The true cost of an education

I come to bury Caesar, not to praise him

Main takeaway: Moloch has killed your curiosity (and hence the cat still lives)

People that are much more intelligent and successful than me have written about the perils of standardized education. Some of them are Paul Graham, Scott Alexander and Bryan Caplan. I would highly recommend that anyone reading this post read these linked articles. There are some of the most eye-opening arguments that I’ve heard on the subject of education.

Some highlights from Paul Graham’s article are given below:

I

Like most other children, I would want constantly want to ask adults questions about the world. However, after trying to humor me for some time, my family would ask me to stop, and my teachers would ask me to “first understand what’s written in the book, and then ask all of these unrelated questions”. I soon learned to shut up and read the textbook.

This approach mostly worked OK for me throughout school. Now I’m a PhD student, and I realize that I have no questions to ask. I train all day to try and become better at answering questions that others ask me. “Can you solve this problem?” I learn theorems and techniques so that I may be able to attack most problems that I see.

I recently came across this blogpost by Zvi Moshwowitz. Zvi is a member of the rationalist community who writes very, very long posts performing detailed statistical analysis of the government’s COVID response. And he posts these extremely detailed statistical analyses every 2-3 days.

My first response on seeing this post was disgust. I was disgusted by the fact that this person, somewhere in the world, spends hours and hours everyday performing statistical analyses, running numbers through some number-crunching software, and then compiling them to post on a blog that he cannot possibly earn much financial or social credit from. Why does he do it? No one asked him to!

When I saw this article a couple of days back, I wanted to write a blogpost right away. And I wanted to call it “The difference between successful people and….me”. This is become it is unfathomable for me that I would put in this much work into anything that wouldn’t go towards my career or oiling my social network. I had absolutely no curiosity about the world around me. There was no question that I’d come up with for a long time, that I wanted to answer. I only aspired to answer questions that other had, so that I could signal some combination of intelligence and hard work, in order to perhaps gain employment, etc.

Over the last couple of days, this made me angry. I have now spent most of my life trying to jump through hoops. I let the people around me kill my curiosity. And as I near the age of 30, my only aspiration is to get better at jumping through these hoops in order to gain employment, or perhaps earn social credit. But what about the education system killed my curiosity? I can only speak about it from an Indian perspective, although these problems seem true for the US (at least as per Paul Graham’s article) as well.

II

An education is mostly supposed to broaden your horizons, and teach you facts about the world that an adult is expected to know. However, in practice, it becomes a system that can be gamed. Although I have learned a lot by going to class in school and college, I ultimately knew that doing well in that course only partially correlated with “loving the subject”. Some combination of intelligence + solving the questions at the back of the chapter + access to notes from class + access to past years’ exams would be required. I don’t really think that any of these factors in themselves are bad. Of course trying to solve problems from the back of the book or from past years’ exams would only strengthen my understanding of the concept. The abuse arose from the fact that it was only through solving the problems at the back of the book or from past years’ exams that one could prepare for the exam or signal an understanding of the subject. Let’s explore this a little bit.

Suppose I’m taking a class in college. I know that if I am able to solve all the questions at the back of the textbook and from past exams, I can realistically be assured of an A/B+. Because humans mostly do the least amount of work required (perhaps because there is an evolutionary advantage to conserving energy that has been hard-coded into our brains), my study strategy would soon evolve into solving just those questions, and not caring as much about being curious about the subject and asking my own questions/reading other unrelated material. Although sometimes there are questions on exams that aim to test whether students have a “deeper” understanding of the material, trial and error soon teaches us what’s the least we have to do to “get by”.

Because curiosity is not really a skill that is required or moulded in school or college, it soon dies out. But what can our education systems really do? Is there really a way to encourage and mould students’ curiosities? Having taught a number of classes myself over the years, I find that this is a difficult problem to solve. I’ve often toyed with the idea of asking students to just “write a detailed summary of the whole course, and any particular problems you like, why you like them, etc”, and then just grade it like a subjective essay rather than an objective assessment. This perhaps sounds silly because science and mathematics are expected to be about “objectivity” and “accuracy”, and do not really lend themselves to long essays filled with “feelings” and such. Although I mostly agree with this, I think that this stance is partly overstated. I would have a much higher opinion of a student’s mathematical understanding if they could write a detailed essay on the development of calculus, why it was shocking for scientists of that time, and what some of their favorite calculus problems are, than one who can differentiate and integrate the problems given on the exam.

Moreover, a lot of hard mathematical problems are just about trying enough things until something clicks. Even if I have to give students numerical problems to solve on an exam, I would perhaps give them most, if not all points if they could write down ten ways that they tried solving the problem but couldn’t. At least in this way, students will be encouraged to try.

III

Education has been a contentious issue for a very long time. Surely a lot of people must have thought of the same points as me. Why haven’t they been implemented yet? Perhaps part of the answer is that it is much easier to test and grade students on numerical problems than on opinion-driven essays. For instance, grading an exam paper consisting only of numerical problems would not take more than 5-7 minutes. However, grading an essay would take perhaps twice as long, because you would often have to address the points made by the student and critically evaluate them. I definitely find this to be true for myself when I grade my students’ exams. There are lots of other ways in which the education of students is harmed by lazy administration, but that perhaps calls for a different post.

I’ve actively tried to be more curious over the last couple of days. This has led me to address fundamental doubts about subjects that I’ve already studied, and has even made research more pleasurable for me. I hope to pass this on to my students who I meet 4 times a week.

Don’t optimize for the world.

Self-propulsion towards the extremes

Consider the following whatsapp forward I received a few years ago:

I’m 25 this year. I’m very pretty, have style and good taste. I wish to marry a guy with 100 crore annual salary or above. You might say that I’m greedy, but an annual salary 2 crore is considered only as middle class now days. My requirement is not high. Is there anyone in this forum who has an income of 100 crore annual salary? Are you all married? I wanted to ask: what should I do to marry rich persons like you? Among those I’ve dated, the richest is 50 crore annual income, and it seems that this is my upper limit.

I’m here humbly to ask a few questions:
1) Where do most rich bachelors hang out? (Please list down the names and addresses of bars, restaurant, gym)
2) Which age group should I target?
3) Why most wives of the riches are only average-looking? I’ve met a few girls who don’t have looks and are not interesting, but they are able to marry rich guys.

4) How do you decide who can be your wife, and who can only be your girlfriend? (my target now is to get married)

Ms. Pooja i Chohan.

A philosophical reply from Mukesh Ambani-

Dear Ms. Pooja,
I have read your post with great interest. Guess there are lots of girls out there who have similar questions like yours. Please allow me to analyse your situation as a professional investor. My annual income is more than 100 crore, which meets your requirement, so I hope everyone believes that I’m not wasting time here. From the standpoint of a business person, it is a bad decision to marry you. The answer is very simple, so let me explain. Put the details aside, what you’re trying to do is an exchange of “beauty” and “money” : Person A provides beauty, and Person B pays for it, fair and square.

However, there’s a deadly problem here, your beauty will fade, but my money will not be gone without any good reason. The fact is, my income might increase from year to year, but you can’t be prettier year after year. Hence from the viewpoint of economics, I am an appreciation asset, and you are a depreciation asset. It’s not just normal depreciation, but exponential depreciation. If that is your only asset, your value will be much worse 10 years later. By the terms we use in Wall Street, every trading has a position, dating with you is also a “trading position”.
If the trade value dropped we will sell it and it is not a good idea to keep it for long term – same goes with the marriage that you wanted. It might be cruel to say this, but in order to make a wiser decision any assets with great depreciation value will be sold or “leased”. Anyone with over 100 crore annual income is not a fool; we would only date you, but will not marry you. I would advice that you forget looking for any clues to marry a rich guy. And by the way, you could make yourself to become a rich person with 100 crore annual income. This has better chance than finding a rich fool.

As Whatsapp forwards go, this is a pretty mediocre “joke”. It obviously is not a true incident, and it is not an original joke either. Similar jokes have been made about other rich men for years now. I’ve known all this for quite a while now. However, for some reason, I’ve carried the joke with me for quite a long time. I’ve always been confounded by why someone would want to make a Whatsapp forward like that in the first place.

Was it Mukesh Ambani himself, who paid someone to create a joke like that? This sounds unlikely. He owns most of Indian media. He doesn’t need to pay people to create flattering Whatsapp forwards for him. Hence, it was probably some clown with a smartphone, who one day decided to plagiarize an already existing joke, hoping that a flattering joke about Mukesh Ambani would catch on and “become viral”.

But what made him think that a flattering joke about Mukesh Ambani would become viral? Was he sure that most, or at least a lot of Indians were fans of Ambani’s? Probably not. Most Indians probably carry a mixed picture of him. “Very successful, probably corrupt – but that’s okay because you have to be slightly corrupt to survive in this country, inherited a lot of his wealth and status, but look how well he’s doing he’s probably smart“, and so on. However, despite this mixed picture, most people lean (at least slightly) towards perceiving Ambani positively rather than negatively. But making this Whatsapp forward go viral would need a very large number of hardcore Ambani fans, forwarding this message to family and friends. How did the person making the Whatsapp forward make the inexplicable jump from “people definitely don’t hate Ambani, and might like him a little bit” to “most people love Ambani, and hence will forward my joke to make it go viral”?

This is because of the following phenomenon: when you and the people around you are slightly sympathetic to a cause, something in your brain clicks, and you assume that everyone loves the cause. Then you make an effort to make statements that project your love for the cause, hoping that you’d fit in with these cause-lovers, and hopefully even be idolized for it.

This is what must have happened with the person who created the crappy Whatsapp forward. He was perhaps subconsciously aware that society was slightly sympathetic towards Ambani. Something in him clicked, and he formed a picture of society in which everyone loved Ambani, and then he created that flattering Whatsapp forward, esconced in the certain belief that it would catch on.

Political polarization

Let us now analyze political polarization in the same light. Imagine that I lean slightly left, and most people in my immediate social group also lean left to varying extents. However, my brain will uniformly characterize my group as far-from-centre left-leaning, and I will incentivize myself to say far-left statements in order to gain their approval. Of course others in my group have the same mental picture that our group is predominantly far-from-centre left-leaning, and my far-left statements will convince them even further of this fact. Soon, they will start agreeing with me and making statements of a similar nature. Our group will progressively become more and more left leaning with time, at least in terms of our opinions (and possibly actions), although individually we might not be as far-left as we pretend to be.

This has happened to me a number of times. Whenever I am hanging out with people who seem concerned with any political issue, say immigration, human rights violations etc, I find myself vehemently expressing my outrage at these issues. Of course I assume that all of them are extremely pro-immigration, pro-human rights even in fringe cases when their stand contravenes state law, and voice far-left opinions in order to perhaps gain their approval and trust. Of course, their true stands might be closer to the centre. However, my statements inevitably lead the group conversation further and further left.

Of course I do meet opposition. Some people do withhold commenting on the issue, or question some of my assertions. However, those people are generally slightly right of centre, and their questions are only disguised disagreements with my stand. Hence, the phenomenon of a group moving more and more to the left is possible only when all the members of the group are at least slightly left of centre on the political spectrum to begin with. When there’s a mix of left-of-centre and right-of-centre people, this problem may be avoidable. Of course, such a varied group is unlikely to exist as people are more likely to hang out with other people with the same political inclinations.

Explaining Chomsky

Noam Chomsky often makes the statement that the media is biased in its reporting of world events. When questioned on how the media acquired its bias, and whether journalists are bribed or otherwise pressured to write these biased reports, Chomsky says that these journalists themselves choose to become biased, whether in school or university, and are then hired by media houses. I was confused by this statement when I heard it for the first time. Now I think it has begun to make sense to me.

If I am an aspiring journalist at a university in the United States, for instance, I will mostly be surrounded by students and professors who are left leaning to various extents (there will be some people who will be right-of-centre of course, but that will be the exception and not the norm). Inevitably, my brain will tell me that the people surrounding me are all heavily left leaning, and all my writing and speaking will henceforth become more left-leaning in order to subconsciously gain their approval. Because it is journalists like me that then go on to join major news outlets, most news outlets will also progressively become more left leaning with time. In this way, I will have chosen to become more left-leaning than I initially intended.

Of course this phenomenon is not restricted to being left-leaning. If I am slightly sympathetic towards any particular world view, and the people around me are the same way, I will for some reason assume that they are very sympathetic to that world view, and will make statements to assert my supreme sympathy for the same. I will have chosen to bias myself.

Shattering to pieces

Any inhomogeneous group of people ultimately fractures into two groups that propel themselves to the opposite ends of the political/opinion spectrum. These groups may again fracture based on some other issue, again self-propelling to the opposite ends of the spectrum of that particular issue. If this happens repeatedly, we end up with multiple groups that have pretty extreme opinions on most issues, and don’t know how to talk to each other. Of course this is currently happening in the world already, and things may only become worse with time.

One way to avoid this is to repeat Eliezer Yudkowsky’s refrain: “Arguments are not soldiers”. You’re allowed to pick out the “best” arguments from both sides of the spectrum. You don’t have to declare yourself part of any ideological group. Of course this goes against our evolutionary instinct of sorting ourselves into cohesive groups rather than remain in inhomogeneous crowds. Hence, the reason why political polarization is such a hard problem despite having our best minds on it is that it is a really hard problem to crack, and goes against the very thing that makes us humans- our proclivity to disintegrate into factions and attack each other.

The neuroscience of meditation

I recently had the chance to read The Neuroscience of Mindfulness Meditation by Tang, Hölzel and Posner. It is effectively a summary of all the research that has been done on the neuroscience of mindfulness meditation, and comments on how a lot of those studies suffer from design flaws, that make their conclusions questionable. In the process of pointing out design flaws in these research papers, the paper fleshes out some clear overarching benefits of meditation that have consistently been seen in research and self-reported experience. I intend to mainly focus on these in this blogpost.

Note that in this paper, the authors consider only mindfulness meditation. Other types of meditation like mantra meditation, chi gong, etc have been ignored. The aim of this paper is to investigate the effects of mindfulness meditation on attention control, emotion regulation and self-awareness.

Main takeaway: Mindfulness meditation helps in accepting the past in an objective light, and moving on. It also improves alertness, helps in dealing with addiction, and obviously reduces stress. Although more evidence is needed for other benefits that people attach with meditation, those mentioned above have ample scientific evidence backing them up.

Challenges in meditation research

Like in other areas of social science, there seems to be a strong bias towards the publication of positive results in the realm of meditation. In addition to this, research on meditation suffers from small samples and post hoc interpretation of results. In other words, researchers collect a bunch of data, and then say “this data probably points to the fact that meditation is beneficial for x”. Their experiment design and hypothesis don’t come from a larger overarching theory that they’re trying to verify or disprove. I will now go into specifics of some of the shortcomings that research into meditation faces:

  1. Cross-sectional versus longitudinal studies: Early research into meditation tended to be cross-sectional: this means that a control group of non-meditators was compared to a group of seasoned and experienced meditators. Differences in their brain structures and neurology would be examined, and many such differences would generally be found. The authors of this paper contend that these neurological differences need not solely be a result of meditation. Maybe people with this particular neurological structure are more likely to meditate, and become seasoned meditators. Hence, the authors propose that scientists perform longitudinal studies. These are studies in which persons are randomly sorted into a meditation group or a general “wellness” group. They’re both made to live a healthy lifestyle. The only difference between them is that one group meditates while another doesn’t. Scientists should then track neurological changes in their brains at regular time intervals. Some researchers have indeed conducted these longitudinal studies, and found that there generally are significant neurological differences between people who meditate and those who don’t. A lot of the evidence presented in this paper will come from longitudinal studies.
  2. Control conditions in functional imaging: How does one find neurological differences between two people? By taking their brain scans of course. However, taking these scans can be tricky. We want to take brain scans in which people are not actively meditating, so that we detect only those neurological features that have been permanently altered, and are not temporarily altered only when a person is meditating. However, if you ask a meditator to enter a “rest state”, they automatically enter a meditative state, or are likely to enter that state at least once. And if we engross our subjects in some other mental activity so that they don’t enter a meditative state, blood flow to their brains increases, causing their brain scans to change. Hence, imaging protocols that do not rely on blood-oxygen-level-dependent contrasts (BOLD contrasts) should be used.

Changes in brain structure

The following areas have consistently been shown to be affected by meditation. Note that other kinds of meditation like Zen, IBMT, etc have also been included in these studies.

  1. Frontopolar cortex: related to meta-awareness (awareness of your attention, and not just the object of your attention)
  2. Sensory cortices and insula: related to body awareness
  3. Hippocampus: related to memory processes
  4. Anterior cingulate cortex (ACC), mid-cingulate cortex and orbitofrontal cortex: related to self and emotion regulation
  5. Superior longitudinal fascicles and corpus callous: involved in intra and inter-hemispherical communication

Although these physical changes in the brain have been consistently found, how these physical changes impact behavior and function are less well understood. Moreover, most studies suffer from treating different regions of the brain as distinct, unrelated entities. It is possible that all of these different regions are parts of a single brain network or pathway. Hence, the neurological structure of the brain needs to be better understood before we can fully understand how meditation is impacting the brain.

Mindfulness and attention

Attention is subdivided into three different components:

  1. Alerting: This can further be subdivided into tonic and phasic effects. This paper does a good job of explaining what those are. Imagine that you’re first given a signal that someone will throw a ball at you, and then after some time a ball is indeed thrown at you. Phasic effects deal with the amount of time it takes for you to get into a suitable fielding position to be ready to catch a ball, and tonic effects deal with fatigue: how much time can you spend catching balls before you start losing your alertness and readiness.
  2. Orienting– This deals with the selection of specific information from multiple sensory stimuli. For instance, imagine that balls of different colors are thrown at you, and you’re told to only catch the red ball. Then you have to be able to ignore the other balls and only go after the red one.
  3. Conflict monitoring– Imagine a timed setting in which you’re asked to pick crayons of colors that are written on a piece of paper. If the word “green” is written in red, the brain will be tempted to pick up the red crayon, although you’re supposed to pick up green. The process of ignoring your initial reaction and going for the green crayon instead of a red one is called conflict monitoring.

Studies have found that early phases of mindfulness meditation might be associated with improvements in conflict monitoring and orienting, whereas later phases might be associated with improved alerting.

Which part of the brain does mindfulness meditation affect though, which causes these changes in attention? The part of the brain that has been most consistently linked to meditation is the anterior cingulate cortex, which will henceforth be abbreviated as ACC. The ACC allows a person to ignore thoughts that keep running in the back of their mind, and focus on the present and the task at hand. This seems pretty useful for people dealing with trauma, who find it difficult to carry on with their daily lives. However, although ACC activation may be enhanced in the early stages of mindfulness meditation, it actually decreases with higher levels of meditation. Does that mean that meditation makes people less capable of dealing with past trauma in the long run? No. Meditation over the long term helps people accept the past and move on. Hence, the suppression of trauma is no longer as important for seasoned meditators. This will be elaborated in a later section of this blogpost.

Mindfulness and emotion regulation

Emotion regulation deals with choosing which emotions rise to the surface, how long those are experienced, and how these emotions may be expressed (in action, for example). Experiments have shown that mindfulness meditation helps in reducing emotional interference by unpleasant stimuli, decreases physiological reactivity, facilitates a return to emotional baseline after stressor films, and decreases self-reported difficulties in emotion regulation. Essentially, it reduces the intensity of negative emotion, and improves overall mood.

What is the neuroscience behind this? Studies have consistently shown that mindfulness practice reduces the activation of the amygdala during stressful situations, along with the activation of the orbitofrontal cortex. Simplistically speaking, the amygdala makes us “sad” and brings up bad memories in stressful situations, and the orbitofrontal cortex helps a person re-frame past traumatic memories in a more positive light. Hence, a reduction in the activation of the amygdala implies a successful suppression of such thoughts and memories, and an activation of the orbitofrontal cortex helps one interpret painful memories in a less traumatic manner. These changes have consistently been shown in less experienced meditators. However, these changes have not been seen in seasoned meditators. Why? Aren’t things supposed to be even better for seasoned meditators? Consider the quote below:

These findings are in line with the assumption that the process of mindfulness meditation is characterized as an active cognitive regulation in meditation beginners, who need to overcome habitual ways of internally reacting to one’s emotions and might therefore show greater prefrontal activation. Expert meditators might not use this prefrontal control. Rather, they might have automated an accepting stance towards their experience and thus no longer engage in top-down control efforts but instead show enhanced bottom-up processing.

In other words, the early stages of meditation help in suppressing negative thoughts. However, the later stages promote acceptance of the past. In a sense, meditation prepares a person to accept the events of the past, and then hopefully move on.

In addition to this, a cross-sectional study has also found that meditation reduces connectivity between the pain-related brain regions and the executive regions. For instance, meditation might help a chain smoker experience the withdrawal pains of giving up nicotine, and still not succumb to start smoking again. Another longitudinal study showed an increased connectivity between the frontal regions of the brain and the amygdala. Hence, the frontal regions of the brain, responsible for modulating thoughts, could more easily modulate the amygdala, which could be thought of as a source of negativity in the brain.

Another area that meditation has been shown to help in is motivation and reward processing. A stronger activity of the putamen and the caudate following mediation suggests a stronger motivation to keep working towards one’s goals, while a lower activation in the caudate nucleus during reward anticipation suggests a heightened ability to not succumb to short-term incentives and rewards. Hence, meditation might help you keep slogging towards your life goals in a fairly stoic manner, without being overly concerned with winning and other “rewards” that you expect to get when you achieve those goals.

Mindfulness and self-awareness

Buddhist philosophy asserts that one should make awareness itself an object at one’s attention. If I’m looking at an orange, I should also be aware of how I’m looking at an orange, and whether other ways of looking at it exist. My thoughts should also go to the nature and limits of my perception. If we can recognize that our limited perception is a major source of misery to us, we may have some hope of seeing our surroundings and circumstances more objectively.

Cue the underlying neuroscience: the default mode network or DMN is considered to be the part of the brain involved in subjective (as opposed to objective) self-referential processing. The DMN shows high activity when one’s mind is wandering or not at peace, and also helps in projecting oneself into another perspective. For instance, if I was bullied as a kid in school, the DMN will help me project myself into my bully’s psyche. I will be able to see exactly how little my bully thought of me (at least according to me. Maybe he was actually bullying me out of insecurity), and the shock of that injustice will lead to trauma and repeated re-processing of that event, causing me greater and greater mental stress. Through fMRI scans, mindfulness meditation has been shown to decrease DMN activity.

The overall findings from multiple studies on mindfulness meditation are that it might alter the self-referential mode so that a previous narrative, evaluative form of self-referential processing is replaced by greater awareness and greater objectivity. Because this is my blog, I am now going to write my personal interpretation of this (plagiarized in part from multiple sources like Sam Harris, Kurt Vonnegut, etc), because I think that this is the main takeaway of the whole paper.

We are often taught to classify things as “good” or “bad”. This is the evaluative narrative that they talk about above. If someone has done something bad to us in the past, we can never get over the injustice of it: how could that person do it? If we have done something bad to someone, and this generally tends to be more traumatic than the former, we can’t get over that either. How could we possibly have wronged this person?! And these thoughts keep gnawing at us day in and out. Mediation helps in destroying this erroneous dichotomy of good and bad. Nothing really is good and bad. It is now a well-established fact that free will doesn’t really exist (I can try and establish this more scientifically in a future blogpost if you’re not convinced by this statement, but Sam Harris has many intelligent things to say about it). We are all Turing machines that have been pre-programmed to do certain tasks in certain situations, with only the illusion that we’re choosing to do these particular things. The person who wronged you was in a state of mind that prompted him to act in that manner in that particular situation. It was inevitable. If you’ve wronged someone, it is because you were in a state of mind that led you to do that thing in that particular situation. We’re not really free agents. We’re just robots gifted/cursed with consciousness. We get to experience our actions, and not really “choose” them. We’re not here to change the world based on our choices. We’re here just to enjoy the show that we put on with other actors. If one can accept this narrative, the acceptance of past and future wrongdoings becomes easier. And this is the acceptance of the past that meditation helps one attain.

References

  1. The Neuroscience of Mindfulness Meditation by Tang, Hölzel and Posner

Evolution and adapting to changing conditions

I read an interesting paper today, titled “Dire wolves were the last of an ancient new world canid lineage” by Frantz et al. Having only heard of dire wolves in badly written fiction about really good looking vampires, I did not even know that these creatures actually existed in real life.

On reading the paper, I realized that dire wolves did actually exist, but became extinct in North America about 13,000 years ago. Grey wolves, on the other hand, survive and thrive to this day. The authors explain that both dire wolves and grey wolves had similar diets 20,000 years ago. They ate large fauna. However, when large fauna slowly disappeared from the North American landmass, grey wolves could adapt to these changes and change their diet to include smaller animals, whilst dire wolves could not. Hence, the former continue to thrive while the latter went extinct thousands of years ago.

This made me think of a blogpost that I’d written on Why is Chlorophyll Green? After doing some complex network analysis, the authors conclude that leaves are not green because this color allows them to maximize energy input, or even minimize energy waste, etc. Is it not the “best” color for any clear criterion. However, evolution has made leaves green because it is the most reliable color. When sunlight or other conditions change, green continues to produce a steady stream of energy for the plant, whilst other colors are prone to failure in such changing conditions.

Evolution, it seems, favors traits that continue to produce results with changing times and conditions. There is a pretty useful life lesson in there somewhere.

Why Grothendieck would say machine learning is mostly overfitting

Introduction

Grothendieck is, by far, the single most influential mathematician of the 20th century. He solved long standing mathematical problems, created whole new fields of human thought, and then spectacularly abandoned it all when his institute refused to accept military funding. The overarching theme of all his research was that when we study mathematical concepts, there are too many extraneous and distracting details. We need to simplify things to their very bare essence.

In this essay, I make the argument that our brain, when processing sensory input, uses this insight naturally. It simplifies things to its bare essentials, and then “fills in” the extraneous details. I then talk about how machine learning engineers designing neural networks may benefit from the same insight

Machine learning and Perceptual Control Theory

Obtaining and storing information is expensive. Hence, when we observe things, we notice only a few of the infinite features of the objects under observation. For instance, when we see a tree, we don’t notice all the leaves on each branch of the tree. We don’t notice each striation on the tree trunk. We just see a basic outline, and we know right away that it’s a tree.

Let us now use Perceptual Control Theory to understand why this may be the case. I have blogged about Perceptual Control Theory before. When we see an object, we don’t really observe every feature of it. In our brain, we only have a grainy outline of the object in front of us. Our brain then superimposes what it “expects” the grainy outline to be filled with. For instance, when we see a conical leafy structure in front of us, we visually process only a very blurry and grainy outline of it. However, our brain then fills in some of the details. There’s probably branches that are supporting the leaves, although we can’t see them. This thing probably has roots that go into the ground, that are preventing it from falling over. We then classify the object as a tree.

It is completely possible that the leafy apparition in front of us is just a conical structure with “leaves” that are actually a weirdly shaped insects, supported by a stone structure in the center. However, our brain only notices a basic outline, and then fills in the details.

But a neural network does something entirely different.

Why machine learning is overfitting

Most of machine learning is overfitting because neural networks are being trained to notice too much. When a convolutional neural network sees a tree, it does not just retrieve a blurry outline and then “fill it in” with expected features. It first processes the outline of the tree. Then it notices smaller features like leaves, etc. It then starts processing even smaller features, until it can classify that object as a tree or not.

Why does the neural network need to continue processing and obtaining information like this? Clearly, this is what makes is to slow and expensive. Why does it also not obtain only bare information, like a bare outline, and then fill it in with expected details? This is because the neural network does not have any input data, that’ll help it fill in this information.

Hence, in order to have a generic neural network that can classify all objects that a human can, we somehow have to give it the “expected fill in” information that a human learns through experience in the real world. Hence, machine learning stands to benefit from pediatric research- how babies learn to identify things when they notice them for the first time. Moreover, Noam Chomsky also argues that babies are born with the adequate equipment to actually learn this information in a fast and efficient way, and that a baby’s brain is never a clean slate. If this is true, passing on this “fill in” information to a machine may be more difficult than expected. However, this is a question that perhaps deserves a closer look.

It is not just what a neural network notices about an object that is important. What it trained to “fill in” into the blurry outline is equally important.

What is the dimension of the space of entrepreneurial innovation?

I was reading a conversation between Sam Harris and Daniel Kahneman, in which Kahneman made the point that if you want people to do what you want, don’t push them to do it. Just make it easier for them to do it instead. If you push people, they will revolt. But if you make it easier for them to do it, you increase the likelihood that they actually do it.

I often catch myself thinking about this line again and again, finding connections with a great number of things around me. I will try and flesh out some aspects of this in this essay

Entrepreneurial innovation

If we take a look at entrepreneurial innovation over the last couple of centuries, almost all of them follow a common pattern- they make life easier for us, often in unexpected ways. We never really demanded these products. However, when we tried them out, we realized that they were easy to use, and provided us with tangible benefits.

Facebook is an obvious example. It made it so easy for us to stay connected with a larger group of friends. It is constantly throwing at us information about what our friends are doing, etc. Of course, it also offers us the aspirational motif of making our lives look the way that we want people to be seeing us. But apart from that, Facebook is popular because it makes life easy. The same goes for AirBnB (makes it easy to arrange cheap accommodation at almost any place in the world), Uber (makes it easy to rent cabs right from your couch), etc.

Of course, there are other entrepreneurial ventures as well that do not just seek to make our lives incrementally easier. Take Tesla and SpaceX, for instance. However, one can agree that a large fraction of new ventures aim to cash in on this idea that there is a lot of money in making our lives easier.

What other low hanging fruit is out there, waiting to be picked? Perhaps something that converts a novel into a movie? A coffee machine that automatically makes coffee at 7 every morning? Something that cooks for us?

It becomes almost obvious in retrospect that the biggest innovation in our daily lives will be an affordable robot that can do all our chores for us. However, creating such a robot has proved to be more difficult than previously thought. Another would be really cheap space travel. But that too seems to be much more difficult than previously thought.

And therein lies the true problem of entrepreneurial innovation. The obvious entrepreneurial ideas have proved too difficult to realistically solve in the near future. Hence, one has to think of new, non-obvious ideas of making our lives easier. For instance, I type around 80-85 wpm. I’ve never really felt the need or desire to type faster than that. However, it is clear to me that I think much faster than that. I usually form whole sentences instantaneously in my mind, which I then take 5-10 second to type out. What if there was a keyboard for less than $100, that helped me type 300 wpm? Would I buy it? Of course! And therein lies some potential for serious entrepreneurial innovation.

How the tech industry hacks this insight

I bought a New York Times subscription last year. I didn’t really wake up one morning and decide to buy one though. I would see really interesting New York Times articles being thrown my way on Facebook, Twitter, you name it. However, on clicking the article, I would find out that all of them were paywalled. And getting access was only one button away. After months of denying myself the information hidden behind the paywall, I finally broke down and got myself a subscription.

A few months later, I realized that I had free access to the articles through my university, and tried to unsubscribe. I couldn’t find the unsubscribe option at all! The only way to unsubscribe was to call them up at a Toll Free number and wait several minutes. Like any other human being, I balked at this idea, and kept paying $10 for several for months, until I finally managed to unsubscribe through a newly enabled internet chat bot.

This is par for the course for most online subscriptions (except, surprisingly, Netflix). Although unsubscribing is possible, it requires effort- much more effort than subscribing does. For instance, deactivating your Facebook profile is essentially a five minute-affair, which involves finding the right spot for de-activation (which Facebook keeps changing), re-entering your password, choosing a reason to de-activate, being sure that you want to de-activate your profile, etc. However, re-activating takes just two seconds. Go to the website, click the login button (I have my login information saved on my computer already), and you’re in!

I have often de-activated my facebook profile, only to re-active it the very next day. Because it is so easy. In fact, the only reason that I no longer have access to my facebook profile right now is that I went on facebook, changed my password to something I would have no hope of remembering, and then de-activating it. Now, in order to get on facebook again, I will have to use the Forgot Password feature, which will require a few additional steps. These steps have been sufficient to keep me off Facebook for about a week now- longer than I’ve ever gone off Facebook in the past!

The same goes for cellphone usage. Although addiction and boredom are surely reasons that I use my phone for 1/5th of my day, the fact that it is just so easy to use is also an equally contributing factor. One swipe, and I’m on. You take something that is really easy to do, and you attach some sort of small Pavlovian reward to it (the dopamine release when you get a Facebook notification, or an email, etc), and you get an unstoppable force pretty much running your life. How do we stop it? The trick that has worked for me the most is just switching off your phone. Although I am able to switch my phone back on when absolutely necessary, I now have to put in greater effort. And sometimes, I’m able to decide that the effort is not worth it. Hence, it is only when we make phone usage more difficult for ourselves that we might be able to de-addict ourselves.

Bureacracy

India is infamous for its corrupt bureaucracy. People often have to resort to bribing to get small things done. Suppose you go to your nearest government office to get an important document. What will happen? Will you be asked for a bribe right away? No. It’s slightly more subtle than that. You will be told that the office responsible for this document is busy, and that you should return later. You do so the next day, and you’re again told the same thing. This keeps happening over multiple days, until you finally offer a small bribe, and then your work gets done instantaneously.

Essentially, bureaucrats offer you two ways of getting your work done. One is an impossibly hard way that requires way too much patience and work. Maybe on your 100th visit, you’ll get your important document. However, you’re loathe to put in so much time and effort, especially if you have an alternate way, which requires you to pay a small sum to get your work done instantaneously. Bureaucrats are effectively hacking that part of your brain that instantly goes for the easier route. They make bribing easy because they’re discreet about it, your work gets done instantaneously, and the alternatives, which are not getting the document at all or visiting the same place 100 times before your work is done, are too expensive. And this is why there is so much bribing in Indian bureaucracy.

Donations and volunteering

Donations and volunteering can also be boosted by making them “easier”. I work for a student organization that asks students to volunteer on weekends in order to raise money for charities at home. We often have a difficult time getting enough volunteers. However, we recently started offering car rides to volunteers to and from the venue, which has definitely helped in recruitment, although getting enough volunteers for our events or raising enough money is still a struggle.

On the other hand, I also donate some money every month to Effective Altruism. It is easy for me to do so, as it is literally just a click away. All my information has been saved already. I punch in my CVV number, click the “donate” button, and I’m done. In fact, they also have a “recurring donation” option, that would make it even easier for me to donate, although I don’t generally use that option as I like having more control over my financial transactions. Over in all, helping out Effective Altruism is much easier for me than on my own student run organization, as it is requires much less effort.

What are some lessons we can learn from this, and implement in our organization? Perhaps we could offer people an “easier” alternative to volunteering. Maybe, along with our weekend volunteering stints which are often tiring and a huge time commitment, we could also offer people the option to pay $5 every month instead? Or we could sell traditional Indian handicrafts door to door, in order to raise money? I’m not sure. However, the easier we make it for people to contribute to our organization, the greater their contributions will be.

Asymmetry of effort

Although I have advocated for making things “easier” for a certain group of people, I have ignored the plight of the group responsible for making it all happen. For instance, thinking up a new way to make our lives easier involves a lot of thinking, planning and work by entrepreneurs. Similarly, implementing all of the actions I describe above for my student group requires a lot of effort from the core members. While entrepreneurs are adequately incentivized to pursue ideas that could be worth a lot of money and power, members of a student group are not as incentivized to take away time from their studies and friends to pursue ideas that might slightly increase the overall funds we raise. Hence, along with making things easier for others, we cannot make them too difficult for ourselves. There’s a delicate optimization game to be played here

We gotta have some more pop philosophy- Mathematics, machine learning and Wittgenstein

In my quest to read all the pop neuroscience available online, I read this fascinating article on Gerald Edelman. It was full of profound quotes like

We don’t have goals. We just have values.

More importantly, it talked about the concept of polymorphous sets as proposed by Wittgenstein.

“Typical Wittgenstein,” Edelman mused. “There is a kind of ostentation in his modesty. I don’t know what that is. He provokes you and it’s very powerful. It’s ambiguous, sometimes, and it’s not cute. It’s riddle, it’s posturing around the riddle.”

A little girl playing hopscotch, chess players, Swedish sailors doing naval exercises, rugby players are all playing games, Edelman continued. To most observers, these phenomena seem to have little or nothing to do with each other, and yet they are all members of the set of possible games.

“This defines what is known in the business as a polymorphous set. It’s a very hard thing. It means a set defined by neither necessary nor sufficient conditions.”

This is something I’ve read about before, and it didn’t strike me that hard before, as it did on reading this article. Most “things” that we talk about in life are polymorphous sets. There is no necessary and sufficient condition for a fruit to be an apple. Does it have to be red? No it can be green. Does it have to be sweet? No it can be sour. Does it have to be of a particular size? No, if you saw a freakishly small apple, you’d still agree that it is an apple.

Why teaching machines how to identify objects is hard

A neural network can be taught to recognize a cat if it is fed millions and millions of images of cats, and asked to choose suitable parameters so that it is able to recognize whether a particular object is a cat or not. I, on the other hand, learned to recognize cats by looking at one cat. Maybe a couple more. And this is true for almost every other human I know. We haven’t seen all cats in the world. However, if you show me an animal, I can almost always tell you right away if it is a cat or not. Does that mean we might have as much computational power as an actual neural network? Not even close.

The fact that we are able to recognize cats after being shown just a handful of cats follows rom the fact that when we see a cat, we automatically form a polymorphous set of cats in our minds. There is no necessary or sufficient condition to be a cat. A cat doesn’t have to be large or small, black or white, agile or lazy. We will just know whether something is a cat when we see one.

This sounds like a spectacularly bad strategy. What if my polymorphous set of cats differs substantially from yours? It is completely possible. Society would stop functioning if our polymorphous sets of various notions were different enough. However, they’re not. Our brains are similar enough that our polymorphous sets are very very similar for most things, if not the same. You and I may have only seen a handful of tigers in our lives, and probably different individual tigers. However, if we’re walking down a road together and see a tiger, we will instantly recognize it as one.

But hang on. Is the animal that we saw really a tiger? What if it is a slightly mutated version of a tiger (it probably is)? Can we still call that a tiger? For instance, humans are mutations of chimps. If humans (mutated chimps) are not the same as other chimps, why are mutated tigers the same as other tigers? Well….you may say that humans have had millions of mutations by now, but that mutated tiger only probably has a small number of mutations. How many mutations does it take for a tiger to stop being a tiger, and become a different species? Well….we don’t know. All we know is that when we see an animal, we will know when it is a tiger and when it is not.

As one can see above, these polymorphous sets that we have formed in our minds are just horrible by design. They’re not precise, and leave way too much ambiguity. But they work. This is because humans are very similar to one another, and form pretty much the same polymorphous sets. Hence, as long as you and I both agree that that particular animal is a tiger, we are fine.

However, machines obviously have very different “minds” as compared to ours. It is not capable of forming polymorphous sets, leave alone polymorphous sets that are the same as ours. Hence, it has to be fed millions of data points for it to have the same sets as our polymorphous sets. This is not really the machine’s fault. We are terribly imprecise in how we name and define things. The machine wasn’t born as a human, and hence does not possess our particular brains that would help it form the same polymorphous sets.

Is there any hope then? Can we ever have machines that would be able to form the same polymorphous sets as humans? One solution is that if we are able to determine all the parameters inside the human brain and pass them on to a machine, we will never have to teach a machine anything ever again. We will possess perfect communication with it. However, this seems like something that can only be realized in the distant future. Maybe we could also somehow communicate our polymorphous sets’ forming apparatus to machines? Again, I am not aware of any research happening in this direction.

Mathematics

Mathematics aims to make things precise. It does so by doing away with the concept of polymorphous sets.

For example, what is a measurable set? It is a set S with the property that for any other set T, we have the property that m^*(T\cap S)+m^*(T\cap S^c)=m^*(T). Of course one would have to define the concept of outer measure m^* before describing this. The point of this definition is that it helps us capture an important property of measurable sets, and explicitly tells us whether a set under consideration is measurable or not. Hence, there is a necessary and sufficient criterion for a set to be a member of the class of measurable sets.

Obviously, no one really started with this definition. Here is a possible development of the concept: do you see this nice set? The unit interval? This has some reasonable properties. What’s crazy is that very broken sets like \Bbb{Q}\cap [0,1] also have these reasonable properties! Alright, so our intuition tells us that very very broken sets can also have all of these properties that we’re talking about. Then someone comes up with the Vitali set. This very broken set clearly does not have the reasonable sounding property you were talking about!

Do we now see that prevents us from forming a polymorphous set of measurable sets? What forces us to come up with precise and bothersome definitions instead? When we form polymorphous sets, we merely attach a nebulous description. We don’t specify any property that the elements of a polymorphous set have to satisfy. For example, the polymorphous set of cats consists of animals that are “feline” in some vaguely defined sense. We don’t say that the polymorphous set of cats has the property that cats are able to jump 1 ft in the air vertically. If we do so, then we are prescribing a necessary condition to the polymorphous set.

In other words, definitions are necessary (and sufficient) conditions. If A is a measurable set, then it should satisfy these nice properties. If it does not, then it cannot be a member of the class of measurable sets.

As Mathematics is built on definitions, which are necessary and sufficient conditions of membership to a class, it cannot have polymorphous sets. But why not? Why does this concept work in the real world, and not in Mathematics? This is because in the real world we want to just describe something, while in Mathematics we want to derive useful properties of things. For instance, in the real world, when we try to classify animals as cats or not, we don’t want to understand the properties of cats (that they should be able to jump a certain height, or weigh this much, etc). However, in mathematics, when we talk about measurable sets, we want to be able to derive useful properties that they possess (that it can be approximated by an open set, that its measure is countably additive, etc). Prescribing any useful properties leads one to form a necessary and sufficient condition for membership in a set, that does away with polymorphous sets and leads to precise definitions.

Hence, although there is perhaps some value in having polymorphous sets of concepts in Mathematics, when it comes down to deriving interesting properties, the vicious cycle of properties-> necessary and sufficient conditions for membership-> non-intuitive definitions seems inevitable. What is slightly tragic about the way that Mathematics is generally taught at the college level and beyond is that this sequence of events is not made explicit. We’re not told that we want our objects to have these nice properties, and hence we need this long winding definitions. We start with the definition, and are then told that these very nice and non-intuitive definitions miraculously lead to these nice properties.

Perhaps in a future post, I can explain how polymorphous sets can still be useful in developing mathematical intuition. However, it seems irrefutable that precise definitions are absolutely integral to mathematical consistency.

Thanks for reading!

Moral asymmetry and Indian politics

I spent part of the morning reading a conversation between Sam Harris and Daniel Kahneman. In an almost textbook example of priming, when I saw something that I already believe, it led me to accord a greater degree of importance to the conversation. Soon I was connecting dots all over the place, and this post is a culmination of that rabbit hole that I hurled myself down.

Moral asymmetry

Harris and Kahneman talk about the asymmetry of morality. How human beings have evolved to avoid loss much more than pursue gain. Consider the following scenarios: we tell a person that they have two options. Out of 100 people, they can either save 60 people, or take a gamble in which we they have 3/5 chance of saving all 100 people. Imagine another scenario in which we tell a person that they can either kill 40 people out of a 100, or take a gamble in which they have a 2/5 chance of killing everyone. The two scenarios are obviously identical. However, in most cases, the person will choose to save 60 people in the first scenario, and choose to take a gamble in the second scenario. Killing 40 people for sure objectively sounds worse than saving 60 people for sure, although these two choices are exactly the same. Actively harming someone seems much worse than refusing to reward someone.

I have referred to this phenomenon in an earlier blogpost as well. Donald Knuth said in an interview that in order to lead a satisfying life, one must reduce loss and regret much more actively than pursue happiness and success. Now Kahneman also reiterates this sentiment, expressing the view that we may have evolutionarily evolved to minimize or avoid losses much more actively than pursue gains. This may be because a loss in the jungle might mean a loss of life or mobility, while a gain might just mean perhaps greater strength or a richer food source. Animals pursuing greater strength or better food sources while jeopardizing their safety would have a lower chance of survival than animals focusing on just watching their backs and focusing on not dying. Hence, more of these animals would have survived through the eons, passing these genes on to us.

Indian politics

How may this apply to politics and and public policy? Take a country like India. We may consider ourselves to be a developing nation. However, roads in many places are full of potholes, women feel unsafe in many areas, water is not potable, there is rampant caste discrimination, etc. However, despite these many hindrances in our daily lives, our voting record would show that a majority of Indian citizens do not vote for development. We mostly vote along caste or religious lines. Why is that? Do we not want better roads or clean drinking water?

This may be because this is the way things have always been. The country has never had much better roads, potable drinking water, etc in the past. Hence, because we’ve never had it, we can’t imagine what losing it would be. The poor family living in the slums does not actively day dream about how living in a better house would be, and how this possibility is being snatched away from them. Hence, people vote based on their deep seated sympathies for their own tribe, whether it be caste, religion, etc.

Now contrast this with the farmer’s protests rocking the country right now. The farmers have been guaranteed a good price for their produce for a very long time. Now the government is threatening to take away that guarantee, at least in the long term if not immediately. The government is snatching away something that farmers have had for a long time. This loss feels much worse than the government not building better roads or infrastructure for the farmers, although objectively the latter is much worse. Hence, farmers have been demonstrating against the ruling government for months, and this is by far the most serious challenge to the government’s authority.

Is this moral asymmetry exploited in politics? All the time. How did India’s BJP sell their Hindutva agenda to the population? They asked us to imagine what a perfect Hindu state or Ram Rajya would be like. It would be a perfect society without vice or corruption, as described in great detail in our mythological stories. Hence, when they claim that this is what our previous governments have denied us, it feels like a personal loss. We feel enraged at other political party (Indian National Congress) for denying what was rightfully ours.

Refugee crisis

How are refugees demonized everywhere in the world? Our political leaders make us imagine refugees come in and steal our property, sexually abuse women, etc. Although refugees have also been consistently known to revitalize the economy and herald unprecedented developments in science and technology, our potential losses, which have never really systematically been seen in data, seem much more unbearable than the benefits that refugees have provided us for more than a century. This prompts large parts of the population to vote against accepting refugees, although they’re aware of the terrible conditions that refugees live in. This is how India justified its refusal to accept Rohingya refugees, and much of Europe refuses to accept refugees from Africa and Asia.

Is there any way to be able to escape this cognitive bias? To perhaps not let our political leaders manipulate us as easily? I’m not sure. But I hope that being aware of this bias in the first place forms part of the solution

Stable systems and managing expectations

In his book Sapiens, Yuval Noah Harari talks about how civilizations in the past fell not because of one error in judgement, but because of multiple such errors. For instance, many empires in ancient China fell because they were not receptive to scientific and military advances from the outside, the bureaucracy was stifled, etc. I have often returned to thinking about this simple observation, and how it relates to much of the world around us.

One way of re-phrasing what Harari was trying to say is that many systems around us are stable. They can absorb small shocks or errors, and still remain relatively unchanged. It takes many errors and misjudgments to completely wreck them. For instance, when we drive on the road, we are generally sensitive to the drivers around us, even if we’re not actively paying attention. If a car suddenly serves into our lane, we will almost involuntary slam our brakes and try to control the outcome. Most times, we will able to do so successfully. However, if we’re intoxicated while behind the wheel, our reaction time will suffer, and we will crash into that car. Hence, just being intoxicated or having a car swerve right into your lane are not by themselves enough to get you into a car accident. Both of these conditions have to come together in order for you to have a decent chance of crashing your car. In other words, when on the road, you’re a stable system. It will take multiple misjudgments on your part or that of others to wreck your vehicle.

Can we also study anger and anxiety from a systems perspective? Imagine that you’re having a bad day at work. Your boss is breathing down your neck for no fault of yours, and the heater has also started malfunctioning, causing you to freeze in your seat for the most of the day. Although this sure will put a damper on your mood, this in itself is generally not enough to make you scream in agony. However, if on your drive back home you get into a fender bender, and on reaching home you realize that there is no electricity and most of the food in the refrigerator has gone bad, you will probably have lost it and will lash out at anyone or anything. It took multiple unfortunate circumstances or “errors” to take you from a sullen face to black rage. If on returning home from work you find your favorite sandwich is waiting for you in the refrigerator, you will soon return to normal. Good food has partially compensated for the bad day at work, and things are alright again.

Hence, although I find myself getting anxious and angry every now at then for seemingly trivial reasons, I have now started thinking that it is a miracle that I don’t get angry or anxious more often. One bad thing is generally not enough to destroy my peace if other things are going well in my life. It is only when bad things line up- car malfunctioning, arguments with friends, problems at home- that I find myself losing my cool. There is probably an evolutionary advantage to not losing your composure over just one thing going wrong. Hence, our moods have evolved to become more stable over eons. It is only when multiple things go wrong that we don’t quite know what to do or who to blame.

Now a small digression: why does it sometimes seem like everything is going wrong for us all at the same time? When we have a bad day at work, we hope that we will at least get good food at home to compensate for it. We hope that we can relax with our partner, tell them about our problems, and that they will soon utter some relaxing words which will make our miseries go away. Hence, our expectations from our life become even more demanding than before. We don’t just want an ordinary day. We want a fantastic day after this in order to forget our troubles. When this does not happen, we get even more dejected, and think that along with a bad boss, we also have an unsympathetic partner and a complete lack of good food in our lives. Hence, one “error” in our life induces us to make narrow, unrealistic expectations in our lives, and when they’re not met, we will that everything is going wrong with us.

So far so good. Our existences are sort-of stable. However, we must ask the following question: how can one become even more stable? Perhaps keep our composure even when very many things go wrong? I struggle with this question because I may have slight anxiety issues. Driving on the road is a struggle because I become nervous when there are cars around me. Even the slightest disturbance when I am working often disturbs my calm. When I’m watching TV, if someone talks to me, I get distracted and irritable. I think all this may be because I only expect to have an easy drive with very few cars around me, complete silence when I work, and no one talking to me when I watch TV. Hence, when these expectations are proved wrong, I get nervous and irritable as I can no longer control my surroundings.

Yesterday, while driving in seemingly erratic conditions, I tried to calm my nerves by trying to expand my range of expectations. I assigned small probabilities to multiple things that could go wrong. Perhaps a car would come and crash against me. Perhaps a car will swerve wildly into my lane. Perhaps I will hit an animal. Of course, thinking about all these possibilities made me mentally prepared to deal with such eventualities. If I do hit an animal, because I had already assigned a non-zero probability to it, I will recover from shock much more quickly, and will probably be able to deal with the situation much better.

This single act of thinking about eventualities calmed my nerves within a few minutes, and I had the rarest of experiences- an enjoyable drive back home, even amongst erratic drivers and the general highway craziness.

Hence, I would like to make the hypothesis that a lot of anxiety and anger may stem from the fact that our range of expectations is often too narrow. Hence, when reality doesn’t meet our very narrow expectations, we lose control of our peace of mind and the situation. If we spend time broadening our range of expectations, we will start expecting in advance more things that happen to us in real life, reducing shock, and hence anxiety in the process.