An Unquiet Mind

Kay Jamison ends An Unquiet Mind not with recovery but with gratitude: gratitude for a mind that, even in its most dangerous states, was also the source of everything she valued about herself. I thought about that a lot while watching N go through what she went through. The same mind that was constructing elaborate systems of meaning from Facebook posts was also, a few years later, doing rigorous theoretical physics work. The illness and the gift were not separate things.

N is a close family member. I was near enough to watch the whole arc.

Bipolar type 1 is frequently misunderstood as a mood disorder in the colloquial sense: extreme happiness followed by extreme sadness. That framing is inadequate. In its most severe presentations, bipolar type 1 involves psychosis: a genuine break from reality that is neurologically indistinguishable, in the moment, from the inside of a healthy mind. This is what makes it so hard to catch and so hard to treat. The person experiencing it has no internal signal that anything is wrong.

N's first symptom, as she later described it, was the conviction that people were listening to her through her phone and laptop. To everyone around her, she seemed normal. She was always a little unconventional, always working on something large and abstract, so the increased intensity, the pacing that clocked 10,000 steps on an average day, read to her family as productivity. Intellectual obsessiveness in someone with a strong scientific background does not look obviously different from early psychosis. That is one of the cruelest features of the illness.

What was actually happening, neurologically, is now reasonably well understood. Bipolar type 1 involves dysregulation of dopaminergic signaling, particularly in the mesolimbic pathway. During manic and psychotic episodes, dopamine transmission is excessive. The brain's pattern-detection machinery, already one of its most powerful features, goes into overdrive. Connections form between things that are not connected. Significance accrues to things that are not significant. In N's case, Facebook posts from a person she knew began to carry the texture of direct communication, of coded messages meant specifically for her. She was writing code during this period and using those imagined messages to validate her work, checking what was right and what was not against signals that existed only in her interpretation of them.

She wrote code that is still publicly visible on GitHub. The work is not without insight. The underlying mathematical intuition was real. But it was untethered from the error-correction that rigorous science requires, because her error-correction system had been replaced by a private system of signs and confirmations.

A friend, K, was the first person N told. N mentioned, in what she likely experienced as a normal disclosure, that this person V was communicating with her through Facebook posts. K responded with extraordinary gentleness. She sent an email to V to confirm that he was not doing this, and then told N, carefully, that what she was experiencing was a hallucination. It did not get through. This is not a failure of communication or of trust. It is simply what psychosis does: the alternative reality is not experienced as alternative. It is experienced as reality, with the same epistemic weight as anything else the person knows.

What did get through, eventually, was contact. K reached N's sister. Her sister told her parents. Her parents took her to a doctor. There followed an extended period of deeper psychosis and then treatment, a process that is neither linear nor clean, and that I will not reduce to a paragraph because it deserves more than that.

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The science of what treatment does is worth understanding. Mood stabilizers like lithium, still after decades among the most effective interventions for bipolar type 1, work in part by modulating intracellular signaling cascades downstream of dopamine and serotonin receptors. They do not simply suppress the highs. They appear to affect neuroplasticity, to slow the kindling process by which untreated episodes make subsequent episodes more likely and more severe. The longer bipolar disorder goes untreated, the harder it becomes to treat.

Early intervention is not just clinically better. It is neurologically better.

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N is now doing theoretical physics again. She works by building mathematical frameworks for things she has cared about since long before the illness. The mind that found hidden messages in Facebook posts is the same mind that finds signal in the universe: the same pattern-detection machinery, now calibrated.

Jamison writes that she would not give up her illness if she could, not entirely, because she cannot untangle it from who she is. I do not know if N would say the same. But watching her now, the continuity is visible. The illness did not interrupt the story. It is part of it.

Mental illness at the level N experienced it is not a character failing, not a lapse of discipline, not the result of too much sensitivity or too little. It is a brain doing what brains do, finding meaning, making connections, maintaining the self, with a biochemistry that has gone out of range. The appropriate response is the same as for any other organ that has gone out of range: diagnosis, treatment, time, and the refusal to let the episode define the person.

N did not let it define her. I watched her not let it.

The I Ching and Synchronicity

I have a small ritual before decisions that matter. Three coins, thrown six times. The resulting pattern is a hexagram, one of sixty-four that tells me something. Not about the future. About the present state of my own thinking. The I Ching is, at its mechanical core, a sampling device. The traditional yarrow stalk method generates lines through a procedure weighted so that not all outcomes are equally likely. The coin method is simpler: three coins, each heads or tails, combined to produce one of four line types. Do this six times and you have drawn a point from a space of sixty-four possibilities. A 6-bit binary string. A hexagram.

What strikes me about this is not the mysticism that has accumulated around it over millennia, but the structure underneath. You are not choosing. You are sampling. And the question you bring to the coins acts as a constraint on how you interpret what you draw, which means you are, without knowing it, doing something very close to what Edwin Jaynes spent his career formalizing.

Jaynes argued that probability is not a property of the world but a property of your state of knowledge. Maximum entropy (his central principle) says this: given what you know, assign probabilities that make the fewest additional assumptions. Don’t pretend to know more than you do. The distribution that satisfies your constraints while assuming nothing else is the honest one.

This is not a mystical idea. It is a discipline. It is, in fact, a form of intellectual honesty that is surprisingly hard to practice, because the mind wants to fill gaps. We over-specify. We build models that know too much. Maximum entropy is the corrective — a formal way of staying inside the boundaries of your actual knowledge.

The I Ching is the same corrective, applied differently.

When you throw the coins, you are not asking the universe for an answer. You are asking yourself a question under conditions that prevent you from cheating. The randomness is the point. It breaks the loop of motivated reasoning. The hexagram you receive is a constraint; not on reality, but on interpretation. You must now find meaning within this shape, not the shape you would have constructed if left alone with your anxieties.

Carl Jung called the moment of fit when the hexagram lands and something clarifies synchronicity. Meaningful coincidence. A connection without causal chain. He meant it seriously, and I think he was pointing at something real, even if the metaphysics he reached for were the wrong container.

What actually happens, I think, is this: the external structure makes internal knowledge legible. You already knew something. The coins gave it a shape you could see. The synchronicity is not between you and the cosmos, it is between two parts of yourself, one of which needed a strange likelihood function to speak.

Bayesian updating with a very strange likelihood function. That is what the I Ching is. And that, I would argue, is not so far from what any good model does.

I don’t throw coins instead of thinking. I throw them when thinking has reached its edge… when I have done the analysis I can do and what remains is genuine uncertainty. That is the correct use of any probabilistic framework. You don’t reach for maximum entropy when you have strong prior information. You reach for it when you don’t, when the honest answer is that several possibilities remain live and you must act anyway.

The coins don’t resolve the uncertainty. They make me sit inside it long enough to hear what I already know. That is, I think, the masterclass. Not in prediction. In the discipline of not pretending to know more than you do and in the strange, rigorous, ancient art of making decisions anyway.

The Long Road to Understanding - Part III

If the first phase was curiosity, and the second was learning how to think, the third has been about learning how to work.

The change was not dramatic. There was no moment where everything suddenly became easy or clear. The way I approached problems stopped depending on who was guiding me and started becoming something I could reproduce on my own.

I began to notice patterns in how I made progress. When something felt confusing, it was usually because I had skipped a definition or was trying to move too quickly. Slowing down helped. Writing things out helped. Returning to first principles helped. These were simple ideas, but applying them consistently made a difference.

Over time, this became a method. Not a rigid system, but a way of working that I could rely on. I would start by grounding myself in the basic objects of a subject, understanding what they were and how they behaved. From there, I would work through problems, not just to get answers, but to see how the ideas moved. When something broke, I would trace it back rather than patch over it.

This approach carried across subjects. Linear algebra, probability, number theory. The details were different, but the process was the same. Progress was still slow at times, but it was no longer directionless. Each piece fit into something larger.

Alongside this, coding remained a constant. Where mathematics required careful construction, programming allowed me to test ideas quickly and build systems that did something tangible. The two began to reinforce each other. Math gave structure to my thinking. Coding gave it a way to express and test that structure.

What feels different now is not that the gaps have disappeared. It is that I know how to work with them. When I encounter something I do not understand, it no longer feels like a dead end. It feels like a signal to slow down and rebuild.

Looking back, the path has not been linear. It has involved false starts, resets, and long periods of confusion. But those phases were not wasted. They shaped the way I approach learning now.

I no longer think of myself as someone trying to catch up. I think of myself as someone building, layer by layer, with a process that holds.

That is what I carry forward.

Reasoning with sticks

One of the recurring patterns in my number theory study has been getting trapped in circular reasoning without noticing it. I read an explanation, restate it in my own words, and feel as if I have understood something. But when I try to justify the idea, the entire argument often turns out to be feeding itself.

This happened most clearly when I was trying to understand why Euclid’s Algorithm works. Textbooks say, “Replacing a pair $(a,b)$ with $(b, \mathrm{a }<mrow><mi\; mathvariant="normal">m</mi><mi\; mathvariant="normal">o</mi><mi\; mathvariant="normal">d</mi></mrow>b)$ does not change the gcd.” I kept trying to explain this using statements like “the gcd stays the same when you subtract multiples,” or “the algorithm preserves common divisors.” Both sounded correct, but both were really just the conclusion restated in slightly different language. Nothing in the reasoning actually began from a place that did not already assume the result.

The loop broke the moment I pictured the numbers as two sticks: one long stick of length $a$ and a shorter stick of length $b$. If you measure the longer stick using the shorter one, the piece left over after laying down the shorter stick repeatedly is exactly $\mathrm{a }<mrow><mi\; mathvariant="normal">m</mi><mi\; mathvariant="normal">o</mi><mi\; mathvariant="normal">d </mi></mrow>b$. Any stick that measures both $a$ and $b$ will also measure the leftover piece, because that piece is created by repeating the shorter stick until it no longer fits. The idea becomes physical at that point. It is not an abstract rule but a direct observation about lengths.

The reverse direction also becomes obvious. If a stick divides $b$ and the leftover piece, then by assembling the leftover pieces and full pieces of $b$, it will divide $a$ as well. The equivalence is suddenly clear, and the reasoning does not run in a circle anymore. There is a concrete starting point that does not depend on the conclusion.

I had a similar experience with linear Diophantine equations. I knew the statement: the equation $ax+by=c$ has a solution exactly when $c$ is divisible by $\gcd (a,b)$. I tried to motivate it by saying that combinations of $\mathrm{an}$ and $b$ somehow determine what is possible, and therefore the gcd must divide $c$. That felt intuitive but it was another loop. I was assuming the existence of the combination in order to justify the condition for the combination.

The picture that fixed it was again based on sticks. Consider all lengths you can create by cutting and taping together sticks of lengths $a$ and $b$ Those lengths do not appear randomly. They form a neat pattern, and the smallest positive one you can create is the gcd. Everything else is a multiple of that smallest value. If you want to create length $c$, it must fit into that pattern. If it does not, no rearrangement of the pieces will ever give you that exact length. This explanation begins somewhere real, so the loop disappears.

What I have learned is that circular reasoning often shows up when I keep everything inside symbols. Symbols can hide gaps because they feel precise even when the underlying logic is not. When I switch to a picture or an analogy, the reasoning becomes grounded, and the loop cannot sustain itself.

Now, when an explanation feels too smooth, I check whether it actually begins from a stable point. If it does not, I translate the idea into something I can visualize. Every time I do that, the reasoning stops circling and finally lands.

Also, here's a painting I made

Why Coding Came Easy (And What That Says About Math)

My coding journey started at 14, when I took computer science as an optional subject in school and learned BASIC. For my final project, I tried to build a simple car racing game. I got stuck trying to generate random obstacle positions and detect collisions and eventually switched to a Hangman game instead. Even then, something about programming clicked.

After school, I moved toward biology, but coding kept reappearing. I took a C++ course in college, then a bioinformatics course and a computational cognitive neuroscience course in graduate school. Over time, programming shifted from being an interest to a necessity. Modern biology, especially bioinformatics and large-scale data analysis, depends heavily on code.

I taught myself Python and R, and during my postdocs in computational biology, both became tools I used fluently. At that point, I was not just using them for my own work but also helping others. Coding had become a natural way for me to think and solve problems.

What has been more difficult to understand is the contrast with my experience in mathematics. Coding and math are often described as closely related. Both require precision, structure, and logical thinking. But my experience of learning them has been very different. Coding became usable and intuitive relatively quickly, while mathematics took much longer to develop into something I could work with comfortably.

My current view is that the difference lies in the type of abstraction involved. Programming often allows you to anchor ideas in concrete systems. You write code, run it, and observe what happens. The feedback loop is immediate, and even complex systems can be built incrementally from smaller, testable pieces.

Mathematics, especially in its more abstract forms, demands a different kind of engagement. The objects are less tangible, and the feedback loop is slower. Progress depends more heavily on internal consistency and precise reasoning without the same level of external grounding.

This difference became clearer when I encountered theoretical computer science. Topics like automata theory, formal languages, and the structure of computation felt much closer to mathematics than to programming. The ease I felt with coding did not carry over. Instead, I had to approach these subjects in the same deliberate way I approached math, building understanding step by step.

Looking back, the contrast is less about ability and more about where I started. Coding allowed me to operate effectively within concrete systems early on. Mathematics required me to develop a deeper level of abstraction over time.

That layer is something I am still building, but now with a clearer understanding of what it demands.

Learning Math: What Worked, What Didn't

Like everyone, I started learning math in school. I wasn't bad at it, but I was no prodigy either. I decided my path lay in biology and only returned to math in 2016. You can read about that journey in my previous post. Today I want to write about the how of learning math: what worked, what didn't, and what I wish I'd known earlier.

I think there is something I'd call a mathematical gaze, a style of thinking that some people access easily and others don't. Everything in learning math, at its core, revolves around developing this gaze. Another word for it is intuition.

What is mathematical intuition, exactly? Does it have anything to do with the real world? For a long time I was convinced that solving enough problems would develop it automatically. The truth is more complicated. Problem-solving alone isn't enough. You need a teacher who already has intuition and can show you how to think like them. That transmission from one mind to another is the only reliable way to generalize beyond the specific equations you've been drilling.

A related insight came to me while thinking about mathematical modelling. People in applied mathematics spend a great deal of time building models of real-world phenomena: abstracting out the parts they care about and expressing relationships between them. Finding the right representations is how they define success. To do that well, you need a solid grasp of the objects mathematics deals with and how they relate, and for that, there is no substitute for practice.

One trick I've found surprisingly powerful: asking which seemingly different problems are actually the same? The right mapping can turn an "impossible" problem into an easy one in seconds.

I also used to binge-watch advanced math lectures on YouTube to "build intuition." You might laugh, but I think it actually works. I'd go in expecting to understand less than 1% of what was being said. Even so, watching people with genuine mathematical intuition think out loud gave me something: a faint but real sense of how math is done, not just the pattern-matching of homework problems, but the branching, exploratory quality of real mathematical thought.

What I've found, in the end, is that for a determined but learner, there is a real path to mathematical understanding, intuition included. It takes only two things: practice, and a teacher who genuinely has the gaze.

My Mathematical Journey

Around early 2016, I decided to learn math. The trigger was a comment I came across about someone who had struggled with math but was able to rebuild their understanding through proofs. That idea stayed with me. I had always been comfortable with biology, and it became clear that a deeper command of mathematics would open up entirely new ways of thinking about it.

I started with enthusiasm but very little structure. Like many beginners, I jumped too far ahead and picked up a book on stochastic methods. That attempt did not go far. At the time, I was finishing graduate school, and the effort faded.

The real shift began during my first postdoc, where I worked with both a physicist and a biologist. My physicist advisor suggested I learn linear algebra and pointed me to Strang’s lectures. I supplemented this with visual material like 3Blue1Brown. That phase gave me an initial intuition for the subject, but it was still shallow. I was beginning to see patterns, but without enough precision to reliably work with them.

For a while, my approach remained inconsistent. I revisited calculus, explored different areas, and often tried to move ahead faster than my foundations allowed. In hindsight, the pattern was clear. I was prioritizing exposure over consolidation.

Around 2023, two things changed. I began a second postdoc at TIFR in Mumbai, and I started learning regularly with a close friend who had trained in physics. This introduced something I had been missing steady pacing and feedback at the right level. Instead of jumping topics, I focused on building depth.

I returned to linear algebra with more discipline, working through Strang’s lectures again and using problem sets to reinforce the material. This time, the concepts became operational rather than just familiar. I also began studying probability and statistics in a more structured way, following recommendations from faculty at TIFR. With consistent practice, I developed a working understanding of both.

Later, I explored number theory using Silverman’s A Friendly Introduction to Number Theory, on the recommendation of a professor. This was challenging in a different way. It required a level of abstraction and precision that exposed remaining gaps in my thinking. Working through it has been slow, but it has also been one of the most valuable parts of the process.

Looking back, the main change has been in how I learn. Early on, I chased exposure and intuition without enough grounding. Now I focus on building foundations, testing understanding through problems, and progressing layer by layer.

Today, I have a solid base in linear algebra, probability, and statistics, along with exposure to other areas. More importantly, I have a process that works. The trajectory is steady, and each layer builds on the last.

I continue from there.