Thursday, 30 August 2018

Book review: Why we sleep

I read this book because I knew that it would tell me to sleep more, and I hoped it would cite enough scary statistics that I'd be likely to actually follow through. Well, it worked - I'm keeping a copy on my bedside table for the foreseeable future, just as a reminder. In addition to the exhortations to get more sleep, it contains a variety of other interesting and important facts about sleep.

What is sleep?
  • Human sleep consists of cycles lasting about 1.5 hours, each of which contains first a period of NREM (Non-Rapid Eye Movement) sleep, then a period of REM sleep. In brain scans, the former consists of slow, deep brain waves, while the latter shows the same frenetic activity as an awake brain. As the night goes on, cycles feature a higher proportion of REM sleep. This means that if you cut your sleep short by 25%, you're actually missing out on somewhere between 60% and 90% of REM sleep. 
  • REM sleep is when the majority of dreams happen. While it's uncommon for dreams to replay events from our everyday lives, they do often reflect our emotional preoccupations. To prevent ourselves from flailing around during dreams, we enter a state of sleep paralysis, where our brains are unable to control our voluntary muscles. Eyes are an exception - hence the name REM. It's definitely not true that REM is the only valuable type of sleep - in fact, immediately after sleep deprivation the brain prioritises catching up on NREM. 
  • The slow waves of NREM sleep are useful for transferring memories from one part of the brain to the other - in particular, from short- to long-term storage. 
  • Walker's theory is that NREM sleep is used to prune away unnecessary connections, while REM reinforces useful connections. He uses the analogy of a sculptor who alternates between carving away whole chunks of marble (NREM) and then adding fine detail on whatever's left (REM). From this perspective, it makes sense that REM sleep is concentrated in later cycles. However, it's unclear whether this is the scientific consensus. 
  • There are two systems controlling sleep and wakefulness. The circadian system follows the day/night cycle, making you tired in the evening and alert in the morning (the exact timings vary by person, making some people "night owls" and some "morning larks"). In addition, "sleep pressure" is controlled by adenosine, which builds up while you're awake and is cleared away during sleep. Caffeine works by temporarily blocking adenosine receptors, but doesn't prevent it from continuing to build up.

What's it good for?
  • There's a very strong link between NREM sleep and memory. The formation of long-term memories suffers if we don't get enough sleep (even several days after the events we want to remember). This is true both for memories about facts and experiences and for "muscle memory" of actions like playing an instrument. When sleep-deprived, we also have worse short-term memory.
  • REM sleep is important in emotional regulation and creativity. After sleep deprivation, the responses of the amygdala (responsible for strong emotions) can be amplified by over 60%, due to weakened links between it and the prefrontal cortex (responsible for "rational" decision-making). Dreams during REM sleep allow us to make unusual and creative connections between different topics - many great intellectuals report that their best ideas just "came to them" upon waking.
  • Sleep deprivation massively reduces our ability to concentrate. In addition to slower reaction times, when tired we lapse into "micro-sleeps" during which we're totally unresponsive. Walker emphasises that tiredness is a far bigger cause of traffic accidents than drunk-driving, that drivers systematically underestimate how tired they are, and that drivers who micro-sleep often don't brake at all before collisions.
  • In the long term, sleep deprivation increases the risk of Alzheimer's (since toxins are flushed from the brain during sleep), heart attacks (by provoking a stress response from the sympathetic nervous system and raising blood pressure) and cancer (by devastating the immune system). All of these seem to be very big effects - e.g. sleep-deprived patients are twice to three times as likely to suffer calcification of their coronary arteries.
  • Note that most of the effects above are noticeable even after small amounts of sleep deprivation, like getting one or two hours less sleep for one or two nights. In fact, even the one-hour sleep reduction from Daylight Savings Time causes a spike in heart attacks.
  • Sleep is also linked to many mental illnesses - e.g sleep deprivation triggers mania or depression in bipolar patients. Most mental illnesses disrupt sleep, which exacerbates their other negative effects.
  • REM sleep promotes the formation of neural links in infants, who have far more neural connections than adults. It is also important for their language learning.
  • Walker's broad answer to the question of what sleep is useful for: EVERYTHING. In addition to the above, sleep helps us overcome traumatic memories, reduces athletes' injury rates, makes us look more attractive, reduces food cravings, and so on and so on...

The evolution of sleep
  • I guess it shouldn't be a surprise that sleep is so broadly useful: once it started, it makes sense that many metabolic processes would take advantage of it. And they've had a long time to do so: sleep is ancient, with all animal species demonstrating some form of sleep-like behaviour. 
  • Even unicellular bacteria have active and passive phases corresponding to the planet's light/dark cycle.
  • However, the length of sleep required varies wildly for different animals, from 4 hours for elephants to 19 for brown bats. 
  • Only birds and mammals have proper REM sleep - it is a relatively recent adaptation. It also seems to be absent in aquatic mammals, whose two brain hemispheres sleep separately. 
  • Humans seem to be naturally biphasic: modern hunter-gatherer tribes sleep for 7-8 hours at night, and then nap for 30-60 minutes in the afternoon. It's biologically natural to be sleepy after lunch. Biphasic sleep significantly decreases mortality from heart disease. 
  • Walker hypothesises that descending from the trees to sleep on the ground allowed us to gain more REM sleep (particularly difficult in trees due to sleep paralysis), and therefore was important in boosting human cognitive development; also, that fire was vital in making ground-sleeping safer.

How to sleep better
  • Alcohol is an extremely powerful suppressor of REM sleep. Since it stays in your system for hours, it's best not to drink in the evenings. 
  • Light, especially blue light, signals your circadian system to wake up. Unfortunately LED screens provide a lot of blue light. Avoid using screens in the hours before bed, or at least phase out the blue light (e.g. using flux). 
  • In addition to light, our bodies use decreasing temperatures as a signal to sleep. Lowering room temperature often helps with insomnia. Apparently your core temperature will also fall after a hot bath. 
  • Caffeine has a half-life of 5 to 7 hours, so if you drink it in the afternoon, a significant amount will still be in your system at bedtime. 
  • The circadian rhythm of a teenager is naturally a few hours later than that of an adult, so teens shouldn't be forced to get up too early. Unfortunately, schools aren't taking much notice of this. 
  • Apparently sleeping pills cause lower-quality sleep and have severe long-term side-effects, so they should be avoided (with the exception of melatonin). 
  • For serious sleep problems, Cognitive Behavioural Therapy for Insomnia (CBT-I) works fairly well and should be the first step.

As you can probably tell from the above, Walker is very much a cheerleader for sleep. This does bias him in some noticeable ways - e.g. his overt scorn towards coffee. He also blurs causation and correlation at some points throughout the book, so I'd be surprised if all of the deleterious effects mentioned above are as significant as he claims. But the overall picture is stark enough that I'm now very worried about the ongoing sleep loss epidemic.

Friday, 24 August 2018

Feeling, complicated

It was very striking to me to contrast the two recent successes of OpenAI: one, OpenAI Five, beating some of the best humans at a complex game in a sophisticated virtual environment; and the other, Dactyl, fumblingly manipulating blocks in ways that children master at young ages. This is not to diminish how much of an achievement Dactyl is - no other reinforcement learning system has come close to this sort of performance in a physical task. But it does show that the real world is very complicated, compared with even our most advanced virtual worlds. To be fair, the graphics and physics engines used to render videos are becoming very good (and as movies show, practically indistinguishable from real life when enough work is put in). Audio generation is worse, except on human voices, which are now very convincing - but background sounds aren't a crucial component of our environment anyway. The biggest experiential difference between current simulations and the real world seems to be tactile sensations, or the lack thereof. OpenAI couldn't get realistic simulation of tactile sensations even in the very simple Dactyl environment (and eventually decided to do without them).

This may be due to the intrinsic difficulty of generating tactile feedback, but may also be because of the type of situation in which it's required. You can get impressive visual output from a static landscape. By contrast, we get tactile feedback mostly from physical interactions with objects in our environment - but modelling objects which can interact with each other is very hard! Consider how many things I can do with a piece of paper: write on it, tear it, crumple it, blow it away, make a paper plane out of it, set it on fire, soak it in water, eat it, cut holes in it, braid it into ropes, and so on. Many of these effects depend on molecular-level physics, which we're very far from being able to simulate on a large scale. And even the macroscopic effects rely on friction, which is also very difficult to model efficiently. If we add in fluid dynamics, then it seems plausible that it will take half a century or more before any simulated world is advanced enough to model all the interactions I listed above in real time. And that's just paper, not machines or electronics!

An alternative approach is to constrain the types of interactions which are allowed - e.g. a simulation with only rigid bodies. In such an environment, we could develop efficient approximations to trade quality for speed (a tradeoff which the graphics community has been wrestling with for some time). Friction would still be a major difficulty, as well as the ability to feel surface textures, but it's likely that immersive, interactive simulations with these properties will be developed within the next decade or two. The reason visual rendering is so advanced is because it's so crucial to the multi-billion-dollar video game and film industries. Now that VR is becoming a thing, those market pressures will be pushing hard for realistic environments with tactile feedback - and in doing so, increasing the effective number of people working on AI even faster than the nominal number.

Monday, 20 August 2018

Book review: The Complacent Class

"The best lack all conviction, while the worst
Are full of passionate intensity."

                                                   W. B. Yeats

The idea that things aren't going great these days is pretty widespread; there's a glut of books pointing out various problems. Cowen's achievement in this one is in weaving together disparate strands of evidence to identify the zeitgeist which summarises the overall trend - in a word, complacency. There are at least two ways in which people can be complacent. Either they're living pretty good lives, and want to solidify their positions as much as possible. Or they're unsatisfied with their lives, but unwilling to mobilise or take the risks which could improve their situations. (People in the middle of the economic spectrum showcase aspects of both). What's the opposite of complacency? Dynamism and risk-taking - traits which have always been associated with immigrants, and with America, the land of immigrants. Such traits aren't always expressed in positive ways, of course. Says Cowen: "Our current decade can be understood by comparing it to the 1960s and early 1970s. The Watts riots of 1965 put 4,000 people in jail and led to thirty-four killed and hundreds injured; during an eighteen-month period in 1971–1972, there were more than 2,500 domestic bombings reported, averaging out to more than five a day. I’m not advocating these tactics, of course. My point is that, today, there is an entirely different mentality, a far more complacent one, and one that finds it hard to grasp that change might proceed on such a basis. Yet in the 1960s and 1970s, not only did riots and bombings happen, but large numbers of influential intellectuals endorsed them, defended them, and maybe led them to some degree." In comparison to this, even people who are passionate about social change lack anywhere near the same sense of urgency today.

Cowen identifies many metrics which support the narrative of increasing complacency. Over the last few decades, interstate migration has gone down, job mobility has gone down, startup formation has gone down, and business churn and turnover have gone down. What's gone up? Market concentration and "matching": our ability to tailor our lives so that we're only exposed to things we're already comfortable with, whether that be music and movies similar to those we've seen before, or partners from the same class background as us. One particularly perverse result of better matching is increasing racial, economic and political segregation, reversing the progress made in the first half of the 20th century. A particularly notable cause of this is NIMBY movements, many of which have succeeded in ossifying their neighbourhoods by stifling new development. Segregation is also very pronounced in the incarceration industry.

In our personal lives, complacency involves prioritising comfort and security above all: physical security, with games like dodgeball and even tag being banned in schools; emotional security, via safe spaces and trigger warnings; and even corporate security, with companies hyper-focused on protecting their brands and other intangible assets (which have gone from less than 20% to over 80% of the value of the S&P 500 over the last 40 years). LGBT activists have moved from pushing the boundaries of societal norms to pursuing the most traditional of institutions, marriage. Nobody really has a bold vision for the future. (Relatedly, the portion of the federal budget allocated for discretionary spending has been falling sharply.)

But, Cowen says, this mindset can't keep limping along indefinitely, and will eventually face a crisis. In fact, we can think of it as a cyclic process: our current appetite for calm was whetted in the riotous and violent 70s and 80s - but as people become more disillusioned, it will eventually give way to similar turmoil, the start of which we're already seeing.

Causes and complacencies

It's instructive to evaluate The Complacent Class with reference to Cowen's last two books. In The Great Stagnation, he argues that America's growth has slowed down because it ran out of "low-hanging fruit" like the technological advances of the early 20th century. Further, the problem is even worse than it seems, because growth in sectors like healthcare, finance and government spending contributes less to people's welfare than it used to. In Average is Over, he predicts the effects of the next low-hanging fruit: AI. He argues that those who can work well with technology - in broad strokes, the smart and the conscientious - will be able to replace dozens of less-skilled workers, and will be richly rewarded for it (which contributes to increasing credentialism). We should expect to see even more middle-class jobs crowded out, and even more wealth captured by a smaller proportion of people. Returns to being based in a good location are also increasing, driving the clustering of university graduates into relatively few cities. Meanwhile, Cowen predicts that the poor will be squeezed into places with much lower housing costs, even if they end up resembling "shantytowns". He notes that America's population is ageing, and that the elderly voting demographic usually gets what it wants, even at the cost of society overall.

Okay, so how does this relate to complacency? I think that's very unclear. If many of the trends cited in The Complacent Class can be explained by the ideas that we're in a "great stagnation" and that "average is over", without reference to individual attitudes, then they're not really evidence for complacency in the psychological sense. In fact, how do we know that there aren't other explanations for all of them? The ageing population comes to mind as a major possibility (although I'm not sure how many of Cowen's statistics already control for age). Perhaps it's useful to identify an overall pattern of "complacent" behaviour even if different changes have different causes, some psychological and some from technological and international shifts - but this sort of pattern has very little predictive power, since we don't know which other domains we can apply it to.

This lack of clarity around what complacency actually means makes it somewhat unfalsifiable. For Cowen, complacency is demonstrated both by the rich erecting barriers to the advancement of the poor, and by the poor not breaking through those barriers. But what if the rich did nothing while their social and financial dominance eroded away - wouldn't that also count as complacency? What if the poor are actually willing to take more risks now (like the financial risk of going to university) but it's just paying off less - would that really make them "complacent"? Cowen claims that more relaxed codes of dress and manners display "a culture of the static and the settled", but don't they also lower implicit class barriers and therefore promote dynamism? There's a case that doing graduate degrees is ambitious and valuable, but there's a similarly strong case that it's a complacent replacement for making things happen in the real world. The very same companies which match us with our preferred options also allow us to sample more variety - whether that's in songs, shopping, or sexual partners. And so on. More generally, I think we should be biased against claims of the form "it's a big problem that the next generation have the wrong attitude towards X", because they have occurred so commonly throughout history, usually sounded convincing, and were usually wrong.

Nevertheless, there's undeniably some truth to Cowen's core argument. Almost none of the physical technologies around us (buildings, cars, trains, rockets, household appliances) have seen significant progress over the last half-century; nor have systems like healthcare, law, politics or education. But more importantly, people aren't even surprised by this stasis: the radical expectations of the mid-20th century have given way to doubt that our lives will be any better than our parents', plus a generous helping of political disillusionment. It's true that IT has made massive leaps, but as Cowen notes, "a lot of the internet’s biggest benefits are distributed in proportion to our cognitive abilities to exploit them". People who don't highly value near-unlimited access to information or niche communities may even find that the downsides of the internet (addiction to games or porn, mental health problems exacerbated by social media, news media's race to the bottom) outweigh its upsides. So I do believe that westerners today are, psychologically, more complacent than they were a few decades ago, and that this shows through in attitudes towards risk and expectations for the future. It's also likely that increasingly complacent behaviour which isn't caused by a complacent mentality still leads to an overall culture of complacency, although disentangling cause and effect here is tricky. Either way, Cowen's ideas are as thought-provoking as usual and should be taken into account by anyone interested in understanding America.

Monday, 13 August 2018

Some summer paper summaries

High-level analysis of reinforcement learning

Building machines that learn and think like people. Lake et al. think that human learners are doing something fundamentally different from machine learners: we carry out tasks in the context of many years of related tasks, whereas ML systems cannot. So, they ask, "how do we bring to bear rich prior knowledge to learn new tasks and solve problems so quickly?" The core ingredients they identify are intuitive models of physics and psychology, which exist from infanthood, and the capacity for rapid building of mental models which can be used for classification, prediction, communication, explanation, and composition. The skill of model-building can be distinguished from pattern recognition, which the authors suggest makes up much of the recent progress in deep learning. In particular, notions of composition, causation and hierarchy which are central to models may be weak or non-existent in pattern recognition. Further, they note that progress in this area may require searching over many structural variations to find new architectures, which currently is done by researchers and seems difficult to automate.

Building machines that learn and think for themselves. DeepMind respond to Lake et al. by arguing for AIs with the autonomy to design their own internal models. They note that there are many domains which, unlike physics, we can't describe in enough detail to hardwire into AIs. Because of this, systems which don't require inbuilt knowledge seem more promising, especially if they can be applied to many different domains. However, Botnivick et al. also defend knowledge being inbuilt in a very generic form, e.g. the translational invariance of CNN's convolutional layers. This allows models to be tailored to both the agent's tasks and its control structures.

A real world reinforcement learning research program. Langford argues against the approach, led by DeepMind and OpenAI, of starting with reinforcement learning for simulated environments like games. He notes that algorithms based on Q learning do badly on certain classes of problems - for example, cases where rewards near the start state favour staying near the start state, or where most transitions lead back to the start state. He also points out that when training in simulation, there's less need to focus on algorithms with good sample complexity - but that simulations are still a long way from being faithful representations of the real world. He worries that even if these approaches work out eventually, less value is being created in the meantime compared with his approach of working on real-world problems informed by fundamental theories of RL. In a comment, Dietterich disagrees and cites the example of SAT, which is theoretically intractable but has still seen exponential speedups.

A roadmap towards machine intelligence. Mikolov et al. identify two characteristics - communication and learning - which they consider crucial to machine intelligence. They argue that we can make progress towards these by training agents in an artificial environment with a teacher who assigns them tasks using natural language. Notably, they also think the agent's only interactions with the environment should be language-based, as in classic text-based adventure games. As the agent progresses through levels, they are assigned more abstract tasks which require previously-learned skills; the authors envisage this culminating in interactions with real people. However, they seem to be overoptimistic about the extent to which an agent can learn from language alone.

Improving RL agents' goals

Intrinsically motivated learning of hierarchical collections of skills and Intrinsically motivated reinforcement learning. This pair of papers introduces the idea of agents which learn for themselves a "knowledge base" of skills, where possessing easier skills can make it quicker to learn harder ones. This approach is inspired by neuroscience - in particular the release of dopamine in response to novelty. Theories of child development also suggest that children are most attracted to moderate novelty, especially when they caused it. In Barto et al.'s toy simulation of this, the RL agent needs hardwired notions of what counts as an interesting event (e.g. changes in light or sound intensity). When one occurs, the agent notes it and from then on is intrinsically rewarded for recreating it (with reward proportional to its error in predicting that event - analogous to how children get bored once they've understood how something works).

Intrinsic motivation and automatic curricula via asymmetric self-play. This paper introduces a new form of unsupervised training for RL agents: Alice proposes a task (by doing it) and then Bob has to either reverse the task (in reversible environments) or repeat it (in resettable environments). Alice's optimal behaviour is to find the simplest task that Bob can't reverse/repeat.

Automatic goal generation for RL agents. Florensa et al. use a generative adversarial network to decide on goals which are at the appropriate level of difficulty for a reinforcement learner. It's started using labelled examples, and then learns to identify goals of intermediate difficulty where the expected reward is within some range.

Hierarchical Deep RL. The authors propose a scheme which simultaneously learns how to choose subgoals and how to achieve subgoals. A controller is trained to achieve its current goal using "intrinsic rewards" for doing so; a meta-controller which chooses new subgoals for the controller is learned using deep reinforcement learning, based on the rewards the controller receives from the environment. Note that subgoals are defined in terms of objects which needed to be identified by a separate system.

Programmable agents. Denil et al. build networks that execute a simple declarative language. A goal is specified as a state of the world that satisfies a relation between two objects, which are associated with sets of properties. They make their boolean operators differentiable by assigning not(x) = 1-x, and(x,y) = xy, or(x,y) = x+y-xy. The particular goal used is for a simulated robotic arm to reach towards certain objects. This is an easy task, but standard deep learning methods totally fail to generalise to unseen objects, whereas apparently this can do so. The paper is somewhat confusing, but it seems like objects are baked in rather than learned.

Improving RL agents' object representations

Interaction networks for learning about objects, relations and physics. Interaction networks are models which can reason about how objects interact in a way analogous to simulation. Objects and the relations between them are stored in the format of a directed multigraph. At each timestep, the effect of each relation on its target object is computed by an MLP. Then another MLP determines how all the relations applied to each object influence its next state. These two neural networks can be learned efficiently because they are shared over all relations and objects respectively. The authors tested interaction networks on their ability to predict simulated physical interactions over many rollout steps. While they end up diverging considerably from the physics engine, the predictions seem fairly realistic.

Discovering objects and their relations from entangled scene representations. Inspired by the above paper, Raposo et al. introduce relation networks, which can be used to reason about objects and their relations. They use a MLP which operates on all pairs of objects, and whose output is then aggregated in an order-invariant way (e.g. addition). Experiments were done with scene descriptions as inputs, as well as inputs pre-processed by variational autoencoders. I didn't quite understand the setup of the experiments, but the results seem promising.

A simple neural network module for relational reasoning. This paper applies relation networks to the CLEVR dataset, both from pixels (which were processed first by a CNN) and from image descriptions. This achieves improves significantly on the state-of-the-art, and also beats human performance - an achievement which seems to be driven by improvements on relational questions in particular.

Schema networks. Researchers at Vicarious created the Schema network, an object-oriented generative physics simulator. It was able to generalise to variations of Breakout with offset or resized paddles, a wall in front of the bricks, and even three balls which needed to be juggled. Their approach is motivated by the gestalt principle: that the ability to perceive objects as a bounded figure in front of an unbounded background is fundamental to all perception. Each schema in the network is a local cause-effect relationship involving one or more objects (which each can possess some attributes); unfortunately, schema networks don't themselves learn how to recognise objects, nor what types of properties and relationships objects can have.

Towards deep symbolic reinforcement learning. Garnelo et al. propose an architecture with a neural back end and a symbolic front end. The neural network is a convolutional autoencoder which is trained to recognise basic patterns of circles and crosses. In a somewhat hacky way which wouldn't scale to any real images, they extract from the autoencoder the locations and types of these objects, and then process them using symbolic logic.

An object-oriented representation for efficient reinforcement learning. Diuk et al. extend the MDP formalism to object-oriented MDPs. When two objects interact, they define a relation between them, which may produce an effect - a change in value of one or multiple attributes in either or both interacting objects. But again, there's no good way of learning what the objects and attributes are...

Other deep learning

Neural Turing machines and Differentiable neural computers. These two papers present neural networks which can write to and read from external memory, in a fully differentiable way. A controller decides at each timestep whether to read or write, and if so where to. It does so using an attention mechanism over all memory locations, determined by the cosine similarity between those locations and a key vector emitted by the controller. In NTMs, there is also a way to shift the focus to the next location. However, since write operations were often not performed at sequential locations, this was of limited use. In DNCs, that mechanism was replaced by a way to shift focus to the location which had been written to immediately after the current location was, and an additional variable was added to keep track of the "usage" of each memory location. Both architectures were tested on question-answering tasks including navigating the London underground based on a graph of the stations. In addition, they were trained via reinforcement learning on a block puzzle game. DNCs did significantly better than both NTMs and the best previous results.

Neural programmer-interpreters. Another DeepMind paper which merges symbolic and neural processing - in this case, by using a controller to decide which program to run and when to stop it. It is applied to tasks like addition and sorting, being trained to maximise the probability of the correct execution trace. The NPI trains faster than a LSTM, and also generalises much better to inputs longer than any seen in training.

Episodic exploration for deep deterministic policies. Usunier et al. work on micromanagement in Starcraft by learning a greedy MDP: an action is chosen for each unit in turn, conditioning on the actions of previous units. Their exploration algorithm (zero-order gradient estimation) samples a vector on the unit sphere and then adds this to the parameters which determine the policy; the estimated gradient is then the cumulative reward times that vector.

Progressive neural networks. Progressive networks instantiate a new neural network for each task being solved, and then connect them laterally to allow transfer learning. It works on variants of Pong, but overall seems like a hacky solution which wouldn't scale.

Taking the human out of the loop: a review of bayesian optimisation. Bayesian optimisation is a way of jointly optimising hyperparameters of black-box functions, by starting with a prior and then describing an acquisition function for sampling from the black box which balances between exploration and exploitation. This can be used for a/b testing, reinforcement learning, combinatorial optimisation, etc.

Neural architecture search with reinforcement learning. In this paper, a controller RNN is used to generate neural network hyperparameters. After an architecture is generated, it is built and trained, and the controller is updated based on how well the architecture did on a test set. As well as variables like number of filters, filter size and stride sizes, the controller can propose skip connections and branching layers using an attention mechanism. A variant of this algorithm generates recurrent cell architectures, including one which outperforms LSTMs (although its method of modifying the computation graph is rather ad-hoc).

Natural language processing

Supervised learning of universal sentence representations from natural language inference data. The authors train sentence representations using the Stanford Natural Language Inference database, which has pairs of sentences labeled either as entailment, contradiction or neutral, and find that their representations outperform Skipthought, FastSent, etc.

A structured self-attentive sentence embedding. This paper tries to make sentence embeddings more interpretable by creating them as a linear combination of hidden states of a bidirectional LSTM, which the authors call a "self-attention" model. This allows identification of which parts of the sentence are being focused on to create the overall embedding.

Just for fun

The Evolution of Ethnocentrism. A cool paper showing that, in a simple model of an evolving population of agents facing prisoners dilemmas, the strategy of ethnocentrism (cooperating with your own tribe, but defecting against others) comes to dominate. The population is set in a 2-dimensional space, with agents interacting locally with others around them; the dominance of ethnocentrism is robust to changes in hyperparameters.

Jack of all trades

Over the last decade and a half, I've spent a lot of time trying out different hobbies. I've gotten pretty good at many of them, but never excellent at any. Now that I've left university, I've decided that I should explore a bit less and focus a bit more, both because I'll have less free time while working, and because you get more out of things when you're very good at them and are very involved in a community around them. But how to choose the optimal combination of hobbies? This is something I think people don't plan well enough, especially for their children. So many girls end up spending a huge amount of time on ballet or gymnastics or figure skating - perhaps the three sports which it's most difficult to continue past childhood, since they're so hard on your body and so youth-focused. And the vast majority of kids who learn instruments - even those who really enjoy playing - end up dropping them a few years down the line. It's true that there is value in experimenting with new things, but I don't want to be an eternal dilettante. Let's see if, from my current position, I can do a bit better in finding things I'll want to do for a long time.

At least one should be a cardio-intensive sport, for the sake of my health. Some people enjoy running, but I find it very difficult to motivate myself to do endurance sports - I just don't get any "runner's high" or particular feeling of achievement. Also, I think I have more fast-twitch muscles than slow-twitch ones - I can exercise at high intensity for a long time, but only if I have frequent breaks. This also rules out cycling, swimming and rowing. There are other outdoorsy sports like hiking, scuba diving and kayaking which aren't such slogs, but unfortunately I don't enjoy nature enough to commit to those.

Team sports are still a good workout while also providing an automatic social environment. Some, like basketball and volleyball, favour tall people too much for my taste. Fortunately, that's less true of sports like rugby, football and field hockey. The former is a bit too physical for me, and the latter not particularly common, but I think it'd be fun to join a casual football team, ideally along with some coworkers. (Actually, for the last few years I've played irregularly for the Oxford Vietnamese Society football team, which I enjoyed a lot). I don't want football to be my main sport though, for a couple of reasons. Firstly, it's too dependent on having an organisational structure - I can imagine changing jobs or cities and not finding a new team to play with. Secondly, I'm quite individualistic at heart, and am more motivated when I'm the one responsible for winning or losing. And thirdly, it's just not as intense as other sports - you spend most of your time without the ball, and some of it on the bench. (To be fair, sports like cricket and baseball are much worse on this metric, to the point where I can't imagine myself actually playing them).

By contrast, when playing racquet sports you're engaged 100% of the time. This is one of the reasons I enjoy them so much - at various points I've played reasonable amounts of tennis, squash, badminton and table tennis. Tennis is obviously the most popular, but I never enjoyed it as much as the others because it's easier to hit the ball out, making the average rally significantly shorter (also true of table tennis). In squash and badminton, on the other hand, rallies can be much longer and very intense. I think I'd enjoy getting better at badminton, but it makes more sense to focus on squash, since I've played it for over a decade now. By default, this is the sport I spend most time on - but I do worry that after another decade or two of squash, I'd end up accumulating knee injuries from constantly sprinting around the court. So perhaps I should play it for a few years more, but phase it out as I get older.

The same is true for my two other favourite sports, ice hockey and skiing. They're both rather tough on the body, and I think it'd be frustrating to be getting worse at them every time I play, so I'll stop before I reach that point. Actually, if I didn't already love skiing, I probably wouldn't let myself do it, because I prefer to avoid sports which are expensive, dangerous, or require travel to special locations - ruling out many water sports, all variants of flying and riding, and most other "exotic" sports (I'd still like to try most of these once or twice, but not as regular hobbies). Speaking of danger, boxing is out for obvious reasons; while less dangerous martial arts require far too much time training, instead of doing the thing you're training to do. This is also true for juggling - keeping a pattern of balls in the air is really fun (and a prime example of being in a state of "flow"), but it's just way too much work to get beyond five. (This is one of the very few cases where the phrase "the difficulty increases exponentially" is mathematically accurate).

Fortunately, I've stumbled on a sport which ticks all the boxes: it's intense, but not hard on your body; individual, but still social; and available everywhere I plan to live. That sport is dancing. Two years ago, I joined the Oxford Dancesport Beginners team, mostly because I felt that it would make my life more aesthetic. I ended up really enjoying both dancing itself and the community around it, and decided to continue dancing outside the team - but of course it wasn't as simple as that. There are dozens of different dance styles - which ones to focus on? So far I've tried waltz, quickstep, tango, jive, rock and roll, swing, rumba, samba, cha-cha, salsa, and bachata. The first three require a statuesque elegance which I'm never going to possess. The next three are American Jazz dances, which tend to be lively and jumpy, and the last five are Latin dances, which tend to be slower and more sensual. In terms of social dancing, the main contenders are swing and salsa, which have regular social nights in most major cities. Personally, I prefer the latter - it's more technically interesting (with fast spins and intricate arm movements), more passionate, and is often played at dance parties which also feature bachata, a particularly romantic dance that's lovely to do with a partner.

Okay, so that's sports sorted. What about more cerebral pursuits? For the last decade I was a competitive debater (and, more recently, a debating coach), but that's very much a student-focused activity, and one which I'd gotten a little bored of besides. Over the same time period I'd also been exploring a variety of classic board games, trying to find one which I wanted to play seriously. I have quite pronounced tastes when it comes to games: I particularly like those with great strategic depth, but without complex or arbitrary rules. The former criterion rules out games like backgammon and checkers; the latter rules out Scrabble and most other modern board games. I also prefer games where the complexity comes from analysing the game itself, not the other players, unlike Diplomacy and poker. Out of the classic strategic games, I played chess at school and Chinese chess with my father. However, for both aesthetic and practical reasons I don't like games where draws are very common, or where it's necessary to memorise many opening sequences to do well. That meant I got bored of those two, and wanted to move on. In my first year at university, I learned shogi from a former US amateur champion, and found it pretty interesting: the fact that captured pieces can be dropped back on the board for the other player adds a whole new level of tactics compared with other forms of chess. The next year, though, I transferred to Oxford, and joined a Go club instead. I find Go to be the deepest and most elegant of all the games I've tried - the rules are amazingly simple, but I could study it for decades and still not grasp all the strategic nuances. So if there's any game which I'll play regularly in the long term, that'll be it. It remains to be seen whether I get bored after a decade or two, but for now, it's fortuitous that DeepMind is probably the one company (outside Asia) with the highest concentration of Go players.

Next, in the words of Abba, who could live without music? Back in school, I dabbled in the violin, french horn and flute (the last of which I still play occasionally), but my main instrument has always been piano. However, I think I went about learning the piano quite badly. I've always loved dramatic Romantic pieces, but they're hard to learn and even harder to play well. It would take regular practice just to maintain the half-dozen pieces I know so that I can play them semi-decently, but I find such practice boring. I'm also pretty bad at sight-reading, so learning new ones is quite an effort. If I want to keep playing piano in the long term, I think I'll need to change my approach to either improve greatly at sight-reading, or else focus on some form of improvisation - perhaps jazz. It would be so much fun to be able to sit down and make up a piece from scratch! I don't know if I'll have time to learn that over the next few years, but whenever I start phasing out the intense sports I mentioned above, this is the obvious replacement. There's also singing in a choir, which is low-effort and communal - it'd be worth signing up in a few years if I find one with cool people singing music I enjoy. But for now, music is on the back-burner (except for whistling, which by now is a deeply-ingrained habit).

Lastly, of course, there are my standard intellectual explorations, which of late have mainly been expressed via blogging - definitely the most rewarding hobby I've ever picked up. Coming up on a year of consistent blogging, I feel like I've made a lot of intellectual progress - and more importantly, that it's progress which I can build on. By contrast, during undergrad I had many fascinating conversations with clever people, but later forgot most of them, and ended up going in circles on many issues. Now, when I have such a conversation I usually manage to incorporate the key ideas into some blog post sooner or later. I still need to spend more time reading more books to pick up a wider range of ideas - but that's always true, because you can never read enough books. Actually, it's fitting to end with the one hobby that has most defined me, and which I still consider to be a core part of my identity. At heart, I'm still the little kid who'd go to the library and come back with a stack of books almost as tall as himself.

Saturday, 11 August 2018

And taxes shall have no dominion

This blog often concerns itself with death, but not so much with that other unyielding constant of life, taxes. Inspired by a conversation with my friend Will, I’ve decided to rectify that imbalance. Apart from complaints, what is there to say about taxes? Economic theory says they should:
  1. Be very difficult to evade.
  2. Not disincentivise the production of things we actually want.
  3. Be progressive - ideally in percentage terms, but at least in absolute terms.
A poll tax (a flat tax on all adults) meets criteria 1 and 2, since I doubt people will take it into account much when having children. But it fails dramatically on 3 - it's a fixed flat sum, which means it can't raise much money without badly hurting the poor. A consumption tax like VAT (value added tax) discourages consumer spending, which may well be good for people's happiness and the environment - but still hurts the poor if implemented badly (because it increases the cost of goods by a fixed percentage). A good way to make VAT more progressive is to have lower rates for goods which the poor spend most of their money on (e.g. food, clothes) and higher rates on luxuries. Unfortunately, classifying every single item gets very bureaucratic, and leads to legal wrangling over bizarre issues like whether Jaffa cakes are cakes or biscuits.

Income taxes and corporate taxes are usually progressive, but are also much easier to evade (especially for the super-wealthy), and penalise productive work on both an individual and a corporate level. More on them later. Carbon taxes can also be dodged, but are otherwise ideal because the thing they disincentivise is a major negative externality - I hope they become more widespread soon.

Land taxes

How about a land value tax? That is, a tax proportional to the value of the land you own - not counting the value of the buildings on that land. It's incredibly difficult to evade - you can't hide your land from the government. It's progressive, because wealthy people tend to own much more land - and by targeting a major source of hereditary wealth, it would reduce inequality more directly and fairly than income taxes. Lastly, it doesn't disincentivise the production of land, because you can't produce land (except via reclamation projects, I guess, but I'm sure an exception could be made for those). In fact, since the tax is equal no matter how well or badly the land is used, it encourages landowners to develop their land, rather than holding it for speculation.

Let's explore that last point a little more. You might think that the lost revenue from leaving a lot empty is enough of a disincentive to prevent it. But construction is very expensive and time-consuming - partly for regulatory reasons (which I detail here) but also because the sort of buildings which bring in revenue in city centers - apartment blocks and skyscrapers - are necessarily large projects. Given how much property prices are rising in cities, you can often make a handsome profit just by hanging on to land for a few years (maybe while using it as a parking lot) without the same cash outlay, time commitment and risk required for a major development.

This is bad, because bustling, vibrant central districts are important to making cities great, and great cities are a public good. Such cities collect and connect clever people to make them more productive and innovative. This has been true for millennia, from the city-states of Ancient Greece to the trading hubs of Renaissance Italy to the glamorous European capitals of the 19th and 20th centuries. It may be even more true now, as winner-takes-all dynamics increase the returns to being in the best locations. More development of city centres would also decrease urban sprawl and all its concomitant problems (long commutes, racially-segregated suburbs, carbon emissions, etc).

There are still some problems with a land value tax. The main theoretical one is that it requires the government to assess underlying land values. Unlike overall property prices, there's no clear market mechanism for doing so, and there's a pretty strong incentive for governments to be optimistic about values when doing evaluations. A second problem is that it makes some projects, like private parks, much costlier. While it would be fairly easy to exempt these, it'd be dangerous to set a precedent of allowing exceptions, which could screw up land allocation. And in fact there's at least one exception which would do so, and also seems quite likely to be included in any proposed land tax - namely, an exemption for primary residences. These are already excluded from the UK's inheritance tax, because otherwise heirs would usually have to sell them to pay the tax. Similarly, the many retirees for whom their house is their major asset would struggle to pay even a small percentage of its land value every year directly out of their incomes.

To be clear, in economic terms this is a feature not a bug. Individual houses are a very unproductive use of central land, but they often can't be put to better use because their owners want to keep living in them for a period of decades. So putting a bit more pressure on them to move speeds up growth. But it's not too coercive, because even income-poor owners could afford to stay if they really wanted to by taking a loan with the house as collateral. Unfortunately, that's the sort of option which people are fairly biased against. And since the elderly are a disproportionately influential voting bloc, I'd bet that a land tax would come bundled with a primary residence exemption. But if other types of building are taxed and those aren't, the net effect might be more of city centers being used unproductively. I guess this would vary by city - London might be fine, since it's nigh-impossible for individuals to buy central land outright. However, that's partly because over 1000 acres of prime real estate is owned by “the Crown, the Church, and five aristocratic estates with a collective wealth of £22 billion.” Any guesses who'd be first in line for exemptions from a land tax? Which is a real shame - I'm usually not in favour of radical wealth redistribution but as far as I can tell these aristocratic estates are pure rentiers who contribute nothing except inequality.

On the other hand, I'm generally loath to recommend the government institute another tax, because even though it'd be an improvement if it replaced an existing one, in practice it's quite likely that both end up coexisting, increasing the overall tax burden. The belief that governments are actually very bad at making use of the taxes they receive is one I’ve had for quite some time, although I admit that its emotional impact rose sharply when I realised just how much of my income I'll be losing to tax next year. (I wouldn't mind nearly as much if I thought the money would actually improve other people's lives - thank goodness charitable donations are tax deductible).

Corporate taxes

I think it's reasonable to say that corporate taxes haven't been working very well lately. Corporations have become incredibly adept at manipulating complex tax laws across many countries to their advantage - and so far the international community has been pretty impotent in taking measures to prevent that. Even when companies can't avoid nominally high taxes, they often leave their money offshore until a "tax holiday" is declared, so effective taxes end up being much lower. In fact, the global average corporate tax rate has fallen from 49% to 24% over the past three decades.

Is this even such a bad thing, though? Corporate tax is a form of double taxation - whatever profits companies earn will eventually translate to gains for their shareholders, who are then taxed again as individuals. (In fact, for multinationals it’s often triple taxation: once in the country where the income is earned, again in their home country, and again when profits are distributed.) So in theory, the total amount collected could be the same whether or not corporations are taxed at all. However, it would be collected by different countries - not the ones in which profits are made, but the ones in which the owners of multinationals are clustered, i.e. mainly America and China. (And if those owners moved to income tax havens, perhaps nobody would be collecting tax from them at all.)

On the other hand, the status quo isn't much better when it comes to fair distribution of corporate taxes. As the graph below shows, the efficacy of corporate tax collection for US tech giants is very low outside the US. Ian Hogarth thinks that the unevenness of corporate tax will be a major concern for other countries as these companies start to automate more and more jobs and therefore constitute a greater share of the global economy. Kai-Fu Lee suggests that such countries will need to become "economic dependents" of the US or China to avoid poverty after their jobs are lost.

AI and taxes

Interestingly, Lee's conclusion that "the solution to the problem of mass unemployment ... will involve ""service jobs of love" ... [which are] jobs that A.I. cannot do, that society needs and that give people a sense of purpose" is pretty similar to my own thinking on the issue. The main difference is that I think these jobs will be financed by wealth increases across society overall, as professional sports teams are, rather than by top-down subsidies. This is informed by my broader belief that, even if the wealth created by technological innovation isn't distributed equally, it'll still benefit the vast majority of people. This has held true for almost all technological developments so far, even ones which seemed elitist when introduced (e.g. the iPhone, which hastened the arrival of budget smartphones). Artificial general intelligence (AGI) may be an extreme enough case that it's an exception to this principle, but I doubt narrow AI is. In fact, it's much easier for poor countries to cultivate CS expertise than other forms of scientific or technological expertise - and even as budgets for computing power shoot up, talent is still the biggest limiting factor. Note also that there’s intense competition in the tech sector, to the point where companies often have to give away valuable software (like map apps or email services) for free, because if they don’t, they’ll be undercut by competitors who do. Assuming that this trend continues - and I see no reason why it won’t - the percentage of the social value of their innovations captured by tech companies will continue to be very low, with most of that value instead going to people across the world.

Nevertheless, it's worth taking Hogarth and Lee's concerns seriously, because even narrow AI has the potential to replace so many jobs; because cutting-edge AI capabilities do seem to be pretty heavily consolidated in a few firms in a few countries; and because worsening international inequality could cause serious global instability. On the other hand, it's very unclear what can be done. Hogarth suggests that countries like the UK and South Korea develop and protect their own AI industries - but at best this extends the potential AI duopoly to an oligopoly. There's a case for openly publishing AI research (which is standard across top research groups) and open-sourcing libraries and training environments (which isn't, although OpenAI seems committed to doing so) - but I worry that these measures increase the risk of catastrophic AI outcomes by allowing wider access to dangerous technology. There's no easy trade-off here, but I am inclined to be more concerned about extreme scenarios which could harm the long-term future of the human race, even if focusing on these increases inequality.

Lastly, there’s the question about which countries will be hit hardest by automation. Hogarth cites the following chart, which claims that amongst OECD countries, poorer ones will lose a greater proportion of their jobs. However, this trend probably reverses when we consider much poorer countries in which the workforces haven't transitioned to white-collar jobs, and where wages are low enough that it's difficult for robots to displace workers. And if the global poor aren't losing their jobs but still indirectly gain the benefits of, say, AI-enhanced R&D inventing better medicines or energy sources, that seems like a good outcome.

Corporate incentives

Overall, we should probably think of corporate taxes as a useful form of international redistribution, and try to strengthen the ability of poorer countries in particular to collect them. In theory, I don’t think this even requires much international coordination, since tax havens aren’t useful without the domestic legal loopholes which allow them to be exploited. However, if only a few countries crack down on those loopholes, they may create pretty significant incentives for multinationals to base themselves elsewhere. I also don’t see any good way to prevent the sort of competition between polities which we saw when Amazon was deciding where to build their new HQ, because that involves local governments offering benefits to companies at their own expense. But as long as those concessions are limited to a few major hubs for each big company, that’s arguably a good thing, since it lowers the tax burden on activities like R&D and expanding global operations.

The last question is whether businesses will actually do those things if they get more money through tax cuts. Oddly enough, it seems not. Over the last few decades, corporations have started to hold much larger cash reserves than they did previously. This is particularly true for the big tech companies - over 25% of Apple’s trillion-dollar valuation is in the form of cash or short-term investments (most of it currently held overseas, although it’s being brought back soon). What makes this even more surprising is that interest rates are very low - surely there’s some way to get more than 2% return on this money? Normally more profitable investments could be found in developing countries - but these days fast-growing China invests much more in the slow-growing US than the other way round. And when Western corporations do spend their money, it’s often on share buybacks to benefit their shareholders. To be fair, the tech titans are also spending exorbitant amounts on research (Amazon leading the pack at $23 billion last year), and so perhaps the gains from that are starting to level off. But all in all, it’s a peculiar situation which I’d quite like to understand better.

Tuesday, 7 August 2018

On first looking into Russell's History

Notes from Bertrand Russell's History of Western Philosophy, in particular the sections on ancient philosophy and theology.
  • Western civilisation began in the city-states of Greece - and there wasn't any comparable intellectual and artistic flourishing until the city-states of Italy during the Renaissance. Russell argues that this isn't a coincidence: that the intellectual climate of a time is bound up in the political and historical circumstances.
  • He also draws several dichotomies: between optimistic and pessimistic times; between individualistic and grouped times; also systematic and piecemeal; also subjective and objective. Some of these are useful perspectives, although they're the sort of categories we should be careful not to over-generalise.
  • Russell holds that the first philosophers created scientific hypotheses which were, if not exactly testable, at least empirically meaningful. These included Thales (around 585 BC; he held that everything was made out of water) and his Milesian School, Anaximander (everything was made of one elemental substance), Anaximenes (air), Heraclitus (fire and change), Parmenides (no change), Empedocles (4 elements), Anaxagoras (infinite divisibility) and eventually Democritus (atoms), who was perhaps the most rigorous, though his correctness was still essentially accidental. These were also, notably, all reductionist doctrines, in that they were concerned with analysing objects in terms of their simpler components; and non-teleological (although Anaximander incorporated a notion of cosmic "justice").
  • We must also include Pythagoras as the founder of mathematics (in the sense of demonstrative deductive arguments), whose influence is a source of the belief in "eternal and exact truth" in philosophy. He forwarded a view of philosophers as contemplative gentleman aristocrats, and foreshadowed Plato's forms.
  • Next, the Sophists, led by Protagoras, who claimed the skeptical hypothesis that "[each] man is the measure of all things."
  • After this, we encounter Socrates, Pluto and Aristotle, the three greatest names in ancient philosophy but also (along with Protagoras) heralds of a turn towards human-centred philosophy. Socrates, insofar as we can separate him from Plato, was largely concerned with ethical questions, which he approached using the Socratic method of conceptual analysis, which teased out details of what people generally agreed were virtues.
  • Plato is best known for his political philosophy, metaphysics and theology. Unfortunately, all were pernicious influences on the next two millennia of intellectual thought. His ideal Republic was based on the myth of Sparta, and essentially totalitarian (based, again, on "justice" as occupying one's natural role) Indeed, it is not surprising that he embraced a unilateral conception of the good, since it is implicit in his doctrine of forms. This metaphysic is not just false but deeply anti-empirical and anti-reductionist. So is his identification of a universal and perfect God.
  • Aristotle was unfortunately similarly theological. Known in the medieval period simply as "The Philosopher", he came up with a competing theory to Pluto's forms, as well as the idea of logical syllogisms. Everything above the moon was indestructible and eternal. The ultimate source of all movement was Will; God's existence could be proved by identifying him as the First Mover. Metaphysics was essentially frozen at this point for two millennia. Aristotle's account of causes was largely teleological; his ethics (particularly the "golden mean") absolutist. Notably, the best individual would be a "proud, great-souled" man who knows his own greatness - in stark contrast to Christianity. Similarly to Plato, this implies an identification of ethics as intrinsically political, because the rest must be subordinate to such great men. The supreme pleasure is contemplation. The aim of the state is to produced cultured gentlemen, such as those of the Athens of Pericles, or the 18th century - but their day is past.
  • Russell argues that many of the errors made in Plato can be corrected using a system of predicate logic - for example, his misunderstanding of relational propositions, and his claims that something can be "one" (or other numbers).
  • After the Alexandrean conquests, the Greek world became chaotic, and philosophers became more specialised, as well as superstitious. Ethics becomes of foremost importance, as men strove to deal with the general confusion - in particular by cultivating mindsets that would help endure the suffering of life, rather than those that would promote any energetic or useful activity.
  • The Cynics, led by Diogenes, taught that we should reject worldly goods and instead focus on virtue. This passed into Zeno's Stoicism, which argued that such pursuit of virtue was independent of all external circumstances. Stoicism greatly influenced a number of Romans, notably Seneca, Epictetus and Marcus Aurelius.
  • By contrast, Epicurus considered pleasure and the avoidance of pain to be the good. Virtue is "Prudence in the pursuit of pleasure" - like the Stoics, he thought attitude incredibly important and argued that, in practice, most desires and extreme pleasures led to more pain than they were worth. Epicurus thought that "death was nothing to us", and religions should be overthrown, since the supernatural causes terror. 
  • Meanwhile Pyrrho, the Sceptic, denied the ability to know anything, and concluded that we should fall back on common practice.
  • These doctrines were all more universal than those of previous philosophers - Rome was the world, and thus it was easy to believe in one universal culture and brotherhood. As Rome declined, Plotinus forwarded Neoplatonism, an important precursor to Christian theology in its focus on another more perfect world, accessed by looking inwards and reflecting.
  • The Church also contained important elements from Judaism - in particular, a sacred history; an identity as God's chosen few; a conception of righteousness; the Messiah and the Kingdom of Heaven. Jews distinguished themselves by their monotheism, and the wickedness of all other religions. This meant that their suffering could only be explained by the sins of the Jewish people in violating their laws. This made them particularly rigid - during the Mecca bean Revolt, many Jews were tortured and killed for refusing to eat pork or stop circumcising their children.
  • Gibbons identifies five factors behind Christianity's rise:
    1. Inflexible religious zeal
    2. Doctrine of future life
    3. A sacred book which testified to a miraculous history
    4. Pure and austere morality
    5. Union and discipline of Christian organisation
  • Doctrinal rigidity caused a number of conflicts over heresies, the most notable being the Arian heresy that God the Father was superior to Jesus. This was condemned at the Council of Nicaea in 325, which (along with Constantine's acceptance of Christianity) heralds a doctrinal consolidation and the end of the early Christian period. It's notable how many of the early heresies made almost entirely opposite claims to other heresies, with only a narrow middle ground being acceptable (e.g. the Nestorian and Monophysite heresies; the Arian and Sabellian hereises).
  • The "four doctors of the Church" from the 4th to 6th centuries were St Ambrose, St Jerome, St Augustine and Pope Gregory the Great. The first initiated the consolidation of power in the Papacy, the second translated the Bible and was a major influence towards monasticism, and the third was the foundation of Catholic theology. Augustine was obsessed by sin: passed down from Adam, God redeems some of us from it via predestination, although none of us deserve redemption. He holds that the Church must be separate from and superior to the State. He is heavily Platonic. Around this time an intense admiration for celibacy developed, and it became essential for the moral authority of the church. Gregory the Great is known for instigating the Gregorian Mission to convert the Anglo-Saxons, as well as his prolific writings.
  • St Benedict founded the most important monastic group, the Benedictine Order, at the beginning of the 6th century. Benedictines did not have to be as austere as previous monks. Around this time Gregory the Great was consolidating power in the papacy, Justinian was compiling Roman law - and Muhammed was born. Thus the men of the 6th century had a disproportionate influence on the world. However, the Dark Ages over the next 5 centuries meant very little intellectual progress occurred. In the 11th century, St Anselm laid out the ontological argument for God. From around then on, ancient philosophy began to be rediscovered, mainly via Islamic scholars.
  • By the 13th century, the popes had lost much of their moral authority, and a number of heretical movements sprouted. However, the rise of the mendicant orders restored some of this faith. St Francis was notably zealous in his austerity; St Dominic similarly zealous in combating heresy. Though their orders were soon corrupted, they contained a number of philosophers, most notably Thomas Aquinas, who was a keen Aristotelian.
I also made a rough diagram of the flow of intellectual influence through the ages - again focusing on ancient philosophers, but with a few modern ones thrown in when there was a particularly strong link. Philosophers most associated with one big idea or virtue have it noted beneath them. The graph is surprisingly neat (and planar!), no doubt because I've simplified a lot of relationships and overlooked many more - don't interpret this as anything more than an outline.


Sunday, 5 August 2018

What we talk about when we talk about maximising utility

Note: this is a slightly edited copy of a post I made on LessWrong a few months ago. I'm putting it here for completeness, and also because my next post will build on the ideas discussed below.

tl;dr: “Utility” is often used to mean what people want, but that’s not what's morally relevant. Utilitarians shouldn't be trying to maximise this sort of utility, but rather "well-being".

Use of the term “utility” as a thing we should maximise implicitly conflates two definitions. Consider person X. In the economic sense, X's utility is the function over possible worlds which X is trying to maximise. For practical purposes, we can often assume that utility functions are roughly linearly separable, and talk about the contribution of each term to the whole sum. For example, if X would save the lives of their family even at the cost of their own life, then we'd say that X assigns higher utility to their family's lives than to their own life. This is perfectly reasonable and normal. (Some people argue that X is actually prioritising their own happiness because if they chose otherwise, they'd be miserable from guilt. But this seems like an implausible model of their actual reasoning; I don't think many people who would save their families over themselves would change their minds even if offered guaranteed happiness afterwards.) A similar definition of utility is used when reasoning about artificial agents - for example, LW Wiki says “Utility is how much a certain outcome satisfies an agent’s preferences”.

However, this makes it very confusing to talk about maximising utility as a moral goal. Taken literally, maximising (economic) utility means wanting the sum of all people’s utility functions to be as high as possible. (In the standard definition of economic utility, this is not well-defined, since utilities can't be compared between people. The following argument is one intuitive reason why we can't maximise even versions of economic-style utility which do allow interpersonal comparision, such as the ones I'll discuss later.) The problem is that by doing so we are double-counting! Let's say I assign utility U to living a happy life, and utility U+1 to my wife living a happy life; my wife does the converse. If we both have happy lives, we have total utility 4U+2, which means that our lives should be prioritised over the lives of four other people who value their own lives just as highly, but don't care much about other people! This is bizarre, and gets more so when we consider that people might have many strong relationships. By this calculation method, a family of five people who all value each other over themselves have more total utility than 25 equally happy loners. Obviously maximising this sort of utility is not what standard utilitarians want.

By contrast, “utility” as usually used in the context of utilitarianism and ethics in general (which I will from now on call well-being) is a metric of how good a life is for the person living it. There are various accounts of well-being; the two most prominent types are desire theories, and hedonic theories. Under the former, a person has high well-being if the things they desire actually occur, even if they never find out about them. This is basically the same as the definition of utility I outlined above - which means it faces exactly the same double-counting problem. Hedonic theories of well-being, on the other hand, imply that your well-being is a function of only your psychological state. There are many different functions that it could be - for example, ones which only care about suffering; or also care about pleasure; or also care about a sense of fulfillment and meaningfulness. The specifics don't matter for our purposes; let's accept the broad idea and see where it leads.

Unfortunately, it immediately leads us to a major problem: since well-being is distinct from utility, people’s actions aren’t a good guide to their actual well-being function. In fact, maximising the well-being of any group of people might be opposed by every person who is affected by the change! Consider first a group of size one: just me. Suppose my life's goal is to write the greatest novel ever, even though I know that slaving away to complete it will make me less happy than I could have been. I also know that if I ever stop working on it, I'll become lazy, my goals will change, and I'll settle for a happy but boring life. You decide that you could maximise my well-being by forcing me to stop working on it - and by the account above, you'd be doing a moral good even though I'd fight you tooth and nail.

One more example, this time with n=2: suppose I am about to suffer torture. Suppose also that I have a wife, who I love deeply, although she doesn't love me nearly as much; also, she has a higher pain tolerance than me. Now you intervene so that instead of me being tortured, my wife is tortured instead, without my knowledge. My well-being is now higher than it would have been, and the total well-being between the two of us is also higher (since she can bear the pain better). Yet if either of us heard about your plan, we would both strongly object.

Some people are willing to bite the bullet and say that we should just maximise hedonic well-being even if all people we are "benefiting" think we're making their lives worse. This implies that, all else being equal, it would be better to force everyone into experience machines, because psychological experiences are all that matter. At a certain point, accepting or rejecting this position comes down to a brute clash of intuitions. I think that that my life would have less value if all my friends were secretly contemptuous of me, and all the things I learned throughout my life were actually wrong, and after my death I was despised - even if I never found out about any of those facts. Your mileage may vary.

The best compromise I can come up with is a solution in which your well-being is the sum of a desire-satisfaction function and a hedonic function - but where the desires we consider are limited to those about your own life. As always with morality, this is somewhat vague. For example, you might desire to have a child, and desire that the child has certain traits, and go into a certain career, and have a good life. Where does this stop becoming "about you"? I don't think there's any clear line to be drawn between desires that are and aren't about your own life, but if we want people’s desires to be morally relevant in a sensible way, we need to pick some boundary; even if they are all well-informed and reflectively consistent, we can't just classify them all as part of the "utility function" which should be maximised.