Why Do I Need to Know Probability and Statistics?

One of the most revealing results from psychology is that we are intuitively horrible statisticians.  In this article, let's explore how poorly we calculate likelihoods of events and why we could derive some benefit from knowing how probability works.

1) You go to see a doctor and she runs a test to see if you have cancer.  If you have cancer, there is a 95% chance that your result will be positive.  If you don't, there is only a 2% chance that your result will be positive.  You are shocked to learn that the result was positive.  How worried should you be?

If you're like most people, you would be terrified because you'd think that the odds of you having cancer is about 95%.  This is a classic example of ignoring the base rate which in this case is the percentage of people in the U.S. who get cancer each year.  It turns out that percentage is roughly 0.5%.  Given this information, you can calculate how likely it is for you to get a positive test result whether you do or don't have cancer.  Despite getting the positive result, you have a probability less than 19.3% of actually having cancer (after applying Bayes' Theorem from elementary probability theory).

2) Here's a simpler one that is deceptively tricky.  There's a couple who has two children and you are told that one of them is a girl.  What are the odds that the couple has two daughters?  Again, most people think 50% since the other child has a 50/50 chance of being male or female.

Let's go through this problem step by step.  Note that there are four possibilities:

OLDER CHILD   YOUNGER CHILD

Girl                        Girl

Girl                        Boy

Boy                        Girl

Boy                        Boy

You know that they have at least one girl so you must get rid of the last possibility; all the others are fair game and they all have equal likelihoods.  Thus, the probability of having two daughters is actually only one-third, not one-half.

3) Ashley majored in English literature at a small liberal arts school where she was active in theater, music, and political activism concerning women's and minorities' rights in America.  It has been over a year since she graduated from college.  Given five possible post-graduation outcomes, place a probability next to each possibility:

A) She is pursuing her dream to become an actress.

B) She is working as a banker.

C) She is working as a banker and auditioning for acting roles at night.

D) She is attending law school.

E) She is unemployed.

Given what you know about Ashley, take the time to actually place a probability for each outcome.  

Okay, done?  Great!  First, make sure that your numbers don't add up to over 100% since that wouldn't make any sense.  Second, what probability did you assign to B?  How does that compare to the probability you assigned to C?  Many people would assign C with a higher probability than to B since Ashley seems like she's very artistically inclined.  However, this is actually impossible.  The probability of her working as a banker AND auditioning for acting roles must be lower than the probability of her working as a banker.  One way to think about it is that the probability of her working as a banker is equal to the probability of her working as a banker and auditioning for roles PLUS the probability of her working as a banker and NOT auditioning for roles.  Thus, the probability of C cannot be greater than the probability of B.

These types of puzzles unveil some of the imperfections of our "rational" minds.  If you are interested in exploring the faulty statistics that go on in our heads, I highly recommend Daniel Kahneman's Thinking: Fast and Slow and Leonard Mladinow's The Drunkard's Walk: How Randomness Rules Our Lives.  I may also post more about these issues in the future.

10 Tips for a Healthier and Fitter Body

After a year and a half of getting out of shape since college graduation, I’ve decided to try to improve my physique and overall health.  During my fitness research, I have encountered several tips that immediately gave me some good results.  I thought that I would share them with you in case you are interested in improving your diet and lifestyle.

1. Avoid fruit juices.  They have a high sugar to fiber ratio that’ll stress out your pancreas from the spike in blood sugar levels.  Also, this will lead to unnecessary levels of fat storage.  Eat fruit instead!

2. Drink less alcohol.  You are probably already aware of this fact but it is true.  Alcoholic beverages are not only calorically dense (hence the beer belly) but are completely void of nutritional value.  If you must, go with light beer or red wine.

3. Consume complex carbohydrates and avoid simple ones.  White bread and white rice are broken down in your body very quickly and lack all the nutrients whole wheat bread and brown rice have.

4. Eat breakfast.  In fact, get into the habit of eating something within the first hour of getting out of bed.  It will kick-start your day’s metabolism and provide you with the energy to engage in your daily activities.  According to Men’s Health magazine, most overweight people skip breakfast.

5. Drink lots of water.   Two-thirds of your body is made up of water so you need a good amount to make sure your body is functioning properly.  A good benefit of being well hydrated is that your appetite will be stable, preventing you from eating unnecessarily.

6. Eat more meals throughout the day.  This one may be counterintuitive so let me explain.  If you only eat one or two meals a day, your metabolism will slow down because you’re body will want to store energy (thus fat) to last you through those long intervals without any food.  If you eat five or six meals a day (eating every 3 hours or so), then your metabolism will keep going throughout the day, burning more calories.  This is a good way to increase your protein intake if you want to add more muscle.

7. Make sure to eat healthy fats.  Your body needs fat to function properly but it is important to keep track of the fat sources.  A general rule of thumb: get your fats from plants (e.g. canola, olives, beans) and fish.  Avoid the fats from dairy and red meat.

8. Stay away from soda.  The diet alternatives are still bad because of the high sugar content.  Sodas have high levels of phosphorous which results in calcium loss, increasing the risk of osteoporosis (i.e. bone density loss).

9. Stop drinking coffee.  Your body should not need caffeine to get you energized in the morning or at any point during the day.  If you feel tired, then that’s your body’s way of telling you to rest.  Dumping coffee into your system is not a healthy way to solve the problem.  If you are addicted, you may experience withdrawal; try to slowly wean yourself off of it.

10. Eat plenty of plants (fruit and vegetables).  If you look at our dental structure, it is more herbivorous than carnivorous; most of our teeth are for cutting and grinding plants.  Evolutionarily speaking, our bodies are adapted to sub-Saharan African jungles and the available food sources there.  A major problem with our diet these days is that we now eat foods that did not exist or were rare in our prehistoric environment.  This is why obesity and diabetes have become so rampant.  Sugar was scarce but provided a lot of energy; thus we developed sweetness to detect sugar, which then inclined us to consume more of it.  Now, sugar is ubiquitous and many devour it carelessly to their demise.

So there you have it.  I have tried to avoid mentioning the obviously unhealthy habits (e.g. smoking tobacco, snorting cocaine, eating fried food, shooting up heroin); if you do any of this already on a regular basis, I highly encourage you to stop.

Do Wealth and Power Corrupt Everyone?

According to my dad, there's no such thing as a good rich person.  Now, I understand that was probably a hyperbole.  However, there might be a certain amount of truth in that statement but I also contend that people in the upper echelons of the socio-economic hierarchy are not inherently more evil than others.  Rather, it is more likely that wealth and power corrupt whoever possesses them.

This came to my attention even more lucidly while reading Howard Zinn's A People's History of the United States.  The first chapter begins with Columbus' arrival to the West Indies and his successful genocide of ALL the Arawak natives on the island.  This chapter is followed by the horrible conditions that African slaves had to endure as well as those of the white indentured servants.

Were the Spanish, the Dutch, the French, the Portuguese, and the English worse people than those from other countries?  I doubt it.  A much more plausible explanation is that they encountered civilizations that had many desirable resources and the former had the ability to take what they wanted by will.  (If you're interested in the exact details of how and why the Europeans dominated the globe, read Guns, Germs, and Steel by Jared Diamond.)  If the Chinese were the first ones to actively explore the New World, then perhaps they would be the ones who would have conquered the Americas and wiped out virtually all of the Native Americans off the two continents.

One of the more interesting ideas from the book had to do with class struggle during America's colonial period under the British.  The basic idea is that well-educated middle and upper-middle class Americans like Sam Adams, James Otis, Jr. (the man who famously coined the phrase "Taxation Without Representation is Tyranny"), and many other famous Bostonians (credited for planting the seeds of the American Revolution) would rally support against the powerful British and Tories in Boston by summoning the American lower class, riding on their angst, grievances, and frustrations caused by the unfair taxes and laws imposed by the British Parliament.  Of course, the leaders of the American Revolution succeeded but the poor remained poor, the slaves remained enslaved, and the oppressed remain oppressed.  Note that the American government continued its territorial expansion by killing off more Indians and witheld women's suffrage, just as the Europeans did.

This social phenomenon of the bourgeoisie using the proletariat by promising the latter a better life under new social rule (followed by the former never following through on their promises after they acquire their power) is usually mentioned in world history classes when discussing the French, Bolshevik, and Cultural Revolutions.  But one should not underestimate the ubiquity of this important pattern for America is not immune.

How might this be relevant to you?  If you're one of my friends reading this, you're probably a Democrat and will vote for Obama this coming election.  You're well-educated and you think that big businesses are the bane of our society and their CEO's are nothing but greedy fat-cats who don't care about Americans.

BUT, would you still be voting for Obama if you were among the super-wealthy in America?  Probably (and statistically), you wouldn't.  It's more likely that you'd vote for Romney who promises not to increase your income tax.  If that's the case, then who are you to morally condemn the millionnaires and billionaires who are simply voting in their interests?  After all, that's what you'd do.

By the way, I am NOT saying that any of the atrocities committed by the rich and powerful are justified.  Wrong is wrong.  Rather, this is merely a reflection on human nature and that maybe we should think twelve times before we judge those who abuse their social advantages.  In a way, they're victims too.

People Are From Africa

I'm surprised by how many very intelligent people don't know that humans are originally from Sub-Saharan Africa.  It's true!  Most of human evolution took place there, even before Australopithecus.  In fact, the two Great Apes that are our closest evolutionary cousins (chimpanzees and gorillas) are still mostly in Africa.

Also, most fossil evidence of early Homo genus members are concentrated in the eastern parts of Africa.  I say "most" because many of them wandered out to parts of Eurasia (i.e. Neanderthals in Europe, Denisovans in Siberia, and Homo erectus in China and India).  There are some competing theories about the precise details of the most recent parts of human evolution, but there is an overwhelming scientific consensus that at least the main bulk of human genetic material came from Africa.  There is some evidence that other human-like species evolved in Eurasia and then interbred with the African Homo sapiens.  Comparing Neanderthal DNA to humans' shows that an estimated 1 to 4 percent of French and Chinese have Neanderthal ancestry.

Just to clear up any confusion: Neanderthals looked almost exactly like modern humans.  In fact, they were probably more intelligent since their craniums were larger than ours, implying that their brains were bigger too.  They were also much stronger than us, especially in terms of upper body strength.  It is unclear why Neanderthals became extinct.  One hypothesis is that humans were more aggressive and vastly outnumbered them.  When the two came into contact, humans would usually kill them or sometimes absorb them into the human gene pool.

One question: why aren't we all black?  Once people started moving out of Africa, they needed to absorb more sunlight since the sun's rays are less intense further from the Equator.  If you had too much pigment in your skin (from melanin), you wouldn't absorb enough sunlight to produce vitamin D in your body.  If this happens at an early age, you develop rickets where your legs become cross-legged.  Thus, natural selection produced people who eventually had fairer skin.

Why does any of this matter?  For starters, it's fascinating!  We now have a better understanding of where we came from and how we developed as a species.  In evolutionary psychology, it is helpful to have a better understanding of prehistoric human conditions and behavior to know how they might have influenced ours.

Secondly, I think this is an important tool in eliminating racism and perhaps nationalism.  The fact that we are all of African descent should liberate us from thinking that one ethnic group is better than another.  At least, that is the hope.

Importance of Core and Lower Body Strength

Walk into a gym and observe the difference between the average man's workout routine from the average woman's.  It seems as though all the benches are always used up by men doing all sorts of bench presses and flyes.  If they are at the squat rack, they are often doing barbell curls to pump up their guns.  Men are the ones doing all the tricep extensions on the cables.  The only core exercises men seem to care even remotely about are all sorts of crunches, sit-ups, and leg raises (if that).  Then you observe the women and you notice that they are far more concerned with cardio and leg strengthening movements (especially the adductor/abductor and leg curling machines).

Men can learn a thing or two from the women at the gym.  Men are so obsessed with how their upper bodies will look at the beach, that they often neglect their lower bodies.  Ironically, their upper bodies would be even more impressive if they incorporated exercises like squats and deadlifts to their regimens.  This is because heavy exercises involving compound movements using the legs and the core produce an anabolic effect that stimulates the whole body to grow.

Let me be honest; my legs are not that impressive.  My upper body strength is decent for my weight, but my core and lower body strength could use improvement.  In fact, the imbalance is so big that my bench has always been higher than my squat.  That is not normal and would explain why I had so much difficulty shooting in effectively in wrestling for single and double leg takedowns (the bread and butter of wrestling).

I looked around for different strength training methods and encountered one that my friend Ryaan started using, Starting Strength (created by Mark Rippetoe).  This remarkably simple program has increased my deadlift AND MY BENCH in a WEEK!!!  It has a strong emphasis on squatting three times a week for three sets of five repetitions each time.  I highly recommend beginners, novices, and intermediate lifters to consider Starting Strength.  (If you're advanced, then you're probably already familiar with this.)  There is a nice wiki for his methods: http://startingstrength.wikia.com/wiki/Starting_Strength_Wiki

WARNING: The only drawback is that the program requires you to do power cleans which most gyms don't allow.  If that is the case, you can substitute rows or hang cleans.

Korean Culture: The Good and the Bad

NOTE: I would like to emphasize that by "Korean culture", I am focusing on South Korean culture.  I am aware that North Korean culture is distinctly different but some of those differences are hard to pin down since there is relatively little information available.

After my freshman year of college, like the good second-generation Korean-American that I am, I made my hajj to the motherland via Harvard Summer School's study abroad program.  The coursework was rather minimal so I had plenty of time to explore various parts of South Korea and meet relatives who I hardly knew.  I was excited to embark on this six-week journey from which my recent ancestry came.  (Of course, most of my human ancestry is from sub-Saharan Africa.)

As much as I enjoyed my visit, there were certain aspects of the culture that caught me off guard.  Upon much reflection, I have concluded that most of their social norms were positive but there were some that I thought were downright immoral.

The Bad:

1. Homophobia- This is one problem that no one can deny.  Yes, homophobia permeates cultures around the globe, but South Korea's is embarrassingly high for a developed country.  There isn't even much formal political discussion dealing with LGBT issues.  Ironically, straight men can hold hands as they walk in public, the traditional clothing could easily fit in a gay pride parade, and a lot of male K-pop stars look quite effeminate and androgynous:

2. Racism- Again, the painful truth comes out.  Many Koreans don't like the Japanese, Chinese, and immigrants from other countries.  They don't even like half-Koreans very much.  What puzzles me even more is why they are racist against blacks.  Here is an interesting video of Hines Ward (half black, half Korean) speaking about this issue: 

However, I think their racism is not much more severe than most other countries'.  Racial tolerance is a relatively new human phenomenon.  I agree with my dad who thinks that the United States has made much more progress in settling racial issues than other countries have because of America's unique history.  I could continue ranting about racism but I'll save it for another post.

3. Sexism- Despite its hyper-patriarchal culture, South Korea has made more progress on this issue than on the two issues mentioned above.  The main reason for this is simple: women are becoming better educated.  More and more women are becoming doctors, lawyers, politicians, and academics.  However, Koreans still have a strong sense of Confucian values and women are expected to be subservient to men.

4. Superstition- This is just more annoying than it is bad.  Koreans have some weird, irrational beliefs about the unluckiness of the number four, fortune-telling, the relationship between blood type and personality, fan death, and many others.


The Good:

1. Family- I was amazed by the strength of family ties in South Korea.  Even relatives who were quite removed from me and had never met me before treated me with unrestrained hospitality.  I was really blown away.  It was from this visit that I began to understand why family values are so important.  Even as I am typing this article, I am thinking about how thankful I am to have such caring relatives abroad.  Wow, I really miss that part of my experience in Korea.

2. Environmentalism- I remember buying a pack of chewing gum and taking out a piece while walking outdoors.  I soon regretted it because I couldn't find a garbage can to throw away my wrapper.  That's when I realized how clean the streets were.  It drove me nuts, but I found a Burger King where I could throw it out.  But then I noticed that people didn't throw away the paper cups in the trash after they finished their drinks.  They put them in a separate area to be reused!  Wow, that's commitment to recycling, my friends.

3. Health- It's just a fact that there are far fewer overweight people in South Korea (including percentage) than there are in North America.  Genetics may be one component but many of them make a conscious effort to stay thin given the stigma attached to being even slightly chubby.  They watch their diets and many of them engage in regular physical activity.

4. Work ethic- The South Korean work ethic is incredible.  Whether they apply it to their jobs or studies, they really push themselves to the limit.  It was one of the Asian Tigers during Asia's economic boom in the mid-late twentieth century and its GDP (at roughly $1.12 trillion) is the fourth highest in Asia (after China, Japan, and India), nearly double Saudi Arabia's.  This is despite the fact South Korea has only 50 million inhabitants (less than a sixth of the US population), spent much of the past century as a developing nation, and was deprived of the little natural resources it had to the Japanese during the latter's colonial occupation.  Their hard work has resulted in certain economic inefficiencies (e.g. education inflation), but overall they are doing quite well.

This was just a short list of the main points I wanted to mention but I might add more on in the future.  Feel free to disagree with me on any of the points but I'm certain that most people who are familiar with the country would agree on all the issues I stated.

Three Subjects Everyone Should Study

School will be back in session in a couple of months so I thought I'd give some early advice on picking classes for the new semester.  This is the same advice I gave to my younger brother who will be a freshman at Harvard this fall and to all of my students.

1. Psychology- This is by far the most important one.  Not only will you have a better understanding of how others think and behave, you will have a deeper understanding of the inner workings of your own mind.  I enjoy almost every subfield of psychology (developmental, abnormal, humanistic, analytical) but the most important ones for the average person to know are social, cognitive, and evolutionary psychology.

2. Economics- You don't have to know it at a highly advanced mathematical level. Knowing the essential concepts will suffice: supply, demand, market equilibrium, taxes, diminishing marginal returns, unemployment, GDP, Keynesianism, et cetera.  Two semesters that cover micro and macro should be more than enough.

3. Statistics- All the sciences use large sums of data that need to be analyzed through statistical methods.  In addition, having a strong grasp of statistics can help you make better decisions in moments of high uncertainty.  It may not come easily to some of you, but it is worth knowing well.

An excellent book that touches upon the importance of each of these subjects is Thinking: Fast and Slow by Daniel Kahneman, the 2002 Nobel laureate in economics for co-founding behavioral economics with Amos Tversky.  Kahneman is a top authority among social scientists, in the same league as John Maynard Keynes, B. F. Skinner, Jean Piaget, Jürgen Habermas, and Noam Chomsky.

(Optional) Computer Science- We live in an era full of computers and their ubiquity will only increase as time goes by.  Unfortunately, most people don't know what computers are or how they work.  They use the Internet, but what is the Internet exactly?  Is it a really just a series of tubes?  Eventually, you will need to know some basics of computer science as they start merging with our bodies and perceptions of reality.  (If you have no idea what I'm talking about, look up The Singularity is Near: When Humans Transcend Biology by Raymond Kurzweil.)