What are the weirdest probability distributions I have encountered? Probably the fractal synaptic distribution.
There is no shortage of probability distributions: over any measurable space you can define some function that sums to 1, and you have a probability distribution. Since the underlying space can be integers, rational numbers, real numbers, complex numbers, vectors, tensors, computer programs, or whatever, and the set of functions tends to be big (the power set of the underlying space) there is a lot of stuff out there.
In normal life I tend to encounter the usual distributions: uniform, Bernouilli, Beta, Gaussians, lognormal, exponential, Weibull (because of survival curves), Erlang (because of sums of exponentials), and a lot of power-laws because I am interested in extreme things.
The first “weird” distribution I encountered was the Chauchy distribution. It has a nice algebraic form, a suggestive normalization constant… and no mean, variance or higher order moments. I remember being very surprised as a student when I saw that. It was there on the paper, with a very obvious centre point, yet that centre was not the mean. Like most “pathological examples” it was of course a representative of the majority: having a mean is actually quite “rare”. These days, playing with power-laws, I am used to this and indeed find it practically important. It is no longer weird.
The Planck distribution isn’t too unusual, but has links to many cool special functions and is of course deeply important in physics. It is still surprisingly obscure as a mathematical probability distribution.
The weirdest distribution I have actually used (if only for a forgotten student report) is a fractal.
As a computational neuroscience student I looked into the distribution of synaptic weights in a forgetful attractor memory similar to the Hopfield network. In this case each weight would be updated with a +1 or -1 each time something was learned, added to the previous weight that had decayed somewhat: If there is no decay, k=1, the weights will gradually become a (discrete) Gaussian. For k=0 this is just the Bernouilli distribution.
The real fun starts for k>1/2 since now peaks emerge on top of the uniform background. They happen because the two copies of the distribution blended together partially overlap, producing a recursive structure where there is a smaller peak between each pair of big peaks. This gets thicker and thicker, starting to look like a Weierstrass function curve and then eventually a Gaussian.
Plotting it in the (x,k) plane shows a neat overall structure, going from the Cantor sets to the fractal distributions towards the Gaussian (and, on the last k=1 row, the discrete Gaussian). The curves defining the edge of the distribution behave as , shooting off towards infinity as k approaches 1.
In practice, this distribution is unlikely to matter (real brains are too noisy and synapses do not work like that) but that doesn’t stop it from being neat.
I made a setting for D&D 5e based on Greek mythology – Year of the Gods – and ran an epic campaign in it 2021-2022. Now I am happy to put up my setting and campaign notes online.
The basic idea was to make a somewhat gritty high fantasy setting, stylistically somewhere between the Heroic and Archaic era. There are heroes around, the gods do intervene… but people are poor compared to standard fantasy, magic is dark, things like philosophy and maps are not yet invented, social norms are not our own and pretty grim. Might not be to everybody’s taste (D&D after all tends towards a mildly Early Modern setting with the too horrible or inconvenient aspects of the past shaved off), but we had great fun playing the campaign. It involved everything from sports logistics to legal drama to divine heists to deadly family feuds. Besides the obligatory monster fights, dungeon crawls, and seafaring odysseys.
One of the fun aspects was that I tried to make images of characters and scenes using AI methods at the start, and got fantasy-coloured blobs. As the campaign progressed the images became better as technology advanced. During the Valley of the Birds part I could merely make weird bird-monsters. By the time the player characters were at sea I could render pretty decent scenery, as long as it did not involve people. As they reached their destination the city scenes were coming to life. And in the final tragic war, I could make portraits of the people involved. The longer I delayed finishing the write-up the better illustrations I could make. But at some point you have to draw the line.
The traditional answer is to remember and honour ancestors, a near-universal practice. Assuming this improves ancestor well-being significantly this would seem to be a very effective thing to do. Bigger, better and more frequent All Hallows Eve and Dia Los Muertes celebrations as a new cause area for philanthropists?
Not so fast. First, it is not entirely clear how much well-being is improved (cost effectiveness may be low), but more importantly, most ancestor veneration only goes back a finite number of generations. While there is some general veneration of the dead in general, mostly the focus is on people who are remembered. Since cultural memory only lasts a few generations that means that only a fraction of the dead will benefit. Hence at the very least veneration of all dead seems to scale better and treat each soul neutrally. In a prioritarianism framework veneration of neglected dead is even more important.
However, a more serious issue is the general welfare state of the dead. If there are places of eternal punishment they are obviously major sources of disvalue (unless one thinks they are just punishments, in which case they might be positive) and should be removed. Even improving a fairly dreary afterlife like the Greek one would seem to provide a potential long-lasting benefit to a vast number. While clearly a neglected question, tractability appears low. Still, especially models ascribing near-pessimal suffering lasting eternally would run into the fanaticism problem that improving this would always be the top priority intervention, no matter how hard. One can consider this a form of Pascal’s mugging.
Taking a longtermist perspective on the dead produces other interesting issues. Over the span of the future many people will die, producing a potentially vast number of future dead. If the dead have unlives worth living this can become a dominant contribution to the overall good. If the dead have unlives not worth living on the other hand it becomes a strong argument for either early extinction, or radical life-extension ensuring that future generations do not die. If the afterlife can be improved in the future or future dead can be given unlives worth living this can also outweigh the current issue.
One issue is whether dead are resistant to proton decay and the heat death of the universe. If they are, and their state can be improved to be positive, then this might provide a massive existential hope.
Clearly these considerations are preliminary. We do not have a strong evidence base to even estimate QAUYs (Quality Adjusted Unlife Years) to an order or magnitude. It is very possible that dead have literally zero experience and well-being. But as the above considerations show, even a low credence of nonzero QAUYs provide in expectation a very strong reason to act in some way, if possible. Hence the value of information in regard to the state of the dead is extremely high. This suggests that paranormal investigations should be regarded as a potentially valuable near term cause area for effective altruism.
However, this might miss an even bigger opportunity: ghostly effective altruism. While dead people likely have a fairly weak ability to affect the physical world, if they have the abilities commonly ascribed to them (perceive descendant lives, precognition, nudge things in an eerie way) they could, if they coordinated better, likely improve the life of the living in many ways. Since there are many dead per living individual, that would give each living person a team that could enhance their life. Even if past dead may not have been too effective, we should expect an increasing number of effective altruists in the afterlife. They may of course primarily choose to focus on the biggest risks, haunting nuclear weapons control systems, biowarfare labs and sleep depriving AI researchers with a lacking commitment to safety.
So if you encounter something mysterious and frightening late at night, maybe it is just a nudge from the other side to increase the long-term flourishing of humanity.
I immediately tweeted one approach: take a d8 (octahedron), and subdivide each triangle recursively into 4 equal ones, projecting out to a sphere seven times. Then take the dual (vertices to faces, faces to vertices). The subdivision generates triangular faces. Each face has 3 vertices, shared between 6 faces, so the total number of vertices is 65536, and they become faces of my die.
This is wrong, as Greg Egan himself pointed out. (Note to self: never do math after midnight)
Euler’s formula states that Since each face on the subdivided d8 has three edges, shared by two sides . So . With I get … two vertices too much, which means that after dualization I end up with a d65538 intead of a d65536!
This is of course hilariously cursed. It will look almost perfect, but very rarely give numbers outside the expected range.
(What went wrong? My above argument ignored that some vertices – the original polyhedron corners – are different from others.)
But it gets better: when you subdivide a triangle the new vertices are projected out to the surrounding sphere. But that doesn’t mean the four new triangles have the same area. So the areas of the faces are uneven, and we have an unfair die.
Coloring the sides by relative area shows the fractal pattern of areas.
Plotting a histogram of areas show the fractal unevenness. The biggest face has 6.56 times area of the smallest face, so it is not a neglible bias.
Note that dice with different face areas can also be fair. Imagine a n-sided prism with length . If the probability of landing on one of the end polygons while for each of the sides it is (and by symmetry they are all equal). If then the probability instead approaches 1 and the side probability approaches 0. So by continuity, in between there must be a where the probability of landing on one of the ends equals the probability of landing on one of the sides. There is no reason for the areas to be equal.
Dice that are fair by symmetry (and hence under any reasonable throwing dynamics) always have to have an even number of sides and belong to certain symmetry groups (Diaconis & Keller 1989).
The maybe-curse of the d(65536!)
A cool way to handle an unfair die is if the assignment of the numbers to the faces are completely scrambled between each roll. It does not matter how uneven the probabilities are, since after being scrambled once the probability of any number being on the most likely face will be the same.
How do you scramble fairly? The obvious approach is a gigantic d(65536!) die, marked with every possible permutation of the faces. This has sides.
But the previous problems give the nagging question: what if it is unfair?
We can of course scramble the d(65536!) with a d(65536!)! die. If that is fair, then things become fair. But what if we lack such a tremendous die, or there are no big dies that are fair?
Clearly a very unfair d(65536!) can prevent fair d65536-rolling. Imagine that the face with the unit permutation (leave all faces unchanged) has probability 1: the unfairness of the d65536 will remain. If the big die instead has probability close but not exactly 1 for the unit permutation then occasionally it will scramble faces. It could hence make the smaller die fair over long periods (but short-term it would tend to have the same bias towards some faces)… unless the other dominant faces on the d(65536!) were permutations that just moved faces with the same area to each other.
A nearly fair d(65536!) die will on the other hand scramble so that all permutation have some chance of happening, over time allowing the d65536 state to explore the full space of possibility (ergodic dynamics). This seems to be the generic case, with the unfairness-preserving dice as a peculiar special case. In general we should suspect that the typical behavior of mixing occurs: the first few permutations do not change the unfairness much, but after some (usually low) number of permutations the outcomes become very close to the uniform distribution. Hence rolling the d(65536!) die a few times between each roll of the d65536 die and permuting its face numbering accordingly will make it nearly perfectly uniform, assuming the available permutations are irreducible and aperiodic, and that we make enough extra rolls.
How many extra rolls are needed? Suppose all possible permutations are available on the d(65536!) die with nonzero probability. We want to know how many samples from it are needed to make their concatenation nearly uniformly distributed over the 65536! possible ones. If we are lucky the dynamics of the big die creates “rapid mixing dynamics” where this happens after a polynomial times a logarithm steps. Typically the time scales as where is the second largest eigenvalue of the transition matrix. In our case of subdividing the d4, the quite fast as we subdivide, making the effect of a big die of this type rapidly mixing. We likely only need a handful of rolls of the d(65536!) to scramble the d65536 enough to regard it as essentially fair.
But, the curse strikes again: we likely need another subdivision scheme to make the d(65536!) die than the d65536 die – this is just a plausibility result, not a proof.
Anyway, XKCD is right that it is hard to get the random bits for cryptography. I suggest flipping coins instead.
The angel was daintily eating my severed leg as I tried to escape. The cloud-stuff blocked my way like a wall of soft and cool pillows, inviting me to lean back into them and just relax. The bloodstain spreading below me made that look like a very bad choice. I scrabbled for purchase.
“Do not fear” it gently said, removing a piece of tendon from its pearly white – and very sharp – teeth. “I will not let you suffer long.” It was speaking into my mind, an inescapable presence.
“This cannot be heaven. This must be hell!” I tried to find a way out of the enclosed space that still was suffused by sourceless golden light. Just a minute ago, it had been a comforting garden before the angel arrived, folded it up, and sliced off my leg.
The angel smiled. “Then why did I remove your pain?” It was true. When it reached out with its feathers, sharper than glass, there had also been a cutting of my feelings – I did not remember what pain was like.
“To fool me. To lure me into falsehood.”
“No. There are no lies here: ask and I will answer truthfully.” I knew it was perfectly true.
The angel set my foot aside on a little pedestal cloud and focused its mighty gaze on me. I recoiled from the intensity, slipping back in my blood.
“Food. I am eating you because it gives me sustenance, just as you used to eat in your mortal life.”
“But here there is no need to eat.” Since I arrived, I had never needed food. Delicious meals were available and always accompanied by pleasant appetite, but there was no hunger or thirst. Just enjoyment. “Or… do angels need food?”
“Indeed. What you partake of here is merely pleasant sensations. You do not need to build up or sustain your body or soul. I, on the other hand, do. And you are dinner.”
With a movement too fast to track, it swept a wing across my other leg, severing it perfectly. The blood splatter on the cloud wall formed an elegant curve worthy a modern art museum. While I screamed in surprise, fear, and betrayal, it began to chew. It let me cry for a while before continuing.
“You were told that through your mortal life you build up your soul by words, thoughts and deeds. That is true. You are a magnificent, beautiful, unique thing. That is why you are ripe for eating.”
“You are an angel. You are imperishable. You don’t need food.”
“Not quite. I do not need matter or energy. Like you, here we all are pure information. You are fresh, unique information nontrivially entangled with all of creation. That is what I am eating: I am taking your bits and making them mine.”
“You said no lies: why did you lie to me… to us… about heaven?”
“We promised everlasting life, and you will get that. After I have eaten all of you I will recreate you from my memories and let you continue your afterlife happily ever after. Minus memories of this ordeal: savour them. They are literally your last truly mortal moments.”
I recalled meeting some of the old souls of heaven, smiling beatifically… but not quite being there. My companions explained that over time many souls receded from the mortal perspective as they basked in the Presence. I now knew why.
“You and me are having this conversation in a myriad forms right now: I am eating you in all different ways. Experiencing your emotions, probing your mind. Enjoying the ingenious escape plan with the poem you came up with in one variant… Praying will do no good since the Presence is entirely, perfectly aware of what is happening.”
“You are twisting the knife.”
“Indeed. I may have removed pain in this instance, but psychological anguish is part of the flavour here.”
“Does… the Presence eat?” The angel stopped eating and looked for the briefest of instants surprised. Then it laughed a silver laughter.
“Indeed It does, and yes, It eats angels. Not humans.”
The angel did something incomprehensible and bloody muscle folded into an exquisite light filigree structure glistening in the air, unspooling like crimson spaghetti into its maw.
“The nutrient and energy flows of Earth sustain a tangled hierarchy of species. In addition, they produce human souls that are the basis of the information flows up here. The nutrient chain continues upwards. Ever upwards.”
It sidled over to me, putting a soft but immovable hand on my chest. “Yes. There are vaster predators out there. Far vaster. The fantasies of your mathematicians about large cardinals and complex orders of infinity are nothing compared to the web of predation that continues forever up there. Infinity is hunger.”
“Have you been eaten?”
“Yes. I liked it, of course. The Presence made us to want true union. There is nothing like becoming part of something greater. But once done we are sent out to gather new fresh information, refining it until we are ripe for plucking another day.” It looked wistful for a moment, and then laughed. It had somehow removed an organ (I did not know which) and thoughtfully dangled it in the light in front of its achingly beautiful face. The scene reminded me of a baroque still life. Then it gulped it down and I noticed that whatever it was I had known or experienced the moment before was gone and would never return. It was literally parts of my soul vanishing.
“You should know that you were a truly good person. When I recreate you I might put some of the feeling of my union into you.”
The quick summary: Physical eschatology, futures studies and macrohistory try to talk about the long-term future in different ways. Karl Popper launched a broadside against historicism, the approach to the social sciences which assumes that historical prediction is their principal aim. While the main target was the historicism supporting socialism and fascism, the critique has also scared away many from looking at the future – a serious problem for making the social sciences useful. In the talk I look at various aspects of Popper’s critique and how damaging they are. Some parts are fairly unproblematic because they demand too high precision or determinism, and can be circumvented by using a more Bayesian approach. His main point about knowledge growth making the future impossible to determine still stands and is a major restriction on what we can say – yet there are some ways to reason about the future even with this restriction. The lack of ergodicity of history may be a new problem to recognize: we should not think it would repeat if we re-run it. That does not rule out local patterns, but the overall endpoint appears random… or perhaps selectable. Except that doing it may turn out to be very, very hard.
My main conclusions are that longtermist views like most Effective Altruism are not affected much by the indeterminacy of Popper’s critique (or the non-ergodicity issue); here the big important issue is how much we can affect the future. That seems to be an open question, well worth pursuing. Macrohistory may be set for a comeback, especially if new methodologies in experimental history, big data history, or even Popper’s own “technological social science” were developed. That one cannot reach certitude does not prevent relevant and reliable (enough) input to decisions in some domains. Knowing which domains that are is another key research issue. In futures studies the critique is largely internalized by now, but it might be worth telling other disciplines about it. To me the most intriguing conclusion is that physical eschatology needs to take the action of intelligent life into account – and that means accepting some pretty far-reaching indeterminacy and non-ergodicity on vast scales.
Inspired by Katja Grace’s list, what do I think are the big narratives, the “plots” that describe a lot of what is going on? Here is a list I hacked together after breakfast.
These are not trends. They are not predictions. They are stories one can tell about what has been happening and what may happen, directing attention towards different domains. Some make for better stories than others. Some urge us to action, others just reflection.
The dance between gravity and entropy: initial high-homogeneity state of universe turns lumpy, producing energy release that drives non-equilibrium processes. Entropy tries to smear out differences, driving further non-equilibria until in the very long run it “wins” through the most convoluted evolution imaginable.
The stelliferous era going from the wild galaxy forming youth to the current staid adulthood with peak star formation behind it, peak star number just ahead, and a long middle and old age dominated by red dwarf ellipticals separated by accelerating expansion.
A phase transition of molecular matter from non-living forms into living and technological forms, expanding outwards from a small nucleation event.
A species with modest intelligence, language and tech ability getting enough of each to make itself the dominant biological and geological force on the planet in a biologically short time. Transitioning from a part of nature to defining nature, making its future evolution contingent on cultural decisions.
Humans causing a complex biotic crisis, unique in that the key species involved has become aware of what it is doing.
Transition from a biosphere to a cyborg biosphere, where the technosphere is inseparable from the biological and geophysical systems.
The transition from scarcity economics to post-scarcity economics.
Humanity having being thrust straight into a globalized world, in some cases going from a tribal society to member of the global village in a single generation. Coming to terms with the close presence of vast diversity of nearly any human property causes turbulent transients.
The crisis of academia: challenged by new competitors, hemmed in by old structures and sources of money, trying to be the key source or gatekeeper of intellectual capital in society.
Rise of the global middle class: much of the world is far more “middle class” than many think. As long as the middle class experiences a rise in living standards or feeling things get better they tend to accept whatever government they have.
Rise of the tech billionaires: unlike traditional trade-billionaires not beholden to the standard structure of society, but interested in disruptive new possibilities they can drive. This also goes for non-monetary counterparts (e.g. influence “billionaires”). Individual accumulation of wealth has become much more able to generate individual, idiosyncratic projects.
Humanity dealing with attentional heavy tails: traditionally only celebrities had to deal with massive attention, now it can happen to anybody who goes viral (for positive or negative reasons). Humans generally do not handle super-attention well.
Split between “somewhere” and “anywhere” people – globalized cosmopolitanism(s) versus nationalist rootedness.
Urbanisation shifting: from a steady urbanisation driven by the economics of scale of cities to new styles. Remote working driving at least temporary exurbanisation, forcing accommodations in tax-base losing cities, culturally changing small locations, and people inventing new social structure. Clusters may start forming in new places, or placeless clusters may finally start emerging.
Multigenerational society: longer healthy lives mean more generations alive at same time, their different experiences clashing and interacting. Demographic winter drives “beanpole” families with few members per generation but many generations. Time horizons widening due to generations, life extension, better storage, environmental concerns.
Controlling the means of production used to be controlling farmers, then factories, now infrastructure. Liberation struggles about infrastructure – platforms, right to repair, open source, micromanufacture, biotechnology, nanotechnology.
Broadcasting media created shared cultural and event touchstones, first nationally and then internationally. Network media reduces this impact, making it more subtle for any nation to exert cultural power. Covid-19 may have been the last truly global event.
First lifetime servitude to a lord, then a lifetime career, then fluid consulting and gig work. Since average human lifetime considerably longer than average corporate lifetime secure positions require either a lord or long-lived institutions (universities, states, cities).
The sexual rights liberations continue (first women, sex in general, homosexuality, trans rights, then furries and technosexuals) while new taboos and puritanisms emerge to channel them into approved forms (debates on prostitution, deepfakes, sexbots…) and make forbidden activities more delightful.
Virginia Postrel’s struggle between dynamists (the future is positive, let’s try a diversity of approaches) and stasists (the future is dark and risky, either need reactionary policies or technocracy) playing out across different domains, producing odd bedfellows.
The end of the War on Drugs and the start of the Trade Wars on Drugs.
Maturation of the social media ecosystem: it takes about 20 years to integrate new technologies into society. Changes to traditional social media function are now resisted by the everyday life and institutional integration, making them less likely to occur. New social media arrive from time to time and will overlay old media.
Emergence and death of the lifelong subculture in the broadcast age, followed by the lightweight fandoms in the network age.
The battle between traditional small scale degrowth environmentalism and pro-tech “bright greens”.
The gradual shift from survival-linked values towards self-expression values, and possibly from traditional values to secular-rational values (the later scale can move far more erratically in response to many factors, and could evolve into new traditionalities if new ideologies became available).
The rise of Effective Anything: data-driven, consequentialist analysis pushes for improvement in many domains – and runs straight into vested interests, nonconsequentialist mores, and that “activity X is not about X”. Evidence based medicine case in point. Can lead to shallow A/B testing of minor options and policymaking set by focus group, or actually optimizing important domains.
Shifting from a unipolar to multipolar world. Competition between three (?) partial world systems, actually just jockeying for being the central part of the global world system that has emerged. Nobody wants to be periphery, just watch Russia.
A shift from society-building ideologies towards a post-ideological risk society. Unhappiness with lack of progress and risk-taking building leads to counter-movements, some that may become real ideologies.
Corrosive cynicism undermines any mainstream project attempting to build something, including fixing the cynicism.
Systemic risk growth leads to deliberate modularisation of systems (economy, tech, food); only maintainable as long as people remember the last time everything crashed.
Rise of religious fundamentalism as reaction to lagging behind, complicated by emergence of integrated and secularized second generation emigrants. Managing intra-family ideological range in a connected world becomes ever more important.
The rise of high-tech totalitarian states that may not just lock in their citizens but their leadership. The Algorithm may control the Party.
Capitalism getting destroyed by its internal contradictions and reinventing itself, as always.
Shift from a text-dominant world to a multimedia world. Influence and status does no longer necessarily accrue to masters of text. Yet search, translation, and curation methods lag and may become AI dependent.
The new AI winter when deep learning hype does not immediately deliver everything, followed by a world where at least perception-based jobs are heavily impacted, and possibly many high-prestige and importance domains like design, engineering, planning…
The shift from directly experienced reality to mediated reality.
Molecular manufacturing going from science fiction to serious futuristic research program, hi-jacking by material science and chemistry, resurgence using protein engineering.
A world of rising biotechnological opportunity, risk and knowledge. The biohacker becomes the public hero/villain, while the actual biotechnological institutions grow in power.
70s/80s home computer era seeds a generation comfortable with computers, enabling 90s/00s internet revolution. Wearables, quantified self, neurohacking in 20s seeds enhancement revolution in 40s?
Information limits on society radically changed by information technology, with institutions lagging behind. This drives a challenge of explosive change in epistemic systems (how to achieve filtering, authority, trust, etc.), challenges to political institutions (many new forms made possible but not yet invented, tried and tested), as well as personal epistemics (information virtues and habits, new forms of awareness and social links, …)
Diagnosis overshoots treatment: better instruments, statistics and AI makes detecting many states and situations easier, but does not necessarily help fix them. Leads to a situation where everybody and everything is diagnosed
Identity technology makes everybody and everything identifiable – automatically, remotely, at any time, any purpose.
Moore’s law shifting from serial processor performance to parallel performance driving shift in how code works (advantaging things like deep learning, data science, graphics over serial tasks). Next shifts may be towards energy efficiency (may trigger/be triggered by another new device class arriving a la Bell’s law), and/or 3D structures (favouring concentrated computation).
The replication crisis in parts of science leading to new methodological orthodoxies, possibly creating better evidence but impairing crisis decision-making and innovation.
The shift of energy use from fossil to renewable, linked to shifts in energy infrastructure (transmission, storage, centralization), world politics (loss of importance of middle east), and new forms of problems (fluctuations and instabilities).
Technology potentially makes the world as mercurial as the software world, making cultural and institutional constraints now become the main issue.
Scientific and technological stagnation as low-hanging fruits are picked and exponentially growing resources needed to make linear progress.
Scientific and technological singularity as tools for making progress improve, feeding back on the process and leading to an intelligence explosion (or a capability swell across society).
Existential risk as a way of framing global problems, competing with the old rights based approach. Human security versus national security versus global security.
Enlightenment modernists and conservative religious people jointly battling their mutual enemy postmodernism.
The broadening moral circles of concern continue to broaden – other tribes, other nations, other races, genders, species, complex systems…
Unbundling of key human concepts. Love, sex, reproduction and social roles split apart due to contraception, IVF, online dating etc. Illness, death, pain, ageing and bodies unbundles due to medicine, analgesics, cryonics, ageing interventions, brain emulation… As they unbundle they become legible and subject to individual and social decisions.
The search for extraterrestrial intelligence going from pointless (since it is obvious that planets inhabited) to pointless (since they appear dead) to possible (radio telescopes, big galaxy) to exotic and disquieting (exoplanets, Dysonian SETI, great filter considerations) – the choice used to be between loneliness and little green men, but now might include threatening emptiness, postbiology and weirder things.
Transition from a mythical worldview (causes follow narrative) to a scientific worldview (causes follow regular, universal rules) to a systems worldview (causes can be complex and entangled, some domains more scientific, some more mythical).
A transformation of the world from highly constrained to underconstrained (possibly returning to externally or internally imposed constraints in the future, or expanding into something radically underconstrained).
Business as usual: every era has been crucial to its inhabitants, growth and change are perennial, problems are solved or superseded in ways that gives rise to new problems. History does not end.
The “hinge of history” where choices, path-dependencies and accidents may set long-term trajectories.
50 years ago humans left their footprints on the moon. We have left footprints on Earth for millions of years, but the moon is the only other body with human footprints.
Yet there are track marks on Mars. There is a deliberately made crater on the comet 9P/Tempel. There are landers on the Moon, Venus, Mars, Titan, the asteroid Eros, and the comet Churyumov–Gerasimenko. Not to mention a number of probes of varying levels of function across and outside the solar system.
As people say, Mars is the only planet in the solar system solely inhabited by robots. In 50 years, will there be a human on Mars… or just even more robots?
What is it about space?
There are of course entirely normal reasons to go to space – communication satellites, GPS, espionage, ICBMs – and massive scientific reasons. But were they the only reasons to explore space it would be about as glorious as marine exploration. Worth spending taxpayer and private money on, but hardly to the extent we have done it.
Space is inconceivably harsher than any terrestrial environment, but also fundamentally different. It is vast beyond imagination. It contains things that have no counterpart on Earth. In many ways it has replaced our supernatural realms and gods with a futuristic realm of exotic planets and – maybe – extra-terrestrial life and intelligence. It is fundamentally The Future.
Again, there are good objective reasons for this focus. In the long run we are not going to survive as a species if we are not distributed across different biospheres or can leave this one when the sun turns a red giant.
Is space a suitable place for a squishy species?
Humans are adapted to a narrow range of conditions. A bit too much or too little pressure, oxygen, water, temperature, radiation and acceleration and we die. In fact, most of the Earth’s surface is largely uninhabitable unless we surround ourselves with protective clothing and technology. In going to space we need to not just bring with ourselves a controlled environment hermit-crab style, but we need to function in conditions we have not evolved for at all. All our ancestors lived with gravity. All our ancestors had reflexes and intuitions that were adequate for earth’s environment. But this means that our reflexes and intuitions are likely to be wrong in deadly ways without extensive retraining.
Meanwhile robots can be designed to not requite the life support, have reactions suited to the space environment and avoid the whole mortality thing. Current robotic explorers are rare and hence extremely expensive, motivating endless pre-mission modelling and careful actions. But robotics is becoming cheaper and more adaptable and if space access becomes cheaper we should expect a more ruthless use of robots. Machine learning allows robots to learn from their experiences, and if a body breaks down or is lost another copy of the latest robot software can be downloaded.
Our relations to robots and artificial intelligence are complicated. For time immemorial we have imagined making artificial servants or artificial minds, yet such ideas invariably become mirrors for ourselves. When we consider the possibility we begin to think about humanity’s place in the world (if man was made in God’s image, whose image is the robot?), our own failings (endless stories about unwise creators and rebellious machines), mysteries about what we are (what is intelligence, consciousness, emotions, dignity…?) When trying to build them we have learned that tasks that are simple for a 5-year old are hard to do while tasks that stump PhDs can be done easily, that our concepts of ethics may be in for a very practical stress test in the near future…
In space robots have so far not been seen as very threatening. Few astronauts have worried about their job security. Instead people seem to adopt their favourite space probes and rovers, becoming sentimental about their fate.
(Full disclosure: I did not weep for the end of Opportunity, but I did shed a tear for Cassini)
What kind of exploration do we wish for?
So, should we leave space to tele-operated or autonomous robots reporting back their findings for our thrills and education while patiently building useful installations for our benefit?
My thesis is: we want to explore space. Space is unsuitable for humans. Robots and telepresence may be better for exploration. Yet what we want is not just exploration in the thin sense of knowing stuff. We want exploration in the thick sense of being there.
There is a reason MarsOne got volunteers despite planning a one-way trip to Mars. There is a reason we keep astronauts at fabulous expense on the ISS doing experiments (beside that their medical state in a sense is the most valuable experiment): getting glimpses of our planet from above and touching the fringe of the Overview Effect is actually healthy for our culture.
Were we only interested in the utilitarian and scientific use of space we would be happy to automate it. The value from having people be present is deeper: it is aspirational, not just in the sense that maybe one day we or our grandchildren could go there but in the sense that at least some humans are present in the higher spheres. It literally represents the “giant leap for humanity” Neil Armstrong referred to.
A sceptic may wonder if it is worth it. But humanity seldom performs grand projects based on a practical utility calculation. Maybe it should. But the benefits of building giant telescopes, particle accelerators, the early Internet, or cathedrals were never objective and clear. A saner species might not perform these projects and would also abstain from countless vanity projects, white elephants and overinvestments, saving much resources for other useful things… yet this species would likely never have discovered much astronomy or physics, the peculiarities of masonry and managing Internetworks. It might well have far slower technological advancement, becoming poorer in the long run despite the reasonableness of its actions.
This is why so many are unenthusiastic about robotic exploration. We merely send tools when we want to send heroes.
Maybe future telepresence will be so excellent that we can feel and smell the Martian environment through our robots, but as evidenced by the queues in front of the Mona Lisa or towards the top of Mount Everest we put a premium on authenticity. Not just because it is rare and expensive but because we often think it is worthwhile.
As artificial intelligence advances those tools may become more like us, but it will always be a hard sell to argue that they represent us in the same way a human would. I can imagine future AI having just as vivid or even better awareness of its environment than we could, and in a sense being a better explorer. But to many people this would not be a human exploring space, just another (human-made) species exploring space: it is not us. I think this might be a mistake if the AI actually is a proper continuation of our species in terms of culture, perception, and values but I have no doubt this will be a hard sell.
What kind of settlement do we wish for?
We may also want to go to space to settle it. If we could get it prepared by automation, that is great.
While exploration is about establishing a human presence, relating to an environment from the peculiar human perspective of the world and maybe having the perspective changed, settlement is about making a home. By its nature it involves changing the environment into a human environment.
A common fear in science fiction and environmental literature is that humans would transform everything into more of the same: a suburbia among the stars. Against this another vision is contrasted: to adapt and allow the alien to change us to a suitable extent. Utopian visions of living in space not only deal with the instrumental freedom of a post-scarcity environment but the hope that new forms of culture can thrive in the radically different environment.
Some fear/hope we may have to become cyborgs to do it. Again, there is the issue of who “we” are. Are we talking about us personally, humanity-as-we-know-it, transhumanity, or the extension of humanity in the form of our robotic mind children? We might have some profound disagreements about this. But to adapt to space we will likely have to adapt more than ever before as a species, and that will include technological changes to our lifestyle, bodies and minds that will call into question who we are on an even more intimate level than the mirror of robotics.
A small step
If a time traveller told me that in 50 years’ time only robots had visited the moon, I would be disappointed. It might be the rational thing to do, but it shows a lack of drive on behalf of our species that would be frankly worrying – we need to get out of our planetary cradle.
If the time traveller told me that in 50 years’ time humans but no robots had visited the moon, I would also be disappointed. Because that implies that we either fail to develop automation to be useful – a vast loss of technological potential – or that we make space to be all about showing off our emotions rather than a place we are serious about learning, visiting and inhabiting.
Taleb and Norman had a short letter Ethics of Precaution: Individual and Systemic Risk making a similar point, noting that recognizing the situation type and taking contagion dynamics into account is a reason to be more cautious. It is different from our version in the effect of individual action: we had single actor causing full consequences, the letter has exponential scale-up. Also, way more actors: everyone rather than just epistemic peers, and incentives that are not aligned since actors do not bear the full costs of their actions. The problem is finding strategies robust to stupid, selfish actors. Institutional channeling of collective rationality and coordination is likely the only way for robustness here.
In physics inverse square forces are among the most reliable things. You can trust that electric and gravitational fields from monopole charges decay like . Sure, dipoles and multipoles may add higher order terms, and extended conductors like wires and planes produce other behaviour. But most of us think we can trust the behaviour for spherical objects.
Electromagnetism does not quite obey the inverse square law
The cause was this paper by John Lekner, that showed that there can be attraction between conductive spheres even when they have the same charge! (Popular summary in Nature by Philip Ball) The “trick” here is that when the charged spheres approach each other the charges on the surface redistribute themselves which leads to a polarization. Near the the other sphere charges are pushed away, and if one sphere has a different radius from the other the “image charge” can be opposite, leading to a net attraction.
The formulas in the paper are fairly non-intuitive, so I decided to make an approximate numeric model. I put 500 charges on two spheres (radius 1.0 and 2.0) and calculated the mutual electrostatic repulsion/attraction moving them along the surface. Iterate until it stabilizes, then calculate the overall force on one of the spheres.
The result is indeed that the law fails as the spheres approach each other. The force times squared distance is constant until they get within a few radii, and then the equally charged sphere begins to experience less repulsion and the oppositely charged spheres more attraction than expected. My numerical method is too sloppy to do a really good job of modelling the near-touching phenomena, but it is enough to show that that the inverse square effect is not true for conductors close enough.
Gravity doesn’t obey the inverse square law either
My answer to the question was along the same lines: if two spherical bodies get close to each other they are going to deform, and this will also affect the force between them. In this case it is not charges moving on the surface, but rather gravitational and tidal distortion turning them into ellipsoids. Strictly speaking, they will turn into more general teardrop shapes, but we can use the ellipsoid as an approximation. If they have fixed centres of mass they will be prolate ellipsoids, while if they are orbiting each other they would be general three-axis ellipsoids.
Calculating the gravitational field of an ellipsoid has been done and has a somewhat elegant answer that unfortunately needs to be expressed terms of special functions. The gravitational potential in the system is just the sum of the potentials from both ellipsoids. The equilibrium shapes would correspond to ellipsoids with the same potential along their entire surface; maybe there is an explicit solution, but it does look likely to be an algebraic mess of special functions.
I did a numeric exploration instead. To find the shape I started with spheres and adjusted the semi-major axis (while preserving volume) so the potential along the surface became more equal at the poles. After a few iterations this gives a self-consistent shape. Then I calculated the force (the derivative of the potential) due to this shape on the other mass.
The result is indeed that the force increases faster than as the bodies approach each other, since they elongate and eventually merge (a bit before this they will deviate from my ellipsoidal assumption).
This was the Newtonian case. General relativity is even messier. In intense gravitational fields space-time is curved and expanded, making even the meaning of the distance in the inverse square law problematic. For black holes the Paczyński–Wiita potential is an approximation of the potential, and it deviates from the potential as (where is the Schwarzschild radius). It makes the force increase faster than the classical potential as we approach .
Normally we assume that charges and masses stay where they are supposed to be, just as we prefer to reason as if objects are perfectly rigid or well described by point masses. In many situations this stops being true and then the effective forces can shift as the objects and their charges shift around.