another big part of what makes life meaningful.
   
4. BE PROACTIVE AND ASSERTIVE. If you want something to happen, make it happen. Don’t wait for opportunities to come your way; rather, actively seek them out and create your own opportunities. Just being good at what you do isn’t enough. People won’t come along and offer you a dream job just because you’re an excellent student. Figure out what you want; then figure out what it will take to get it; and then do it. You have to be willing to take risks. I was never very good at this, and I regret that I didn’t understand earlier what it meant to be proactive. I was a “great” student who always made good grades, and so I always got funneled automatically to the advanced classes at the next level. I made very few decisions on my own. I expected everything to be handed to me automatically because I was a good, hardworking student. But when it came time for me to graduate from college, I didn’t have a plan. Other people had made plans much earlier on: medical school, graduate school, law school, internships, and engineering jobs. While they were starting their dream careers, I still had no idea what I wanted to do. That was a huge mistake — one that I don’t want you to make as well. So, figure out what you want to do, and make it happen.
   
5. EXERCISE YOUR MIND. Your intelligence level is not fixed; never stop raising it. Push yourself to master knowledge and skills that are difficult to understand, and you will become smarter. Stay in the “zone of proximal development” — the region where things are neither too easy nor too hard, but challenging enough to make you grow. If you feel that everything you’re doing is easy, then you’re not challenging yourself enough, and you should find more difficult problems to tackle. Actively and intentionally develop your problem-solving, comprehension, and communication skills. Be informed, be discerning, and expose yourself to a variety of viewpoints.
   
6. PROTECT YOUR HEALTH. Take good care of your physical and mental health. Poor health is an obstacle to success, because health problems can eat up time, energy, and money that could be better spent on other things. You can’t control everything about your health, but there is plenty you can do to maximize your chances of staying healthy. There are four keys: diet, exercise, sleep, and companionship. Don’t pollute your body with smoke, excessive alcohol, or too much sugar and fat. Don’t eat too much or too little. Play sports that exercise your heart and lungs; lift weights enough to be strong; stretch enough to be flexible. Take care of your appearance so that you will always feel good about the way you look. Get enough sleep so that you’ll be mentally sharp and have plenty of energy. And surround yourself with people who push you to be a better person and make you feel good about yourself. Your health has multiple components, all of which will affect your success; don’t neglect any of those components.
   
7. MANAGE YOUR MONEY WISELY. Always spend less than you earn. Whenever you receive money, save and invest a portion of it. Obtain assets, and avoid liabilities. An asset is an investment that brings more money into your pocket. A liability is something that drains money out of your pocket. An expensive car is a liability, not an asset. A fancy house is a liability, not an asset. A stock or mutual fund that grows in value and pays dividends is an asset. A house or condo that you rent out is an asset. Don’t worship money, but manage it wisely so that you’ll always have enough to take care of your family and do things that you enjoy.

Of course, success is not the only important thing in life. There are plenty of highly successful, wealthy people who are miserable, who hate life, and who drag everyone around them down. Don’t be one of those people. Happiness is more important than success or wealth — though of course, success and wealth can make it easier to be happy. Below are some additional principles that will help you to be as happy as possible.

KEYS TO HAPPINESS

1. Surround yourself with cheerful people who work hard and like to help others. The friends you choose will have a tremendous influence on the kind of person you become. Make sure you’re always surrounded by people who make you a better, happier person. If you surround yourself with unhappy people, then you’ll be unhappy too. If you surround yourself with lazy and unsuccessful people, then you’ll be lazy and unsuccessful. On the other hand, if you surround yourself with people who are just like the person you want to be, then you will become the person you want to be. Here’s a good rule of thumb: If you like the person you are when you’re with someone else, then keep spending time with them. If you don’t like the person you are when you’re with someone else, then stop hanging out with them.
   
2. Don’t compare yourself to others. There will always be people above you and people below you; people who are faster, and people who are slower; people who are richer, and people who are poorer. If you focus on the people who are “ahead of you” in life, it will be easy to become afflicted by envy, bitterness, and despair. If you focus on the people who are “behind you,” you may be tempted to feel an undeserved sense of superiority and pride. Neither is beneficial. Focus instead on being the best you can be. Take satisfaction in your own unique identity, the special roles that you fill, and the never-ending process of striving to become a better person.
   
3. Find enjoyment in your present circumstances. A lot of people spend too much time focusing on what they want next. First, they can’t wait to grow up and become an adult. Then they can’t wait until they finish school. Then they can’t wait until they have a job. Then they can’t wait until they’re married. Then they can’t wait until they have kids. Then they can’t wait until their kids grow up. Then they can’t wait until they retire. Before they know it, their life is over, and they didn’t enjoy much of it because they never savored what they were doing in the present. Satisfaction was always one step ahead of them, so they never reached it. Instead of dwelling on where you want to be next, focus on where you are now. Find enjoyment in the process rather than the goal. If you’re doing the right thing now, you’ll end up in the place where you want to be next.
   
4. Hold onto the good, and let go of the bad. Your memories will be your most precious treasures. The ones you choose to focus on will determine whether you are happy or bitter. Every night, as you drift off to sleep, open up your treasure chest of happy memories, and fill your heart with them. Think back on the bad times just enough to learn from them, and then let go of them so that they will never bother you again. This can be difficult to do, since we can’t always control our thoughts; but what we can do is notice negative thoughts when they arise (without passing judgment), notice how they make us feel, and then redirect our attention toward something more positive. Do not try to stop thinking about bad things. (There’s a classic joke about this: If someone tells you not to think about an elephant, they have just made you think of an elephant — and so it is impossible to avoid thinking about an elephant by trying to avoid thinking about one. In the same way, if you are focusing your attention on trying not to think about something painful, then you will necessarily be continuing to think about that painful thing.) Instead, start thinking about something else; the only way to get rid of negative thoughts is by replacing them with something positive. Don’t punish yourself for mistakes you’ve made. If you feel bad about them, then you’ve already learned from them. Let go, and move on.
   
5. Never allow bitterness, resentment, contempt, or anger to take root in your mind. Don’t let any event — a horrible illness, the loss of a friend or loved one, or any kind of conflict or tragedy — make you bitter. Your life is too precious and too short to allow any significant part of it to be ruled by bitterness or anger. You may not be able to stop yourself from having these feelings temporarily, but the important thing is that you not let them take root and grow. Notice the bitterness or anger when it arises, and then let go of it and actively replace it with something positive.

Here are some other miscellaneous pieces of advice that I think are extremely valuable. Many of them are things you’ve heard me say many times, and I repeat them here unapologetically. They will also contribute to success and happiness.

OTHER MISCELLANEOUS RULES

1. Never complain or make excuses, even when there are legitimate complaints and excuses to be made. Complaining is unattractive. If you have a positive attitude and lift others up rather than dragging them down, then people will like you more, and you’ll be happier and more successful. Bad attitudes are contagious; if you get infected by one, try to cure it before you spread it around. And avoid catching a bad attitude from others, just as you would avoid catching a cold from them.
   
2. Observe other people carefully, and pay attention to their motives. Do this in both the short term and the long term. It will help you identify dangerous people, and it will also help you make deals with people. If you’re on a bus and you see a woman taking care of her baby, then you know what is motivating her: the desire to keep her baby safe, happy, and healthy. She’s not going to hurt someone else on the bus unless she feels threatened or desperate; and if she does feel threatened or desperate, that’s something you should be able to see. But if there’s a young man who is all by himself and is eyeing everyone else’s bags, purses, and pockets, then maybe he’s looking for something to steal. Pay attention to what people are looking at. Watch their eyes, watch their body language, and listen to their words. Think, what is this person trying to accomplish right now? This habit can be useful in working with other people. If you know what someone really wants, you can make a deal with them; they might be willing to do something for you if you help them get what they want. Just be ethical, and avoid shady deals that will cause trouble.
   
3. Don’t be afraid to take risks. This old saying is true: “Nothing ventured, nothing gained.”Often, it’s worth it to give up something of value to get what you want, just as you might sacrifice a valuable piece in chess in order to win the game. Just be wise, not reckless, in the risks you take and the sacrifices you make.
   
4. Be a player in life, not a spectator. Theodore Roosevelt put this idea best in the following quote:
   “It is not the critic who counts; not the person who points out how the strong one stumbles, or where the doer of deeds could have done them better. The credit belongs to the one who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again; who spends oneself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if one fails, at least fails while daring greatly, so that one’s place shall never be with those cold and timid souls who know neither victory nor defeat.“
5. Avoid motivated reasoning. “Motivated reasoning” is one of the most harmful things to human society. It undermines truth itself. And yet it is something that we do naturally, so we must watch for it in ourselves and try to avoid it. What is it? It’s the tendency to fabricate logical reasons for believing the things we want to believe. The following statement is counterintuitive but true: Intelligence doesn’t necessarily bring you closer to the truth; rather, it just enables you to construct clever reasons to continue believing the things you want to be true. A man once said to me, “My IQ is just a few points shy of Einstein’s. If you give me any argument against the Bible, I’ll be able to prove it wrong.” All this really meant was that he was committed to using his high intelligence to buttress the dogmas he had already decided were true before examining the evidence. His mistake was this: He never approached the Bible with an open mind and used his intelligence to consider the question, “What is actually true?” Instead, he was tackling the question, “How do I interpret the evidence in a way that won’t conflict with my cherished beliefs?” If he had been born into a Muslim family, he would have said the same about Islam: “If you give me any argument against the Qur’an, I’ll be able to prove it wrong.” And indeed, there are many people just as intelligent as he is who are just as certain that the Qur’an is true and whose arguments for its veracity are just as clever. The honest pursuit of truth is NOT about searching for evidence to prove your hypothesis correct. It is about going where the evidence takes you — whether that’s where you wanted to go or not. Good scientists search just as hard for evidence that will disprove their theories as for evidence that will support them.
   
6. Avoid tribalism of all forms — especially political, racial/ethnic, and religious tribalism. Just like motivated reasoning, tribalism is tremendously harmful. It exists naturally within you, and you have to work hard to avoid falling victim to it. What is it? It’s a tendency to fall in line with people in your group — something we all do without being aware of it. Think about this: If you know what people believe about one particular issue, such as abortion, then you can usually guess what they believe about most other issues — even totally unrelated ones. Take guns and abortion, for example. You might think that someone who wants to protect the lives of unborn babies would also want to limit the availability of guns. But as it turns out, most people who are against abortion are also in favor of widespread gun ownership. And the reason is purely political. Most people are born into a political tribe, or they join one when they grow up. They think they’ve arrived at their beliefs through logical reasoning, but the actual truth is that they’re going along with their tribe, and they’re just employing motivated reasoning (without knowing it) to convince themselves that they arrived at their positions via rational thought.
   
7. Become adept at defusing tense situations and disarming agitated people. It is in our nature to escalate tensions and repay offenses with greater offenses. Be strong and creative enough to step out of such destructive cycles. Interactions with people are like games of chess. You can be a slave to your nature and make expected moves that bring about expected conflicts — or you can master yourself and make unexpected moves that take everyone by surprise and change the direction and outcome of the game. In fact, most people are trapped in petty games without even realizing it. They are trying to score points for themselves and for their tribe. They spout insults and broadcast false virtues (which will win them esteem in the eyes of their tribe) without any regard for what is actually true. They cannot see their way to exit the game and play by a different, higher set of rules, putting an end to the point-scoring and the tribalism. Once they are locked in conflict, they cannot even see the possibility of ending it and working together. They cannot see the possibility of admitting they are wrong or apologizing. Get in the habit of watching for ways to transcend the games that others play. This is how you turn enemies to friends. This is how you get people to come together and accomplish more than anyone ever would have believed possible.

Life, the Universe, and Everything

(Click here for the PDF version of this presentation.)

Math is everywhere, hidden in places where we don’t even expect to see it. For example, take a look at the following image:

What do you see?

Most people say “music.” People who have studied the piano might recognize this as a piano score. And a true enthusiast might recognize it as the third movement of Beethoven’s Moonlight Sonata.

What you’ve probably never thought of before, though, is that a musical score is actually a form of graph. It tells the performer what combination of notes to play at a given moment in time. In other words, it shows sound as a function of time.

In the image below, I’ve added labeled axes to draw attention to this:

Now consider a photograph. Below is one of the most spectacular images I found when Googling “photograph.” (Thanks to whoever posted it!) I love how it shows the strings of mucus frozen in time.

Anyway, a photograph itself is also just a type of graph — and not just metaphorically. In fact, even the way images are produced in our brains is just a way of numerically graphing the intensity and frequency of light that falls on different portions of our retinas. In essence, your retina is the x-y plane and the light is the quantity being graphed.

Below is what the photograph looks like when graphed in three dimensions from different angles, with the colors changed to a different color scale:

Now here is the same graph when viewed from directly above, so that the tiger is easier to make out:

Here’s another example of a great photo:

And here it is with the same procedure applied to it. This one works a little better than the tiger because it isn’t filled with little white spots that end up looking like noisy spikes in the graph.

Below is the graph when viewed from directly above, just as I did for the tiger. Pretty cool, huh?

Now consider something that really seems to have nothing to do with math: a piece of literature. Below is the first paragraph from A Tale of Two Cities, by Charles Dickens.

It, too, can be considered as a type of graph. It’s a graph that tells the reader what words to speak or think as a function of time:There are, of course, many other examples of graphs:

What I’m saying is that anything can be thought of as a kind of graph. Really, though, it’s not just graphs that are so powerful, but numbers themselves. This is because numbers encode information. For example, an entire song can be encoded in a single number. So can a photograph, or even a movie.

What’s particularly fascinating is that physicists now believe that physical reality itself is composed of information. In fact, the universe might even be digital. And since numbers encode information, it is possible that the entire universe could be represented by a single number.

Take a minute to meditate on that.

If that’s true, then there’s only one thing we can conclude…

* * * * *

This post is based on a PowerPoint presentation I made for my math students in an attempt to inspire them. Here it is in PDF form:

Math Is Everything (PDF version)

An Apology for Imaginary Numbers

WHY, IN THE NAME OF EUCLID’S BRIDGE OF ASSES, DO WE HAVE TO STUDY NUMBERS THAT AREN’T EVEN REAL?

For as long as imaginary numbers have been taught in schools, frustrated math students around the world have asked the above question in some form or another. The creation (or was it a discovery?) of these imaginary mathematical constructs — a set of so-called “numbers” that could not possibly have any useful applications in the real, physical world — is surely an offense grave enough to warrant a life sentence at the very least. I mean, we’re talking torture here. Right?

Well, as a math teacher, I am here to offer an apology for imaginary numbers on behalf of the entire mathematics community. But wait. I mean the word “apology” in the Classical sense, as Plato used it. It means “defense.”

Against whom (or what) do imaginary numbers need defending? Well . . . against you, if you are one of the many people who assume that because they are called “imaginary,” they are not real. Actually, it’s not you personally at which I’m taking aim, but rather this misguided and pernicious belief that appears to be holding your mind captive.

Allow me to set you free.

The words “imaginary number” constitute one of the greatest misnomers in all of history. The truth is that imaginary numbers are every bit as real as what we call the “real numbers” (which are also poorly named). This whole thing is really just a big misunderstanding, and we should all be blaming the idiot who named them “imaginary numbers.”*

First, imaginary numbers are, to use a technical term, freakin’ useful. Among other things, they crop up all the time in describing waves. Electrical engineers use them particularly frequently when working with oscillating currents and voltages.

Second, imaginary numbers are downright unavoidable in Quantum Mechanics, which is the fundamental theoretical framework underlying the fabric of our universe’s very existence (along with General Relativity and possibly some additional physical theories that will have to be developed to explain dark matter and dark energy, and perhaps a depressingly, even infinitely, large number of further theories to describe phenomena that we haven’t discovered yet — but never mind that).

Where was I? Oh, yes . . . The fact that imaginary numbers are unavoidable in Quantum Mechanics seems to imply that they are more than just useful concepts, but are actually an indispensable component of physical reality itself — in which case there’s no denying that they are real in every sense of the word.

This is borne out by the simple fact that i appears in Schrodinger’s equation, which is the centerpiece of Quantum Mechanics:

Obviously, the content of the above equation is so trivial that no explanation is needed.** So I will only point out that there is an i — that’s right, the ol’ square root of negative one — contained in it. And there’s no way to get rid of the i (short of renaming it, but that doesn’t count). I challenge anyone to reformulate Quantum Mechanics in a way that doesn’t necessitate the use of imaginary numbers. If you can do it, I’ll give you twenty bucks — which will be nothing compared to the Nobel Prize you’ll also receive. But you might as well try to cut down a tree with a herring, because it can’t be done.

Now let us seek further enlightenment by meditating on how certain other sets of numbers — with which you may be more familiar — were assimilated into our present system of mathematics, and how those sets of numbers came to be accepted as “real.”

First, note that numbers in general are not “real” things (or at least, the extent to which they are real is a matter of definitions and philosophical considerations). The “real numbers” themselves, and even the more fundamental set of “counting numbers” (positive integers) are just conceptual constructs that are useful for making both descriptive and predictive calculations about the world.

The utility of the counting numbers is obvious, because you can have 5 apples, for example. Rational numbers (fractions), too, are clearly applicable since you can divide an apple into, say, four quarters. And so it’s easy to see why these numbers are considered “real.”

Along these lines, the utility of imaginary numbers is not obvious. After all, you can’t have i apples (or can you?). But then, you can’t have negative two apples, either; and yet negative numbers are accepted as “real.” Let’s proceed by analogy.

A good analogue for imaginary numbers is the set of irrational numbers (yet another poorly named set). These are numbers that can’t be written as fractions of integers. The square root of two is a good example. Let’s take a moment to see why the square root of two can be argued to exist (i.e., be “real”).

Suppose you need to make a square with a certain area. Could you make a square with an area of 4? Yes. Just give each side a length of 2. How about an area of 1? Yes, with a side length of 1. It seems intuitively obvious that you should be able to make a square with any area between 1 and 4. Just choose an appropriate side length between 1 and 2.

Well, what if you want to make a square with an area of 2? You need a side length that, when squared, gives you 2. Unfortunately, such a number can’t be found among the “rational numbers.” It must exist, though — otherwise there could be no such thing as a square with an area of 2.

And so the set of irrational numbers is born.

Back when this was first done, people complained that such numbers didn’t make sense — which is why they were called “irrational” — and irrational numbers were initially treated with the same contempt that today’s math students direct at imaginary numbers. But the fact is, irrational numbers are just plain useful. And because of this usefulness, the set of irrational numbers joined the other sets in our system of numbers.***

Imaginary numbers come about when you go one step further and define numbers whose squares are negative. Just like irrational numbers, they are simply another set of numbers that have been added to the existing collection of sets. And just like irrational numbers, the reason they were added is that they have been proved to be useful in describing the physical world around us.

In other words, imaginary numbers are real.

END OF APOLOGY

Notes:

*No, I’m not seriously calling him an idiot. And in fact, it’s not clear that he was the first person to call them imaginary. He did perpetuate the name, though.

**If you must know, the equation says that the rate at which a system changes over time is proportional to the energy of the system. Sort of. If you want a better explanation than that, I can only tell you that even Richard Feynman, a guy who won a Nobel Prize for his work in Quantum Mechanics, said that he didn’t understand Quantum Mechanics.

***Incidentally, it’s interesting to note that in a sense, irrationals are less “real” than imaginary numbers because in real life, due to the uncertainty principle, physical quantities generally don’t have perfectly precise values, so most of those digits way out toward infinity are meaningless anyway. And while we’re on the topic of irrational numbers, I’d like to share that one of the most interesting facts that I’ve learned is that the vast majority of real numbers are not just irrational but uncomputable, which is a word with special mathematical meaning (see The Information by James Gleick).

BWYA Graduation Speech – May 2009

In the spring of 2009, I had the honor of being asked to give the graduation speech at the Beijing World Youth Academy, where I taught physics from 2007 to 2009. It is (or was at the time) their tradition to ask one of the departing teachers to be the main speaker at the ceremony. They probably asked other people first, but no one else was willing, as we were all busy with our end-of-the-year insanity. And so they turned to me.

With my characteristic modesty, I declare that I did a pretty good job coming up with a simple and inspiring message. Here it is:

BWYA Graduation Speech 2009 – Olen Rambow

Preparing Students for Real Life

The Houston Chronicle published an article about a new plan to train students, especially in low-income areas, for specific careers. The skills listed in the article are “process technology” (in “chemical, refining, and manufacturing careers”), “electronic engineering,” “network and computer administration,” “logistics and global supply,” and “pharmacy technology.”

Now this is what I’m talking about. If executed well, programs like this could have a significant positive impact on our education system and society in general. This is right in line with some of my proposals in my education essay, namely:

1. Make the curriculum more practical.
2. Encourage early specialization.
3. Reduce the emphasis on “preparation for college.”
4. Develop trade schools.

The most important thing here is that we give kids something constructive to do. If we give them practical skills and enable them to start working, kids who otherwise might have felt worthless and directionless and turned to gangs and drugs would instead feel like contributing members of society who have some say. That’s the kind of change that will make America a better place to live in.

I hope this program receives the support it needs in order to have a chance at success.

Here’s a link to the article in the Chronicle:

HISD looking to help graduates land jobs