Of the subtle things in life, status signaling is one of the subtlest. It is mostly a delicate art refined in the forging fires of one-upmanship (and perhaps envy), but it can become quite unpleasant in the hands of brutes.
So what is status signaling? Well if I am earning a lot more than you, or went to a better school than you, or perhaps can stake some claim to professional success, I will need to signal that in some way, lest you think you’re better than me.
There are a couple of things about status that one needs to carefully consider before we get into status signaling. Status in a varied society is not a completely ordered set. There is not just one parameter by which you can compare the statuses of two people. For example, a rich person is not necessarily better than an MIT professor. However, an MIT professor in a particular field may be considered to be “better” than a professor at a lesser known school who works in the same field.
This, too, is not the complete picture. Some communities do give greater importance to some parameters over others. For instance, my own community in India gives much more importance to wealth than academic achievement. Hence, status may be thought of as a weighted sum of all parameters, and these weights vary amongst communities and cultures.
Secondly, status signaling is mostly a defensive strategy, and not an offensive strategy. If my social group already accords my a high social status for my unique talents and personality, and I do not feel that another person has been accorded a higher social status than me, I will mostly be comfortable, and will not feel the need to compete with another person for status. However, if my group accords me a lower status than someone else, or if someone slights me and hence challenges me to a status duel, I will feel a need to somehow pull myself up (or maybe pull them down) in order to gain higher status than them.
As an adult, I spend a lot of my time watching other people signaling their status, or perhaps doing some signaling of my own. Such signaling is mostly subtle. If I went to reputed school for my education, I cannot just bring it up right away. I’ll need to find the right opportunity to bring it up: maybe when the conversation meanders to the topic of education, I can casually talk about how I had a terrible time in college. This of course would lead to “where did you go for college?”, in which instance I would bring it up. Some people may casually slip in where they went for vacation, what senior administrative managerial position they occupy in their company, how they once beat the odds and got that very coveted job, etc.
The delicate art of signaling, however, can get less subtle in the hands of brutes. I once saw two math professors compete for status by comparing the scores they got on some standardized exams two decades ago. I’ve seen multiple students from reputed institutes in India bring up their entrance exam ranks in their very first conversations with me (I’ve seen profs do that too). I’m sure that brutes may also signal wealth and professional achievement in a similar manner, although I do not have real life examples of these sort.
What is perhaps even more interesting is not status signaling, but status slapping. What is status slapping, you ask? I’d thought of a similar concept myself a couple of months back, but then I came across Eliezer Yudkowsky’s comment on slatestarcodex that perhaps expressed it much better. If society thinks that you have a status , and you try to convey that your status is , people around you will push you down/make fun of you, etc until you begin to accept that your status is indeed . Consider the following example: someone in my college cohort did very well on a standardized exam in India. Everyone was suitably impressed. Then she said something to the effect of “I think I have the potential to become a tech genius like Ironman”. Predictably, this led to a lot of derision until that person accepted their lower “true” status.
Another aspect of status slapping/signaling is status by association. If you signal that you have higher status than me, I can remind you that there are people who have even higher status than you, so that you don’t feel all high and mighty. For instance, if you casually let slip that you went to Berkeley for grad school, I might bring up the fact that I had a close friend who went to Harvard last year. Hence, I know people that “are better than you”. Why is this a successful form of status slapping? Even though I know someone who went to Harvard, I myself remain where I am! Why does bringing up this overachieving friend reduce our mutual status gap? Maybe status can also be earned by association. Although going to Harvard/being rich/being athletic may give me direct social status, being a spouse/friend/family member of someone with high status may also accord some secondary status to me. This feels weird in our supposedly individualistic societies. However, it exposes the fact that we still possess monkey brains, and status by association is a real thing.
It is important to note that status signaling is a lost battle for most people. If you are rich/well educated/etc, you are likely to socialize with people who enjoy the same status as you, if not more. For instance, if I went to Yale and joined a law firm right after, I am likely to work with other well educated college graduates, perhaps some from Harvard, who may go on to do much better than me. Hence, status signaling will mostly be a lost battle for me in the long run. However, status signaling does not affect those people (as much) who accept their status. If I accept my position in the status hierarchy and do not try to compete with another for status, I will mostly be left alone. Everyone I know who refuses to status signal actually has a much better time socializing, fitting in, etc.
So what should be the best strategy for life, as far as social signaling is concerned? Should I just stop signaling status? Sure. That plan should work for most people…..until the next jerk who comes along and signals their superior status. Faced with such a situation, we may feel an irresistible urge to either challenge them to a status duel, or perhaps pull off a “status by association” move. I would perhaps give some zen advice on how not to care about status, and that we’re all stupid mortals anyway, etc…but this would run directly opposed to our fundamentally simian brains that have been hardwired to indulge in status challenges for literally millions of years. Can we subdue our monkey brains? Can we not care when someone of a supposedly higher social status slights us? Can we just keep learning and growing forever, exploring our fascinating universe and ourselves, and not competing for status?Thus ends my status signaling post on status signaling.
Let me detail some of the many ways in which I am basically a hypocrite.
I am a “liberal”. Does that mean that I fight for women’s rights? Do I work tirelessly for the downtrodden? Well I got into an argument with a family member once in which I said that men and women deserved equal professional opportunities. I sometimes post articles on social media when I’m particularly “disgusted” by women not getting a chance. A lot of people see it for what it is- a stab at the social applause meter.
However, let us imagine a better version of me. Imagine a (slightly better-looking) version of me who went on long marches advocating for equal pay for men and women, gave money to the poor, etc. I would probably do all of that, and then expect some social capital out of it. Although I’d be discreet enough to not bring it up myself in conversations, people would eventually “come to know”, and then they’d think of me as passionate about equality of justice, etc. Come to think of it, even this slightly better version of me is not that great.
Well let’s imagine an even better version of me (who’s even better looking). I maintain strict anonymity, but work really hard to serve the marginalized sections of society. I go on long marches (perhaps wearing a Guy Fawkes mask), and distribute a lot of my income to the poor who I think have better use for it than I do. Although people don’t really know my true identity, I feel pretty good at the end of the day. A true savior. The closest thing to Batman a baniya from Kolkata can get. Is this guy “good”?
Moloch is probably the word/feeling that most closely resembles what this much better version of me is trying to do. “I will defend the rights of all the marginalized sections of society. And I will do so because I matter, and my chosen actions are exactly what are needed to correct these evils.” The sheer arrogance of it. What if going on marches and redistributing my income are not what is needed to cure these problems?
If I really wanted to help, I would have made an effort to discover what actually helps. And what actually helps is often counter-intuitive, and can only be found after experimentation. For instance, Abhijit Banerjee discovered that it was very difficult to convince people in India to have their kids take the Polio vaccine. However, when they started a policy of giving away 2 kgs of rice free after administering the vaccine, this relatively inexpensive intervention convinced hundreds of thousands of people to buy much more expensive tickets, and brave hours and hours of journeying to travel to the polio administration centers, kids in tow.
What actually helps in improving the general condition of people is not redistributing wealth to the poor, but allowing the rich to hoard it (Capitalism)! This is perhaps one of the most counter-intuitive ideas in history. If you allow the rich to hoard wealth, they pump in so much money into a country’s infrastructure that the poor are bettered as a consequence. Who’d have thunk!
Did this much-much better version of me care about finding out what actually helps? No. He was mostly invested in an ineffective cocktail of arguing with family members, sharing updates on social media, and perhaps going on marches and redistributing income.
Most people don’t really want to do anything! Whether it be helping others, doing meaningful research, basically anything at all! They mostly want to be thought of as doing something meaningful or important. If I can shut down a “male chauvinist” uncle at a family gathering, I will have emancipated all women alive. Because it is I, the emancipator of women, that stands at the crossroads of history, on whose actions the future arc of humanity depends. What if I am basically a stupid and inconsequential bystander, who is too stupid to realize this?
What if asking that uncle to shut up is not the best intervention? In fact, I will only have further alienated him. Instead of taking the higher moral ground at family functions, what if I look up ways that actually work to emancipate women? What if I help my mother cook? What if I *really listen* to her with full attention, as she tells me stories of her past? What if I devote more time and effort to what the women in my life want me to do to help them? What if I stop assuming that the only way that women can be made equal to men is if they’re doing the same jobs, because I, me, myself think that way? What if it is not my f@#king place to make that choice for them? What if I just shut up, listen and learn?
One of my favorite things in life is to discover counterintuitive truths. Hence, I was happy to recently learn about mimetic desire, as discovered by the French polymath René Gerard.
Let me reproduce some real zingers from the article:
We borrow our desires from others. Far from being autonomous, our desire for a certain object is always provoked by the desire of another person—the model—for this same object. This means that the relationship between the subject and the object is not direct: there is always a triangular relationship of subject, model, and object. Through the object, one is drawn to the model, whom Girard calls the mediator: it is in fact the model who is sought.
Mediation is external when the mediator of the desire is socially beyond the reach of the subject or, for example, a fictional character, as in the case of Amadis de Gaula and Don Quixote. The hero lives a kind of folly that nonetheless remains optimistic. Mediation is internal when the mediator is at the same level as the subject. The mediator then transforms into a rival and an obstacle to the acquisition of the object, whose value increases as the rivalry grows. This is the universe of the novels of Stendhal, Flaubert, Proust and Dostoevsky, which are particularly studied in this book.
What Paris wanted, then, was not Helen, but to be a great king like Agamemnon. A person who desires seeks to be like the subject he imitates, through the medium of object that is possessed by the person he imitates.
This was, and remains, a pessimistic view of human life, as it posits a paradox in the very act of seeking to unify and have peace, since the erasure of differences between people through mimicry is what creates conflict, not the differentiation itself.
It is the last quote in particular that seems like a fundamentally counter-intuitive fact about the world. I was always taught that it is our differences that create strife and conflict, and that if we could reduce the differences amongst ourselves, we could be peaceful. However, it now seems clear on reflection that conflicts are the harshest between people that are similar or close to each other. This is because, at least according to mimetic theory, all conflict is a desire to become someone- someone who you envy. You desire what they have. And hence you’re ready to maim them, insult them, somehow occupy the exalted position that they currently command.
If we could accept our differences, and accept that we are unique and incomparable with everyone else, we would perhaps have peace. It is this acceptance of our differences that would reduce conflict. However, we do not consider ourselves to be fundamentally incomparable with people that we envy or despise. We want to become them, and think that we indeed can become them. And it is in this act of aspirational mimicry that we shatter any hope of peace or contentment.
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:
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.
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.
Frontopolar cortex: related to meta-awareness (awareness of your attention, and not just the object of your attention)
Sensory cortices and insula: related to body awareness
Hippocampus: related to memory processes
Anterior cingulate cortex (ACC), mid-cingulate cortex and orbitofrontal cortex: related to self and emotion regulation
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:
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.
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.
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.
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.
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.
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 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 with the property that for any other set , we have the property that . Of course one would have to define the concept of outer measure 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 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 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.
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.
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.
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.
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
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.