From Nielsen to Thurston by way of Cummings, ft Terry Tao

I was reading Dominic Cummings’ blog post On the referendum #33: high performance government, ‘cognitive technologies’, Michael Nielsen, Bret Victor, & ‘Seeing Rooms’, and at one point he references a nice passage by Nielsen that immediately reminded me of Bill Thurston’s experience trying to communicate his ways of thinking in his seminal retrospective On proof and progress in mathematics, one of the highest wisdom-density (not just insight-density!) opinion pieces I have ever had the privilege of reading, so I thought I’d record it here. In doing so I went to Nielsen’s essay Thought as a technology where Cummings got the passage from, and discovered that Nielsen directly references Thurston right then and there. It is with supreme modesty that I henceforth claim that for one blindingly-inspired moment of reasoning-by-vague-association, I was precisely as bright as a man who in his mid-twenties co-wrote one of the ten most cited physics texts of all time.

(NOT! After all, a stopped clock is still right twice a day. But don’t you dare deny me my time in the sun.)

Cummings’ post itself is an interesting infodump. I am somehow turned on by infodense run-on sentences, because they’re the most reliable way to sound Stereotypically Ferociously Smart on paper. He certainly delivers there. But more so than that, he’s one of the very few people ‘in politics’ (broadly construed) who understands the need for quantitative literacy and complex systems intuition (in particular as it relates to high-performance grand-scale complex project management, like the Apollo mission). Also I’m biased, because he checks all the Right Names – Nielsen, Bret Victor, Alan Kay, Colonel ‘OODA loop’ Boyd, Tetlock etc – in other words, despite me having almost nothing else in common with him he is firmly One Of My People (albeit clearly better endowed in the grey matter department). His introduction to On the referendum #33 certainly promises loads:

This blog looks at an intersection of decision-making, technology, high performance teams and government. It sketches some ideas of physicist Michael Nielsen about cognitive technologies and of computer visionary Bret Victor about the creation of dynamic tools to help understand complex systems and ‘argue with evidence’, such as ‘tools for authoring dynamic documents’, and ‘Seeing Rooms’ for decision-makers — i.e rooms designed to support decisions in complex environments. It compares normal Cabinet rooms, such as that used in summer 1914 or October 1962, with state-of-the-art Seeing Rooms. There is very powerful feedback between: a) creating dynamic tools to see complex systems deeper (to see inside, see across time, and see across possibilities), thus making it easier to work with reliable knowledge and interactive quantitative models, semi-automating error-correction etc, and b) the potential for big improvements in the performance of political and government decision-making.

It is relevant to Brexit and anybody thinking ‘how on earth do we escape this nightmare’ but 1) these ideas are not at all dependent on whether you support or oppose Brexit, about which reasonable people disagree, and 2) they are generally applicable to how to improve decision-making — for example, they are relevant to problems like ‘how to make decisions during a fast moving nuclear crisis’ which I blogged about recently, or if you are a journalist ‘what future media could look like to help improve debate of politics’. One of the tools Nielsen discusses is a tool to make memory a choice by embedding learning in long-term memory rather than, as it is for almost all of us, an accident. I know from my days working on education reform in government that it’s almost impossible to exaggerate how little those who work on education policy think about ‘how to improve learning’.

Fields make huge progress when they move from stories (e.g Icarus)  and authority (e.g ‘witch doctor’) to evidence/experiment (e.g physics, wind tunnels) and quantitative models (e.g design of modern aircraft). Political ‘debate’ and the processes of government are largely what they have always been — largely conflict over stories and authorities where almost nobody even tries to keep track of the facts/arguments/models they’re supposedly arguing about, or tries to learn from evidence, or tries to infer useful principles from examples of extreme success/failure. We can see much better than people could in the past how to shift towards processes of government being ‘partially rational discussion over facts and models and learning from the best examples of organisational success‘. But one of the most fundamental and striking aspects of government is that practically nobody involved in it has the faintest interest in or knowledge of how to create high performance teams to make decisions amid uncertainty and complexity. This blindness is connected to another fundamental fact: critical institutions (including the senior civil service and the parties) are programmed to fight to stay dysfunctional, they fight to stay closed and avoid learning about high performance, they fight to exclude the most able people.

That passage is tempting to dive further into, but I am trying to discipline my blogging/associative note-taking output by ‘modularizing’ it to better build upon it in the future (a long-term personal knowledge management project of mine), so I’ll save that for a later post.

Back to the topic at hand with a relevant quote:

Language and writing were cognitive technologies created thousands of years ago which enabled us to think previously unthinkable thoughts. Mathematical notation did the same over the past 1,000 years. [A math problem that took al-Khawarizmi a convoluted paragraph to express can now be written as a quadratic equation an inch long.]

Michael Nielsen uses a similar analogy. Descartes and Fermat demonstrated that equations can be represented on a diagram and a diagram can be represented as an equation. This was a new cognitive technology, a new way of seeing and thinking: algebraic geometry. Changes to the ‘user interface’ of mathematics were critical to its evolution and allowed us to think unthinkable thoughts.

Similarly in the 18th Century, there was the creation of data graphics to demonstrate trade figures. Before this, people could only read huge tables. …

Segue to Nielsen’s essay elaborating on the above, then noting that visual thinking is another great example of a cognitive technology:

Language is an example of a cognitive technology: an external artifact, designed by humans, which can be internalized, and used as a substrate for cognition. That technology is made up of many individual pieces – words and phrases, in the case of language – which become basic elements of cognition. These elements of cognition are things we can think with.

Language isn’t the only cognitive technology we internalize.

Consider visual thinking. If, like me, you sometimes think visually, it’s tempting to suppose your mind’s eye is a raster display, capable of conceiving any image. But while tempting, this is wrong. In fact, our visual thinking is done using visual cognitive technologies we’ve previously internalized.

For instance, one of the world’s best-known art teachers, Betty Edwards, explains that the visual thinking of most non-artist adults is limited to what she refers to as a simple “symbol system”, and that this constrains both what they see and what they can visually conceive:

[A]dult students beginning in art generally do not really see what is in front of their eyes — that is, they do not perceive in the way required for drawing. They take note of what’s there, and quickly translate the perception into words and symbols mainly based on the symbol system developed throughout childhood and on what they know about the perceived object.

It requires extraordinary imagination to conceive new forms of visual meaning – i.e., new visual cognitive technologies. Many of our best-known artists and visual explorers are famous in part because they discovered such forms. When exposed to that work, other people can internalize those new cognitive technologies, and so expand the range of their own visual thinking.

For example, cubist artists such as Picasso developed the technique of using multiple points of view in a single painting. Once you’ve learnt to see cubist art, it can give you a richer sense of the structure of what’s being shown…

Another example is the work of Doc Edgerton, a pioneer of high-speed photography, whose photographs revealed previously unsuspected structure in the world. If you study such photographs, you begin to build new mental models of everyday phenomena, enlarging your range of visual thought…

Another class of examples comes from the many cartographers who’ve developed ways to visually depict geography. Consider, for example, the 1933 map of the London Underground, developed by Harry Beck. In the early 1930s, Beck noticed that the official map of the Underground was growing too complex for readers to understand. He simplified the map by abandoning exact geographic fidelity, as was commonly used on most maps up to that point. He concentrated instead on showing the topological structure of the network of stations, i.e., what connects to what…

Images such as these are not natural or obvious. No-one would ever have these visual thoughts without the cognitive technologies developed by Picasso, Edgerton, Beck, and many other pioneers. Of course, only a small fraction of people really internalize these ways of visual thinking. But in principle, once the technologies have been invented, most of us can learn to think in these new ways.

Why, you know who was good at visual thinking, perhaps the best geometric thinker in the history of mathematics (a tall claim!)? Bill Thurston. In Thinking and explaining, one of the most upvoted MathOverflow questions of all time, Thurston asked:

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you’re thinking? Please give either personal examples of how your thoughts and words differ, or describe how they are connected for you.

I’ve been fascinated by the phenomenon the question addresses for a long time. We have complex minds evolved over many millions of years, with many modules always at work. A lot we don’t habitually verbalize, and some of it is very challenging to verbalize or to communicate in any medium. Whether for this or other reasons, I’m under the impression that mathematicians often have unspoken thought processes guiding their work which may be difficult to explain, or they feel too inhibited to try.

One prototypical situation is this: there’s a mathematical object that’s obviously (to you) invariant under a certain transformation. For instant, a linear map might conserve volume for an ‘obvious’ reason. But you don’t have good language to explain your reason—so instead of explaining, or perhaps after trying to explain and failing, you fall back on computation. You turn the crank and without undue effort, demonstrate that the object is indeed invariant.

Here’s a specific example. Once I mentioned this phenomenon to Andy Gleason; he immediately responded that when he taught algebra courses, if he was discussing cyclic subgroups of a group, he had a mental image of group elements breaking into a formation organized into circular groups. He said that ‘we’ never would say anything like that to the students. His words made a vivid picture in my head, because it fit with how I thought about groups. I was reminded of my long struggle as a student, trying to attach meaning to ‘group’, rather than just a collection of symbols, words, definitions, theorems and proofs that I read in a textbook.

There’s a reason this question matters so much to Thurston, and it’s exactly what this post of mine is building up to. But I like my foreplay, so I shall prolong it just a tad further with more related-ish quotes. (Also, “Connect Everything!” can be a hard impulse to resist.)

It turns out that Nielsen’s essay Thought as a technology also quotes part of the Thurston passage above (before Tao), just without referencing the MO question. (I knew it anyway because I’d seen it before. Gosh, yet another instance where my thoughts rise to Nielsen’s level! Where do I collect my MacArthur Fellowship??) He paraphrases Thurston like so:

… mathematicians often don’t think about mathematical objects using the conventional representations found in books. Rather, they rely heavily on what we might call hidden representations, such as the mental imagery Thurston describes, of groups breaking into formations of circular groups. Such hidden representations help them reason more easily than the conventional representations, and occasionally provide them with what may seem to others like magical levels of insight.

Nielsen notes that “the use of hidden representations occurs in many fields”. In electrical engineering, for instance, Gerald Sussman has the following quote about analyzing electrical circuits:

I was teaching my first classes in electrical engineering at MIT, in circuit theory… and I observed that what we taught the students wasn’t at all what the students were actually expected to learn. That is, what an expert person did when presented with a circuit… was quite different from what we tell [the students] to write down – the node equations… and then you’re supposed to grind these equations together somehow and solve them, to find out what’s going on. Well, you know, that’s not what a really good engineer does. …

Nielsen himself is a theoretical physicist, so he can draw from personal experience:

The energy surface prototype is based on the kind of hidden representation described by Thurston and Sussman. In particular, it’s based on the way I often visualize one-dimensional motion, in my work as a theoretical physicist. The visuals are not original to me: when I’ve shown the prototype to other physicists, several have told me “Oh, I think about one-dimensional motion like this”. But while this way of understanding may be common among physicists, they rarely talk about it. For instance, it’s not the kind of thing one would use in teaching a class on one-dimensional motion. At most, you might make a few ancillary sketches along these lines for the students. Certainly, you would not put this way of thinking front and center, or expect students to answer homework or exam questions using energy surfaces. Nor would you use such a representation in a research paper.

The situation is strange. A powerful way of thinking about one-dimensional motion is largely absent from our shared conversations. The reason is that traditional media are poorly adapted to working with such representations.

Okay, why not just share those representations? The answer is that they do, but it’s hard nonetheless, and there can be reasons why they don’t. Nielsen:

To answer that question, suppose you think hard about a subject for several years – say, cyclic subgroups of a group, to use Thurston’s example. Eventually you push up against the limits of existing representations. If you’re strongly motivated – perhaps by the desire to solve a research problem – you may begin inventing new representations, to provide insights difficult through conventional means. You are effectively acting as your own interface designer. But the new representations you develop may be held entirely in your mind, and so are not constrained by traditional static media forms. Or even if based on static media, they may break social norms about what is an “acceptable” argument. Whatever the reason, they may be difficult to communicate using traditional media. And so they remain private, or are only discussed informally with expert colleagues.

This is the passage I alluded to at the very beginning. It’s precisely what Thurston ran up against, and the answer to it will be the climax of this post.

But one last interlude – Terry Tao has also expressed the same sentiments, which is to be expected given the highly collaborative nature of his research style. He describes these in his answer to Thurston’s MO question, which is fantastic in its sheer range:

I find there is a world of difference between explaining things to a colleague, and explaining things to a close collaborator. With the latter, one really can communicate at the intuitive level, because one already has a reasonable idea of what the other person’s mental model of the problem is. In some ways, I find that throwing out things to a collaborator is closer to the mathematical thought process than just thinking about maths on one’s own, if that makes any sense.

One specific mental image that I can communicate easily with collaborators, but not always to more general audiences, is to think of quantifiers in game theoretic terms. Do we need to show that for every epsilon there exists a delta? Then imagine that you have a bag of deltas in your hand, but you can wait until your opponent (or some malicious force of nature) produces an epsilon to bother you, at which point you can reach into your bag and find the right delta to deal with the problem. Somehow, anthropomorphising the “enemy” (as well as one’s “allies”) can focus one’s thoughts quite well. This intuition also combines well with probabilistic methods, in which case in addition to you and the adversary, there is also a Random player who spits out mathematical quantities in a way that is neither maximally helpful nor maximally adverse to your cause, but just some randomly chosen quantity in between. The trick is then to harness this randomness to let you evade and confuse your adversary.

Is there a quantity in one’s PDE or dynamical system that one can bound, but not otherwise estimate very well? Then imagine that it is controlled by an adversary or by Murphy’s law, and will always push things in the most unfavorable direction for whatever you are trying to accomplish. Sometimes this will make that term “win” the game, in which case one either gives up (or starts hunting for negative results), or looks for additional ways to “tame” or “constrain” that troublesome term, for instance by exploiting some conservation law structure of the PDE.

For evolutionary PDEs in particular, I find there is a rich zoo of colourful physical analogies that one can use to get a grip on a problem. I’ve used the metaphor of an egg yolk frying in a pool of oil, or a jetski riding ocean waves, to understand the behaviour of a fine-scaled or high-frequency component of a wave when under the influence of a lower frequency field, and how it exchanges mass, energy, or momentum with its environment. In one extreme case, I ended up rolling around on the floor with my eyes closed in order to understand the effect of a gauge transformation that was based on this type of interaction between different frequencies. (Incidentally, that particular gauge transformation won me a Bocher prize, once I understood how it worked.) I guess this last example is one that I would have difficulty communicating to even my closest collaborators. Needless to say, none of these analogies show up in my published papers, although I did try to convey some of them in my PDE book eventually.

ADDED LATER: I think one reason why one cannot communicate most of one’s internal mathematical thoughts is that one’s internal mathematical model is very much a function of one’s mathematical upbringing. For instance, my background is in harmonic analysis, and so I try to visualise as much as possible in terms of things like interactions between frequencies, or contests between different quantitative bounds. This is probably quite a different perspective from someone brought up from, say, an algebraic, geometric, or logical background. I can appreciate these other perspectives, but still tend to revert to the ones I am most personally comfortable with when I am thinking about these things on my own.

ADDED (MUCH) LATER: Another mode of thought that I and many others use routinely, but which I realised only recently was not as ubiquitious as I believed, is to use an “economic” mindset to prove inequalities such as X≤Y or X≤CY for various positive quantities X,Y, interpreting them in the form “If I can afford Y, can I therefore afford X?” or “If I can afford lots of Y, can I therefore afford X?” respectively. This frame of reference starts one thinking about what types of quantities are “cheap” and what are “expensive”, and whether the use of various standard inequalities constitutes a “good deal” or not. It also helps one understand the role of weights, which make things more expensive when the weight is large, and cheaper when the weight is small.

ADDED (MUCH, MUCH) LATER: One visualisation technique that I have found very helpful is to incorporate the ambient symmetries of the problem (a la Klein) as little “wobbles” to the objects being visualised. This is most familiarly done in topology (“rubber sheet mathematics”), where every object considered is a bit “rubbery” and thus deforming all the time by infinitesimal homeomorphisms. But geometric objects in a scale-invariant problem could be thought of as being viewed through a camera with a slightly wobbly zoom lens, so that one’s mental image of these objects is always varying a little in size. Similarly, if one is in a translation-invariant setting, one’s mental camera should be sliding back and forth just a little to remind you of this, if one is working in a Euclidean space then the camera might be jiggling through all the rigid motions, and so forth. A more advanced example: if the problem is invariant under tensor products, as per the tensor product trick, then one’s low dimensional objects should have a tiny bit of shadowing (or perhaps look like one of these 3D images when one doesn’t have the polarised glasses, with the slightly separated red and blue components) that suggest that they are projections of a higher dimensional Cartesian product.
One reason why one wants to do this is that it helps suggest useful normalisations. If one is viewing a situation with a wobbly zoom lens and there is some length that appears all over one’s analysis, one is reminded that one can spend the scale invariance of the problem to zoom up or down as appropriate to normalise this scale to equal 1. Similarly for other ambient symmetries.

This sort of wobbling of symmetries is also available in less geometric settings. … In analysis, one often only cares about the order of magnitude of some very large or very small quantity X, rather than its exact value; so one should view this quantity as being a bit squishy in size, growing or shrinking by a factor of two or so every time one looks at the problem. If there is some probability theory in one’s problem, and some of your objects are random variables rather than deterministic variables, then you can imagine that every so often the “game resets”, with the random variables jumping around to different values in their range (and any quantities depending on these variables changing accordingly), whereas the deterministic variables stay fixed. Similarly if one has generic points in a variety, or nonstandard objects in a space (with the point being that if something bad happens if, say, your generic point is trapped in a subvariety, you can “reset the game” in which the generic point is now outside the subvariety; similarly one can “reset” an unbounded nonstandard number to be larger than any given standard number, etc.).

Hot damn, Terry!

I have digressed enough. Here’s Thurston’s reminiscences, the answer to the prompt at the beginning of this post.

First, foliations, where Thurston “did wrong”:

First I will discuss briefly the theory of foliations, which was my first subject, starting when I was a graduate student. (It doesn’t matter here whether you know what foliations are.)

At that time, foliations had become a big center of attention among geometric topologists, dynamical systems people, and differential geometers. I fairly rapidly proved some dramatic theorems. I proved a classification theorem for foliations, giving a necessary and sufficient condition for a manifold to admit a foliation. I proved a number of other significant theorems. I wrote respectable papers and published at least the most important theorems. It was hard to find the time to write to keep up with what I could prove, and I built up a backlog.

An interesting phenomenon occurred. Within a couple of years, a dramatic evacuation of the field started to take place. I heard from a number of mathematicians that they were giving or receiving advice not to go into foliations—they were saying that Thurston was cleaning it out. People told me (not as a complaint, but as a compliment) that I was killing the field. Graduate students stopped studying foliations, and fairly soon, I turned to other interests as well.

I do not think that the evacuation occurred because the territory was intellectually exhausted—there were (and still are) many interesting questions that remain and that are probably approachable. Since those years, there have been interesting developments carried out by the few people who stayed in the field or who entered the field, and there have also been important developments in neighboring areas that I think would have been much accelerated had mathematicians continued to pursue foliation theory vigorously.

Today, I think there are few mathematicians who understand anything approaching the state of the art of foliations as it lived at that time, although there are some parts of the theory of foliations, including developments since that time, that are still thriving.

What happened?

I believe that two ecological effects were much more important in putting a damper on the subject than any exhaustion of intellectual resources that occurred.

First, the results I proved (as well as some important results of other people) were documented in a conventional, formidable mathematician’s style. They depended heavily on readers who shared certain background and certain insights. The theory of foliations was a young, opportunistic subfield, and the background was not standardized. I did not hesitate to draw on any of the mathematics I had learned from others. The papers I wrote did not (and could not) spend much time explaining the background culture. They documented top-level reasoning and conclusions that I often had achieved after much reflection and effort. I also threw out prize cryptic tidbits of insight, such as “the Godbillon-Vey invariant measures the helical wobble of a foliation”, that remained mysterious to most mathematicans who read them. This created a high entry barrier: I think many graduate students and mathematicians were discouraged that it was hard to learn and understand the proofs of key theorems.

Second is the issue of what is in it for other people in the subfield. When I started working on foliations, I had the conception that what people wanted was to know the answers. I thought that what they sought was a collection of powerful proven theorems that might be applied to answer further mathematical questions. But that’s only one part of the story. More than the knowledge, people want personal understanding. And in our credit-driven system, they also want and need theorem-credits.

And secondly, 3-manifolds and hyperbolic geometry, where Thurston “did right”:

I’ll skip ahead a few years, to the subject that Jaffe and Quinn alluded to, when I began studying 3-dimensional manifolds and their relationship to hyperbolic geometry. (Again, it matters little if you know what this is about.) I gradually built up over a number of years a certain intuition for hyperbolic three-manifolds, with a repertoire of constructions, examples and proofs. (This process actually started when I was an undergraduate, and was strongly bolstered by applications to foliations.) After a while, I conjectured or speculated that all three-manifolds have a certain geometric structure; this conjecture eventually became known as the geometrization conjecture. About two or three years later, I proved the geometrization theorem for Haken manifolds. It was a hard theorem, and I spent a tremendous amount of effort thinking about it. When I completed the proof, I spent a lot more effort checking the proof, searching for difficulties and testing it against independent information.

I’d like to spell out more what I mean when I say I proved this theorem. It meant that I had a clear and complete flow of ideas, including details, that withstood a great deal of scrutiny by myself and by others. Mathematicians have many different styles of thought. My style is not one of making broad sweeping but careless generalities, which are merely hints or inspirations: I make clear mental models, and I think things through. My proofs have turned out to be quite reliable. I have not had trouble backing up claims or producing details for things I have proven. I am good in detecting flaws in my own reasoning as well as in the reasoning of others.

However, there is sometimes a huge expansion factor in translating from the encoding in my own thinking to something that can be conveyed to someone else. My mathematical education was rather independent and idiosyncratic, where for a number of years I learned things on my own, developing personal mental models for how to think about mathematics. This has often been a big advantage for me in thinking about mathematics, because it’s easy to pick up later the standard mental models shared by groups of mathematicians. This means that some concepts that I use freely and naturally in my personal thinking are foreign to most mathematicians I talk to. My personal mental models and structures are similar in character to the kinds of models groups of mathematicians share—but they are often different models. At the time of the formulation of the geometrization conjecture, my understanding of hyperbolic geometry was a good example. A random continuing example is an understanding of finite topological spaces, an oddball topic that can lend good insight to a variety of questions but that is generally not worth developing in any one case because there are standard circumlocutions that avoid it.

Neither the geometrization conjecture nor its proof for Haken manifolds was in the path of any group of mathematicians at the time—it went against the trends in topology for the preceding 30 years, and it took people by surprise. To most topologists at the time, hyperbolic geometry was an arcane side branch of mathematics, although there were other groups of mathematicians such as differential geometers who did understand it from certain points of view. It took topologists a while just to understand what the geometrization conjecture meant, what it was good for, and why it was relevant.

This is the answer! Continuing:

At the same time, I started writing notes on the geometry and topology of 3-manifolds, in conjunction with the graduate course I was teaching. I distributed them to a few people, and before long many others from around the world were writing for copies. The mailing list grew to about 1200 people to whom I was sending notes every couple of months. I tried to communicate my real thoughts in these notes. People ran many seminars based on my notes, and I got lots of feedback. Overwhelmingly, the feedback ran something like “Your notes are really inspiring and beautiful, but I have to tell you that we spent 3 weeks in our seminar working out the details of §n.n. More explanation would sure help.”

I also gave many presentations to groups of mathematicians about the ideas of studying 3-manifolds from the point of view of geometry, and about the proof of the geometrization conjecture for Haken manifolds. At the beginning, this subject was foreign to almost everyone. It was hard to communicate—the infrastructure was in my head, not in the mathematical community. There were several mathematical theories that fed into the cluster of ideas: three-manifold topology, Kleinian groups, dynamical systems, geometric topology, discrete subgroups of Lie groups, foliations, Teichmuller spaces, pseudo-Anosov diffeomorphisms, geometric group theory, as well as hyperbolic geometry.

We held an AMS summer workshop at Bowdoin in 1980, where many mathematicans in the subfields of low-dimensional topology, dynamical systems and Kleinian groups came. It was an interesting experience exchanging cultures.

It became dramatically clear how much proofs depend on the audience. We prove things in a social context and address them to a certain audience. Parts of this proof I could communicate in two minutes to the topologists, but the analysts would need an hour lecture before they would begin to understand it. Similarly, there were some things that could be said in two minutes to the analysts that would take an hour before the topologists would begin to get it. And there were many other parts of the proof which should take two minutes in the abstract, but that none of the audience at the time had the mental infrastructure to get in less than an hour.

At that time, there was practically no infrastructure and practically no context for this theorem, so the expansion from how an idea was keyed in my head to what I had to say to get it across, not to mention how much energy the audience had to devote to understand it, was very dramatic.

In reaction to my experience with foliations and in response to social pressures, I concentrated most of my attention on developing and presenting the infrastructure in what I wrote and in what I talked to people about. I explained the details to the few people who were “up” for it. I wrote some papers giving the substantive parts of the proof of the geometrization theorem for Haken manifolds—for these papers, I got almost no feedback. Similarly, few people actually worked through the harder and deeper sections of my notes until much later.

The result has been that now quite a number of mathematicians have what was dramatically lacking in the beginning: a working understanding of the concepts and the infrastructure that are natural for this subject. There has been and there continues to be a great deal of thriving mathematical activity. By concentrating on building the infrastructure and explaining and publishing definitions and ways of thinking but being slow in stating or in publishing proofs of all the “theorems” I knew how to prove, I left room for many other people to pick up credit. There has been room for people to discover and publish other proofs of the geometrization theorem. These proofs helped develop mathematical concepts which are quite interesting in themselves, and lead to further mathematics.

What mathematicians most wanted and needed from me was to learn my ways of thinking, and not in fact to learn my proof of the geometrization conjecture for Haken manifolds. It is unlikely that the proof of the general geometrization conjecture will consist of pushing the same proof further.

The ascended economy civilizational failure mode, ft Scott Alexander and Charlie Stross

Scott Alexander’s short speculative depiction of a possible Goodhart’s law-style civilizational failure mode – where “the imperative of economic growth” becomes the end rather than the means, becomes, indeed, totalizing – in his book review of Robin Hanson’s Age of Em has stuck with me like a low-grade nightmare ever since I read it all those years ago:

Imagine a company that manufactures batteries for electric cars. The inventor of the batteries might be a scientist who really believes in the power of technology to improve the human race. The workers who help build the batteries might just be trying to earn money to support their families. The CEO might be running the business because he wants to buy a really big yacht. And the whole thing is there to eventually, somewhere down the line, let a suburban mom buy a car to take her kid to soccer practice. Like most companies the battery-making company is primarily a profit-making operation, but the profit-making-ness draws on a lot of not-purely-economic actors and their not-purely-economic subgoals.

Now imagine the company fires all its employees and replaces them with robots. It fires the inventor and replaces him with a genetic algorithm that optimizes battery design. It fires the CEO and replaces him with a superintelligent business-running algorithm. All of these are good decisions, from a profitability perspective. We can absolutely imagine a profit-driven shareholder-value-maximizing company doing all these things. But it reduces the company’s non-masturbatory participation in an economy that points outside itself, limits it to just a tenuous connection with soccer moms and maybe some shareholders who want yachts of their own.

Now take it further. Imagine there are no human shareholders who want yachts, just banks who lend the company money in order to increase their own value. And imagine there are no soccer moms anymore; the company makes batteries for the trucks that ship raw materials from place to place. Every non-economic goal has been stripped away from the company; it’s just an appendage of Global Development.

Now take it even further, and imagine this is what’s happened everywhere. There are no humans left; it isn’t economically efficient to continue having humans. Algorithm-run banks lend money to algorithm-run companies that produce goods for other algorithm-run companies and so on ad infinitum. Such a masturbatory economy would have all the signs of economic growth we have today. It could build itself new mines to create raw materials, construct new roads and railways to transport them, build huge factories to manufacture them into robots, then sell the robots to whatever companies need more robot workers. It might even eventually invent space travel to reach new worlds full of raw materials. Maybe it would develop powerful militaries to conquer alien worlds and steal their technological secrets that could increase efficiency. It would be vast, incredibly efficient, and utterly pointless. The real-life incarnation of those strategy games where you mine Resources to build new Weapons to conquer new Territories from which you mine more Resources and so on forever.

But this seems to me the natural end of the economic system. Right now it needs humans only as laborers, investors, and consumers. But robot laborers are potentially more efficient, companies based around algorithmic trading are already pushing out human investors, and most consumers already aren’t individuals – they’re companies and governments and organizations. At each step you can gain efficiency by eliminating humans, until finally humans aren’t involved anywhere.

He goes into more detail in his followup post, Ascended Economy, which has the following line of argument:

… we can hope that things will get so post-scarcity that governments and private charities give each citizen a few shares in the Ascended Economy to share the gains with non-investors. This would at least temporarily be a really good outcome.

But in the long term it reduces the political problem of regulating corporations to the scientific problem of Friendly AI, which is really bad.

Even today, a lot of corporations do things that effectively maximize shareholder value but which we consider socially irresponsible. Environmental devastation, slave labor, regulatory capture, funding biased science, lawfare against critics – the list goes on and on. They have a simple goal – make money – whereas what we really want them to do is much more complicated and harder to measure – make money without engaging in unethical behavior or creating externalities. We try to use regulatory injunctions, and it sort of helps, but because those go against a corporation’s natural goals they try their best to find loopholes and usually succeed – or just take over the regulators trying to control them.

This is bad enough with bricks-and-mortar companies run by normal-intelligence humans. But it would probably be much worse with ascended corporations. They would have no ethical qualms we didn’t program into them – and again, programming ethics into them would be the Friendly AI problem, which is really hard. And they would be near-impossible to regulate; most existing frameworks for such companies are built on crypto-currency and exist on the cloud in a way that transcends national borders.

(A quick and very simple example of an un-regulate-able ascended corporation – I don’t think it would be too hard to set up an automated version of Uber. I mean, the core Uber app is already an automated version of Uber, it just has company offices and CEOs and executives and so on doing public relations and marketing and stuff. But if the government ever banned Uber the company, could somebody just code another ride-sharing app that dealt securely in Bitcoins? And then have it skim a little bit off the top, which it offered as a bounty to anybody who gave it the processing power it would need to run? And maybe sent a little profit to the programmer who wrote the thing? Sure, the government could arrest the programmer, but short of arresting every driver and passenger there would be no way to destroy the company itself.)

The more ascended corporations there are trying to maximize shareholder value, the more chance there is some will cause negative externalities. But there’s a limited amount we would be able to do about them. This is true today too, but at least today we maintain the illusion that if we just elected Bernie Sanders we could reverse the ravages of capitalism and get an economy that cares about the environment and the family and the common man. An Ascended Economy would destroy that illusion.

How bad would it get? Once ascended corporations reach human or superhuman level intelligences, we run into the same AI goal-alignment problems as anywhere else. Would an ascended corporation pave over the Amazon to make a buck? Of course it would; even human corporations today do that, and an ascended corporation that didn’t have all human ethics programmed in might not even get that it was wrong. What if we programmed the corporation to follow local regulations, and Brazil banned paving over the Amazon? This is an example of trying to control AIs through goals plus injunctions – a tactic Bostrom finds very dubious. It’s essentially challenging a superintelligence to a battle of wits – “here’s something you want, and here are some rules telling you that you can’t get it, can you find a loophole in the rules?” If the superintelligence is super enough, the answer will always be yes.

From there we go into the really gnarly parts of AI goal alignment theory. Would an ascended corporation destroy South America entirely to make a buck? Depending on how it understood its imperative to maximize shareholder value, it might. Yes, this would probably kill many of its shareholders, but its goal is to “maximize shareholder value”, not to keep its shareholders alive to enjoy that value. It might even be willing to destroy humanity itself if other parts of the Ascended Economy would pick up the slack as investors.

Charlie Stross picks up where Scott left off in the ‘Economic 2.0’ scenario run amok he depicts in Accelerando, the post-singularity novel that’s featured in the last few posts. He takes this speculative viewpoint further than Scott does, or at least in a different direction – as an answer to the Fermi Paradox:

… while all this is going on, the damnfool human species has finally succeeded in making itself obsolete. The proximate cause of its displacement from the pinnacle of creation (or the pinnacle of teleological self-congratulation, depending on your stance on evolutionary biology) is an attack of self-aware corporations. The phrase “smart money” has taken on a whole new meaning, for the collision between international business law and neurocomputing technology has given rise to a whole new family of species – fast-moving corporate carnivores in the Net.

Consider for instance one of the more imaginatively alien aliens in science fiction – a defaulting corporate instrument disguising itself from creditors as a naturally-evolved alien, called ‘the Slug’:

“How much for just the civilization?” asks the Slug.

Pierre looks down at it thoughtfully. It’s not really a terrestrial mollusk: Slugs on Earth aren’t two meters long and don’t have lacy white exoskeletons to hold their chocolate-colored flesh in shape. But then, it isn’t really the alien it appears to be. It’s a defaulting corporate instrument that has disguised itself as a long-extinct alien upload, in the hope that its creditors won’t recognize it if it looks like a randomly evolved sentient. One of the stranded members of Amber’s expedition made contact with it a couple of subjective years ago, while exploring the ruined city at the center of the firewall. Now Pierre’s here because it seems to be one of their most promising leads. Emphasis on the word promising – because it promises much, but there is some question over whether it can indeed deliver.

“The civilization isn’t for sale,” Pierre says slowly. The translation interface shimmers, storing up his words and transforming them into a different deep grammar, not merely translating his syntax but mapping equivalent meanings where necessary. “But we can give you privileged observer status if that’s what you want. And we know what you are. If you’re interested in finding a new exchange to be traded on, your existing intellectual property assets will be worth rather more there than here.”

The rogue corporation rears up slightly and bunches into a fatter lump. Its skin blushes red in patches. “Must think about this. Is your mandatory accounting time cycle fixed or variable term? Are self-owned corporate entities able to enter contracts?”

“I could ask my patron,” Pierre says casually. He suppresses a stab of angst. He’s still not sure where he and Amber stand, but theirs is far more than just a business relationship, and he worries about the risks she’s taking. “My patron has a jurisdiction within which she can modify corporate law to accommodate your requirements. Your activities on a wider scale might require shell companies –” the latter concept echoes back in translation to him as host organisms – “but that can be taken care of.”

The translation membrane wibbles for a while, apparently reformulating some more abstract concepts in a manner that the corporation can absorb. Pierre is reasonably confident that it’ll take the offer, however. When it first met them, it boasted about its control over router hardware at the lowest levels. But it also bitched and moaned about the firewall protocols that were blocking it from leaving (before rather rudely trying to eat its conversationalist). He waits patiently, looking around at the swampy landscape, mudflats punctuated by clumps of spiky violet ferns. The corporation has to be desperate, to be thinking of the bizarre proposition Amber has dreamed up for him to pitch to it.

“Sounds interesting,” the Slug declares after a brief confirmatory debate with the membrane. “If I supply a suitable genome, can you customize a container for it?”

“I believe so,” Pierre says carefully. “For your part, can you deliver the energy we need?”

“From a gate?” For a moment the translation membrane hallucinates a stick-human, shrugging. “Easy. Gates are all entangled: Dump coherent radiation in at one, get it out at another. Just get me out of this firewall first.”

“But the lightspeed lag –”

“No problem. You go first, then a dumb instrument I leave behind buys up power and sends it after. Router network is synchronous, within framework of state machines that run Universe 1.0; messages propagate at same speed, speed of light in vacuum, except use wormholes to shorten distances between nodes. Whole point of the network is that it is nonlossy. Who would trust their mind to a communications channel that might partially randomize them in transit?”

Pierre goes cross-eyed, trying to understand the implications of the Slug’s cosmology. But there isn’t really time, here and now: They’ve got on the order of a minute of wall-clock time left to get everything sorted out, if Aineko is right. One minute to go before the angry ghosts start trying to break into the DMZ by other means. “If you are willing to try this, we’d be happy to accommodate you,” he says, thinking of crossed fingers and rabbits’ feet and firewalls.

“It’s a deal,” the membrane translates the Slug’s response back at him. “Now we exchange shares/plasmids/ownership? Then merger complete?”

Pierre stares at the Slug: “But this is a business arrangement!” he protests. “What’s sex got to do with it?”

“Apologies offered. I am thinking we have a translation error. You said this was to be a merging of businesses?”

“Not that way. It’s a contract. We agree to take you with us. In return, you help lure the Wunch into the domain we’re setting up for them and configure the router at the other end …”

and, further down:

Amber finds the Slug browsing quietly in a transparent space filled with lazily waving branches that resemble violet coral fans. They’re a ghost-memory of alien life, an order of thermophilic quasi fungi with hyphae ridged in actin/myosin analogues, muscular and slippery filter feeders that eat airborne unicellular organisms. The Slug itself is about two meters long and has a lacy white exoskeleton of curves and arcs that don’t repeat, disturbingly similar to a Penrose tiling. Chocolate brown organs pulse slowly under the skeleton. The ground underfoot is dry but feels swampy.

Actually, the Slug is a surgical disguise. Both it and the quasi-fungal ecosystem have been extinct for millions of years, existing only as cheap stage props in an interstellar medicine show run by rogue financial instruments. The Slug itself is one such self-aware scam, probably a pyramid scheme or even an entire compressed junk bond market in heavy recession, trying to hide from its creditors by masquerading as a life-form.

except that the Slug is just a particular instance of the corporation-as-lifeform, per this dialogue between two of the main characters:

“Corporations are life-forms back home, too, aren’t they? And we trade them. We give our AIs corporations to make them legal entities, but the analogy goes deeper. Look at any company headquarters, fitted out with works of art and expensive furniture and staff bowing and scraping everywhere –”

” – They’re the new aristocracy. Right?”

“Wrong. When they take over, what you get is more like the new biosphere. Hell, the new primordial soup: prokaryotes, bacteria, and algae, mindlessly swarming, trading money for plasmids.” The Queen passes her consort a wineglass. When he drinks from it, it refills miraculously. “Basically, sufficiently complex resource-allocation algorithms reallocate scarce resources … and if you don’t jump to get out of their way, they’ll reallocate you. I think that’s what happened inside the Matrioshka brain we ended up in: Judging by the Slug it happens elsewhere, too. You’ve got to wonder where the builders of that structure came from. And where they went. And whether they realized that the destiny of intelligent tool-using life was to be a stepping-stone in the evolution of corporate instruments.”

“Maybe they tried to dismantle the companies before the companies spent them.” Pierre looks worried. “Running up a national debt, importing luxurious viewpoint extensions, munching exotic dreams. Once they plugged into the Net, a primitive Matrioshka civilization would be like, um.” He pauses. “Tribal. A primitive postsingularity civilization meeting the galactic net for the first time. Overawed. Wanting all the luxuries. Spending their capital, their human – or alien – capital, the meme machines that built them. Until there’s nothing left but a howling wilderness of corporate mechanisms looking for someone to own.”


“Idle speculation,” he agrees.

“But we can’t ignore it.” She nods. “Maybe some early corporate predator built the machines that spread the wormholes around brown dwarfs and ran the router network on top of them in an attempt to make money fast. By not putting them in the actual planetary systems likely to host tool-using life, they’d ensure that only near-singularity civilizations would stumble over them. Civilizations that had gone too far to be easy prey probably wouldn’t send a ship out to look … so the network would ensure a steady stream of yokels new to the big city to fleece. Only they set the mechanism in motion billions of years ago and went extinct, leaving the network to propagate, and now there’s nothing out there but burned-out Matrioshka civilizations and howling parasites like the angry ghosts and the Wunch. And victims like us.”

So another answer to “where is everyone?” is “they got dissembled by corporations”.

Stross’ Accelerando by the decade: a blow-by-blow executive summary of the Singularity

Passages to make my heart race. A reread for old times’ sake.


Europe has achieved peaceful political union for the first time ever: They’re using this unprecedented state of affairs to harmonize the curvature of bananas. The Middle East is, well, it’s just as bad as ever, but the war on fundamentalism doesn’t hold much interest for Manfred. In San Diego, researchers are uploading lobsters into cyberspace, starting with the stomatogastric ganglion, one neuron at a time. They’re burning GM cocoa in Belize and books in Georgia. NASA still can’t put a man on the moon. Russia has re–elected the communist government with an increased majority in the Duma; meanwhile, in China, fevered rumors circulate about an imminent rehabilitation, the second coming of Mao, who will save them from the consequences of the Three Gorges disaster. In business news, the US Justice Department is – ironically – outraged at the Baby Bills. The divested Microsoft divisions have automated their legal processes and are spawning subsidiaries, IPOing them, and exchanging title in a bizarre parody of bacterial plasmid exchange, so fast that, by the time the windfall tax demands are served, the targets don’t exist anymore, even though the same staff are working on the same software in the same Mumbai cubicle farms.

Welcome to the twenty-first century.


Welcome to the early twenty-first century, human.

It’s night in Milton Keynes, sunrise in Hong Kong. Moore’s Law rolls inexorably on, dragging humanity toward the uncertain future. The planets of the solar system have a combined mass of approximately 2 x 1027 kilograms. Around the world, laboring women produce forty-five thousand babies a day, representing 1023 MIPS of processing power. Also around the world, fab lines casually churn out thirty million microprocessors a day, representing 1023MIPS. In another ten months, most of the MIPS being added to the solar system will be machine-hosted for the first time. About ten years after that, the solar system’s installed processing power will nudge the critical 1 MIPS per gram threshold – one million instructions per second per gram of matter. After that, singularity – a vanishing point beyond which extrapolating progress becomes meaningless. The time remaining before the intelligence spike is down to single-digit years ..


Welcome to the second decade of the twenty-first century; the second decade in human history when the intelligence of the environment has shown signs of rising to match human demand.

The news from around the world is distinctly depressing this evening. In Maine, guerrillas affiliated with Parents for Traditional Children announce they’ve planted logic bombs in antenatal-clinic gene scanners, making them give random false positives when checking for hereditary disorders: The damage so far is six illegal abortions and fourteen lawsuits.

The International Convention on Performing Rights is holding a third round of crisis talks in an attempt to stave off the final collapse of the WIPO music licensing regime. On the one hand, hard-liners representing the Copyright Control Association of America are pressing for restrictions on duplicating the altered emotional states associated with specific media performances: As a demonstration that they mean business, two “software engineers” in California have been kneecapped, tarred, feathered, and left for dead under placards accusing them of reverse-engineering movie plot lines using avatars of dead and out-of-copyright stars.

On the opposite side of the fence, the Association of Free Artists are demanding the right of perform music in public without a recording contract, and are denouncing the CCAA as being a tool of Mafiya apparachiks who have bought it from the moribund music industry in an attempt to go legit. FBI Director Leonid Kuibyshev responds by denying that the Mafiya is a significant presence in the United States. But the music biz’s position isn’t strengthened by the near collapse of the legitimate American entertainment industry, which has been accelerating ever since the nasty noughties.

A marginally intelligent voicemail virus masquerading as an IRS auditor has caused havoc throughout America, garnishing an estimated eighty billion dollars in confiscatory tax withholdings into a numbered Swiss bank account. A different virus is busy hijacking people’s bank accounts, sending ten percent of their assets to the previous victim, then mailing itself to everyone in the current mark’s address book: a self- propelled pyramid scheme in action. Oddly, nobody is complaining much. While the mess is being sorted out, business IT departments have gone to standby, refusing to process any transaction that doesn’t come in the shape of ink on dead trees.

Tipsters are warning of an impending readjustment in the overinflated reputations market, following revelations that some u-media gurus have been hyped past all realistic levels of credibility. The consequent damage to the junk-bonds market in integrity is serious.

The EU council of independent heads of state has denied plans for another attempt at Eurofederalisme, at least until the economy rises out of its current slump. Three extinct species have been resurrected in the past month; unfortunately, endangered ones are now dying off at a rate of one a day. And a group of militant anti-GM campaigners are being pursued by Interpol, after their announcement that they have spliced a metabolic pathway for cyanogenic glycosides into maize seed corn destined for human-edible crops. There have been no deaths yet, but having to test breakfast cereal for cyanide is really going to dent consumer trust.

About the only people who’re doing well right now are the uploaded lobsters – and the crusties aren’t even remotely human.


Welcome to the eve of the third decade: a time of chaos characterized by an all-out depression in the space industries.

Most of the thinking power on the planet is now manufactured rather than born; there are ten microprocessors for every human being, and the number is doubling every fourteen months. Population growth in the developing world has stalled, the birth rate dropping below replacement level. In the wired nations, more forward-looking politicians are looking for ways to enfranchise their nascent AI base.
Space exploration is still stalled on the cusp of the second recession of the century. The Malaysian government has announced the goal of placing an imam on Mars within ten years, but nobody else cares enough to try.

The Space Settlers Society is still trying to interest Disney Corp. in the media rights to their latest L5 colony plan, unaware that there’s already a colony out there and it isn’t human: First-generation uploads, Californian spiny lobsters in wobbly symbiosis with elderly expert systems, thrive aboard an asteroid mining project established by the Franklin Trust. Meanwhile, Chinese space agency cutbacks are threatening the continued existence of Moonbase Mao. Nobody, it seems, has figured out how to turn a profit out beyond geosynchronous orbit.

Two years ago, JPL, the ESA, and the uploaded lobster colony on comet Khrunichev-7 picked up an apparently artificial signal from outside the solar system; most people don’t know, and of those who do, even fewer care. After all, if humans can’t even make it to Mars, who cares what’s going on a hundred trillion kilometers farther out?


Getting back to the history lesson, the prospects for the decade look mostly medical.

A few thousand elderly baby boomers are converging on Tehran for Woodstock Four. Europe is desperately trying to import eastern European nurses and home-care assistants; in Japan, whole agricultural villages lie vacant and decaying, ghost communities sucked dry as cities slurp people in like residential black holes.

A rumor is spreading throughout gated old-age communities in the American Midwest, leaving havoc and riots in its wake: Senescence is caused by a slow virus coded into the mammalian genome that evolution hasn’t weeded out, and rich billionaires are sitting on the rights to a vaccine. As usual, Charles Darwin gets more than his fair share of the blame. (Less spectacular but more realistic treatments for old age – telomere reconstruction and hexose-denatured protein reduction – are available in private clinics for those who are willing to surrender their pensions.) Progress is expected to speed up shortly, as the fundamental patents in genomic engineering begin to expire; the Free Chromosome Foundation has already published a manifesto calling for the creation of an intellectual-property-free genome with improved replacements for all commonly defective exons.

Experiments in digitizing and running neural wetware under emulation are well established; some radical libertarians claim that, as the technology matures, death – with its draconian curtailment of property and voting rights – will become the biggest civil rights issue of all.

For a small extra fee, most veterinary insurance policies now cover cloning of pets in the event of their accidental and distressing death. Human cloning, for reasons nobody is very clear on anymore, is still illegal in most developed nations – but very few judiciaries push for mandatory abortion of identical twins.

Some commodities are expensive: the price of crude oil has broken eighty Euros a barrel and is edging inexorably up. Other commodities are cheap: computers, for example. Hobbyists print off weird new processor architectures on their home inkjets; middle-aged folks wipe their backsides with diagnostic paper that can tell how their cholesterol levels are tending.

The latest casualties of the march of technological progress are: the high-street clothes shop, the flushing water closet, the Main Battle Tank, and the first generation of quantum computers. New with the decade are cheap enhanced immune systems, brain implants that hook right into the Chomsky organ and talk to their owners through their own speech centers, and widespread public paranoia about limbic spam. Nanotechnology has shattered into a dozen disjoint disciplines, and skeptics are predicting that it will all peter out before long. Philosophers have ceded qualia to engineers, and the current difficult problem in AI is getting software to experience embarrassment.

Fusion power is still, of course, fifty years away.


Welcome to the fourth decade. The thinking mass of the solar system now exceeds one MIPS per gram; it’s still pretty dumb, but it’s not dumb all over. The human population is near maximum overshoot, pushing nine billion, but its growth rate is tipping toward negative numbers, and bits of what used to be the first world are now facing a middle-aged average. Human cogitation provides about 1028 MIPS of the solar system’s brainpower. The real thinking is mostly done by the halo of a thousand trillion processors that surround the meat machines with a haze of computation – individually a tenth as powerful as a human brain, collectively they’re ten thousand times more powerful, and their numbers are doubling every twenty million seconds. They’re up to 1033 MIPS and rising, although there’s a long way to go before the solar system is fully awake.

Technologies come, technologies go, but nobody even five years ago predicted that there’d be tinned primates in orbit around Jupiter by now: A synergy of emergent industries and strange business models have kick-started the space age again, aided and abetted by the discovery of (so far undecrypted) signals from ETs. Unexpected fringe riders are developing new ecological niches on the edge of the human information space, light-minutes and light-hours from the core, as an expansion that has hung fire since the 1970s gets under way.

Amber, like most of the postindustrialists aboard the orphanage ship Ernst Sanger, is in her early teens: While their natural abilities are in many cases enhanced by germ-line genetic recombination, thanks to her mother’s early ideals she has to rely on brute computational enhancements. She doesn’t have a posterior parietal cortex hacked for extra short-term memory, or an anterior superior temporal gyrus tweaked for superior verbal insight, but she’s grown up with neural implants that feel as natural to her as lungs or fingers. Half her wetware is running outside her skull on an array of processor nodes hooked into her brain by quantum-entangled communication channels – her own personal metacortex. These kids are mutant youth, burning bright: Not quite incomprehensible to their parents, but profoundly alien – the generation gap is as wide as the 1960s and as deep as the solar system. Their parents, born in the gutter years of the twenty-first century, grew up with white elephant shuttles and a space station that just went round and round, and computers that went beep when you pushed their buttons. The idea that Jupiter orbit was somewhere you could go was as profoundly counterintuitive as the Internet to a baby boomer.

Most of the passengers on the can have run away from parents who think that teenagers belong in school, unable to come to terms with a generation so heavily augmented that they are fundamentally brighter than the adults around them. Amber was fluent in nine languages by the age of six, only two of them human and six of them serializable; when she was seven, her mother took her to the school psychiatrist for speaking in synthetic tongues. That was the final straw for Amber: using an illicit anonymous phone, she called her father. Her mother had him under a restraining order, but it hadn’t occurred to her to apply for an order against his partner …


Half a light-hour away, tired Earth wakes and slumbers in time to its ancient orbital dynamics. A religious college in Cairo is considering issues of nanotechnology: If replicators are used to prepare a copy of a strip of bacon, right down to the molecular level, but without it ever being part of a pig, how is it to be treated? (If the mind of one of the faithful is copied into a computing machine’s memory by mapping and simulating all its synapses, is the computer now a Moslem? If not, why not? If so, what are its rights and duties?) Riots in Borneo underline the urgency of this theotechnological inquiry.

More riots in Barcelona, Madrid, Birmingham, and Marseilles also underline a rising problem: the social chaos caused by cheap anti-aging treatments. The zombie exterminators, a backlash of disaffected youth against the formerly graying gerontocracy of Europe, insist that people who predate the supergrid and can’t handle implants aren’t really conscious: Their ferocity is equaled only by the anger of the dynamic septuagenarians of the baby boom, their bodies partially restored to the flush of sixties youth, but their minds adrift in a slower, less contingent century. The faux-young boomers feel betrayed, forced back into the labor pool, but unable to cope with the implant-accelerated culture of the new millennium, their hard-earned experience rendered obsolete by deflationary time.

The Bangladeshi economic miracle is typical of the age. With growth rates running at over twenty percent, cheap out-of-control bioindustrialization has swept the nation: Former rice farmers harvest plastics and milk cows for silk, while their children study mariculture and design seawalls. With cellphone ownership nearing eighty percent and literacy at ninety, the once-poor country is finally breaking out of its historical infrastructure trap and beginning to develop: In another generation, they’ll be richer than Japan.

Radical new economic theories are focusing around bandwidth, speed-of-light transmission time, and the implications of CETI, communication with extraterrestrial intelligence. Cosmologists and quants collaborate on bizarre relativistically telescoped financial instruments. Space (which lets you store information) and structure (which lets you process it) acquire value while dumb mass – like gold – loses it. The degenerate cores of the traditional stock markets are in free fall, the old smokestack microprocessor and biotech/nanotech industries crumbling before the onslaught of matter replicators and self-modifying ideas. The inheritors look set to be a new wave of barbarian communicators, who mortgage their future for a millennium against the chance of a gift from a visiting alien intelligence. Microsoft, once the US Steel of the silicon age, quietly fades into liquidation.

An outbreak of green goo – a crude biomechanical replicator that eats everything in its path – is dealt with in the Australian outback by carpet-bombing with fuel-air explosives. The USAF subsequently reactivates two wings of refurbished B-52s and places them at the disposal of the UN standing committee on self-replicating weapons. (CNN discovers that one of their newest pilots, re-enlisting with the body of a twenty-year-old and an empty pension account, first flew them over Laos and Cambodia.) The news overshadows the World Health Organization’s announcement of the end of the HIV pandemic, after more than fifty years of bigotry, panic, and megadeath.


Greetings from the fifth decade of the century of wonders.

The solar system that lies roughly twenty-eight trillion kilometers – just short of three light-years – behind the speeding starwisp Field Circus is seething with change. There have been more technological advances in the past ten years than in the entire previous expanse of human history – and more unforeseen accidents.

Lots of hard problems have proven to be tractable. The planetary genome and proteome have been mapped so exhaustively that the biosciences are now focusing on the challenge of the phenome: Plotting the phase-space defined by the intersection of genes and biochemical structures, understanding how extended phenotypic traits are generated and contribute to evolutionary fitness. The biosphere has become surreal: small dragons have been sighted nesting in the Scottish highlands, and in the American midwest, raccoons have been caught programming microwave ovens.

The computing power of the solar system is now around one thousand MIPS per gram, and is unlikely to increase in the near term – all but a fraction of one percent of the dumb matter is still locked up below the accessible planetary crusts, and the sapience/mass ratio has hit a glass ceiling that will only be broken when people, corporations, or other posthumans get around to dismantling the larger planets. A start has already been made in Jupiter orbit and the asteroid belt. Greenpeace has sent squatters to occupy Eros and Juno, but the average asteroid is now surrounded by a reef of specialized nanomachinery and debris, victims of a cosmic land grab unmatched since the days of the wild west. The best brains flourish in free fall, minds surrounded by a sapient aether of extensions that out-think their meaty cortices by many orders of magnitude – minds like Amber, Queen of the Inner Ring Imperium, the first self-extending power center in Jupiter orbit.

Down at the bottom of the terrestrial gravity well, there has been a major economic catastrophe. Cheap immortagens, out-of-control personality adjuvants, and a new formal theory of uncertainty have knocked the bottom out of the insurance and underwriting industries. Gambling on a continuation of the worst aspects of the human condition – disease, senescence, and death – looks like a good way to lose money, and a deflationary spiral lasting almost fifty hours has taken down huge swaths of the global stock market. Genius, good looks, and long life are now considered basic human rights in the developed world: even the poorest backwaters are feeling extended effects from the commoditization of intelligence.

Not everything is sweetness and light in the era of mature nanotechnology. Widespread intelligence amplification doesn’t lead to widespread rational behavior. New religions and mystery cults explode across the planet; much of the Net is unusable, flattened by successive semiotic jihads. India and Pakistan have held their long-awaited nuclear war: external intervention by US and EU nanosats prevented most of the IRBMs from getting through, but the subsequent spate of network raids and Basilisk attacks cause havoc. Luckily, infowar turns out to be more survivable than nuclear war – especially once it is discovered that a simple anti-aliasing filter stops nine out of ten neural-wetware-crashing Langford fractals from causing anything worse than a mild headache.

New discoveries this decade include the origins of the weakly repulsive force responsible for changes in the rate of expansion of the universe after the big bang, and on a less abstract level, experimental implementations of a Turing Oracle using quantum entanglement circuits: a device that can determine whether a given functional expression can be evaluated in finite time. It’s boom time in the field of Extreme Cosmology, where some of the more recherché researchers are bickering over the possibility that the entire universe was created as a computing device, with a program encoded in the small print of the Planck constant. And theorists are talking again about the possibility of using artificial wormholes to provide instantaneous connections between distant corners of space-time.
Most people have forgotten about the well-known extraterrestrial transmission received fifteen years earlier. Very few people know anything about the second, more complex transmission received a little later. Many of those are now passengers or spectators of the Field Circus: a light-sail craft that is speeding out of Sol system on a laser beam generated by Amber’s installations in low-Jupiter orbit. (Superconducting tethers anchored to Amalthea drag through Jupiter’s magnetosphere, providing gigawatts of electricity for the hungry lasers: energy that comes, in turn, from the small moon’s orbital momentum.)

Manufactured by Airbus-Cisco years earlier, the Field Circus is a hick backwater, isolated from the mainstream of human culture, its systems complexity limited by mass: The destination lies nearly three light-years from Earth, and even with high acceleration and relativistic cruise speeds, the one-kilogram starwisp and its hundred-kilogram light sail will take the best part of seven years to get there. Sending a human-sized probe is beyond even the vast energy budget of the new orbital states in Jupiter system – near-lightspeed travel is horrifically expensive. Rather than a big, self-propelled ship with canned primates for passengers, as previous generations had envisaged, the starship is a Coke-can-sized slab of nanocomputers, running a neural simulation of the uploaded brain states of some tens of humans at merely normal speed. By the time its occupants beam themselves home again for download into freshly cloned bodies, a linear extrapolation shows that as much change will have overtaken human civilization as in the preceding fifty millennia – the sum total of H. sapiens sapiens‘ time on Earth.

But that’s okay by Amber, because what she expects to find in orbit around the brown dwarf Hyundai +4904/-56 will be worth the wait.

Take a brain and put it in a bottle. Better: take a map of the brain and put it in a map of a bottle – or of a body – and feed signals to it that mimic its neurological inputs. Read its outputs and route them to a model body in a model universe with a model of physical laws, closing the loop. René Descartes would understand. That’s the state of the passengers of the Field Circus in a nutshell. Formerly physical humans, their neural software (and a map of the intracranial wetware it runs on) has been transferred into a virtual machine environment executing on a honking great computer, where the universe they experience is merely a dream within a dream.

Brains in bottles – empowered ones, with total, dictatorial, control over the reality they are exposed to – sometimes stop engaging in activities that brains in bodies can’t avoid. Menstruation isn’t mandatory. Vomiting, angina, exhaustion, and cramp are all optional. So is meatdeath, the decomposition of the corpus. But some activities don’t cease, because people (even people who have been converted into a software description, squirted through a high-bandwidth laser link, and ported into a virtualization stack) don’t want them to stop. Breathing is wholly unnecessary, but suppression of the breathing reflex is disturbing unless you hack your hypothalamic map, and most homomorphic uploads don’t want to do that. Then there’s eating – not to avoid starvation, but for pleasure: Feasts on sautéed dodo seasoned with silphium are readily available here, and indeed, why not? It seems the human addiction to sensory input won’t go away. And that’s without considering sex, and the technical innovations that become possible when the universe – and the bodies within it – are mutable.


Greetings from the last megasecond before the discontinuity.

The solar system is thinking furiously at 1033 MIPS – thoughts bubble and swirl in the equivalent of a million billion unaugmented human minds. Saturn’s rings glow with waste heat. The remaining faithful of the Latter-Day Saints are correlating the phase-space of their genome and the records of their descent in an attempt to resurrect their ancestors. Several skyhooks have unfurled in equatorial orbit around the earth like the graceful fernlike leaves of sundews, ferrying cargo and passengers to and from orbit. Small, crab like robots swarm the surface of Mercury, exuding a black slime of photovoltaic converters and the silvery threads of mass drivers. A glowing cloud of industrial nanomes forms a haze around the innermost planet as it slowly shrinks under the onslaught of copious solar power and determined mining robots.

The original incarnations of Amber and her court float in high orbit above Jupiter, presiding over the huge nexus of dumb matter trade that is rapidly biting into the available mass of the inner Jovian system. The trade in reaction mass is brisk, and there are shipments of diamond/vacuum biphase structures to assemble and crank down into the lower reaches of the solar system. Far below, skimming the edges of Jupiter’s turbulent cloudscape, a gigantic glowing figure-of-eight – a five-hundred-kilometer-long loop of superconducting cable – traces incandescent trails through the gas giant’s magnetosphere. It’s trading momentum for electrical current, diverting it into a fly’s eye grid of lasers that beam it toward Hyundai +4904/-56. As long as the original Amber and her incarnate team can keep it running, the Field Circus can continue its mission of discovery, but they’re part of the posthuman civilization evolving down in the turbulent depths of Sol system, part of the runaway train being dragged behind the out-of-control engine of history.

Weird new biologies based on complex adaptive matter take shape in the sterile oceans of Titan. In the frigid depths beyond Pluto, supercooled boson gases condense into impossible dreaming structures, packaged for shipping inward to the fast-thinking core.

There are still humans dwelling down in the hot depths, but it’s getting hard to recognize them. The lot of humanity before the twenty-first century was nasty, brutish, and short. Chronic malnutrition, lack of education, and endemic diseases led to crippled minds and broken bodies. Now, most people multitask: Their meatbrains sit at the core of a haze of personality, much of it virtualized on stacked layers of structured reality far from their physical bodies. Wars and revolutions, or their subtle latter-day cognates, sweep the globe as constants become variables; many people find the death of stupidity even harder to accept than the end of mortality. Some have vitrified themselves to await an uncertain posthuman future. Others have modified their core identities to better cope with the changed demands of reality. Among these are beings whom nobody from a previous century would recognize as human – human/corporation half-breeds, zombie clades dehumanized by their own optimizations, angels and devils of software, slyly self-aware financial instruments. Even their popular fictions are self-deconstructing these days.

None of this, other than the barest news summary, reaches the Field Circus: The starwisp is a fossil, left behind by the broad sweep of accelerating progress. But it is aboard the Field Circus that some of the most important events remaining in humanity’s future light cone take place.

Seven – awaken:

Outside the light cone of the Field Circus, on the other side of the spacelike separation between Amber’s little kingdom in motion and the depths of empire time that grip the solar system’s entangled quantum networks, a singular new reality is taking shape.

Welcome to the moment of maximum change.

About ten billion humans are alive in the solar system, each mind surrounded by an exocortex of distributed agents, threads of personality spun right out of their heads to run on the clouds of utility fog – infinitely flexible computing resources as thin as aerogel – in which they live. The foggy depths are alive with high-bandwidth sparkles; most of Earth’s biosphere has been wrapped in cotton wool and preserved for future examination. For every living human, a thousand million software agents carry information into the farthest corners of the consciousness address space.

The sun, for so long an unremarkable mildly variable G2 dwarf, has vanished within a gray cloud that englobes it except for a narrow belt around the plane of the ecliptic. Sunlight falls, unchanged, on the inner planets: Except for Mercury, which is no longer present, having been dismantled completely and turned into solar-powered high-temperature nanocomputers. A much fiercer light falls on Venus, now surrounded by glittering ferns of carbon crystals that pump angular momentum into the barely spinning planet via huge superconducting loops wound around its equator. This planet, too, is due to be dismantled. Jupiter, Neptune, Uranus – all sprout rings as impressive as Saturn’s. But the task of cannibalizing the gas giants will take many times longer than the small rocky bodies of the inner system.

The ten billion inhabitants of this radically changed star system remember being human; almost half of them predate the millennium. Some of them still are human, untouched by the drive of meta-evolution that has replaced blind Darwinian change with a goal-directed teleological progress. They cower in gated communities and hill forts, mumbling prayers and cursing the ungodly meddlers with the natural order of things. But eight out of every ten living humans are included in the phase-change. It’s the most inclusive revolution in the human condition since the discovery of speech.

A million outbreaks of gray goo – runaway nanoreplicator excursions – threaten to raise the temperature of the biosphere dramatically. They’re all contained by the planetary-scale immune system fashioned from what was once the World Health Organization. Weirder catastrophes threaten the boson factories in the Oort cloud. Antimatter factories hover over the solar poles. Sol system shows all the symptoms of a runaway intelligence excursion, exuberant blemishes as normal for a technological civilization as skin problems on a human adolescent.

The economic map of the planet has changed beyond recognition. Both capitalism and communism, bickering ideological children of a protoindustrial outlook, are as obsolete as the divine right of kings: Companies are alive, and dead people may live again, too. Globalism and tribalism have run to completion, diverging respectively into homogeneous interoperability and the Schwarzschild radius of insularity. Beings that remember being human plan the deconstruction of Jupiter, the creation of a great simulation space that will expand the habitat available within the solar system. By converting all the nonstellar mass of the solar system into processors, they can accommodate as many human-equivalent minds as a civilization with a planet hosting ten billion humans in orbit around every star in the galaxy.

A more mature version of Amber lives down in the surging chaos of near-Jupiter space; there’s an instance of Pierre, too, although he has relocated light-hours away, near Neptune. Whether she still sometimes thinks of her relativistic twin, nobody can tell. In a way, it doesn’t matter, because by the time the Field Circus returns to Jupiter orbit, as much subjective time will have elapsed for the fast-thinkers back home as will flash by in the real universe between this moment and the end of the era of star formation, many billions of years hence.


Welcome to the downslope on the far side of the curve of accelerating progress.

Back in the solar system, Earth orbits through a dusty tunnel in space. Sunlight still reaches the birth world, but much of the rest of the star’s output has been trapped by the growing concentric shells of computronium built from the wreckage of the innermost planets.
Two billion or so mostly unmodified humans scramble in the wreckage of the phase transition, not understanding why the vasty superculture they so resented has fallen quiet. Little information leaks through their fundamentalist firewalls, but what there is shows a disquieting picture of a society where there are no bodies anymore. Utility foglets blown on the wind form aerogel towers larger than cyclones, removing the last traces of physical human civilization from most of Europe and the North American coastlines. Enclaves huddle behind their walls and wonder at the monsters and portents roaming the desert of postindustrial civilization, mistaking acceleration for collapse.

The hazy shells of computronium that ring the sun – concentric clouds of nanocomputers the size of rice grains, powered by sunlight, orbiting in shells like the packed layers of a Matrioshka doll – are still immature, holding barely a thousandth of the physical planetary mass of the system, but they already support a classical computational density of 1042 MIPS; enough to support a billion civilizations as complex as the one that existed immediately before the great disassembly. The conversion hasn’t yet reached the gas giants, and some scant outer-system enclaves remain independent – Amber’s Ring Imperium still exists as a separate entity, and will do so for some years to come – but the inner solar system planets, with the exception of Earth, have been colonized more thoroughly than any dusty NASA proposal from the dawn of the space age could have envisaged.

From outside the Accelerated civilization, it isn’t really possible to know what’s going on inside. The problem is bandwidth: While it’s possible to send data in and get data out, the sheer amount of computation going on in the virtual spaces of the Acceleration dwarfs any external observer. Inside that swarm, minds a trillion or more times as complex as humanity think thoughts as far beyond human imagination as a microprocessor is beyond a nematode worm. A million random human civilizations flourish in worldscapes tucked in the corner of this world-mind. Death is abolished, life is triumphant. A thousand ideologies flower, human nature adapted where necessary to make this possible. Ecologies of thought are forming in a Cambrian explosion of ideas: For the solar system is finally rising to consciousness, and mind is no longer restricted to the mere kilotons of gray fatty meat harbored in fragile human skulls.

Somewhere in the Acceleration, colorless green ideas adrift in furious sleep remember a tiny starship launched years ago, and pay attention. Soon, they realize, the starship will be in position to act as their proxy in an ages-long conversation. Negotiations for access to Amber’s extrasolar asset commence; the Ring Imperium prospers, at least for a while.

But first, the operating software on the human side of the network link will require an upgrade.


Welcome to decade the sixth, millennium three. These old datelines don’t mean so much anymore, for while some billions of fleshbody humans are still infected with viral memes, the significance of theocentric dating has been dealt a body blow. This may be the fifties, but what that means to you depends on how fast your reality rate runs. The various upload clades exploding across the reaches of the solar system vary by several orders of magnitude – some are barely out of 2049, while others are exploring the subjective thousandth millennium.

While the Field Circus floats in orbit around an alien router (itself orbiting the brown dwarf Hyundai +4904/-56), while Amber and her crew are trapped on the far side of a wormhole linking the router to a network of incomprehensibly vast alien mindscapes – while all this is going on, the damnfool human species has finally succeeded in making itself obsolete. The proximate cause of its displacement from the pinnacle of creation (or the pinnacle of teleological self-congratulation, depending on your stance on evolutionary biology) is an attack of self-aware corporations. The phrase “smart money” has taken on a whole new meaning, for the collision between international business law and neurocomputing technology has given rise to a whole new family of species – fast-moving corporate carnivores in the Net. The planet Mercury has been broken up by a consortium of energy brokers, and Venus is an expanding debris cloud, energized to a violent glare by the trapped and channeled solar output. A million billion fist-sized computing caltrops, backsides glowing dull red with the efflux from their thinking, orbit the sun at various inclinations no farther out than Mercury used to be.

Billions of fleshbody humans refuse to have anything to do with the blasphemous new realities. Many of their leaders denounce the uploads and AIs as soulless machines. Many more are timid, harboring self-preservation memes that amplify a previously healthy aversion to having one’s brain peeled like an onion by mind-mapping robots into an all-pervading neurosis. Sales of electrified tinfoil-lined hats are at an all-time high. Still, hundreds of millions have already traded their meat puppets for mind machines, and they breed fast. In another few years, the fleshbody populace will be an absolute minority of the posthuman clade. Sometime later, there will probably be a war. The dwellers in the thoughtcloud are hungry for dumb matter to convert, and the fleshbodies make notoriously poor use of the collection of silicon and rare elements that pool at the bottom of the gravity well that is Earth.

Energy and thought are driving a phase-change in the condensed matter substance of the solar system. The MIPS per kilogram metric is on the steep upward leg of a sigmoid curve – dumb matter is coming to life as the mind children restructure everything with voracious nanomechanical servants. The thoughtcloud forming in orbit around the sun will ultimately be the graveyard of a biological ecology, another marker in space visible to the telescopes of any new iron-age species with the insight to understand what they’re seeing: the death throes of dumb matter, the birth of a habitable reality vaster than a galaxy and far speedier. Death throes that, within a few centuries, will mean the extinction of biological life within a light-year or so of that star – for the majestic Matrioshka brains, though they are the pinnacles of sentient civilization, are intrinsically hostile environments for fleshy life.


Welcome to decade eight, third millennium, when the effects of the phase-change in the structure of the solar system are finally becoming visible on a cosmological scale.

There are about eleven billion future-shocked primates in various states of life and undeath throughout the solar system. Most of them cluster where the interpersonal bandwidth is hottest, down in the water zone around old Earth. Earth’s biosphere has been in the intensive care ward for decades, weird rashes of hot-burning replicators erupting across it before the World Health Organization can fix them – gray goo, thylacines, dragons. The last great transglobal trade empire, run from the arcologies of Hong Kong, has collapsed along with capitalism, rendered obsolete by a bunch of superior deterministic resource allocation algorithms collectively known as Economics 2.0. Mercury, Venus, Mars, and Luna are all well on the way to disintegration, mass pumped into orbit with energy stolen from the haze of free-flying thermoelectrics that cluster so thickly around the solar poles that the sun resembles a fuzzy red ball of wool the size of a young red giant.

Humans are just barely intelligent tool users; Darwinian evolutionary selection stopped when language and tool use converged, leaving the average hairy meme carrier sadly deficient in smarts. Now the brightly burning beacon of sapience isn’t held by humans anymore – their cross-infectious enthusiasms have spread to a myriad of other hosts, several types of which are qualitatively better at thinking. At last count, there were about a thousand nonhuman intelligent species in Sol space, split evenly between posthumans on one side, naturally self-organizing AIs in the middle, and mammalian nonhumans on the other. The common mammal neural chassis is easily upgraded to human-style intelligence in most species that can carry, feed and cool a half kilogram of gray matter, and the descendants of a hundred ethics-challenged doctoral theses are now demanding equal rights. So are the unquiet dead; the panopticon-logged Net ghosts of people who lived recently enough to imprint their identities on the information age, and the ambitious theological engineering schemes of the Reformed Tiplerite Church of Latter-day Saints (who want to emulate all possible human beings in real time, so that they can have the opportunity to be saved).

The human memesphere is coming alive, although how long it remains recognizably human is open to question. The informational density of the inner planets is visibly converging on Avogadro’s number of bits per mole, one bit per atom, as the deconstructed dumb matter of the inner planets (apart from Earth, preserved for now like a picturesque historic building stranded in an industrial park) is converted into computronium. And it’s not just the inner system. The same forces are at work on Jupiter’s moons, and those of Saturn, although it’ll take thousands of years rather than mere decades to dismantle the gas giants themselves. Even the entire solar energy budget isn’t enough to pump Jupiter’s enormous mass to orbital velocity in less than centuries. The fast-burning primitive thinkers descended from the African plains apes may have vanished completely or transcended their fleshy architecture before the solar Matrioshka brain is finished.

It won’t be long now …

Interlude – a passage I remember from my first reading of Accelerando many years ago:

“More than that,” says Amber, idly kicking at a tussock of grass. She squints at Sirhan. “My mother is dead,” she remarks quietly. Louder: “She never really asked what we found beyond the router. Neither did you, did you? The Matrioshka brains – it’s a standard part of the stellar life cycle. Life begets intelligence, intelligence begets smart matter and a singularity. I’ve been doing some thinking about it. I figure the singularity stays close to home in most cases, because bandwidth and latency time put anyone who leaves at a profound disadvantage. In effect, the flip side of having such huge resources close to home is that the travel time to other star systems becomes much more daunting. So they restructure the entire mass of their star system into a free-flying shell of nanocomputers, then more of them, Dyson spheres, shells within shells, like a Russian doll: a Matrioshka brain. Then Economics 2.0 or one of its successors comes along and wipes out the creators. But. Some of them survive. Some of them escape that fate: the enormous collection in the halo around M-31, and maybe whoever built the routers. Somewhere out there we will find the transcendent intelligences, the ones that survived their own economic engines of redistribution – engines that redistribute entropy if their economic efficiency outstrips their imaginative power, their ability to invent new wealth.”


Welcome to decade the ninth, singularity plus one gigasecond (or maybe more – nobody’s quite sure when, or indeed if, a singularity has been created). The human population of the solar system is either six billion, or sixty billion, depending on whether you class the forked state vectors of posthumans and the simulations of dead phenotypes running in the Vile Offspring’s Schrödinger boxes as people. Most of the physically incarnate still live on Earth, but the lily-pads floating beneath continent-sized hot-hydrogen balloons in Saturn’s upper atmosphere already house a few million, and the writing is on the wall for the rocky inner planets. All the remaining human-equivalent intelligences with half a clue to rub together are trying to emigrate before the Vile Offspring decide to recycle Earth to fill in a gap in the concentric shells of nanocomputers they’re running on. The half-constructed Matrioshka brain already darkens the skies of Earth and has caused a massive crash in the planet’s photosynthetic biomass, as plants starve for short-wavelength light.

Since decade the seventh, the computational density of the solar system has soared. Within the asteroid belt, more than half the available planetary mass has been turned into nanoprocessors, tied together by quantum entanglement into a web so dense that each gram of matter can simulate all the possible life experiences of an individual human being in a scant handful of minutes. Economics 2.0 is itself obsolescent, forced to mutate in a furious survivalist arms race by the arrival of the Slug. Only the name remains as a vague shorthand for merely human-equivalent intelligences to use when describing interactions they don’t understand.

The latest generation of posthuman entities is less overtly hostile to humans, but much more alien than the generations of the fifties and seventies. Among their less comprehensible activities, the Vile Offspring are engaged in exploring the phase-space of all possible human experiences from the inside out. Perhaps they caught a dose of the Tiplerite heresy along the way, for now a steady stream of resimulant uploads is pouring through the downsystem relays in Titan orbit. The Rapture of the Nerds has been followed by the Resurrection of the Extremely Confused, except that they’re not really resurrectees – they’re simulations based on their originals’ recorded histories, blocky and missing chunks of their memories, as bewildered as baby ducklings as they’re herded into the wood-chipper of the future.


Welcome to the afterglow of the intelligence supernova, little tapeworm.

Tapeworms have on the order of a thousand neurons, pulsing furiously to keep their little bodies twitching. Human beings have on the order of a hundred billion neurons. What is happening in the inner solar system as the Vile Offspring churn and reconfigure the fast-thinking structured dust clouds that were once planets is as far beyond the ken of merely human consciousness as the thoughts of a Gödel are beyond the twitching tropisms of a worm. Personality modules bounded by the speed of light, sucking down billions of times the processing power of a human brain, form and re-form in the halo of glowing nanoprocessors that shrouds the sun in a ruddy glowing cloud.

Mercury, Venus, Mars, Ceres and the asteroids – all gone. Luna is a silvery iridescent sphere, planed smooth down to micrometer heights, luminous with diffraction patterns. Only Earth, the cradle of human civilization, remains untransformed; and Earth, too, will be dismantled soon enough, for already a trellis of space elevators webs the planet around its equator, lifting refugee dumb matter into orbit and flinging it at the wildlife preserves of the outer system.

The intelligence bloom that gnaws at Jupiter’s moons with claws of molecular machinery won’t stop until it runs out of dumb matter to convert into computronium. By the time it does, it will have as much brainpower as you’d get if you placed a planet with a population of six billion future-shocked primates in orbit around every star in the Milky Way galaxy. But right now, it’s still stupid, having converted barely a percentage point of the mass of the solar system – it’s a mere Magellanic Cloud civilization, infantile and unsubtle and still perilously close to its carbon-chemistry roots.

It’s hard for tapeworms living in warm intestinal mulch to wrap their thousand-neuron brains around whatever it is that the vastly more complex entities who host them are discussing, but one thing’s sure – the owners have a lot of things going on, not all of them under conscious control. The churning of gastric secretions and the steady ventilation of lungs are incomprehensible to the simple brains of tapeworms, but they serve the purpose of keeping the humans alive and provide the environment the worms live in. And other more esoteric functions that contribute to survival – the intricate dance of specialized cloned lymphocytes in their bone marrow and lymph nodes, the random permutations of antibodies constantly churning for possible matches to intruder molecules warning of the presence of pollution – are all going on beneath the level of conscious control.

Autonomic defenses. Antibodies. Intelligence bloom gnawing at the edges of the outer system. And humans are not as unsophisticated as mulch wrigglers, they can see the writing on the wall. Is it any surprise, that among the ones who look outward, the real debate is not over whether to run, but over how far and how fast?


Somewhere in the gas-sprinkled darkness beyond the local void, carbon-based life stirs. A cylinder of diamond fifty kilometers long spins in the darkness, its surface etched with strange quantum wells that emulate exotic atoms not found in any periodic table that Mendeleyev would have recognized. Within it, walls hold kilotonnes of oxygen and nitrogen gas, megatonnes of life-infested soil. A hundred trillion kilometers from the wreckage of Earth, the cylinder glitters like a gem in the darkness.

Welcome to New Japan: one of the places between the stars where human beings hang out, now that the solar system is off-limits to meatbodies.

I wonder who we’ll find here?

It has been a long time since Aineko passed this way, and in the meantime the space around Hyundai +4904/-56 has changed out of all recognition. Back when the great lobster-built starships swept out of Sol’s Oort cloud, archiving the raw frozen data of the unoccupied brown dwarf halo systems and seeding their structured excrement with programmable matter, there was nothing but random dead atoms hereabouts (and an alien router). But that was a long time ago; and since then, the brown dwarf system has succumbed to an anthropic infestation.

An unoptimized instance of H. sapiens maintains state coherency for only two to three gigaseconds before it succumbs to necrosis. But in only about ten gigaseconds, the infestation has turned the dead brown dwarf system upside down. They strip-mined the chilly planets to make environments suitable for their own variety of carbon life. They rearranged moons, building massive structures the size of asteroids. They ripped wormhole endpoints free of the routers and turned them into their own crude point-to-point network, learned how to generate new wormholes, then ran their own packet-switched polities over them. Wormhole traffic now supports an ever-expanding mesh of interstellar human commerce, but always in the darkness between the lit stars and the strange, metal-depleted dwarfs with the suspiciously low-entropy radiation. The sheer temerity of the project is mind-boggling: notwithstanding that canned apes are simply not suited to life in the interstellar void, especially in orbit around a brown dwarf whose planets make Pluto seem like a tropical paradise, they’ve taken over the whole damn system.

New Japan is one of the newer human polities in this system, a bunch of nodes physically collocated in the humaniformed spaces of the colony cylinders. Its designers evidently only knew about old Nippon from recordings made back before Earth was dismantled, and worked from a combination of nostalgia-trip videos, Miyazaki movies, and anime culture. Nevertheless, it’s the home of numerous human beings – even if they are about as similar to their historical antecedents as New Japan is to its long-gone namesake.


Their grandparents would recognize them, mostly. The ones who are truly beyond the ken of twentieth-century survivors stayed back home in the red-hot clouds of nanocomputers that have replaced the planets that once orbited Earth’s sun in stately Copernican harmony. The fast-thinking Matrioshka brains are as incomprehensible to their merely posthuman ancestors as an ICBM to an amoeba – and about as inhabitable. Space is dusted with the corpses of Matrioshka brains that have long since burned out, informational collapse taking down entire civilizations that stayed in close orbit around their home stars. Farther away, galaxy-sized intelligences beat incomprehensible rhythms against the darkness of the vacuum, trying to hack the Planck substrate into doing their bidding. Posthumans, and the few other semitranscended species to have discovered the router network, live furtively in the darkness between these islands of brilliance. There are, it would seem, advantages to not being too intelligent.
Humanity. Monadic intelligences, mostly trapped within their own skulls, living in small family groups within larger tribal networks, adaptable to territorial or migratory lifestyles. Those were the options on offer before the great acceleration. Now that dumb matter thinks, with every kilogram of wallpaper potentially hosting hundreds of uploaded ancestors, now that every door is potentially a wormhole to a hab half a parsec away, the humans can stay in the same place while the landscape migrates and mutates past them, streaming into the luxurious void of their personal history. Life is rich here, endlessly varied and sometimes confusing. So it is that tribal groups remain, their associations mediated across teraklicks and gigaseconds by exotic agencies. And sometimes the agencies will vanish for a while, reappearing later like an unexpected jape upon the infinite.


Welcome to the twenty-third century, or the twenty-fourth. Or maybe it’s the twenty-second, jet-lagged and dazed by spurious suspended animation and relativistic travel; it hardly matters these days. What’s left of recognizable humanity has scattered across a hundred light-years, living in hollowed-out asteroids and cylindrical spinning habitats strung in orbit around cold brown dwarf stars and sunless planets that wander the interstellar void. The looted mechanisms underlying the alien routers have been cannibalized, simplified to a level the merely superhuman can almost comprehend, turned into generators for paired wormhole endpoints that allow instantaneous switched transport across vast distances. Other mechanisms, the descendants of the advanced nanotechnologies developed by the flowering of human techgnosis in the twenty-first century, have made the replication of dumb matter trivial; this is not a society accustomed to scarcity.

But in some respects, New Japan and the Invisible Empire and the other polities of human space are poverty-stricken backwaters. They take no part in the higher-order economies of the posthuman. They can barely comprehend the idle muttering of the Vile Offspring, whose mass/energy budget (derived from their complete restructuring of the free matter of humanity’s original solar system into computronium) dwarfs that of half a hundred human-occupied brown dwarf systems. And they still know worryingly little about the deep history of intelligence in this universe, about the origins of the router network that laces so many dead civilizations into an embrace of death and decay, about the distant galaxy-scale bursts of information processing that lie at measurable red-shift distances, even about the free posthumans who live among them in some senses, collocated in the same light cone as these living fossil relics of old-fashioned humanity.

James Patterson, author-corporation

I forget how I came across James Patterson. I’m not talking about first encounters with his books – they fill entire shelves at Kinokuniya, a feat paralleled by no other author, and have done so since time immemorial – I’m talking about the particular narrative thread that culminates in this blog post. But somehow or another I was led to his Wiki page, where there are descriptions like this:

His books have sold more than 300 million copies[1] and he was the first person to sell 1 million e-books.[2] In 2016, Patterson topped Forbes‘s list of highest-paid authors for the third consecutive year, with an income of $95 million.[3] His total income over a decade is estimated at $700 million.

and this:

Patterson has written 147 novels since 1976.[12] He has had 114 New York Times bestselling novels,[13] and holds The New York Times record for most #1 New York Times bestsellers by a single author, a total of 67, which is also a Guinness World Record. His novels account for one in 17, roughly 6%, of all hardcover novels sold in the United States; in recent years his novels have sold more copies than those of Stephen KingJohn Grisham, and Dan Brown combined.[14] His books have sold approximately 305 million copies worldwide.[1] In 2008, he replaced Jacqueline Wilson as the most borrowed author in Britain’s libraries.[15] He retained this position at least until 2013.

This is obscene commercial success for a writer. Imagine the most borrowed author in Britain not even being British. Imagine accounting, personally, for one in every seventeen hardcover novels sold in one of the largest countries in the world. Before reading this Wiki page, I would’ve laughed this off as impossible. Jim is a monster of a writer. How does he do it?

By not writing his own books, it turns out. This makes Patterson the equivalent of one of those PIs of huge research labs with dozens or even hundreds of postdocs and grad students cranking out dozens of massively-collaborative papers a year in particle physics or the biomedical sciences – the kind of people who inspired Alessandro Strumia to invent improvements to the h-index, like citation coins and AuthorRank, in his paper Biblioranking fundamental physics.

(Stephen King doesn’t much like Patterson’s methods. In a recent interview with Stephen Colbert, he noted how Patterson needed only twelve hours for two books, and how they both had “a mutual respect – sort of”. Elsewhere he’s even more blunt, calling him “a terrible writer”. Patterson’s response, in the WSJ, is diplomatically generous: “He’s taken shots at me for years. It’s fine, but my approach is to do the opposite with him—to heap praise.”)

Writing novels is pretty different from writing particle physics papers. And Patterson is the only author so far to have perfected this art for novels. (Partly this is because authors don’t write to maximize book count, they write because they want to write. But even then I’d expect more authors to go down the Patterson path, forced by their finances.) So again: how does he do it?

From the WSJ:

Mr. Patterson works seven days a week out of a two-room office suite at his Palm Beach oceanfront home. White bookshelves line the first room, where he does the bulk of his writing, all in pencil on white legal pads. There’s no computer; just a telephone, fax machine, an iPad, and a bag of bubble gum. The second room looks like a traditional bedroom, but the bed is covered by books, loose-leaf papers, and manuscripts.

When it comes to writing, he has a well-practiced system: he writes a detailed outline and then hires someone—often a former colleague from his advertising days—to write the ensuing scenes, usually in 30 to 40 page chunks. He will review those pages every few weeks, sometimes providing notes on them and other times re-writing them entirely.

When he’s not writing, the 65-year-old author can be found on one of Palm Beach’s premier golf courses, at the movies (he sees almost everything), or at home having dinner with his wife, Sue, and their 14-year-old son, Jack. Sometimes, Mr. Patterson will retire to write into the night, particularly if he’s excited—or anxious—about a new project.

(I can’t read more of the article, because I don’t have a subscription.)

A more informative source is O’Sullivan & Fuller’s paper Structure over style: collaborative authorship and the revival of literary capitalism. The part about “literary capitalism” is hinted at in the last sentence of the abstract:

James Patterson is the world’s best-selling living author, but his approach to writing is heavily criticised for being too commercially driven — in many respects, he is considered the master of the airport novel, a highly-productive source of commuter fiction.

A former marketing professional, Patterson uses his business acumen to drive sales of his novels, which are largely written in conjunction with lesser-known co-authors.

Using stylometry, this paper analyses the extent to which Patterson actually contributes to the writing of his novels, situating his process within the context of literary capitalism and the novel as a force of modernity

Midway through the introduction this is elaborated upon a bit more:

Patterson’s background is in marketing, and indeed he makes unapologetic use of advertising techniques to increase sales. His writing style is largely considered to be simplistic; his subject matter excessively emotive. Moreover, he hires collaborators, who, according to our analysis, complete much of the actual writing.

However, as we will describe in this paper, it is in such a context that we can situate Patterson as working within structures of literary production indissociable from the capitalist forces which drive most literary production. His re-discovery and refinement of the novel’s popular traditions is accompanied by a choice of style and subject matter that make his works exemplary of the experience of leisure-time in late capitalism.

Patterson’s particular achievement is to be both author and producer; creator, brand, and corporation. Patterson is, in many respects, as much a trademark as he is a writer. His name is a stamp of approval. What does this mean for our constructions of “the author”? Does Patterson’s name on the cover mean that a particular novel is written by Patterson, or that it has been approved by Patterson? Is his name an indicator of the style of a novel, or a gesture towards its structure and content?

I’m not very familiar with reading humanities papers, so some of the phrase choices and questions raised irritate me a bit, but on the whole that’s an interesting passage for sure.

More on Patterson’s commercial success:

At the time of writing, he is the world’s most successful living author, outselling J. K. Rowling, Dan Brown, and John Grisham combined [Wood 2009]. Between 2006 and 2010, one in every seventeen novels sold in the United States was authored by Patterson [Mahler 2010]. He has achieved this feat by publishing copious numbers of reasonably successful novels rather than a select few blockbusters. His most successful release, 1993’s Along Came A Spider, only reached number two on the bestseller charts. Its five million print-run is small compared to that of say, Dan Brown’s The Da Vinci Code; however, by 2014 he had published in excess of 100 novels.

I instinctively respect replicated success, as opposed to jackpot-winners, so props to him here.

Patterson turns out to be a master marketer:

Patterson wrote his first thriller in 1976, but before the 1990s his main employment and source of income lay in marketing. He worked at J. Walter Thompson, where he became its youngest ever creative director and eventually chief executive of North American operations [Mahler 2010].

His marketing continues to inform his approach to promotion and writing. In fact, the two processes, Patterson’s writing and his marketing, are somewhat indistinguishable. For Along Came A Spider, he took the unusual step of using television advertising [Wroe 2013], paying for it out of his own pocket [Deighton 2006, 8].

Since then, he has taken control of his own marketing from his publisher, Little, Brown and Co., a division of Hachette [Mahler 2010]. Two editors and three full-time Hachette employees, plus assistants, work exclusively for Patterson. According to Michael Pietsch, his editor and publisher, “Jim is at the very least co-publisher of his own books”  [Deighton 2006, 5]. Patterson, in this sense, is bigger than his publisher.

In outranking his publisher, he differs significantly from many forms of commercial fiction. Mills and Boon, for instance, employ writers to create romance novels that conform to a limited horizon of reader expectation. Watt describes how in the eighteenth-century, the bookseller-publishers of Grub street used to employ writers, often paying by the word, to churn out novels and translate works from French [Watt 2001, 55]. Commercial fiction has always been driven by the demands of its readership.

What makes Patterson different, is that he exerts personal control over the publishing apparatus which seek to match literary content to the market. Patterson brings a new level of rigour to marketing within the publishing industry. This is acknowledged by Larry Kirschbaum, former head of Little, Brown: “Until the last 15 years or so, the thought that you could mass-merchandise authors had always been resisted… Jim was at the forefront of changing that”  [Mahler 2010].


What Patterson shares with the writers of Mills and Boon novels, the forgotten eighteenth-century hack pieces, and the dime novels and penny dreadfuls of the nineteenth-century, is that he writes simple, populistic works with no pretensions of academic literary quality, designed to sell.

But, like the publishers of Grub Street, he has a greater number and variety of books to sell than most authors can produce. As we will discuss, he achieves this in part by hiring collaborators. Patterson therefore has properties of the traditional popular author, properties of the publishing house, as well as those of the modern marketing executive.

If the development of the form and content of popular fiction is explainable to a large extent by the socio-economic factors that drive its production,[1] then Patterson is in the unusual position of possessing an overview of these factors, and writing and commissioning fiction accordingly.

As such, economic forces do not simply shape his work externally or deterministically, but are put to play by him from the outset to determine a written product that will be popular, marketable, and replicable.

(so this is what a commercial-success optimizer looks like for fiction writing…)

More than that:

In an effort to broaden his following, Patterson has commissioned his own studies into the demographics of his audience [Deighton 2006, 5]. Such research has even directly influenced the content of his work — in one case, in order to make up for a lag of sales on the West coast of the United States, where John Grisham was the dominant author, he decided to locate his second thriller series, The Women’s Murder Club, in San Francisco [Mahler 2010].

In a generally complimentary assessment, Jonathan Mahler says of Patterson’s TV campaign for his breakthrough work, Along Came A Spider: “It’s entirely possible, even quite likely, that without those ads, Along Came a Spider never would have made the bestseller list, and that James Patterson would now be just another thriller writer”  [Mahler 2010]. The problem with such an appraisal is not that it ascribes Patterson’s success to his marketing alone, but that it considers Patterson’s literary work and the surrounding marketing as separate in the first place. Rather, the literary and commercial facets of his work reinforce each other to the point where, as in the case of his choice of location for The Women’s Murder Club
series, they are indistinct.

Recall this snippet from the WSJ:

When it comes to writing, he has a well-practiced system: he writes a detailed outline and then hires someone—often a former colleague from his advertising days—to write the ensuing scenes, usually in 30 to 40 page chunks. He will review those pages every few weeks, sometimes providing notes on them and other times re-writing them entirely.

O’Sullivan & Fuller go into more detail:

When producing a novel, Patterson uses about a dozen readers as a soundboard for the work in progress, making alterations as they point to the “weaker” elements of a story [Deighton 2006, 5].

His writing is designed to arrest readers’ attention, and to encourage them to buy into a series of novels, typically based around a primary, re-occurring character or characters. As Nicholas Wroe explains: “His prose is doggedly functional with short sentences and chapters relentlessly working to propel the plot”. His use of short chapters, says Mahler, “creates a lot of half-blank pages; his books are, in a very literal sense, page-turners”.

The development of this approach is premeditated. Patterson himself describes how, after his earlier, less successful works, he is “less interested in sentences now and more interested in stories”. Of his first work, The Thomas Berryman Number, he says that he “couldn’t have supported [himself] on that kind of book”, and that his writing is now “very self-consciously commercial”.

In developing a formula that has seen him become the world’s most successful writer, Patterson’s new releases often do not receive press reviews, but they attract a large number of reader reviews across online media. Here, it is quickly apparent that his works are praised by readers for the qualities he has intentionally fostered. An excerpt from an Amazon review for I, Alex Cross reads: “This is well written — using Patterson’s usual quick and easy chapters,” evidently equating brevity with quality. Another review for the same work concludes: “The thriller is written in short chapters, which I like, and the font is large enough to make reading enjoyable. The prose is clear, succinct, and paints a picture of full-blown evil and terror. A fast read.”

Even more detail on the collaborative assembly line:

A much-noted aspect of Patterson’s approach is his use of collaborators for his novels. In 2000 he published three books, all of which were successful, and this prompted him to focus upon collaboration in order to dominate the market. As a result of this process, he produced 13 distinct publications in 2012 and the same number in 2013.

The co-authors are directly employed by Patterson, assigned to a particular genre or series, and paid out of Patterson’s own pocket at what is rumoured to be a flat rate with bonuses and no royalties. For many, such as Gross and De Jonge who feature in our stylometric analysis, it has provided a launching pad for their solo careers.

While Patterson does not like the term “boss”, he concedes that he is the senior figure in any collaboration, and defends his position by way of employee satisfaction: “nobody quits”, and “nobody asks for a raise”. Indeed, he primarily assumes a managerial role in the creative process itself: “I write an outline for a book. The outlines are very specific about what each scene is supposed to accomplish. I get pages from [the collaborator] every two weeks, and then I re-write them. That’s the way everything works. Sometimes I’ll just give notes…”. Patterson appears to be part creator, part editor, and also part guarantor of satisfaction — a sort of Alfred Hitchcock Presents stamp of quality. In his own words: “my name on the cover is the assurance of a good read”.

Defending his process, Patterson points out that collaboration has also been used in other creative outlets, such as television, newspapers, cinema, and even the masonic guilds behind the medieval cathedrals. In employing collaborative methods, Patterson has in fact aligned novel writing with the creative norm in contemporary culture. As Hobsbawm says of the late twentieth-century: “Creation was now essentially cooperative rather than individual, technological rather than manual”. A crucial juncture in the establishment of this modern paradigm, and of its rise in the field of professional writing, was the introduction of the producer system in early Hollywood cinema, wherein the producer takes precedence over the director, overseeing a process in which labour is divided along lines established in heavy industry, with the same goals of increased efficiency and profit.

But is Patterson’s approach unprecedented? No. Consider the prolific French writer Alexandre Dumas, whose “factory of novels” churned out 400 books and 35 plays in 20-odd years with the assistance of around 8,000 people in total:

Division of labour was in fact adopted in literature from at least the mid-nineteenth-century. Benjamin frequently discusses the growing application of industrial methods on nineteenth-century French literature as the commercial returns for literature increased. As such, the French novel, for Benjamin, appears to build upon the commercial origin of the British novel, industrializing the already commercial form. The most commercially successful writers of the era included Sue, Scribe, and Dumas, each of which employed collaborators in order to increase output. …

Dumas took simultaneous contracts for serialised novels from different journals, once occupying “almost simultaneously, with three of his novels, the feuilleton sections of La Presse, Le Constitutionnel, and Le Journal des debats”. He designated the writing task to others in order to keep up with demand. As a caricature puts it: “It was said that Dumas employed a whole army of poor writers in his cellars” while he drank champagne with actresses. He was accused by de Mirecourt of running “a factory of novels” and the Revue des Mondes  questioned whether he even knew the names of all the titles published in his name. De Mirecourt writes: “his novels are by Maquet, Fiorention, Meurice, Malefille, or Paul Lacroix … [he] dares, monster that he is, to sign his name alone.”

As a consequence of this criticism, Dumas was obliged to publicly recognise Maquet and others as collaborators. In his defence, Dumas sought credit for providing so much employment: “In twenty years, he said, he had written 400 novels and 35 plays. He had created jobs for 8160 people — proofreaders, typesetters, machinists, wardrobe mistresses”.

Even Marx and Engels approved of Dumas’ methods, since the latter’s industrialization of the novel was seen as “formally aligning popular culture with the modes of production”. (I would’ve dismissed this as a Tumblr joke to be honest, if I didn’t see it in the paper.)

Another example of Patterson’s optimization of his novels for his specific audience (taking “know thy audience” to the limit, as it were):

The form of his novels also appears to be moulded by contemporary experience.

In particular, his work is perhaps best described as “commuter fiction”. Nicholas Paumgarten describes how the average time for a commute has significantly increased. As a result, reading has increasingly become one of those pursuits that can pass the time of a commute. For example, a truck driver describes how “he had never read any of Patterson’s books but that he had listened to every single one of them on the road”.

A number of online reader reviews also describe Patterson’s writing in terms of their commutes. One such reviewer of Patterson’s The Postcard Killers directly relates the writing style to the realities of modern transitional life: “As a consequence of such short chapters I whizzed through this book in under two hours and it was a fairly decent thriller and a good way to spend time commuting to work.”[3] With large print, and chapters of two or three pages, Patterson’s works are constructed to fit between the stops on a metro line.

O’Sullivan & Fuller conclude:

Patterson, like Dumas, has commodified his reputation as an author and met demand through delegation. However, it appears that Patterson has generally been transparent regarding his collaborative process, and has offered sufficient accreditation, tutelage, opportunity, and financial reward to those with whom he works.

The novel has always been a commercial form. Its rise was a product of the rise of the bourgeoisie. But Patterson has perhaps brought the novel to its logical conclusion. In a certain sense, Patterson’s works are not reducible to their socio-economic context. Rather, wresting marketing control from his publisher, hiring his own soundboard readers, and employing subsidiary writers, Patterson generates pulp far more concentratedly than the vagaries of traditional historical materialism would generally allow. While we might see “high literature” as irreducible to its immediate socio-economic context because the author is in a kind of dialogue with the whole literary and even metaphysical canon, Patterson’s work is irreducible in the sense that he creates his fiction in accordance with his own manipulations of its economic base.

As Patterson says: “above all my brand stands for story. I became successful when I stopped writing sentences and started writing stories. Editors think it’s about style. It’s not. It’s all story”.

Robot shell companies in Stross’ Accelerando

Believe it or not, my first introduction to the notion of shell companies was actually from Charlie Stross’ Accelerando, which I read a couple of years ago (without understanding much) and which has featured in the last few blog posts. In particular, it was this excerpt:

Manfred is jolted awake by the hotel room phone shrilling for attention.

“Hello?” he asks, fuzzily.

“Manfred Macx?” It’s a human voice, with a gravelly east coast accent.

“Yeah?” Manfred struggles to sit up. His mouth feels like the inside of a tomb, and his eyes don’t want to open.

“My name is Alan Glashwiecz, of Smoot, Sedgwick Associates. Am I correct in thinking that you are the Manfred Macx who is a director of a company called, uh, agalmic dot holdings dot root dot one-eight-four dot ninety-seven dot A-for-able dot B-for-baker dot five, incorporated?”

“Uh.” Manfred blinks and rubs his eyes. “Hold on a moment.” When the retinal patterns fade, he pulls on his glasses and powers them up. “Just a second now.” Browsers and menus ricochet through his sleep-laden eyes. “Can you repeat the company name?”

“Sure.” Glashwiecz repeats himself patiently. He sounds as tired as Manfred feels.

“Um.” Manfred finds it, floating three tiers down an elaborate object hierarchy. It’s flashing for attention. There’s a priority interrupt, an incoming lawsuit that hasn’t propagated up the inheritance tree yet. He prods at the object with a property browser. “I’m afraid I’m not a director of that company, Mr. Glashwiecz. I appear to be retained by it as a technical contractor with non-executive power, reporting to the president, but frankly, this is the first time I’ve ever heard of the company. However, I can tell you who’s in charge if you want.”

“Yes?” The attorney sounds almost interested. Manfred figures it out; the guy’s in New Jersey, it must be about three in the morning over there.

Malice – revenge for waking him up – sharpens Manfred’s voice. “The president of is The secretary is, and the chair is All the shares are owned by those companies in equal measure, and I can tell you that their regulations are written in Python. Have a nice day, now!”

He thumps the bedside phone control and sits up, yawning, then pushes the do-not-disturb button before it can interrupt again. After a moment he stands up and stretches, then heads to the bathroom to brush his teeth, comb his hair, and figure out where the lawsuit originated and how a human being managed to get far enough through his web of robot companies to bug him.

A bit more on how it all works:

One of his e-mail accounts is halfway to the moon with automatic messages, companies with names like screaming for the attention of their transitive director. Each of these companies – and there are currently more than sixteen thousand of them, although the herd is growing day by day – has three directors and is the director of three other companies. Each of them executes a script in a functional language Manfred invented; the directors tell the company what to do, and the instructions include orders to pass instructions on to their children. In effect, they are a flock of cellular automata, like the cells in Conway’s Game of Life, only far more complex and powerful.

Manfred’s companies form a programmable grid. Some of them are armed with capital in the form of patents Manfred filed, then delegated rather than passing on to one of the Free Foundations. Some of them are effectively nontrading, but occupy directorial roles. Their corporate functions (such as filing of accounts and voting in new directors) are all handled centrally through his company-operating framework, and their trading is carried out via several of the more popular B2B enabler dot-coms. Internally, the companies do other, more obscure load-balancing computations, processing resource-allocation problems like a classic state central planning system.

Manfred Macx, venture altruist

I really liked this paragraph from Charlie Stross’ Accelerando for some reason, perhaps because it’s a slightly more fleshed out version of the fantasy that instead of creative work being 1% inspiration and 99% perspiration, you can outsource/delegate the latter and focus entirely on the former, increasing your throughput a hundredfold. (This also describes senior management at big firms, except the fantasy Charlie spins is different.)

Manfred has a suite at the Hotel Jan Luyken paid for by a grateful multinational consumer protection group, and an unlimited public transport pass paid for by a Scottish sambapunk band in return for services rendered. He has airline employee’s travel rights with six flag carriers despite never having worked for an airline. His bush jacket has sixty-four compact supercomputing clusters sewn into it, four per pocket, courtesy of an invisible college that wants to grow up to be the next Media Lab. His dumb clothing comes made to measure from an e-tailor in the Philippines he’s never met. Law firms handle his patent applications on a pro bono basis, and boy, does he patent a lot – although he always signs the rights over to the Free Intellect Foundation, as contributions to their obligation-free infrastructure project.

In IP geek circles, Manfred is legendary; he’s the guy who patented the business practice of moving your e-business somewhere with a slack intellectual property regime in order to evade licensing encumbrances. He’s the guy who patented using genetic algorithms to patent everything they can permutate from an initial description of a problem domain – not just a better mousetrap, but the set of all possible better mousetraps. Roughly a third of his inventions are legal, a third are illegal, and the remainder are legal but will become illegal as soon as the legislatosaurus wakes up, smells the coffee, and panics. There are patent attorneys in Reno who swear that Manfred Macx is a pseudo, a net alias fronting for a bunch of crazed anonymous hackers armed with the Genetic Algorithm That Ate Calcutta: a kind of Serdar Argic of intellectual property, or maybe another Bourbaki math borg. There are lawyers in San Diego and Redmond who swear blind that Macx is an economic saboteur bent on wrecking the underpinning of capitalism, and there are communists in Prague who think he’s the bastard spawn of Bill Gates by way of the Pope.

Manfred is at the peak of his profession, which is essentially coming up with whacky but workable ideas and giving them to people who will make fortunes with them. He does this for free, gratis. In return, he has virtual immunity from the tyranny of cash; money is a symptom of poverty, after all, and Manfred never has to pay for anything.

There are drawbacks, however. Being a pronoiac meme-broker is a constant burn of future shock – he has to assimilate more than a megabyte of text and several gigs of AV content every day just to stay current. The Internal Revenue Service is investigating him continuously because it doesn’t believe his lifestyle can exist without racketeering. And then there are the items that no money can’t buy: like the respect of his parents. He hasn’t spoken to them for three years, his father thinks he’s a hippy scrounger, and his mother still hasn’t forgiven him for dropping out of his down-market Harvard emulation course. …

Accelerando’s origin story

I love Charlie Stross’ origin story for his novel Accelerando, from this page:

“Accelerando” is a creature of its time, and that time is the late 1990s. I spent most of the 90s on a kind of sabbatical from writing fiction (my first love), with my head stuck up the fundament of the software industry. In the early 90’s I worked for SCO (back when it was a UNIX company, rather than the unholy terror that came back from the dead to haunt the free software movement).

Then I discovered the web, back around 1993. I remember a wee daily email bulletin titled “what’s new on the web” that came from an address at NCSA; I used to visit all the interesting new web sites every day, until the volume grew too great some time in late 1994. I was supposed to be writing UNIX manuals, but I distracted myself by learning Perl – and was inadvertently responsible for the development of the robot exclusion protocol (by writing a web spider that annoyed people who knew more about what they were doing than I did). I moved to Scotland to join a web startup that went bust, freelanced for a couple of years while writing a web architecture book, landed myself a magazine column about Linux, and joined another start-up that turned into a successful dot com, went public, and much to my surprise is still in business.

The last sentence covers a multitude of sins. I signed on with the company two weeks before its official formation, and left two months after the IPO – three and a half years later. Along the way I bolted together about thirty thousand lines of object oriented perl that swallowed credit card numbers at one end and talked to obscure British banking systems in strange protocols. And it had a psychotherapy bot wired into the middle just to help me de-stress when things got too heavy, which was almost every other day, because …

You’ve probably never had to work inside a business that’s growing of 30% per month. Take it from me, it’s an experience you don’t need. Especially when you’re not a brilliant programmer, you know damn well your code has bugs in it – it’s actually a prototype that they pressed into service six months too early – and it’s handling millions of pounds of other people’s money. If things go wrong they scream at you. And exponential growth means the workload is always growing faster than the budget for hiring minions to do the donkey-work. At first it’s fun, a buzz like a caffeine high: but it goes on too long and you get old and feel stupid, and at some point you find you can’t stop running because your feet are locked to the treadmill and there’s a wall of spikes right behind you.

The germ of “Accelerando” dates to that time. To be specific, it dates to a particularly bad month in early 1999, when I was trying to brainwash Datacash into talking to a French credit card system (and if you think obscure 1970’s-vintage British credit card protocols sound awful, you’ve never dealt with the French equivalent). I was under a lot of pressure, not aided by the French bank programmers not actually wanting to expose the guts of their communication protocol to, gasp, developers who were trying to communicate with their servers … things were not looking good. One Thursday when things had been not been going well in an especially emphatic manner, I wandered over to my boss the CTO’s desk and said, “I’m taking tomorrow off.”

“But what if we need you – ” he began.

“I’ll be in Amsterdam.”

He looked at me. Then he did a double-take: “Amsterdam. Okay.” I hadn’t taken any vacation time in the preceding year, my caffeine intake was measured in the direction of gallons of coffee per day, and I was developing an uncontrollable facial tic and a tendency to jump at loud noises. “Take tomorrow off.”

This was very sensible of him. Most directors of a company that’s going public in six months and has a server development team consisting of 1 (one) geek who is developing an incontrolable facial tic and demanding days off in Amsterdam might actually get a little bit nervous about the idea of said server development team fleeing the country on short notice. But my prepared fallback position to taking a long weekend somewhere with lots of beer and no French bank managers to scream at was to try to quit on the spot, and if that failed I was going to spring a full-scale nervous breakdown … and it probably showed.

“Just come back on Monday,” he said.

I think I nodded, but maybe it was just the caffeine pulling my strings.
Anyway, I was wandering around Amsterdam the next day – on a rainy Friday – trying not to fall apart at the seams. I’d spent the whole night lying awake, looping on re-drafting my resignation letter, and I had the shakes. Then my phone rang.

“What’s gone wrong?” I asked, my heart sinking.

It was my boss the CTO. “The French fuckwits,” he said.

I got that sinking feeling. “What have they sprung on us now?” I asked.

“Their parent institution is so unhappy with them that they’re being shut down! I thought you might like to know …” (In the background, I could hear the entire office cheering.)

I immediately headed for the nearest pub, and my girlfriend and I celebrated in time-honoured fashion. For a couple of bright hours in the middle of a rainy afternoon, the high pressure bubble in the core of the dot com boom actually looked like an optimistic, cheerful place to be.

And something about the sudden release of stress took root, and began to germinate. I got far enough away from the coal seam to blink, look at it in amazement, and ask once more the classic science fictional question, what happens if this goes on? What happens if you keep piling on the changes? What kind of person can actually live on the edge of a singularity, keeping pace while all around them the world is melted down and re-forged monthly, daily, hourly?

I pulled out my Psion 5MX and scribbled a brief paragraphs about a very strange guy named Manfred. Then I proceeded to get side-tracked by beer for the next couple of days.

Scattered quotes on Buddhism and meditation

Below are some scattered quotes about Buddhism and meditation, broadly construed. Note that I have never grokked either, or even really understood anything more than smidgens here and there, but the little tidbits I find are tantalizing enough for me to want to learn more. A lot of them are in the form of ‘unlearning’ – I had certain assumptions arising from stereotypes or whatever, which turn out (delightfully/intriguingly/confusingly) to be untrue.

Here’s a comment by batbdotb from the Reddit thread Important message from the Dharma Treasure Board of Directors. Some context by the Board:

Dear Dharma Treasure Sangha,

It was recently brought to the attention of Dharma Treasure Board members that John Yates (Upasaka Culadasa) has engaged in ongoing conduct unbecoming of a Spiritual Director and Dharma teacher. He has not followed the upasaka (layperson) precepts of sexual harmlessness, right speech, and taking what is not freely given.

In a series of Board meetings as well as written correspondences with Mr. Yates, he admitted to being involved in a pattern of sexual misconduct in the form of adultery. There is no evidence that this adultery involved improper interactions with students or any form of unwanted sexual advances. Rather, adultery with multiple women, some of whom are sex workers, took place over the past four years. The outcome was extended relationships with a group of about ten women. Relationships with some continue to the present day.

He has provided significant financial support to some of these women, a portion of which was given without the prior knowledge or consent of his wife. Mr. Yates also said he engaged in false speech by responding to his wife’s questions with admissions, partial truths, and lies during these years.

After we brought this misconduct to the attention of Mr. Yates, he agreed to write a letter to the Sangha disclosing his behavior, which would give students informed consent to decide for themselves whether to continue studying with him. However, after weeks of negotiations, we were unable to come to an agreement about the content and degree of transparency of his letter.

At the end of this entire process, we are sadly forced to conclude that Mr. Yates should not be teaching Dharma at this time. Likewise, we are clear that keeping the upasaka (layperson) vows is an absolutely essential foundation for serving as the Spiritual Director of Dharma Treasure. With heavy hearts, the Board has voted to remove him from this role, from the Board, and from all other positions associated with Dharma Treasure.

We know people may feel disbelief and dismay upon learning about this pattern of behavior. However, it is our strong wish that we all use this time as an opportunity to practice patient inquiry, compassion, and discernment. Our goal in sharing this information with the Sangha is to provide each of you with enough information to make your own informed decision about whether or how to work with Mr. Yates as a teacher. We hope this transparency about Mr. Yates’ behavior can help us all move toward a place where we honor teachers for their gifts while acknowledging they are complex human beings who make mistakes.

Finally, we hope this disclosure about Mr. Yates’ conduct does not shake your confidence in the Buddha, Dharma, and Sangha.

It was in this context that batbdotb wrote the following comment:

To anyone feeling disillusioned, I would offer these words: goodDisillusionment is the stripping away of illusions. We collectively had a certain narrative of the way things were and now that narrative is being challenged; this is the way of the world-stream — The world-stream often disappoints. Don’t get me wrong, I am in no way speculating whether Culadasa did or did not do these things – what is more intriguing than the situation itself is each of our own respective responses to the situation.

The ultimate goal of The Way is complete and total transcendence. In my view, even attachment to Buddhism is another attachment that is open to being stripped away. Nothing that is “content” is safe from this. I know this runs counter to the notion of taking refuge in the 3-jewels, so I suppose this is where I would differ from a Buddhist. The Way does not belong to any particular teacher, religion, or tradition. No tradition owns the state of Revelation, Inner Peace, or egolessness; any situation can be used towards Realizing these modes of being – including this situation. Take whatever life gives you and use it as fuel to further your advancement towards these modes of being.

Regardless of what happens here, I would extend and open invitation for us all to engage in these 2 things:

Be aware of your attachments relating to these matters and let go of them. Be like a stone, which perpetually becomes more purified every-time it is put into the furnace, perhaps one day to be transformed into a full-fledged gem.

Clarify your Intention; the reactive mind becomes easily swayed by the arising-and-passing of content in the world-stream. Know what you value; decide what is important, and let your intention carry you forward in peace.

And finally, I wanted to send my sincere love and gratitude to Culadasa. To be honest, the facts of the situation make no personal difference to me. Only Culadasa will know the truth of the situation with absolute certitude; it is none of my business. His teachings have worked incredibly well for me so regardless of how things unfold, I am unspeakably grateful.

Lotusofthebuck raises a valid response:

It’s easy to say for you that it makes no personal difference. And surely with the presence you’ve amassed via your contributions here, that people will agree with you and feel less conflicted about a teacher who has broken vows…it’ll perhaps pacify their doubts and help them sleep at night, despite their gut feeling. And yet, if even some of these allegations are false but there remains some truth, what about his wife?

Batbdotb’s response:

Hey there,

I appreciate your inquiry; context often gets distorted when we communicate via text like this. If we had the opportunity to communicate in-person this would not be the case. So before I continue, I will declare my intention here is dialogue rather than debate — I trust you hold similar attitudes in mind.

that people will agree with you and feel less conflicted about a teacher who has broken vows…it’ll perhaps pacify their doubts and help them sleep at night, despite their gut feeling.

The implication of using the word “pacify” is that people are ignoring wrongdoing under the guise of “mindfulness” or “its not my problem”. But no one is really ignoring anything – clearly, as this very active discussion demonstrates.

To your point, we shouldn’t ignore things that conflict with our model of the world for the sake of reducing cognitive dissonance; this is not my stance. A new narrative threatens our collective narrative, rather than deny this – we should learn from it and move on. Together we can make this world a better place – we have an amazing group of people here. Disillusionment is inevitable in any collective thought-system; but the question is – will we use this to get bitter or get better?

what about his wife?

Let her grieve in peace.

If she requires anything from the community, of course we shall be there for her. My guess would be she prefers not to have all this attention, hence – why I refrain from getting involved in the personal matters of others.

More context for why I’m interested in this thread of discussion: I found it in Scott’s Open Thread 135, where commenters were saying stuff like

I got into meditation because of TMI and I don’t think this changes much about how I feel about meditation or TMI. But then, I don’t think meditation makes you into a perfect person (and I’m not even sure it has much benefit for the average person), so the story reads as “human does typical human things” (not that it isn’t sad and upsetting for everyone involved).


I suppose the less one expects from meditation, the less devastating this news is. And by “expect less” I don’t mean a weaker effect, but rather a narrower effect. Regular exercise at breathing and concentration should make you better at… well, breathing and concentration… and maybe closely related things, such as relaxation and perhaps improved memory. Why expect anything else?

If you want your meditation gurus to be nice people, perhaps don’t skip doing the loving-kindness meditation for a few years before moving on to concentration and insight exercises.

From Redditor thatisyou in the thread This is not an appropriate time for me to respond to the DT Board. Therefore…, started by Culadasa himself:

“Suppose a man was struck by an arrow thickly smeared with poison. Their friends and colleagues, relatives and kin would get a field surgeon to treat them. The surgeon would cut open the wound with a scalpel, probe for the arrow, extract it, and expel the poison, leaving some residue behind. Thinking that no residue remained, the surgeon would say: ‘My good man, the dart has been extracted and the poison expelled without residue. It’s not capable of harming you. Eat only suitable food. Don’t eat unsuitable food, or else the wound may get infected. Regularly wash the wound and anoint the opening, or else it’ll get covered with pus and blood. Don’t walk too much in the wind and sun, or else dust and dirt will infect the wound. Take care of the wound, my good sir, heal it.’

They’d think: ‘The dart has been extracted and the poison expelled without residue. It’s not capable of harming me.’ They’d eat unsuitable food, and the wound would get infected. And they wouldn’t regularly wash and anoint the opening, so it would get covered in pus and blood. And they’d walk too much in the wind and sun, so dust and dirt infected the wound.And they wouldn’t take care of the wound or heal it. Then both because they did what was unsuitable, and because of the residue of unclean poison, the wound would spread, resulting in death or deadly pain.

In the same way, it’s possible that a certain mendicant might think: ‘The Ascetic has said that craving is a dart; and that the poison of ignorance is inflicted by desire and ill will. I have given up the dart of craving and expelled the poison of ignorance; I am rightly intent on extinguishment.’ Having such conceit, though it’s not based in fact, they would engage in things unconducive to extinguishment: unsuitable sights, sounds, smells, tastes, touches, and thoughts. Doing so, lust infects their mind, resulting in death or deadly pain.

For it is death in the training of the noble one to reject the training and return to a lesser life. And it is deadly pain to commit one of the corrupt offenses.”- With Sunnakkhata, Middle Discourses, 105 .

No matter how far I get in meditation, may I always remember this Sutta. Buddha was pointing to a challenge of very advanced practitioners: they have practiced to such a level of precision that there is a belief of being beyond the allure of vedana and formations. However, craving vedana and formations never stops being poison.

Comment chain from same thread, different subthread:

I’ve met rough people through volunteer work who turned their lives around via prison ministry and other Christian efforts. Many of them are not very intelligent, and have (as far as I can tell) non-heroic levels of metacognitive awareness. However, what they do have is a sharpened awareness of how their actions have hurt other people, and a resolve to do better and be a force of good in the world. I think this sense of ethical dedication – a less grandiose sort of Bodhisattva’s vow – seems to work better at producing ethical human beings than any amount of meditation.

followed by

I think you may be right. Focusing on meditation may be putting the cart before the horse. I’m really reevaluating my own practice in light of this situation. Considering drastically reducing my commitment to meditation and putting those energies into work on cleaning up my own act, looking at my own blind spots. Focus on step one, clean conduct across the board.

Backtracking a bit: Culadasa is the author of The Mind Illuminated, which Scott reviewed last year. Some excerpts – I just wanted another excuse to quote Scott’s enjoyably droll reviewing:

I usually hate meditation manuals, because they sound like word salad. “One attains joy by combining pleasure with happiness. Pleasure is a state of bliss which occurs when one concentrates focus on the understanding of awareness. Happiness is a state of joy that occurs when one focuses concentration on the awareness of understanding. By focusing awareness on bliss, you can increase the pleasure of understanding, which in turn causes concentration to be pleasant and joy to be blissful, and helps you concentrate on understanding your awareness of happiness about the bliss of focus.” At some point you start thinking “Wait, were all the nouns in that paragraph synonyms for each other?”

Culadasa avoids this better than most people. Whenever he introduces a term, he puts it in bolded italicized letters, and includes it in a glossary at the back. He tries to stick to multiple-word-phrases that help clarify the concept, like “bliss of physical pliancy” or “meditative joy”, instead of just calling one thing “joy” and the other thing “bliss” and hoping you remember which is which. He includes a section on what he means by distinguishing “awareness” from “attention”, and admits that some of these are tough choices that do not necessarily cooperate with the spirit of the English language. And his division of the material into stages helps ensure you’re not reading a term until you’re somewhere around the point of personally experiencing the quality being discussed.

This is characteristic of the level of care taken in this book, which despite its unfortunate acronym does a good job of presenting just the right amount of information. For example, when people say “meditate on the breath”, I can only do this for a little while until I notice that the breath doesn’t really exist as a specific object you can concentrate on. Really there are just a bunch of disconnected sensations changing at every moment. What do you concentrate on? I had previously dismissed this as one of several reasons why obsessive-compulsive people shouldn’t do meditation, but TMI describes exactly this issue, says that it is normal and correct to worry about it, and prescribes solutions: concentrate on the disconnected sensations of the breath in whatever way feels easiest for the first few stages, and once you’ve increased awareness to the point where you can notice each subpart of the breath individually, do that.

This is a nice example of what commenter OpenHand_ClosedFist probably meant in the above Reddit thread in writing about Culadasa:

I don’t see him as anything other than a fucked up dude with probably a lot of trauma who happened to also write a meditation manual light years beyond anything else I’ve ever read.

More examples in this vein:

TMI also solves a whole slew of my obsessive questions and concerns with its “attention vs. awareness” dichotomy.

I had always been confused by instructions like “concentrate on the breath until you feel joy, then notice the joy”. Usually what would happen was: I would concentrate on the breath, ask myself “am I feeling joy yet?”, spend some time trying to figure this out, realize my attention had deviated from the breath, put my attention back on the breath, then feel bad because I wasn’t checking to see if I was feeling joy or not. How could I both have 100% of my attention on the breath, but also be checking my joy? If I came up with the policy “check once per minute for joy, then go back to the breath”, how would I avoid checking arbitrarily often whether it felt like a minute had gone by? This was another issue I just dismissed as “maybe meditation is not for obsessive-compulsive people”.

But TMI distinguishes between “attention” (sometimes “focused attention”) as the one thing in the foreground of your brain, and awareness (sometimes “peripheral awareness”) as the potentially many things in the background of your brain. Think of it working the same way as central vs. peripheral vision. When given instructions like “concentrate on the breath until you feel joy, then notice the joy”, you should be focusing your entire attention on the breath, but potentially noticing joy in your peripheral awareness. These instructions are no more contradictory than “look at this dot on the wall straight ahead, but notice if a dog runs past”.

Skipping to the comments section, here’s one by Hoopyfreud that I liked:

There is a tendency within certain circles (this one alone among those that I frequent) to regard enlightenment as an economic attainment. To suppose that it is something that can be acquired with the proper investiture of time and energy. That enlightenment is fundamentally a skill that can be applied in one’s life, like mathematics or CBT. “Judo of the mind” type shit. That it will change what you can do more than it changes who you are.
I cannot accept, based on personal experience, that it works like that. I know several people who I regard as enlightened, Deepak Chopra not among them. The degree of awareness and present-ness that a word like “enlightenment” implies to me is… incomparable, I think, to what’s described here.

Can you imagine, really, complete awareness? The dissolution of the self? Using the word, “I” to mean, “the piece of the world that makes up my body and mind?” Knowing, deep inside, at the level that you know that you are sad when you’ve spent the last hour crying, that there is nothing in this world that is more or less than a fragment of universal consciousness? Can you imagine maintaining your equanimity in the face of a holocaust? In the face of the birth of your child? On the first good day that your father has had in the last year? Can you imagine never wanting anything with the kind of hunger that keeps you awake at night?

I can, and it sounds like dying to me.

And yet I meditate. Not because I want to attain enlightenment, but because there’s enough in meditation that is worthwhile. It’s nice, I think, to know myself. But I’m too much of an egoist to follow the other path, and I’m under no illusions that enlightenment is anything close to what I seek. And it raises my hackles to see it treated like the one thing when it really seems to me quite another.

A completely unrelated observation I had some years back, my recollection of it triggered by the above comment:

I was at Joshua Tree National Park with some friends, watching the Milky Way and the occasional meteor. It was a Class 2-3 sky on the Bortle dark sky scale. I was trying to grok Sagan’s quote about the Earth being a mote of dust suspended in a sunbeam, and the observation that we (humans) are part of the universe that awoke, became capable of looking outward and inward and selfward, becoming Is. And then I looked at myself and saw a bag of meat and minerals animated by electricity. I looked at my friends and saw the same. Pieces of the landscape, as it were, moving about, making noises. Building things that amplified their wills over millennia. Reshaping vast tracts of land, touching the moon. There was nothing more to it, nothing less; it wasn’t profound or meaningful; the observation just was. But I felt it deeply in my bones. And then it passed.

Saunders Mac Lane’s attempt to define mathematics, along with how it came about

Saunders Mac Lane was, with Sam Eilenberg, one of the cofounders of category theory. Random biographical tidbits: he was originally Leslie Saunders Maclean, the name his nurse suggested, but his mom didn’t like it and his dad eventually dismissed it with “Leslie forget”; he added the space in his surname at his wife’s behest. His favorite subject in high school was chemistry, but he got disillusioned with it as a freshman at Yale and majored in physics and math instead, co-authoring his first paper (in physics) with Nobel Prize winner Irving Langmuir before graduation. Apparently his GPA was a Yale record. He was approached at a Yale football supporters party (where he was being presented with a prize for the GPA thing) by the University of Chicago’s president, who encouraged him to go there for graduate studies; he didn’t apply, but showed up and got admitted anyway, on a scholarship too. (Things were different back then.) Then he went to Göttingen and studied under more giants: Weyl, Noether. He wrote a thesis in mathematical logic. He toured around giving visiting lectures, and met Eilenberg just as Pearl Harbor happened. They bonded over their shared appreciation for Immanuel Kant’s work, and originated category theory as the war ended.

Fun as his bio is, it’s not what this post is about. This post is about his 10-page paper Mathematical models: a sketch for the philosophy of mathematics, published in The American Mathematical Monthly in 1981.

Mac Lane begins by saying that phil of math has been dormant for exactly 50 years, since 1931. (That was the year Godel published his incompleteness theorems.) This is no good, he says. It needs reviving. The three major schools, logicism, formalism and intuitionism, as well as the more general and longstanding platonism and empiricism, are all deficient. Recent contributions from such names as Putnam, Quine and Wang he dismisses in a single sentence as showing “little new insight”. Mac Lane wants to start afresh, by looking at “the actual state of mathematics”, since “a sound philosophy of mathematics ought to start with a description of what is really there” (good thinking). To be fair, this was also how the various schools above started, math just looked different then:

The various earlier philosophies of mathematics listed above each arose out of the dominant aspects of mathematics as then understood. For example, Platonism arose in Greece and applied to mathematics there because it fitted Greek geometry; it has been popular among mathematicians recently because it fitted well with the view that mathematics derives from axioms for sets. Logicism arose together with the discovery and formalization of mathematical logic. Intuitionism was the child of emphasis on numbers as the starting point of mathematics and on intuition as a basis of topology. Formalism arose with the development of axiomatic methods and the discovery that proof theory might give consistency proofs for abstract mathematics. Empiricism sprang from the 19th-century view of mathematics as almost coterminal with theoretical physics; it was much influenced by Kant’s dichotomy between analytic and synthetic.

Now we search for a philosophy of mathematics better attuned to the present state of the subject.

This segues directly into one of the most interesting passages on the evergreen topic “where did math come from?” that I’ve seen:

Mathematics begins with puzzles and problems dealing with combinatoric and symbolic aspects of the general human experience. Some of these aspects turn out to be systematic and intrinsic, rather than arbitrary and tied to one context. They become the stuff of elementary mathematics. From this starting point, the subject has developed to be a deductive analysis of a large number of very different but interlocking formal structures. These structures have been derived from experience in many successive stages; by abstractions from various observations of the world, its problems, and the interconnections of these problems. These observations can be described as starting with a variety of human activities, each one of which leads more or less directly to a corresponding portion of mathematics:

Counting : to arithmetic and number theory;

Measuring : to real numbers, calculus, analysis;

Shaping : to geometry, topology;

Forming (as in architecture) : to symmetry, group theory;

Estimating : to probability, measure theory, statistics;

Moving : to mechanics, calculus, dynamics;

Calculating : to algebra, numerical analysis;

Proving : to logic;

Puzzling : to combinatorics, number theory;

Grouping : to set theory, combinatorics.

These various human activities are by no means completely separate; indeed, they interact with each other in complex ways. Table 1 gives only a partial view of this complexity, to indicate how various human activities lead to the concepts now present in algebra. The two parts of this table should (and do) fit together by many crosslinks

This is the excitingly broad Table 1:

Mac Lane continues:

On the basis of many more elaborate tables such as this, giving the origin and interconnection of mathematical ideas, we conclude that mathematics started from various human activities which suggest objects and operations (addition, multiplication, comparison of size) and thus lead to concepts (prime number, transformation) which are then embedded in formal axiomatic systems (Peano arithmetic, Euclidean geometry, the real number system, field theory, etc.). These systems turn out to codify deeper and nonobvious properties of the various originating human activities.

For example, the notion of a group, though axiomatically very simple, reveals common properties of motion (rotation and translation groups), of symmetry (crystal groups), and of algebraic manipulations (Galois groups, Lie groups for differential equations). Many other mathematical concepts (function, partial order) are similarly both simple in structuretand pervasive in application. The simplicity and the applicability are made effective by the formal treatment of the notions involved.

In this view, mathematics is formal, but not simply “formalistic”- since the forms studied in mathematics are derived from human activities and used to understand those activities.

Formal but not just “formalistic”. What a neat distinction! Elaborating:

The actual structure of mathematical ideas is an incredibly elaborate development of this simple description. Consider just the case of algebra. Algebra first involved manipulation to solve equations. Then geometry was reduced to coordinates, and thus geometrical problems to algebraic ones. Next, simple Euclidean spaces are described by vectors in two, three, and then higher dimensions. The resulting notion of a vector space, often one equipped with a (quadratic) inner product, worked even in infinite dimensions and then served to codify some of the methods of solving functional equations. The linear transformations acting on these vector spaces could be represented by matrices, which also cropped up in group theory, in numerical analysis, and in number theory. Presently vector spaces over a field were subsumed under modules over a ring.

Such spaces and modules were needed to measure connectivity phenomena in topology. These topological concepts were then borrowed again by algebraists to become homological algebra and to settle questions in ring theory and in number theory-or at least in the higher reaches of class field theory. Groups represented by matrices had extensive applications in physics, while finite groups had an elaborate structure all their own, reflecting both geometry and number theory. Additional number systems like the complex numbers or the quaternions were impossible, in view of topological arguments-but the p-adic numbers arose from a marriage of algebraic functions and algebraic numbers. This is but a small sample of the extraordinary way in which the various ideas of mathematics interlock.

Because of ths elaborate interlocking pattern of ideas, each mathematical notion is tied to its empirical origins in multiple ways. As a result, no simplistic description of mathematics is adequate.

At each stage of development in mathematics, the structure at issue can be recorded as a formal deductive system. Such a system starts with axioms on a suitable list of undefined terms; in principle, it uses explicit rules of a specified logical system in order to deduce theorems and other conclusions from these axioms. Such an emphasis on the axiomatic method was not always present in mathematics. Moreover, it may seem more natural for some parts of mathematics than for others. Nevertheless, it is now always available for any part of mathematics. Our description of such systems is intended to cover use of intuitionistic or finitistic logic as alternatives to the more classical propositional and predicate calculus.

I’m wholly convinced by now of his case. (Perhaps this is just epistemic learned helplessness, given that Mac Lane happens to be a giant. Whatever.) Mac Lane summarizes:

At this point, we can make a first summary of our position. Mathematics starts from a variety of human activities, disentangles from them a number of notions which are generic and not arbitrary, then formalizes these notions and their manifold interrelations. Thus, in the narrow sense, mathematics studies formal structures by deductive methods which, because of the formal character, require a standard of precision and rigor

(Julie Moronuki expands upon this at the start of her beautiful essay The unreasonable effectiveness of metaphor, where I actually got Mac Lane’s paper here from.)

Mac Lane covers a lot more in his otherwise-short paper – the above is only the first quarter of it – but time runs short, so I’ll skip to the very end, where he attempts to define mathematics (ambitious!):

We hold that logicism, formalism, and Platonism have been too much dominated by the notions of set theory and deductive rigor. A balanced philosophy of mathematis should complement these ideas with others. The others we tended to list as three: breadth, clarity, and depth.

All three become important because of the extent of abstraction in mathematics. Abstraction consists in formulating essential aspects of some subject matter in terms of suitable axioms. Such abstraction can take place in several successive stages, interlocking different branches of mathematics. However, to be well directed or relevant that abstraction needs these three qualities.

The breadth of a mathematical notion refers to the variety of the situations in which it is to apply and to the pertinence and relevance of the abstraction made. It carries also the caution that deductions of theorems are guided not just by rigor but by the intent of the applications or by the origin of the abstraction.

Second, abstraction has increased the need for clarity in presentation; if the object of study is abstract, it must be understood not by its intuitive content but by its precise and abstract description.

Clarity goes beyond the precision of rigor to a clear ordering of ideas. The development of abstract mathematics, especially after 1920, is in this view a reflection of the necessity for such clarity. When geometry was the geometry of a three-dimensional real world, there could be continual appeals to the real world. Now, done in greater generality, it must be done rigorously and exactly; this means also that it must be clear and perspicuous.

The depth of a mathematical notion refers to the way in which that notion gets at the nonobvious, more fundamental structures and concepts underlying the problems at issue-as group theory underlies symmetry or as uniform continuity is subtly involved in many questions of real analysis. The study of manifolds in differential geometry and in algebraic geometry offers another example of the discovery of deeper notions. Initially one thinks of a manifold as a suitable smooth set of points spread out in some given ambient space. Later on one forgets the ambient space and considers the manifold in terms of the well-behaved functions which can be defined on it, as well as the germs of such functions at each point. This study in turn leads to the sheaf of germs of well-behaved functions on the manifold, and so to the deeper ideas of sheaf theory.

The depth of a mathematical notion may well change with time. For example, in the late nineteenth century the notion of uniform continuity seemed hard. It now seems easier, and is often dismissed as being simply a change in the position of an existential quantifier.

On the basis of this observation, we attempt a definition of mathematics about as follows:

Mathematics consists in the discovery of successive stages of the formal structures underlying the world and human activities in that world, with emphasis on those structures of broad applicability and those reflecting deeper aspects of the world.

In detail, mathematical development uses experience and intuitive insights to discover appropriate formal structures, to make deductive analyses of these structures, and to establish formal interconnections between them. In other words, mathematics studies interlocking structures. Because of the depth and of the distance from immediate concerns, mathematical treatments need be not only rigorous but also endowed with conceptual clarity.

Applied category theory: behavioral mereology

Lots of blogs are worth browsing even if (as an outsider/layperson) you only barely understand what’s going on. One of them is The n-Category Cafe, which I first stumbled upon many years ago while trawling through everything posted by John “Grandfather of Math Blogs” Baez.

Yesterday I swung by again and found a delightful post: Behavioral Mereology, by Toby Smithe and Bruno Gavranovic, introducing the eponymic paper by Spivak(!), Fong and Myers. The intro is clickbait, followed by a promise:

What do human beings, large corporations, biological cells, and gliders from Conway’s Game of Life have in common?

This week in the Applied Category Theory School, we attempt some first steps towards answering this question. We turn our attention to autopoiesis, the ill-understood phenomenon of self-perpetuation that characterizes life. Our starting point is Behavioral Mereology, a new take on the ancient question of parthood: how should we understand the relationship between a part and a whole? 

(There’s more words, but lacking the context to appreciate them my eyes glazed over to the main content.)

A digression: I first came across the term ‘mereology’ as a college freshman skimming the SEP, in particular the Holes page. Even back then I thought the discussion hard to take seriously, but I do remember the following line of reasoning:

If holes are entities of a kind, then, they appear to be spatiotemporal particulars, like cookies and tins and unlike numbers or moral values. They appear to have a determinate shape, a size, and a location. (‘These things have birthplaces and histories. They can change, and things can happen to them’, Hofstadter & Dennett 1981: 6–7.) On the other hand, if holes are particulars, then they are not particulars of the familiar sort. For holes appear to be immaterial: every hole has a material “host” (the stuff around it, such as the edible part of a donut) and it may have a material “guest” (such as the liquid filling a cavity), but the hole itself does not seem to be made of matter. Indeed, holes seem to be made of nothing, if anything is. And this gives rise to a number of conundrums. For example:

It is equally difficult to account for the mereology of holes. Take a card and punch a hole in it. You have made one hole. Now punch again next to it. Have you made another hole? In a way, yes: now the card is doubly perforated. But what prevents us from saying that we still have one hole, though a hole that comes in two disconnected parts? After all, material objects can be disconnected: a bikini, your copy of the Recherche, a token of the lowercase letter ‘i’. Perhaps holes may be disconnected, too? If so, perhaps we have just punched a single, disconnected hole?

This brought me to the Mereology page and this opening line:

Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole.

But that was half a lifetime ago. This is now. And Smithe and Gavranovic suddenly got my wandering attention again with the following introduction:

When we look at the world, we notice that it is full of objects. Some of these objects are immediate to our senses — such as a coffee cup, a bicycle, or your pet rabbit. Other objects we only come to know after reflection, or through the use of tools — such as the atoms of the cup, the ecosystem that led to the evolution of the rabbit, or the cells of the rabbit’s body. These objects are related by a kind of compositionality that we call parthood: the parts of the bicycle include its gears and pedals; the parts of the ecosystem include its population of rabbits; in turn, the rabbits are composed of organs and thence cells. Indeed, all of these objects are tautologically parts of the whole that we call ‘the universe’.

Behavioral Mereology seeks to formalize the intuitions behind these ascriptions of parthood. Its starting point is the observation that parthood captures a kind of behavioral coherence: “when you pull on a part, the rest comes with”. That is to say, being a part entails a restriction on possible behaviors. For instance, consider a cup together with its contents: as long as the two parts can be considered together as a whole, the possible movements of the contents are constrained by the those of the cup. In general, the behavior of a part is not only constrained by its corresponding whole, but also by the parts around it. For instance, the behavior of the rabbit’s brain constrains the behavior of its muscles; and because the muscles change the relation of the rabbit to its environment, and the environment constrains the rabbit’s senses, we can say transitively that the rabbit’s muscle-behavior constrains its sense-behavior. Consequently, we can think of the whole ‘rabbit’ system as providing a context for the passage of constraints between parts of the rabbit, and we will see how this gives rise to a lattice structure on the corresponding category of parts.

That last line was quite the conceptual leap. Unfortunately my lack of category-theoretic background fails me on the next paragraph:

These ideas sit at the confluence of two traditions of applied category theory. On one side, following Lawvere, we can conceptualize the aforementioned constraint passing as a formal change of context, via the pullback functor; precisely put, constraint passing is modelled by pulling a predicate back along the epi representing the parthood relation, from which we obtain two new adjoint inter-modalities, called compatibility and ensurance. On the other side of the confluence lies a behavioral approach to the categorical modelling of open and interacting systems. Let’s see how these two parts of applied category theory interact. We’ll start with the behavioral approach, which supplies the objects for the logic of constraint passing.

Damn! I don’t get it but wish I did. It gets friendlier for a while, before getting meaty again:

In our everyday lives, we do not need to know the internal workings or detailed structure of objects in order to distinguish them. Instead, we perform a kind of informal ‘black-boxing’, and declare that “if it looks like a duck and quacks like a duck, then it probably is a duck.” This is to say, we distinguish objects by observational equivalence, calling two systems the same when they produce the same observations under our measurements; in the field of coalgebra, this idea gives rise to the concept of bisimulation.

It gets really meaty from here on out, which in my case means I’m lost. Sighs. If you know category theory though, definitely check it out! Anything involving Spivak tends to be fun.