Chapter three
A few years ago, in a phase of my life that the rest of this book has more or less prepared you for, I walked into a bookshop and had a small private crisis in the self-help section.
The crisis was not dramatic. It was the quiet, technical kind of crisis a software engineer has when he realizes a system he has been debugging for hours is, in fact, working exactly as designed, and the bug is somewhere upstream of where he has been looking.
I was standing in front of a shelf approximately fifteen feet long, organized loosely by promise. Books promising peace. Books promising calm. Books promising that I was, despite the evidence, enough. Books promising to teach me to honor my journey. Books promising that I could heal my inner child, which I had not realized was injured and which now, suddenly, I was anxious about. Books with one-word titles in lowercase. Books with three-word titles in capital letters. Books written by people on book tours. Books written by people who had recently been on book tours and were processing the experience.
I had, at this point in my life, read perhaps thirty of these. Possibly forty. I am not proud of the number. None of them had worked.
What I want to say carefully, because the temptation to be unkind to these books is enormous and entirely unhelpful, is that they had not worked on me. Many of them have worked on many people. They work on the kind of mind for which the language of self-help is a native language. That is a real and beautiful kind of mind. It is not mine.
My mind has the unfortunate property of treating sentences like "you are enough" as logical propositions. It asks enough for what. It asks enough by which metric. It asks enough compared to whom. It then notices that the sentence has not specified an answer to any of these questions, files the sentence under statements pending further clarification, and goes on being anxious. The book has done nothing to it, because the book was not written in a language it accepts as input.
I stood in the bookshop. I considered, for the hundredth time, the possibility that the problem was me. That the language of self-help was the only language available, and that my failure to be helped by it was a personal defect. That there were no other languages.
This was not true. I just did not, at the time, know that.
It turns out there is another language. It turns out it has been sitting on a different shelf, in a different section of the same bookshop, for several thousand years. It turns out it is, for a particular kind of mind, considerably more useful than the language on the self-help shelf, for reasons that I am going to lay out in this chapter, one at a time, with the dignity each of them deserves.
The language is mathematics. The chapter you are reading is, in essence, an argument for why mathematics, of all the unlikely candidates, is the right toolkit for the brain we diagnosed in Chapter 1.
I want to make this argument carefully, because the version of it that is easy to make, namely mathematics is rigorous and therapy is not, is not the argument I am making, and it is also not true. There are forms of therapy that are extraordinarily rigorous. There are mathematicians who are extraordinarily lost. The argument is not about rigor. The argument is about fit. Some minds metabolize feelings well. Other minds metabolize feelings badly, but metabolize structure well. For the second kind of mind, mathematics is not a substitute for emotional work. It is a translation layer, between an interior life that is too noisy to read directly and a notation that holds still long enough to be examined.
Here are the five reasons it works.
Reason one. Mathematics is precise where feelings are not.
When you tell a friend you are anxious, the word anxious is doing the work of approximately forty distinct internal states, all of which feel similar from the inside and which are, in fact, different machines. The anxiety that is your body responding to a real deadline is not the same machine as the anxiety that is your nervous system relitigating a conversation from 2014. They feel the same. They are not the same. They have different causes, different mechanisms, and different fixes.
Mathematics refuses this kind of conflation. It cannot. It has no available word that means forty things. Every symbol has one meaning, and the meaning is determined by the context, and the context is itself defined. When you write down what is happening to you in mathematical notation, the first thing the notation does is force you to distinguish between things you had been blurring. The anxiety that was a single word becomes, on paper, a function with arguments. The arguments turn out, on inspection, to be different in different cases. The single word was hiding a dozen different problems. The notation cannot help itself. The notation insists.
This is, for a certain kind of mind, an enormous relief. You did not know what was wrong with you because your only available label was a word that meant too many things. Once you have a notation that refuses to mean too many things, you can finally see the shape of what you are dealing with. You may not yet know how to fix it. But you can, at last, see it.
Reason two. Mathematics is unsentimental.
Mathematics has no opinion about you. It does not want you to feel better. It does not want you to feel worse. It does not have a podcast. It is not trying to sell you a course. It does not know your name, does not care about your story, has never met your mother, and would not be moved by your suffering even if it could be, which it cannot.
This is, again, for the right kind of mind, an enormous relief.
The trouble with much of the language available for talking about anxiety is that it comes pre-loaded with emotional charge. The words trauma, boundaries, healing, journey, growth, are not neutral words. They are weighted. They imply a particular posture, a particular kind of person speaking, a particular set of values you are expected to share before the conversation can usefully continue. For some minds, this weighting is helpful, because it creates a sense of belonging to a community of people who care. For other minds, the weighting is exactly the problem, because the mind cannot tell whether it is responding to the content or to the connotation, and so it suspects, correctly, that it is being managed.
Mathematics is the opposite. The integral sign does not care about you. The equals sign is incorruptible. When you write down P(A | B), the notation will not flatter you, will not patronize you, and will not pretend, for your benefit, that the answer is going to be the one you wanted. The notation just tells you what is true, on the assumptions you have given it. If you do not like the answer, the notation does not mind. It is happy to compute a different one if you give it different assumptions. It is not invested in the outcome. It is, in this respect, the most polite professional you have ever met.
Reason three. Mathematics is non-negotiable.
The anxious mind is, among many other things, an extraordinary negotiator. It will negotiate with any premise. It will negotiate with reality. It will negotiate with the people who love it, with the evidence in front of it, with the calendar, with the laws of physics. It will produce, on demand, a perfectly reasonable sounding argument for why the catastrophe it is currently rehearsing is the catastrophe that will, this time, actually happen, contrary to all available data.
The therapist's gentle but is that really true? is a wonderful question, and it works on many minds, and it bounces off the negotiator like a feather off a cathedral. The negotiator has been ready for that question since the cradle. The negotiator has prepared a paragraph.
Mathematics does not ask. Mathematics asserts. If you have stated your premises honestly, and the premises imply a conclusion, the conclusion is the conclusion. You can dislike it. You can be unmoved by it. You can write a long letter to the editor about it. The conclusion will still be the conclusion. There is no version of mathematics in which two plus two becomes, with sufficient effort, three. The negotiator, faced with this, has nothing to negotiate with. It can, of course, refuse to accept the conclusion. But the refusal is now visible as a refusal. The negotiator can no longer pretend it is being reasonable. The mathematics has, in the politest possible way, called its bluff.
Reason four. Mathematics is patient.
Therapists have schedules. Friends have lives. Partners eventually need to sleep. Mathematics is available at three in the morning, in your kitchen, with a pen and the back of an envelope, and will not be tired, will not be busy, will not have opinions about your texts, and will not require you to call ahead.
This is, frankly, the reason I survived several years of my life. There were nights, more than I would like to count, in which the only available adult in the building was a notebook full of equations. The equations were better company than they had any right to be. They listened. They held still. They did not move while I looked at them. They could be returned to, the next morning, in exactly the state I had left them in.
The patience of mathematics is, in some quiet way, the most underrated of its virtues. It is the only conversational partner you have ever had who will not be exhausted by the version of you that calls at three in the morning. It will not, in fact, even notice you are calling. The mathematics will be there in the morning, the same as the night before, holding still, ready to be examined again with whatever fresh eyes you have managed to bring it.
Reason five. Mathematics is yours.
This is, in my private estimation, the most important of the five reasons. The previous four are about what mathematics is. This one is about what it does to you.
When a good therapist helps you, the help is, in part, on loan. They lend you their attention, their training, their pattern recognition, their hour, their room. Some of what they give you, you do, over time, internalize. The best therapists make a point of working themselves out of a job by transferring as much of the toolkit into you as they can. But there is, inescapably, a portion of the help that runs through them and is replenished by them, the way a particular doctor refills a particular prescription. This is not a flaw in therapy. It is the nature of the modality. Some kinds of healing happen only in the presence of another human being, and there is no shortcut, and the people who try to find one usually end up worse off.
Mathematics is different. When you work out, for yourself, with your own hand, that the function called more has no fixed point, the working out is yours. The result is yours. The argument that produced the result is yours. Nobody can take it away from you. Nobody can revoke your access to it. Nobody can charge you, the second time around, for using it. You can carry it from your twenties into your fifties, from your kitchen into your hospital room, from your worst night into your best morning, and the math will be the same math, and the math will still be yours.
For someone whose childhood was, as mine was, an extended demonstration that the things you were allowed to have could be taken back at any time, this property is not a small property. It is the entire property. The thing I love most about mathematics is that, once you have understood a proof, no one alive can repossess it.
Now the necessary caveat, because the version of this chapter that pretends there isn't one would be dishonest, and a dishonest opening to Part two would sink the rest of the book.
Mathematics is not enough.
I want to say this with the same precision I have been demanding of mathematics. Mathematics can describe an emotion. It cannot feel one. It can model rumination. It cannot make rumination stop. It can show you, with unanswerable clarity, that the function you have been running on yourself for thirty years has no fixed point and therefore cannot converge. It cannot, by itself, get you to stop running the function. That part is on you. The mathematics is the diagnostic. You are still the surgeon.
There are also, I want to acknowledge, kinds of suffering that mathematics has nothing to say about. The first morning after someone you love has died is not a mathematical event. The afternoon you find yourself unable to get out of a chair is not a problem with a closed-form solution. The middle stretch of a long depression, in which everything is grey and the future is grey and the past is grey and the only thing not grey is the carpet, which is also grey, is not a place where calculus is, on its own, going to be very useful. I have been in all three rooms. I did not, in any of them, reach for a textbook.
What I reached for in the rooms was not mathematics. I survived the rooms because of a particular therapist, named Anna, and because of the work of a particular organization, called the Live Love Laugh Foundation, both of whom I will properly thank in Chapter 5, where their work has a chapter of its own and the right to be discussed at length. I want to be honest about this, because the version of this book that pretends mathematics alone saved me would be insulting to both you and them. Mathematics did not save me. People did. Specifically, the right people, found at the right time, doing the right work, after another kind of therapy, applied with the best of intentions in a much earlier context, had not been the right fit.
What mathematics did, in parallel and on a longer timeline, was something different. In the notebook, in the weeks and months and years after the rooms, I worked out what had happened to me, in a language I could finally read. The mathematics did not get me through the worst nights. It got me through the longer, less dramatic project of understanding what the worst nights had been, and arranging my life so that fewer of them arrived.
This is, I think, the honest case for the toolkit. It is not an emergency tool. It is a maintenance tool. It is what you reach for, in partnership with whatever else has been working for you, in the long quiet hours between emergencies, to slowly rebuild the system so that the next emergency is smaller, and the one after that smaller still, and the one after that, if you are very lucky and you do the work, does not arrive at all.
I want to close this chapter with one small demonstration, on the page, in real time, of what I am claiming the toolkit can do. Otherwise the rest of this chapter is a promise, and you have already been promised a great deal in this book, and you have a right to ask for something concrete before Part two begins.
Here is a feared outcome. I am going to use a small one, on purpose, because the technique is the same regardless of scale, and a small example fits on the page.
The feared outcome is that you have sent a slightly awkwardly worded email to a colleague, and you are now lying in bed at one in the morning, convinced that the colleague is going to think less of you for it, and that this lower opinion will, over time, cost you the project, the promotion, and eventually the career.
The anxious brain is, at this moment, treating this chain of events as approximately certain. The body is responding accordingly. The body does not know how to respond to a probability. The body only knows how to respond to yes this is happening or no it is not. The brain, lacking better information, has rounded the probability to one.
Mathematics, asked the same question, refuses to round.
Let us compute what the brain is actually claiming. Let p be the probability that the colleague even noticed the awkward wording. Be generous. Say p is one in three. Let q be the probability, given they noticed, that they formed a negative impression rather than ignoring it, as adults usually do. Say q is one in five. Let r be the probability, given a negative impression, that they remember the impression beyond the next forty-eight hours, during which they will read approximately two hundred other emails. Say r is one in ten. Let s be the probability, given that they still remember it, that it affects a concrete decision about your career rather than evaporating in the general background noise of office politics. Say s is one in twenty.
The probability your brain has been treating as essentially one is, on even moderately honest accounting, approximately one in three thousand.
Three thousand. The probability of being struck by lightning at some point in your life, in many countries, is higher than this. The probability of choking on a small piece of food at dinner tonight is higher than this. You are, statistically speaking, not in the slightest danger.
Now I want to say something carefully, because the version of this technique that pretends it has solved the problem is the version that fails. The calculation does not, on its own, make the anxiety go away. The body is still in the bed. The heart is still at ninety. The math has not entered the bloodstream. What the math has done is something smaller and more useful. It has given the anxiety a number it cannot dispute. The negotiator in the brain can no longer say but what if it really is the end of my career, because the negotiator has been handed, in writing, a number that says it is, by your own admission, one in three thousand. The negotiator can refuse the number. But the negotiator can no longer pretend the number does not exist.
Over time, with practice, the brain begins to recognize this pattern. The cascade starts. The body notices. The mind reaches, almost reflexively now, for the back of an envelope. The numbers come out. The numbers are usually absurd. The cascade slows. It does not always stop. But it slows. And, in the long quiet project of recovering from a life like the one I described in the previous chapter, slowing the cascade is, most days, exactly enough.
This is what mathematics does for the anxious brain. Not magic. Not enlightenment. Not a cure. A small, dependable, available, three in the morning sort of clarity, in a language the brain cannot negotiate with, applied by your own hand, in a notebook nobody can repossess.
That is the end of Part one.
The diagnosis is in. The brain is legacy code. The author has, for better or worse, lived through enough of it to have the credentials. The toolkit is mathematics, with the necessary caveat that the toolkit is a partner, not a replacement, and that on the worst days you will still need the other tools, which is fine, because the other tools are real and they are good and they have their place.
From here on, we are no longer diagnosing. We are debugging.
Part two opens with the question of why anxiety is the derivative, and not the function, and why that one small piece of calculus, properly understood, is the difference between a life of constant emergency and a life that occasionally remembers it is allowed to sit down.
Bring the notebook. Bring the envelope. Bring the worst question your brain has asked you this week.
We are about to compute.