Appendix E
A small explanation of the title, because it is going to do some work in this appendix.
A directed acyclic graph, in computer science, is a structure of nodes connected by directional arrows, with the additional property that no chain of arrows ever loops back on itself. The structure is, on inspection, the natural form for representing dependencies. Each node points at the nodes that depend on it. Each node is, in turn, pointed at by the nodes it depends on. The whole graph has a topological order, which is the order you would have to do things in to make the whole structure resolve: start at the roots, the nodes with no incoming arrows, and work downstream through everything that depends on them.
I want to use this structure for the acknowledgments, because the alternative is a flat list of names, and a flat list of names is, on inspection, a piece of compression that loses information the structure preserves. The information it loses is who depends on whom. Some of the gratitudes in this appendix are roots. They have no incoming dependencies. Others are downstream of those roots, and would not exist in the form they exist in without the roots being where they are. The structure honors the people and the relationships in a way that a flat list cannot.
The appendix is therefore organized in topological order. The roots come first. Each subsequent layer depends, in some way, on the layer above it. The order is not a hierarchy of importance. The order is a hierarchy of antecedence. Some things had to come first for the rest to be possible.
A note before the names. The naming is deliberate and complete to the extent the book is in my power to make it so. If anyone whose name should be here is not here, the omission is my failure of memory, not a comment on what they did. The graph, like any model, is approximate.
Layer one
The roots.
Who died when I was four. The book is, in some sense I have not been able to write about directly, a long letter to a person I do not remember well enough to write a letter to. The fact that I am the person who wrote this book, rather than some other person, has, on inspection, an enormous amount to do with the four years she had. I do not have many memories. I have, by what I am told, what she gave me in those four years, which I am still using.
Held in my life since I was four and she was one. The book has, for reasons I tried to be honest about in Chapter 16, not told her side of any of the same events it told mine. Her side exists. Her version of the same childhood is, in many ways, the version this book has been a careful compression around the edges of. She has, over four decades, been the one person who has known the source material the same way I have, and the only person who could, on inspection, accurately fact-check most of my memory. Whatever the book gets right, she is part of the reason. Whatever it gets wrong, she has been kind about.
Layer two
The people without whom the writer would not have survived to write.
Who took two children he had not asked for, and kept them, and made sure they had a roof and an education, despite the fact that the ledger in his head was, by his own standards, not balancing. The book has been honest about the complications, in Chapter 8 and Chapter 20, and I want to be equally honest here. He did what he could do. He did, in retrospect, more than the equation he was solving could reasonably have asked of him. He was a finite person in a non-integrable system, and the system did not, on inspection, give him the tools to be the man he might have liked to be. He is in this graph because, on the cleanest reading, I am alive because of him.
Who hired me on the afternoon I walked in, at eighteen, with a few clothes and a few pairs of chappals in a small bag, and gave me a job teaching the basics of computing to other people, on the theory, mostly correct, that I knew enough to be useful and would learn the rest under pressure. The three years at that institute are, in some sense, the years in which the writer of this book was being assembled. He is in this graph because every subsequent layer required, as a precondition, the small piece of professional dignity that he extended to a teenager who had nowhere else to go.
Who has been thanked, by name, in Chapter 5 and in Appendix C. She earns another mention here, in the appendix structure, because the order is dependency and not importance, and the writing of this book depends, in a particular technical sense, on the work she did with me during the worst eight months of my life. The book would not have been written without that work. She did not, of course, write the book. She did, however, install some of the procedures that the writer of the book has been running ever since. Her own book, Battles in the Mind, is recommended in Appendix C, and is one of the things this book has been quietly conversing with throughout.
For the work that, in the worst months, was within reach when nothing else was, and for the years since, during which the relationship has been the kind one builds with an institution that has, on inspection, become part of one's actual life. The foundation knows me. I know them. That is a piece of good fortune that not every person who has received their help has had, and I am, in the appropriate technical sense, grateful for it. Their work in the country is among the most important pieces of mental-health infrastructure I have ever encountered, and the fact that it exists, in the form it exists in, is, on inspection, the result of a great many people deciding, year after year, that it should continue to. They are at this node in the graph because several of the downstream nodes, including the writer of this book, would not exist without them.
Whose names are repeated here, not because I have anything to add to what was said in the interlude, but because the structure of this graph would, on inspection, be wrong if they were not at this layer. The two of them are the reason a particular man, at three in the morning of a particular night during the worst stretch of his adult life, did not, on inspection, choose what he was considering choosing. The downstream graph, including this book, including this paragraph, including the reader's hands turning to this page, depends on the two of them having been who they were, on that night, in his small apartment, asking only that he get up in the morning and put food in their bowls.
Koko. Knoppix. The graph is still pointing at you.
Layer three
The intellectual ancestors.
The next layer is the writers and thinkers, most of whom I have never met and several of whom are no longer alive, whose work the book has been built on top of. The list is, by construction, incomplete. The writers below are the ones whose voices I can, on close listening, still hear in the prose of the chapters.
To Carl Sagan, who taught a generation that science could be written about with warmth, and whose Cosmos was, on a small black-and-white television in a small house in Bhilai, the first thing I had ever encountered that made me believe an inner life of ideas was available to a person like me.
To Richard Feynman, who taught me that being playful was not, on inspection, the opposite of being serious, and whose autobiographical books are still my model for how an intelligent person should sound when telling stories about themselves.
To Isaac Asimov, whose science writing across four decades shaped a great many of the sentences in this book without my having quite noticed they were being shaped, and whose patience with the reader is, in my honest estimation, the most underrated feature of his prose.
To Stephen Hawking, for the courage of trying to explain things that, on inspection, were harder to explain than even he knew. To Neil deGrasse Tyson, for taking up the work after Sagan. To Richard Dawkins, for the early books, which are still the early books. To Ursula K. Le Guin, for the prose, which I have never been able to imitate but have, on every page, tried to honor. To Michael Crichton, for the discipline of the working novelist who never stopped explaining the science he was working with.
To the mathematicians and computer scientists whose actual work the book uses: Isaac Newton, Thomas Bayes, Henri Poincaré, Claude Shannon, Alan Turing, John McCarthy, Donald Knuth, Martin Fowler, Kent Beck. Each of them contributed, by their work, the substance of a chapter I would not otherwise have known how to write.
The intellectual ancestor list is, of course, much longer than this. I have named the ones whose names appear, in some form or other, in the text. The rest are upstream of the named ones, and are honored by extension.
Layer four
The current network.
To the friends who read drafts of these chapters with attention, who told me when a sentence was too clever, who pointed out, gently, when an argument was less complete than I thought it was, and who, in several cases, gave the manuscript more sustained attention than they have given to most of the published books they have read in the same year. You know who you are. You are the reason the book reads the way it reads, rather than the way the first drafts read.
To the people who, during the eight months I lived through after the marriage ended, were quietly available. Some of them I called. Some of them I did not call, but they were where I knew I could call if it came to that, and the fact that they were there was, in a way that did not require me to call them, enough. Some of them are still in my life. Some of them are not, by the ordinary attrition of adult friendships. To all of them, then and now, my thanks.
To the small handful of professional collaborators, designers, programmers, and editors who have, over the years, put up with the man this book has been a long attempt to refactor away from. You were the test cases. You suffered the unreviewed code. I have, since you knew me at my worst, tried to do better. The book is in part what doing better looks like.
To my ex-wife. The marriage ended. The years were real. The years contained a great deal that I have not written about and will not, and they also contained two dachshunds whose introduction was, on inspection, the single greatest piece of practical wisdom anyone has ever offered me in any context. Thank you for the years. Thank you for the suggestion that led, by a route neither of us could have predicted, to Koko and Knoppix.
Layer five
The reader.
You are, structurally, at the end of the graph. You are also, in the relevant sense, the reason all the upstream nodes have done their work, because the work of all the upstream nodes assembles, in your hands, into a thing that may or may not be useful to you. The arrows have all been pointing, eventually, at you.
I want to say a small thing about this, because the chapter would be incomplete without it. The book in your hands is, on inspection, the longest letter I have ever written. The recipient was, for most of the writing, abstract. Toward the end, the recipient began to feel, in some quiet way, more real. By the time of this appendix, the recipient is you. You are the node at which the work resolves, or, in some cases, fails to resolve. Either outcome is yours to determine. The work is no longer mine to do.
I hope it has, in some small way, been useful. I hope, more than that, that on some Tuesday evening in some future month, you reach for a piece of mathematics this book has put into your hands, and you find that the mathematics is there when you reach for it, in the patient way that mathematics is, and that the reaching makes the evening, by some small amount, more livable. If that happens, the book has done what books like this can do, which is, in technical terms, not much, but enough.
Thank you for reading.