Effing the Ineffable

I think it’s interesting that language, despite it being a powerful way of communication, cannot express a lot of things.

To use a cliched example, language cannot express what love is. People resort to saying, “No one needs to tell you you are in love, you just know it, through and through.” Same with art, which people can only know it when they see it (or obscenity).

That’s not the same as saying that language cannot lead to such things. We may not be able to describe love, but we can tell stories about it, and depend on our shared neuron structure for the reader to get in the character’s shoes. More indirectly, language can express instructions that leads to the reader to have unexpressable feelings. We may not be able to tell someone how to be effortless or be spontaneous, but we can tell them to do things that will eventually lead them to be effortless or spontaneous.

Buddhist koans are, in theory, exactly this, another level down. Language cannot express what enlightenment is. It can’t even describe the process of attaining enlightenment in any useful way. Instead, koans try to make you think differently by denying its normal way of thinking. The reader is supposed to then think on the koan and, eventually, adopt the requisite state of mind. In a sense, a koan describes the shape of unexpressable directions that lead to unexpressable states of mind.

All in all, it’s amazing that we can induce patterns of thought in other people, even for things that language fail to describe. Maybe, this is why sometimes a passage appears vague and unclear to us; maybe it’s not that the author is doing a bad job, but that language itself is incapable of expressing what the author wants to say.

PS. The title of this post is, of course, paraphrased from Douglas Adams.

Unteachables

A partial list of things that cannot be taught:

• Effortlessness
• Heroism
• Subversiveness
• Resoluteness
• Commitment
• Individuality
• Sympathy
• Spontaneity

This is not to say that you can't induce people to be some of these things, it's just unclear how they can be taught them without already knowing how. Some teachable things, but difficultly so, include:

• Detachment
• Critical Thinking
• Inner Peace
• Creativity 
• Responsibility

The only line I can draw is that the second list seem to be more about ways of thinking, while the first list contains ways of being or feeling. If anyone can draw a better line, or has ways of teaching things on the first list, leave a comment below.

Nerd Sniped by Nerd Sniping

I got nerd sniped today reading Paul Lockhart’s A Mathematician’s Lament. It’s an excellent rant on the state of mathematics education, but it also contains a short essay on why he finds mathematics fun. It contained this problem:

Do all undirected graphs (of order > 2) contain at least two nodes with the same degree?

Actually, the precise problem that got me is not important (I just wanted to nerd snipe you too). As I was getting coffee and thinking about it though, I wondered if the susceptibility of being nerd sniped is correlated with the breadth of interest. It makes sense that the more things you are interested, the more easily you’d be distracted by a random, sufficiently difficult question. Of course, the “sufficiently difficult” part is hard to measure, but we’ll let that go for now.

But then it occurred to me that all the nerd sniping questions I know are (at least somewhat) logical in nature. I can’t imagine someone being nerd sniped by a history question. For example, I don’t know anything about the causes of World War I, other than that it involved the assassination of Archduke Ferdinand (wow, I even got the name right; I wrote that without checking my sources). But I can’t imagine myself dropping everything to think about this problem. I don’t think this is a lack of interest, either; I can’t even imagine my historian friends doing this. (Yes, I have friends. Shut up.)

I feel the difference is that, for the logic-based questions, it’s not the answer that matters, but the process of getting there. I can tell you the answer to the graph problem: yes (…probably. I haven’t solved it yet). But that answer is not satisfying. It’s like looking at the solution of a solved Sudoku puzzle; the only thing it tells you is that the board can be solved. (For this reason, I think it's pointless to print Sudoku solutions, as long as I trust them to be solvable.) For both the original infinite-grid-of-resistors problem and the graph problem, I want to know how that answer was derived. I might not even believe your answer until you’ve shown me the proof. (By the way, the answer to the resistor problem is 4/pi - 0.5 ohms.)

But that’s not true of the question about World War I. If you tell me (to whatever detail) why WWI occurred, and I would nod and go on my way. I wouldn’t question your explanation (unless it contradicts something I already know), and I wouldn’t question your source of knowledge.

I first thought that this is because the answer is trivially obtainable from, say, Wikipedia; but then, I could also have looked up the proof and be done with it. It’s also not the case that the question about WWI requires a long explanation (eg. it asks “why/how”), while the graph question requires just a binary answer (eg. it asks “do”). I can transform both questions the other way (“Was the assassination of Archduke Ferdinand a factor in starting WWI?” and “Why do all undirected graphs have two nodes with the same degree?”), and the feeling remains the same. Notice, though, that the reworded graph question now presumes an answer, so the new question actually gives more information than the old one.

As I thought more about this, I realized that I get nerd sniped by questions outside of the maths and sciences as well. I’ve nerd sniped someone before with the question, “Is the statement “Unicorns have one horn” true or false?”. I myself have spent entire afternoons thinking about questions from psychology/philosophy, the latest being the nature of vulnerability. Although, if I apply the same reasoning of whether I’d want to know the reasoning behind the answer, I’m not sure if the psychology question is truly a nerd sniper.

Maybe there are also shades of being sniped too. While I wouldn’t think too long on the question of, say, the significance of socks in the Harry Potter series, I can imagine myself disagreeing with someone else’s answer, leading to an afternoon of debate. It’s not as powerful a sniper as the logical questions, and there’s confusion between the appeal of the problem itself with the appeal of a good discussion. I wouldn’t call it nerd sniping for this reason, but it’s still something that would cause me to stop what I’m doing.

I don’t have any answers to my questions about nerd sniping raised here. I am curious whether and how much my mathematical and scientific background has biased me in what I get sniped by. I would love to hear from people in history or anthropology or related subjects, and see if there are questions that get them but don’t get me.

…Once you get over how I’ve just nerd sniped all of you, of course.

Regret and Responsibility

A couple months ago I had a conversation with a friend. In that conversation, I ended up expressing a belief that hurt them, leading to a month of tense interactions. But, we eventually sorted it out, and in the resulting conversation, my friend asked me, “Do you regret saying what you did?” I replied, “I’m sorry that you were hurt, but I don’t feel guilty about saying it.”

The words “sorry” and “regret” have several related meanings. ”Sorry” can be used to express condolence without implying guilt, as in “I’m sorry for your loss.” It can, of course, also be used as an apology, as in “I’m sorry I yelled at you.” Although “regret” can be used in the same manner (”I regret yelling at you yesterday.”), it can also simply express a wish for a different outcome, as in “I regret not getting the chocolate ice cream.” I take my friend’s question to use the apologetic meaning of “regret”.

Let’s assume that hurtful behavior is considered bad by both parties. I posit that when someone (the “perpetrator”) apologizes, they must believe they had somehow wronged the “victim”. The question is, could the perpetrator have hurt the victim without having done the wrong thing?

Here’s an example. It turns out that, in the story at the beginning (which is a true story, by the way), my friend had previously told me that they “would always rather have the truth than ignorance”. So, in our conversation, when they had asked me for my thoughts, I had simply told them what I believed, explicitly as a belief of mine (that is, without implying whether that belief was correct). Of course, they then took it personally, leading to the episode above.

Who was at fault in this scenario? It’s true that my friend was hurt because of what I said, and that I had said what I did intentionally. Intuition suggests that, if that was the full story, I probably did something wrong and should apologize and feel bad.

What throws this intuition off is that my friend had asked what I thought, and that they had stated that they “always” prefer the truth. For past-me, the choice between telling and not telling is obvious: there’s no reason I should withhold what I was thinking. I could argue that, even if I had known that what I said would hurt them, given their preference of truth, I should still have told them. Since I had considered my choice before acting, and since a reasonable person would have done the same, I don’t feel guilty about saying what I believed.

But I could argue the other way. Clearly, I hadn’t fully considered my choice; if I had, I would have realized that my friend’s previous statement was not true. They could have been lying then, or more plausibly, they themselves had not considered all the options before making that statement. That is, while they believed they always prefer the truth, their belief was incorrect. Knowing what I know about human psychology (ie. that people don’t know much about themselves), I should have foreseen that they would be hurt despite their statement, and that should have influenced my decision. I was, in other words, negligent.

The question here is not whether I knew that my friend would be hurt; clearly I didn’t know, which is what caused this problem. The question is whether I should have known that my friend would be hurt, whether I am responsible for having that knowledge, and therefore ultimately responsible for their suffering. But on this question I’m stuck. On one hand, I can’t be telepathic or clairvoyant; there must be a limit to what I can know, and whether my friend had told the truth as they knew it, or had actually told the truth truth, seems to be past this limit. Plus, having to decide between correct and incorrect beliefs for every statement anyone ever makes about themselves seems overly cynical. On the other hand, it is true that people often have incorrect beliefs about themselves, particularly ones that give a more generous picture, in this case, that they are more “rational” than they actually are. Moreover, I know this from reading papers in cognitive bias, and have had enough personal conversations to observe it occurring multiple times.

Personally, I lean towards the position that I should have known, or at least should have doubted the veracity of the statement. At least, I do now that I’ve experienced this whole episode, and I will keep an eye out for these situations in the future. As for the episode itself, I do want to support my friend in their pain, and I do wish something else had happened. In that sense, I’m sorry and I’m regretful, but I still don’t think that I did anything wrong.

EDIT 2013-08-11: It occurred to me that intentionality seems to have nothing to do with regret. Either the perpetrator knew the victim will be hurt, and had therefore deliberately acted to hurt the victim (even if it is the lesser of two evils), or the perpetrator did not know the victim will be hurt, and had therefore chosen as well as they could have. Neither case seems to fit the template of someone who should be regretful, although apologies may be necessary in both cases. This suggests that either regret (or lack thereof) does not depend on intentionality, or the whole concept of regret is faulty.

Regardless, the passages about responsibility still hold, although personally I think both concepts of regret and responsibility are incoherent.

Defining Objectification

I want to discuss an interesting example of objectification. The point of this post is not to show that the incident is not an example of objectification, but to encourage crisper and more nuanced divisions between what is objectification and what isn’t. I will start with the original behavior, then describe why one might consider the behavior objectifying, then point out gray areas in the reasoning which goes against intuition.

Somewhat ashamedly, I was actually the “perpetrator” of this incident. Instead of repeating exactly what I said, however, I’m going to expand on the scenario. Let’s say that I know someone through reading their blog, enough to know their personality and thoughts. From that, I find that their intelligence, desires and life choices has artistic/aesthetic appeal, and therefore think of the author as a work of living art. Is that objectification?

I asked a friend this question. She told me that yes, it is objectification, and as explanation linked me to this blogpost on the Pervocracy, which offered a simplified definition (emphasis in original):

Objectification is focusing on a person’s usefulness to you with total disregard for their desires. In the context of compliments, it’s not saying “You turn me on.” It’s saying “You turn me on, and whether you want to turn me on is utterly irrelevant."

Saying “nice ass” to a person who’s deliberately wiggling their ass at you is a compliment; saying “nice ass” to a person who’s just walking by is objectification. “I want to sleep with her” is expressing desire; “I’d hit it” is objectification. “You’re sexy” is nice to say on a date because it’s a compliment; “you’re sexy” is hideously undermining to say at a business meeting because it’s objectification.

These examples suggest that the definition should be further qualified by adding the phrase, “when they have not given you explicit consent” – setting aside whether non-verbal behavior could be considered consent. Back to my incident, this assumes (let’s say correctly) that the author of the blog did not intend their audience to appreciate them as art. By thinking of them as art, without their explicit consent, I am therefore objectifying them.

There are two unintuitive implications of this logic. The first one has to do with the features with which I’m objectifying the author, namely, their intelligence and life choices. These are not the usual features for objectification and, crucially, are things that people consider crucial parts of personhood. It would therefore seem that by focusing on exactly the things that make a person a person (without consent), I am still objectifying them.

The second unintuitive implication focuses on the fact that I don’t know the author, but have only read their blog. Let’s say that, a couple days later, I found out that the blog is actually a work of fiction, and that the real author had written it for their own amusement (that is, I still don’t have consent to admire it). My actions haven’t changed, and in fact now I could never have gotten the fictional character’s consent. Intuition suggests that I am still objectifying something – but it’s unclear whether it is possible to objectify fictional characters. And if the answer is that yes, it’s possible, how is that different from any the analysis of any character in any novel?

Reflections on Wittgenstein

I just finished David Stern's introduction to Wittgenstein's Philosophical Investigations, and my mind got blown in a non-minor way. I want to share some of the thoughts that went through my head while going through the book. I am not a philosopher, and I didn't read the original text (English or German), so I can't say I am representing Wittgenstein's views. But what I can do is to play both the role of what I think I read, and how I respond to that those particular ideas. This will be presented as a short dialog between a devil's advocate (indented) and a god's advocate, where the former takes a skeptical position. The devil's advocate should be taken as one would Zeno in proposing his paradoxes: he is trying to show how something that "obviously" happens as an impossibility. The god's advocate will then propose explanations as solutions.

---

It is impossible to learn a language. Consider how we understand a new word: we look it up in a dictionary, or ask someone for a definition. The definitions themselves are words, however, which means that the learner needs to already know some words in order to understand this new word. This is true of all words - all their definitions depend on knowledge of other words. In order to learn a language, at least one word must be learned first, but learning it already requires partially knowing the language. Thus it is impossible to learn a language.

Of course, words don't have to be learned by definition. The teacher may point to a car and say "car", or may wave a fork in front of the baby and say "fork"; nouns could be learned in this way. Similarly, the teacher can repeat a verb while performing a motion, or repeat an adjective while pointing to successive objects that the word describes. This method of teaching avoids words, and so avoids the need for a priori knowledge of the language.

The problem with this approach is that impossibility covers not only language, but all communication. When the teacher points to a car and says "car", how does the learner know that the word "car" is the object pointed to, and not the act of pointing? The act of pointing itself requires knowledge that it is only a reference, not the object itself - prior knowledge that the learner does not have. Repeating a word may be used to indicate subtle differences, that the learner believes they have not yet learned to distinguish. Even gestures of affirmation or of denial - nods and shakes of the head, for example - has meaning which can only be explained through additional communication.

Example-based learning - such as pointing to red objects for "red" - has an additional problem of induction. For any finite set of examples, there is an infinite number of patterns that can describe those examples. 1, 2, and 3 may describe the set of natural numbers, or the set of real numbers, or the set of all glyphs, or the set of all objects.

There is always the possibility of misinterpretation for any communication. This gets worse with interaction units that do not represent concrete objects or actions. The verbs "think", "feel", and "remember" has no demonstrable behavior, and one cannot point to "imaginary numbers". These concepts must be transmitted through existing common ground, and since that does not exist, communication is impossible.

Common ground is necessary, but it is a mistake to assume that common ground must be some form of communication. Any two strangers, in any culture in any period of history, already have a common ground: their shared evolutionary history.

Any two humans, when they communicate, already share 3.5 billion years of ancestral cohabitation on earth. Our physiology and psychology have been shaped by common forces, leading to similarities before even the first grunt. Our brains interpret - and misinterpret - perception in the same way; we process information through similar algorithms with similar biases. When a teacher waves a fork, the learner is biologically programmed to pay attention to the movement. In fact, this behavior is so primitive that it is a shared trait between a large portion of animals. We also associate and cluster stimuli that occur together, sufficiently so to mistake the ring of a bell for the presence food - and perhaps the audio signal "car" for a wheeled vehicle. Again, this is common ground with many other animals.

Other traits are more recent in evolutionary history. A number of vertebrates - cats, dogs, great apes, dolphins - are also social in nature, and our brains are also adapted for such an environment. We are biased to mimic other people's behavior, and project ourselves into their position to understand them. At least a partial understanding of facial expression is inborn, allowing infants to replicate certain expressions. There are theories which hypothesize the hard-wiring of stronger forms of communication structure, but it is clear regardless that common ground for communication exists. The information processing commonalities above, together with the correct assumption that the teacher operates in the same way, allows the listener to infer the meaning that the teacher intended.

It goes without saying that this shared evolutionary history does not rely on further prior common ground. It can therefore safely serve as the foundation for the building of communication and language.

This explanation of common-ground puts the burden of communication on the brain, and therefore leaves out one thing: precision in communication. For one, evolution does not account for everything in a particular brain; its structure is also determined by the specific genetic inheritance as well as the environment in which the brain matured. There is no guarantee that these differences will keep the biases for communication intact. Even if the neural machinery were all there, these differences make it impossible to recreate exactly what the speaker meant.

The more fundamental problem, though, is that brains are fuzzy. People not begin with definitions of words they want to communication, but general ideas that they themselves cannot define. All that exists in the brain are approximations and conglomerations of previous experiences. "Humans" are not "feather bipeds with broad nails", but some incoherent mixture of all humans the speaker has seen. This concept cannot be transmitted through any communication, language, gesture, or otherwise. What does gets communicated is itself misinterpreted by the listener for a different mixture of people. What two people call "human" may not in fact be the same thing at all.

All that occurs during communication is a double illusion of transparency, both sides thinking they understand the other, but neither getting the point across.

Brains are probabilistic, but so is the world! It is a fallacy to assume that communication needs to be precise exactly; it is sufficient for it to be precise enough. Precision is a double-edged sword: too little precision and there remains ambiguity, too much precision and the communication cannot be generalized. Language is learned and used in the real world, where nothing is clear cut. It is in fact a power of communication to capture these ambiguities.

That language is ambiguous doesn't mean that language is unlearnable. Language is not learned as a whole, but slowly, piecemeal, over a long time. The first word doesn't need to be precise - and as pointed out, it can't be. All it needs to be is a first approximation, and this approximation can be refined over time. The fuzzy concepts between the speaker and the listener do not need to match up exact, but just needs to have sufficient overlap. As long as this overlap is precise enough for the world, then communication is meaningful.

Most of the world may be ambiguous enough for communication, but not all of it is. That two speakers can get meaning overlap is not good enough. From whence does the logical calculus of mathematical symbols?

---

The first arguments from the devil's advocate is somewhat close to my understanding of Wittgenstein. Given that most of the counter-arguments are made decades after Wittgenstein's death, I don't know how much of it was known to Wittgenstein. The idea that human physiology and psychology has such unescapable influence on everything was a new thought to me. A smaller version of the idea, that no one sees an object/event in the same way, has been pushed on me before, but this is different. It suggests that even concepts we find "objective" - for example, the maxim of Ockham's razor - may be the result of our evolutionary history (although a Bayesian explanation exists). I have been occasionally interested in how cunning linguists propose we establish communication with aliens. Most schemes begin by establishing numbers, then showing mathematical concepts. But how does mathematics arise from probabilistic biology?

Generative Protection (aka. Graduate School in Midsight)

I feel like I should talk about grad school and how my fourth year has somehow crept up on me, but really what interests me is the idea of generative protection, so I'll talk about that and use examples from grad school to illustrate it.

I first came across the idea of generative protection - or more generally, generativity - while I was working in Web Communications back at Northwestern, in 2006. We handled the website redesign for Northwestern Magazine, and one article I had to check was Elizabeth Blackwell's Redemption. The article was about Dan McAdams, a Northwestern psychology professor doing research on how people tell their life stories. One trait he points out is generativity, which is a measure of how much people want to leave a legacy. At the time, the only thing I noticed was that generative people also tend to be narcissistic. About a year later, I came across an article in the New York Times, This is Your Life (and How You Tell It). That article focused more on telling life stories and how it is healthy, but one quote about generativity stuck with me: "Often, too, [generative adults] say they felt singled out from very early in life - protected, even as others nearby suffered."

That sentence put words to an idea I've had since high school. An episode from 2004-01-16 in my journal, when someone asked me how I did in my chemistry exam and it was better than the scores they've heard so far, I wrote, "I knew, and I kind of felt sorry, like survivor's guilt, since every did so poorly but I was unscathed." This feeling was touched on in an earlier blog post about grad school. A month later, a friend asked me why I think I'm not good at taking compliments, and I replied:

I think my reaction to compliments comes from not being able to return the compliment. This happened a lot in high school and early in college, when I would get really good grades without really trying. Inevitably someone would ask me what I got, and after telling them they would say good job or something similar. But I know intuitively that they didn't do as well, so I feel guilty about it. Kinda like survivor's guilt, I guess. I've gotten better at just saying thankyou though.

I used the word "guilt", but the feeling was never explicitly negative. If I had to explain it, I would say that it's a sort of puzzlement - about why other people didn't do as well as I did, about why people find things so difficult while I have barely exerted myself. It was only recently that the phrase "generative protection" came to mind, but it conveys how I feel very well. It was as though I am detached from the situation in some way, so hardships that affect other people only pass through me.

The idea of generative protection came back to me at the end of last year, after I worked to pass my prelim that summer. The previous post on grad school might suggest that this feeling of easy accomplishment would have completely disappeared by then (and more so now, another year of the PhD grind later); this is true with research, but not with grad school in general.

In research, even by the first semester, I was feeling the full force of the impostor syndrome. So named because people feel like they're merely faking it, grad school is an environment that pumps out these kinds of people. As a result, every grad student thinks everyone else is doing better than they are, and no one feels like they know what they're doing. In a lab with three senior students, who seem to talk knowledgeably about their research areas, I was understandably intimidated. The funny thing was, after knowing them a little better, I learned that they were also intimidated by me, as I was quiet and always seemed to be working. It took me another long while before I understood that I was as smart as other people in the lab, that we were good at different things, and that we all tend to only notice the times when other people were smarter than us but not vice versa. This depression and later rebound in confidence fixed my feeling of generative protection. I now have a healthy, and hopefully relatively objective, view of my abilities and my own research.

But being a grad student is more than about research; it is also about being able to strike that balance between work and everything else. There are, I think, three reasons why this balance comes easily to me. The first is that I'm not afraid to take time off. I spent three of the last four weekends away from Ann Arbor: the first was part of a week-long bouldering trip to Georgia, while two more weekends were spent in Kentucky. I do feel slightly ashamed that I'm not working, but not enough to stop me from going. I am, of course, writing this post when I could be reading papers. The second reason is that I find other non-research grad school activities to busy myself with. I am the secretary for the computer science graduate students group (CSEG), so I have a non-passive role organizing events for the department. This semester I'm also an engineering teaching consultant (ETC), so I spend time observing and giving suggestions to teaching assistants. Doing "work" for these roles gives me a break from research without inflicting too heavy a sense of guilt. The final reason work-life balance is easy is that, to be honest, work is fun. I enjoy separating theoretical confounds and laying down theory for my research, and to some extent am willing to spend "play" time doing so. I've previously mentioned the spars with my dad about the work-play distinction; my relative lack of such distinction greatly reduces how stressful I feel. Plus, as Larry Birnbaum said, one doesn't have to be brilliant all the time; if one is brilliant ten minutes a day, that's already pretty good.

In truth, the work-life balance issue isn't what makes me feel protected. I have yet to talk to a grad student who truly feels that their work is destroying their non-work life. I wrote the previous paragraph because I felt like humblebragging, but also because I promised I would talk about grad school. What makes me feel protected is that I am still in grad school at all. In the past year and a half, I know four people who left grad school without their (PhD) degrees. I only know two of them with any depth, but both of their reasons for leaving are the same: they are not sure whether grad school is right for them. Keep in mind that this is after three years into the program, after what most people consider the horrible second year; they have both passed their prelims (and will therefore likely get a Master's), and are capable of conducting independent research. For them, it wasn't a matter of ability, but a matter of desire. Neither of them have found a topic they are willing to invest time in, and they are not sure it's worth the time to continue banging their heads against the wall to figure it out. At least one of them is not sure whether it's the research topic (or lack thereof) or the research process that is putting them off, and feels it's better to try something new. Their stories made me realize how easily I have taken on the role of a grad student and how I feel grad school is, if not the right choice, at least not the wrong choice for me.

The descriptions I have given so far of why I might feel I am protected have been about events in my life. One could ask what it was that led me to excel in school and to be so sure that I want to teach at the university level. The only answers I have for these two questions are that "I am good at recognizing patterns" (which is something someone else said of me) and that "I am introspective". These answers do not provide any insight, at least not at this level, and I am not prepared to explore them at this time. Another path of questioning, one I am more interested in, is why I perceive myself as being protected. Equivalently, one might ask why I don't feel as though I have tried very hard in my accomplishments. After all, generative protection is a subjective feeling, not an objective fact; the same event of remaining in grad school could be interpreted as the result of hard work and perseverance. I spend a lot of weekends coding or writing papers, and evenings are often spent sitting at coffee shops exploring the theoretical foundations of my work. Given that I do invest time in research (or climbing), why do I still feel shielded from the difficulties of life - that, to quote from Atlas Shrugged, I've "never suffered"?

I don't have a clear answer to that question, but I do have two related hypotheses. The first is that, once I have accomplished something difficult, that task seems much easier in hindsight. The closest approximation to this idea is what education psychologists call the curse of knowledge. It describes the phenomenon where experts - people who are good at a particular task - find it difficult to explain how to perform that task to novices. The underlying reason for this curse is that expertise changes the neural pathways in the brain, making what previously required conscious thought into something that is automatic and instinctive. For me, the same mechanism may lead to a strong myopic bias, leading me think that the task was never difficult, despite the memory of how I struggled to accomplish it in the first place. I had tweeted this idea some months ago: "It turns out that - for someone with a pretty huge ego - I tend to trivialize my accomplishments."

The second theory is encapsulated by this quote from the climber Adam Ondra in the film Progression, when he compared himself to Chris Sharma: "I think I'm basically weak." Ondra was comparing their ability to do strength-based climbing moves, in which there might be a legitimate difference in their ability. Objectively, however, Ondra remains one of the strongest (if not the strongest) climber in the world; his accomplishments alone is strong evidence that he is not a weak climber. I have come to call this the weakness mindset: the idea that there is nothing special about our ability despite being extremely competent. The perception of weakness, together with my continued survival despite that weakness, leads to the conclusion that I am protected. A second implication of this belief is that I must not have worked very hard or trained very long, as otherwise I would not be weak. This elegantly explains both the feeling of protection and the feeling that no effort was exerted.

My suspicion is both the hindsight explanation and the weakness mindset are expressions of something deeper, a get-it-done-at-all-cost mentality that makes any effort worthwhile. That, however, is the subject of another post.

Postscript: There are at least two omissions in this essay, which were realized only in the process of writing (hence, an essay). First, I realized that there are two ways to define the lack of suffering: that of not having worked hard, and that of not having encountered difficult external circumstances. This ambiguity in the meaning of "suffer" is important, as it is the quote from Atlas Shrugged that first inspired this subject. Second, I acknowledge that there is no immediate connection between not exerting oneself and feeling protected. Their relationship will have to be cleared up at a later date.