One Second Left

I really enjoyed Edge of Tomorrow (an 8 on my movie list), but one plot detail really bugged me. If you haven’t seen it yet, I’m not going to spoil anything directly.


(Image link—pretty funny.)

It’s part of a larger category that happens in most action movies actually. This particular example doesn’t happen in Edge of Tomorrow: every time there is a countdown timer where something really, really bad will happen (typically an explosion), the protagonist will save the day with one second left til destruction, whether the timer was originally set to five minutes or five hours. In every action movie there are several of these “just in time” moments. And yes, I understand, this is what makes the movies suspenseful.

That really annoys me.

Did the aliens annoy me? Nope. Time travel loops? Nope. But impeccable luck and timing? Yes.

Is there any deeper meaning behind this? People have said that I over-criticize movie meanings, but I think this does have some harmful effects. The “protagonist always gets the girl” cliché is the worst in terms of social damage for obvious reasons, but “one second left” has its own issues. It distorts our views of luck and chance, thereby affecting our risk judgment, and it turns the extremely improbable into the probable.

A bigger issue still is that the “protagonist wins” cliché, which is in 99% of movies, may warp our sense of justice. There is a known cognitive bias called the just-world bias, where we falsely expect justice to be served (we unconsciously believe in karma), and movies can really take advantage of this. How do you explain why the good side was able to defuse the bomb at the last second? Easy, the good side deserved it. (How might this translate into real life? We feel that we deserve something great, so instead of trying for it, we wait for the universe to give it to us.)

Of course, I still enjoy action movies and TV that use “one second left.” But it just gets difficult to keep up suspension of disbelief when the most absurd chance events happen over and over again.

On the Video Games and Violence Discussion

With three recent deadly shootings (one in Isla Vista and the second in Seattle; a third in Las Vegas as I was writing this post), I’ve once again heard many ignorant statements thrown around regarding video games and violence. Much of the ignorance comes from making blanket statements completely lacking in nuance, from both sides.


Here is what’s wrong with the current discussion:

1. The anti-video game side ignores the actual crime statistics.

Whether you look at the past decade or past two decades (when video games arose and flourished), you see that general crime, violent crime, and juvenile crime are all down significantly.


Violent juvenile crime in the United States has been declining as violent video game popularity has increased. The arrest rate for juvenile murders has fallen 71.9% between 1995 and 2008. The arrest rate for all juvenile violent crimes has declined 49.3%. [1]

Of course, this does not mean that (violent) video games are causing the reduction in violence. Here is a graph that goes forward by several more years [2]:


The point is that even if a study comes out demonstrating a link between video games and aggression, it is another step to go from aggression to actual violent crime, which is hard to measure because we can’t just run experiments on violent crime. To show that video games have a strengthening effect on the crime rate, you must show that in the absence of video games, the crime rate would be decreasing faster than it already is (or something equivalent to that).

2. Both sides have a wrong assumption about overall crime.

Because our media gives plentiful attention to violent crimes—the more deaths, the better—we get a sense that the nation is becoming more violent, and we desperately look for any changes that could have caused this increase in violence.

In fact, the violence rate was fairly constant until 1994, when it began dropping steadily [3]:


The public does not see it this way. According to the same Gallup poll [3]:

Despite a sharp decline in the United States’ violent crime rate since the mid-1990s, the majority of Americans continue to believe the nation’s crime problem is getting worse, as they have for most of the past decade. Currently, 68% say there is more crime in the U.S. than there was a year ago, 17% say less, and 8% volunteer that crime is unchanged.

Not as relevantly, but shockingly, even our long-term historical assessment is wrong. A poll was done in the UK on perceptions of violence [4]:

When I surveyed perceptions of violence in an Internet questionnaire, people guessed that 20th-century England was about 14 percent more violent than 14th-century England. In fact it was 95 percent less violent.

This flawed assumption significantly changes the way we approach the video games and violence discussion. Instead of asking, “What is responsible for the recent rise in crime rates?” and noting that video games exist now whereas they didn’t exist before and then drawing the facile conclusion, we should ask, “Do video games hold back an even greater decline in violence?”

3. The pro-video game side ignores the link between video games and aggression.

Just like ignoring crime statistics, one can also ignore psychological effects of violent video games.

In a meta-analysis of the psychological literature, Craig A. Anderson and Brad J. Bushman, violent video games were generally found to be associated with aggression [5].

One concern of violent video games is that violence is often rewarded. A study [6,7] shows a difference in player aggression between a game where violence is rewarded and one where violence is punished.


It would be nice if psychological results were not ignored by the pro-video game side. On the other hand, psychological results are often tenuous and likely to be wrong. So it would also be nice if the anti-video game side took these results with a bit more caution. After all, some studies are skeptical of the video game-aggression link [8,9].

Finally, even if we assume that violent video games definitely lead to increased aggression, this is one step removed from deducing that video games actually lead to violent crimes such as shootings.

4. Mechanisms are argued instead of statistics.

I wrote about this topic before in my blog post “Mechanisms vs Statistics,” which incidentally used video games and violence as the example.

The gist is, if you don’t use statistics or real evidence, then you can argue anything you want. If you are anti-video games, you could argue that gamers imitate the characters they play, hence they become more prone to going on shooting rampages. If you are pro-video games, you could argue that someone who otherwise would have committed a violent crime satisfied their aggression in video games instead of in real life, thus decreasing crime. Without data, it’s hard to say which of these stories is more correct, or correct at all. (And you could come up with dozens of such plausible-sounding stories for either side.)

Even with statistics, we have to make sure to interpret the data carefully. Being relaxed with statistics will lead us to believe the wrong things.





[5] Anderson, C.A. & Bushman, B.J. (2001). Effects of Violent Video Games on Aggressive Behavior, Aggressive Cognition, Aggressive Affect, Physiological Arousal, and Prosocial Behavior: A Meta-Analytic Review of the Scientific Literature Psychological Science September 2001 12: 353-359.

[6] Carnagey, N.L., & Anderson, C.A. (2005). The effects of reward and punishment in violent video games on aggressive affect, cognition, and behavior. Psychological Science, 16(11), 882-889.


[8] Williams, D. & Skoric, M. (2005). Internet fantasy violence: A test of aggression in an online game. Communication Monographs, 72, 217-233.


Confirmation Bias and the Illuminati

Check out this hilarious Buzzfeed article, “28 Shocking Pictures That Prove That The Illuminati Is All Around Us.”


While it may seem comical at best, it is the only time I have seen such a sustained visual depiction of confirmation bias, satirical or not. The popularity of the article demonstrates that everyone can and does understand what confirmation bias is. Unfortunately, people tend to think they are less biased than everyone else (which is itself a bias), so that they simultaneously enjoy this Buzzfeed article and make fun of conspiracy theorists and superstitious worshipers, yet often believe in equally ridiculous things.

Namely, if you change the title to “28 Shocking Pictures That Prove That God Does Good Things All Around Us,” I have a feeling it would be much less satirical, and if it was, people would call to burn the writer at the stake. Of course, the punchline of the Illuminati images is that the criterion for being the Illuminati, i.e., being a triangle, is so vague that it can literally appear anywhere. Sound familiar?

(To be fair, at least there is definitive evidence that the Illuminati existed.)

Statistics in the Social Sciences

I’ve always wondered whether the rigorous application of statistics is underutilized in the social sciences. This is less so a problem in economics, where the subject is, by nature, highly quantitative. But in fields like psychology, sociology, and political science, where a background in mathematics is not common (unlike for biology, chemistry, and physics), researchers can intentionally or, very often, unintentionally (this is a really good Economist article) produce wrong results by abuse or misunderstanding of statistical inference.


As an onlooker whose training is in mathematics, I cannot help but to feel frustrated by the lack of numeracy in our “scientists.” The Economist article does a good job at showing how failure to understand statistical concepts leads to false results being published, even past peer review.

What triggered me to write this post was an assigned reading for a comparative politics class. In it, Adam Przeworski discusses the inherent selection bias in matching countries for experimentation. Noting that democracies have higher economic growth rates than authoritarian regimes, Przeworksi brings in the relevant data that democracies have a significant chance to die off when faced with economic failure whereas authoritarian regimes are not as affected. Hence, observing that democracies have higher growth rates does not signify that democracy leads to economic growth, but rather that economically failing democracies are not observed because they tend to disappear.

“What we are observing here is what the statistical literature calls ‘selection bias.’ Indeed, I am persuaded that all the comparative work we have been doing may suffer potentially from selection bias.”  (p. 19, stable JSTOR link)

In context of a comparative politics theory symposium, this makes a lot of sense to state. But the phrasing is really interesting to a math person: selection bias is a given, and is one of the tools we use to analyze anything. My instinctual reaction to the reading was “Duh, obviously there is selection bias.” While I am sure the field of comparative politics is more aware of selection bias than Przeworski makes it appear to be, the fact that Przeworski framed it as such (“what the statistical literature calls ‘selection bias'”), as if to imply that the formal tools of statistical inference are generally beyond the scope of comparative politics theory, is a bit unnerving.

Przeworski, Adam in The Role of Theory in Comparative Politics: A Symposium, World Politics, Vol. 48, No. 1 (Oct., 1995), pp. 1-49.

Big Picture vs Detail Oriented Thinking


Big picture vs detail oriented thinking is usually portrayed as a dichotomy. It is one or the other, and even when the need for both is acknowledged, the two are still considered separate forces. Here is a section of an article that is one of the first google search results:

Typical of the Big Picture Thinker

  • You can quickly see patterns in complex problems.
  • You like to come up with new ideas and new projects.
  • You have a low tolerance for busywork, tedious errands, and filling out forms.
  • You are great at outlining what needs to be done, but filling in the details can feel exhausting.
  • You may have been described as right-brained.
  • When you have taken the Myers-Briggs assessment, you were an N.

Typical of the Details Thinker

  • You think about things in great detail and sometimes miss the big picture.
  • While you are certainly smart, others may joke that you lack common sense.
  • You would prefer to edit or tweak a plan than to come up with it from scratch.
  • Highlighting study notes doesn’t work for you, because you end up highlighting everything.
  • You may have a tendency to over-think things.
  • You have excellent attention to detail.
  • You may have been described as left-brained.
  • When you have taken the Myers-Briggs assessment, you were an S.

While this may be a good indicator of which type of thinking is more dominant, it doesn’t look at the two in combination. For me, big picture and detail thinking are very intertwined.

I’ve always considered myself a big picture thinker, and I even have the N on the Myers-Briggs test. In addition, I consider some of the worst arguments to be the ones where something is taken out of context. Generally I don’t try to bog myself down with details, but often the two types of thinking aren’t mutually exclusive; sometimes the application of big picture thinking requires an enormous attention to detail. Whether a large-scale plan succeeds often depends on the tiny details.

In chess, the big picture vs the details is analogous to strategy vs tactics. Strategy provides you with overall guidance: should I attack the kingside or the queenside, should I seek to trade a bishop for a knight? Tactics govern how such plans actually take place: if I attack the kingside this way, then my opponent will play this counter, then I will play this move, etc. I try to keep a balance of strategy and tactics, as having one without the other can lead to disaster.

I guess an analogy would be that to get somewhere, you need a map and a car. Having a map without the transportation is useless, and having a car but no idea how to get to your destination is futile. Though if you had to pick only one, I guess having the car is a better idea.

Big Picture Thinking Requires Details, and Vice Versa

The big picture vs detail oriented thinking comes up a lot in political/economic/social debates. Often it’s the knowledge of many related facts that leads to a more accurate big picture understanding. To take a not super-controversial topic, consider the funding and effectiveness of NASA. We know that it has declined significantly since landing on the moon. And we know that landing a human on Mars should be done soon, and we could argue that if only NASA had more funding, we could be much further in space exploration.

Of course, the previous is a pretty naive representation of the NASA situation. During the 1960s, we were at the height of the space race in the Cold War, and NASA was considered not only as an institution for scientific research, but also an institution for national security. Landing on the moon was inspirational not just as a feat of humanity, but also as a feat of us beating them. In addition, as many inventions come from military purpose, there are obvious military implications of having satellites in orbit around the earth, but there are much fewer in having any on Mars. And the economic investment would take much longer to return. You could keep piling on more relevant details to get a better picture.

The point is, to get a good high-level understanding of something requires extensive knowledge of the details surrounding it.

On the other hand, making sense of small details often relies on seeing the big picture. Every bit and fragment of the news makes more sense the more you understand current trends. Events that seem unrelated may very well be correlated, but the correlation may only be visible from bird’s eye view.

For example, LGBT rights and the abortion/women’s rights may seem unrelated, but there is a common denominator: religion. Resistance against LGBT rights and abortion are both connected to religious beliefs in the same way, and even the arguments for resisting either movement come almost solely from religious arguments. This is why on this blog I discuss religion a lot but rarely LGBT rights or abortion—dealing with the root cause is more imperative than dealing with the symptoms.

In all, both big picture and detail oriented thinking are important, and one needs both of them to have a deeper understanding. Without the big picture or the details, one has a limited grasp of the situation.

Spontaneous Decision Making


This post is about my own decision-making habits. In particular, I don’t plan ahead details ahead of time, as I abhor fixed schedules or fixed paths. Perhaps an interesting case is from a 2011 post:

For example, last semester, to get to one of my classes from my dorm I had two main paths, one going over the Thurston Bridge and the other over a smaller bridge that went by a waterfall. For the first couple weeks I took the Thurston Bridge path exclusively, as I thought it was shorter than the waterfall path. But then one day I went the other path and timed it, with about the same time, maybe a minute slower (out of a total of 15 minutes). So I started taking the waterfall path exclusively. But eventually that got boring too, so I started alternating every time. You might think that’s how it ended.

But a consistent change like that is still… consistent. Still the same. It was still repetitive, and still very predictable. Perhaps the mathematical side of me started running pattern-search algorithms or something. Eventually, I ended up on a random schedule, not repeating the same pattern in any given span of 3 or 4 days.

This example involved physical paths, but it is true for figurative paths as well. I can’t stand any repetitive task for a long time, including for things that I might like.

Another set of examples comes from video games. I tend to play extremely flexible classes/builds that have multiple purposes, and I try to have multiple characters or styles to be able to adapt quickly and to know what other people are thinking:

  • World of Warcraft: 8 (out of 11) classes at level 85+; raided as tank, dps, and heal.
  • Diablo 3: all 5 classes at level 60.
  • Path of Exile: all 6 classes at level 60+.
  • DotA: every hero played (up to a certain version).
  • Starcraft 2: all 3 races to level 30.

In WoW, the game I have definitely spent the most time on, my two main characters when I raided were a Priest (disc/shadow) and Paladin (prot/holy), having all 3 roles covered. Even within one specialization, I switched out strategies all the time: one day I would stack haste, the next day I would stack crit, and so on. Even so, I was usually very indecisive about what to do until the last moment.

My blogging follows a similar pattern. I find it hard to focus on one topic to write about in consecutive posts, and I generally cover whatever topic comes to mind. Yes, I set a schedule of one post per week. However, I usually don’t come up with a topic until the last day. The topic for this post did not arise until yesterday, from the suggestion of a friend (whom we were visiting also as a result of a spontaneous decision).

Being too spontaneous, however, also didn’t work well. In 2011 I decided to blog spontaneously (see the first link). Largely due to indecision, I ended up writing only 33 posts the entire year, 20 of which were written in the first two months. By contrast, in the December of 2010, I wrote 38 posts. The current system of sticking with a posting schedule but not a topic schedule is working much better, as every once in a while it forces me to make a decision and choose some topic to write about. This removes indecision from the equation.

(Edit: Due to an inordinate amount of spam on this page, the the comments are disabled.)


This is a review of Susan Cain’s Quiet: The Power of Introverts in a World That Can’t Stop Talking (2012).


Being an introvert in almost every way, I wasn’t expecting to learn too much about my own behavior from the book. Indeed, the personality descriptions and key features of introversion are mentioned in the book. There was, however, still much to learn about introversion vs extroversion from a societal perspective.

What got me interested in the book was a line from Amazon’s interview:

Q: Why did you write the book?
A: For the same reason that Betty Friedan published The Feminine Mystique in 1963. Introverts are to extroverts what women were to men at that time–second-class citizens with gigantic amounts of untapped talent. Our schools, workplaces, and religious institutions are designed for extroverts, and many introverts believe that there is something wrong with them and that they should try to “pass” as extroverts. The bias against introversion leads to a colossal waste of talent, energy, and, ultimately, happiness.

I had never thought about this before. After all, introversion is almost a societal taboo: from the first day of school to the last day of one’s job, there are boundless social encouragements to be an extrovert—or at least to pretend to be an extrovert. I’ll go through some of the book’s main results.

The Team Environment

One of the most interesting points of the book is that extroverts are overrated in teamwork skills. Cain relates a game called the Subarctic Survival Situation, given to incoming students at the Harvard Business School. Individuals within a team are supposed to rank the items in a list of tools based on which would be the most important for survival in a freezing condition. Then the team can collaborate and come up with a team ranking. If the team ranking is better than every individual’s ranking, the team is said to have synergy and be successful. Otherwise, if one person on the team had a better individual ranking than the team ranking, it means the team did not cooperate well enough.

In this game, those who were the most assertive (i.e. the extroverts) dominated the discussions. As a result, sometimes when one person who may have had tons of wilderness experience speaks too softly, they are ignored and the team fails. An interview with a participant in the game:

“Our action plan hinged on what the most vocal people suggested,” recalls the classmate. “When the less vocal people put out ideals, those ideas were discarded. The ideas that were rejected would have kept us alive and out of trouble, but they were dismissed because of the conviction with which the more vocal people suggested their ideas. Afterwards they played us back the videotape, and it was so embarrassing.” (50)

Here are more unsurprising results:

If we assume that quiet and loud people have roughly the same number of good (and bad) ideas, then we should worry if the louder and more forceful people always carry the day. This would mean that an awful lot of bad ideas prevail while good ones get squashed. Yet studies in group dynamics suggest that this is exactly what happens. We perceive talkers as smarter than quiet types—even though grade-point averages and SAT and intelligence test scores reveal this perception to be inaccurate. In one experiment in which two strangers met over the phone, those who spoke more were considered more intelligent, better looking, and more likable. (51)

And yet more:

All of this would be fine if more talking were correlated with greater insight, but research suggests that there’s no such link. In one study, groups of college students were asked to solve math problems together and then to rate one another’s intelligence and judgment. The students who spoke first and most often were consistently given the highest ratings, even though their suggestions (and math SAT scores) were no better than those of the less talkative students. These same students were given similarly high ratings for their creativity and analytical powers during a separate exercise to develop a business strategy for a start-up company.  (51)

In addition, Cain cites studies which show that extroverts and introverts both make good leaders, but of different people. Extroverts were more effective when leading passive types, that is, those who did their job without exercising initiative. However, introverts were more effective when leading those who did actively try to improve work performance. This makes sense. Those who are more passive may need extra guidance, while those who take initiative don’t need to be bogged down by micromanagement.

The style of “groupthink” took its own chapter: “When Collaboration Kills Creativity.” Study after study show that ideas might be better if extroverts weren’t so overvalued.

Physiological Differences

Cain cites the work of Jerome Kagan, a developmental psychologist, who was able to successfully predict whether babies would turn into extroverts or introverts based on reactiveness.  Counterintuitively, it was the high-reactive who became introverts. It makes sense though, as the high-reactive are more moved by external stimuli, while the low-reactive are unfazed. Hence the low-reactives are the extroverts: they handle unfamiliar social situations with calm, while the high-reactives tend to stay away from such situations.

Some of the evolutionary principles behind the different behaviors are also explored.

In fact, public speaking anxiety may be primal and quintessentially human, not limited to those of us born with a high-reactive nervous system. One theory, based on the writings of the sociobiologist E.O. Wilson, holds that when our ancestors lived on the savannah, being watched intently meant only one thing: a wild animal was stalking us. And when we think we’re about to be eaten, do we stand tall and hold forth confidently? No. We run. In other words, hundreds of thousands of years of evolution urge us to get the hell off the stage, where we can mistake the gaze of the spectators for the glint in a predator’s eye. (107)

The difference can be detected even in something as innocuous as noise sensitivity:

In another famous study, introverts and extroverts were asked to play a challenging word game in which they had to learn, through trial and error, the governing principle of the game.  While playing, they wore headphones that emitted random bursts of noise.  They were asked to adjust the volume of their headsets up or down to the level that was “just right.”  On average, the extroverts chose a noise level of 72 decibels, while the introverts selected only 55 decibels.  When working at the volume that they had selected—loud for the extroverts, quiet for the introverts—the two types were about equally aroused (as measured by their heart rates and other indicators).  They also played equally well.

When the introverts were asked to work at the noise level preferred by the extroverts, and vice versa, everything changed.  Not only were the introverts over-aroused by the loud noise, but they also underperformed—taking an average of 9.1 trials rather than 5.8 to learn the game.  The opposite was true for the extroverts—they were under-aroused (and possibly bored) by the quieter conditions, and took an average of 7.3 trials, compared with the 5.4 they’d averaged under noisier conditions. (124)


How do introverts and extroverts compare on academic tasks?

Introverts’ disinclination to charge ahead is not only a hedge against risk; it also pays off on intellectual tasks. Here are some of the things we know about the relative performance of introverts and extroverts at complex problem-solving. Extroverts get better grades than introverts during elementary school, but introverts outperform extroverts in high school and college. At the university level, introversion predicts academic performance better than cognitive ability. One study tested 141 college students’ knowledge of twenty different subjects, from art to astronomy to statistics, and found that introverts knew more than the extroverts about every single one of them. Introverts receive disproportionate numbers of graduate degrees, National Merit Scholarship finalist positions, and Phi Beta Kappa keys. (167)

The following contains what I found to be perhaps the most significant result:

Introverts are not smarter than extroverts. According to IQ scores, the two types are equally intelligent. And on many kinds of tasks, particularly those performed under time or social pressure or involving multitasking, extroverts do better. Extroverts are better than introverts at handling information overload. Introverts’ reflectiveness uses up a lot of cognitive capacity, according to Joseph Newman. On any given task, he says, “if we have 100 percent cognitive capacity, an introvert may have only 75 percent on task and 25 percent off task, whereas an extrovert may have 90 percent on task.” This is because most tasks are goal-directed. Extroverts appear to allocate most of their cognitive capacity to the goal at hand, while introverts use up capacity by monitoring how the task is going.

This speaks very true for me.