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Additive, multiplicative, and exponential economics

(Based on this Twitter thread. Epistemic status: fairly plausible, I would teach this to kids)Image

A simple, and hardly unique economic observation: when you are poor, money is additive. As you get more, it becomes multiplicative. And eventually exponential.

To a kid or a very poor person every coin is a treasure, worth something just by being itself.

When you get a few coins they instead sum into fungible numbers. These are additive – you add or subtract to your wallet or account, and if the inflow is larger than the outflow your number will get bigger. You dream of finding the big pile of gold. Saving makes sense.

Then loans, investment, and interest show up. You can buy something and sell it for more, and the more you can buy and resell it the more profit. You can use existing money as security to borrow more. Good quality things you can now afford save money. It is multiplicative.

Eventually you get into the exponential domain where the money keeps on growing since it is being invested and the time horizon is long. A short horizon means that compound interest or reinvestment has little effect, a long one leads to a fairly predictable growth.

Obvious complications from things like risk and uncertainty. Many people move between these thoughts depending on context, saving cents on coffee filters while losing time and money driving across town to get them on a sale… while having massive invested savings.

There can also be “boots theory” that being poor increases your expenses and this acts as a trap. As you get richer you get easier or free access to a lot of things (airport lounges, better service), not necessarily making up for the higher price goods you buy but reducing some forms of friction. The nature of difficulties shift from finding money to maintaining an income stream to managing a system of growth.

I think this division maps roughly to mindset and social class. Additive thinking is about getting more input or paying less, mercantilism, and avoiding going to zero. Everything is a zero-sum game. Very much a precariat situation.

Multiplicative thinking is about finding big multipliers – the realm of the smart business idea, the good investment, removing bottlenecks and improving efficiency. This is where win-win trades begin to make sense. Classical rising middle class.

Exponential thinking is all about maximizing growth rates (or their growth), long time horizons, boosting GDP growth. Modern upper class. (Premodern feudal upper classes were far closer to multiplicative or even additive modes – they were poor by our standards!)

Could there be a realm beyond this, an economic world of tetration? It might be about creating entirely new opportunities. This is the from zero to one VC/entrepreneur world, although in practice it often descends into the previous ones most of the time. The cryptocurrency people think they are here, of course.

Note that in fiction and games the creators often want to keep things simple and understandable. Many (board and computer) games start out in the clear additive world and you are gathering coins and optimizing what to buy. The treasure is added to your wealth, not increasing it by a percentage. Often they eventually move into the multiplicative world (better equipped RPG characters can buy +1 longsword of monster killing, giving higher revenues; in Saint Petersburg your workers leverage into buildings leveraging into nobles), where computer games typically lose interest (unless they are trading games) and it acts as an endgame in the boardgame since the exponential state usually doesn’t make for an interesting competitive dynamics. Still, MMoRPGs often show heavyish tails of wealthy player characters.

What kind of “rich get richer” phenomena do the different domains produce? Obviously, exponential growth amplifies differences enormously: the growth rate of the wealthiest will be highest. But even in the additive domain wealth tends to accumulate. If people randomly meet and exchange random amounts, wealth tends to accumulate into an exponential distribution. It seems that the power-law tails one gets in real economies are due to non-conservation of money: there is new wealth flowing in.

Are there limiting factors to economic growth in general, or individually? In the additive world it is all set by the amount of resources – and your ability to grab them and hold on to them. Typically diminishing returns emerge soon. In the multiplicative world you want to boost productivity, and this goes even further in the exponential world. Considering an endogenous growth model, you start out by using more labour to get higher yields, then use capital, and eventually might boost the knowledge/tech… and typically this last step makes the model blow up to infinity if you can reinvest the yield. What actually happens is that there is a limited absorptive capacity of the economy and diminishing returns or delays set in. Whether this always holds is an important question, but for practical everyday economics it is worth keeping in mind.

Plus the very important issue of what you want the money for. Money is instrumentally useful, but not a final value. When you start treating it as the goal, Goodhart bites you.

What is going on in the world?

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.

Earth

  • 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.

Water

  • 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.

Air

  • 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).

Fire

  • 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.

 

Stuff I have been up to

I have been busy everywhere except on this blog. Here are a few highlights, mostly my public outreach:

Long term survival

On BBC Future I have an essay concluding their amazing season on long term thinking where I go really long-term: The greatest long term threats facing humanity.

The approach I take there is to look at the question “if we have survived X years into the future, what problems must we have overcome before that?” It is not so much the threats (or frankly, problems – threat seems to imply a bit more active maliciousness than the universe normally brings about) that are interesting as just how radically we need to change or grow in power to meet them.

The central paradox of survival is that it requires change, and long-term that means that what survives may be very alien. Not so much a problem for me, but I think many disagree. A solid state civilization powered by black holes in a starless universe close to absolute zero, planning billions of years ahead may sound like a great continuation of us, or something too alien to matter.

Debunking doom

Climate doom is in the air, and I am frankly disturbed by how many think that we are facing an existential threat to our survival in the next decade or so – both because it is based on a misunderstanding of the science (which is not entirely easy to read), and how it breeds fatalism. As a response to a youngster question I wrote this piece on the Conversation: Will climate change cause humans to go extinct?

Robots in space

In Quartz, I have an essay about the next 50 years of space exploration and whether we should send robots instead: We should stop sending humans into space to do a robot’s job.

As often the title (not chosen by me, I prefer “A small step for machinekind”) makes it seem I am arguing for something different than I am actually arguing. As I see it, sending machines to space makes much more sense than sending humans… but given the very human desire to be the ones exploring, we will send humans in any case. Long-term we should also become multiplanetary if only to reduce extinction risks, but that might require sending robots ahead – except that in order to do that we need a lot of cheap, low-threshold experimentation and testing.

See also my chat with John Ellis and Kierann Shah about space at the How The Light Gets In Festival.

Good versus evil, Moloch versus Maria

Last year I participated in the Nexus Instituut “intellectual opera” in Amsterdam, enjoying myself immensely. I ended up writing an essay AI, Good and Evil… and Moloch (Official version Sandberg, A. (2019) Kunstmatige intelligentie en Moloch. Tijdschrift Nexus 81: De strijd tussen goed en kwaad. Nexus Instituut, Amsterdam (Tr. Laura Weeda)).

My main point is that evil is usually seen as active maliciousness or neglecting others, suffering itself, or meaningless/removal of meaning. Bad AI is unlikely to be actively malicious and making machines that can experience suffering is likely tricky, but automation that perform bad actions without caring is all too simple. The big risk is getting systems that are effective at implementing pointless goals too efficiently, destroying value (human or other) for no gain, not even to themselves. A further problem is also that these systems are systems, not individuals. We tend to think of AI as robots, “the AI” and other individual entities, when it just as well can be an ambient functionality of the wider techno-social world – impossible to pull the plug, with everybody complicit. We need better ways of debugging adaptive technological systems.

Life extension

On Humanity 2.0 I discussed/debated digital afterlives with Steve Fuller, Sr. Mary Christa Nutt, James Madden and Matthew Harvey Sanders. Got a bit intense at some points, but there is an interesting issue in untangling exactly what we want from an extended life. Not all forms of continuity count for all people: a continuity of consciousness is very different from a continuity of memory, a continuity of social interactions or functions, or leaving the right life projects in order.

Other stuff

Polish translation of my chapter on limits of morphological freedom.

Hacking the Brain: Dimensions of Cognitive Enhancement. A paper on cognitive enhancement, the final fruit of the “comparing apples to oranges” Volkswagen foundation project I participated in.

The GoCAS existential risk project final outputs arrived in the journal Foresight. I have two pieces, There is plenty of time at the bottom: The economics, risk and ethics of time compression and the group-written Long-term trajectories of human civilization.

I have also helped a bit with an Oxford project on sensitive intervention points for a post-carbon society. Not all tipping points are bad, and sometimes cartoon heroes may help.

Grand futures

Behind the scenes, my book is expanding… whether that is progress remains to be seen.

I have given various talks about some contents, but there is so much more. I think I have to do a proper lecture series this fall.

A bit of existential hope for Christmas (and beyond)

Slide from the Foresight Vision Weekend 2018. Image by Robert McCall.

Existential hope is in the air. The term was coined by my collegues Toby and Owen to denote the opposite of an existential catastrophe: the chance that things could turn out much better than expected.

Recently I had the chance to attend a visioning weekend with the Foresight Institute where we discussed ways of turning dystopias into utopias. It had a clear existential hope message, largely because  it was organised by Allison Duettman who is writing a book on the topic. I must admit that I got a bit nervous when I found out since I am also writing my own grand futures book, but I am glad to say we are dealing with largely separate domains and reasons for hope.

Now I extra am glad to add a podcast to the list of hopeful messages: the Future of Life Institute had me on the podcast Existential Hope in 2019 and beyond. It includes not just me and Allison, but also Max Tegmark, Anthony Aguirre, Gaia Dempsey, and Josh Clark (who also interviewed me for his podcast series End of the World).

I also participated in the Nexus Instituut event “The Battle between Good and Evil”. I assume the good guys won. I certainly had fun. I ended up arguing that good is only weak compared to evil like how water is weak compared to solid object – in small amounts it will deform and splash. In larger amounts it is like the tide or a tsunami: you better get out of the way. In retrospect that analogy might have been particularly powerful in the Netherlands. They know their water and how many hands (and windmills) can reshape a country.

Do we really have grounds for existential hope?

A useful analysis of the concept of hope can be found in Jayne M. Waterworth’s A Philosophical Analysis of Hope. He defines that hoping for something requires (1) a conception of an uncertain possibility, (2) a desire for an objective, (3) a desire that one’s desire be satisfied, and (4) that one takes an anticipatory stance towards the objective.

One can hope for things that have a certain or uncertain probability, but also for things that are merely possible. Waterworth calls the first category “hope because of reality” or probability hope, while the second category is “hope in spite of reality” or possibility hope. I might have probability hope in fixing climate change, but possibility hope in humanity one day resurrecting the dead – in the first case we have some ideas of how it might happen and what might be involved, in the second case we have no idea even where to begin.

Outcomes can also be of different importance: hoping for a nice Christmas present is what Waterworth calls an ordinary hope, while hoping for a solution of climate change or death is an extraordinary hope.

We may speak of existential hope in the sense that “existential eucatastrophes” can occur, or that our actions can make them happen. This would represent the most extraordinary kind of hope possible.

But note that this kind of hope is potentially “hope because of reality” rather than “hope in spite of reality”. We can affect the future to some extent (there is an interesting issue of how much). There doesn’t seem to be any law of nature dooming us to early existential risk or a necessary collapse of civilization. We have in the past changed the rules for our species in very positive ways, and may do so again. We may discover facts about the world that greatly expand the size and value of our future – we have already done so in the past. These are good reasons to hope.

Hope is a mental state. The reason hope is a virtue in Christian theology is that it is the antidote to despair.

Hope is different from optimism, the view that good things are likely to happen. First, optimism is a general disposition rather than directed at particular hoped for occurrences. Second, hope can be a very small and unspecific thing: rather than being optimistic about everything going the right way, a hopeful person can see the overwhelming problems and risks and yet hope that something will happen to get us through. Even a small grain of hope might be enough to fend of despair.

Still, there may be a psychological disposition towards being hopeful. As defined by Snyder in regarding motivations towards goals this involves a sense of agency (chosen goals can be achieved) and pathways (successful plans and strategies for those goals can be generated). This trait predicts academic achievement in students beyond intelligence, personality, and past achievement. Indeed, in law students hope but not optimism was predictive for achievement (but both contributed to life satisfaction). This trait may be more about being motivated to seek out good future states than actually being hopeful about many things, but the more possibilities are seen, the more likely something worth hoping for will show up.

If there is something I wish for everybody in 2019 and beyond it is having this kind of disposition relative to existential hope. Yes, there are monumental problems ahead. But we can figure out ways around/through/over them. There are opportunities to be grabbed. There are new values to be forged.

The winter solstice has just passed and the days will become brighter and longer for the next months. Cheers!

Blueberry Earth

[Update: I have a paper version of this essay on arXiv:1807.10553, extending and correcting some of the results.]

On Physics Stackexchange billybodega asked the question:

BlueberrySupposing that the entire Earth was instantaneously replaced with an equal volume of closely packed, but uncompressed blueberries, what would happen from the perspective of a person on the surface?

Unfortunately the site tends to frown on fun questions like this, so it was in my opinion prematurely closed while I was working out the answer. So here it is, with some extra extensions:

The density of blueberries has been estimated to 625.56 kg/m3, WillO on Stackexchange estimated it to 13% of Earth’s density (5510*0.13=716.3 kg/m3), so assuming it to be around \rho_{berries}=700 kg/m3 appears to be reasonable. Blueberry pulp has a density similar to water,  980 to 1050 kg per m3 although this is both temperature dependent and depends on how much solids there are. The difference to the whole berries is due to the air between the berries. Note that these are likely the big, thick-skinned “American” blueberries rather than the small wild thin-skinned blueberries (bilberries) I grew up with; the latter would have higher density due to their smaller size and break far more easily.

So instantaneously turning Earth into blueberries will reduce its mass to 0.1274 of what it was. Gravity will become correspondingly weaker, g_{BE}=0.1274 g.

However, blueberries are not particularly sturdy. While there is a literature on blueberry mechanics (of course!), I did not manage to find a great source on their compressive strength. A rough estimate is possible: stacking a sugar cube (1 g) on a berry will not break it, while a milk carton (1 kg) will; 100 g has a decent but not certain chance. So if we assume the blueberry area to be one square centimetre the breaking pressure is on the order of P_{break}=0.1 g / 10^{-4} \approx 10,000 N/m2. This allows us to estimate at what depth the berries will start to break: z=P_{break}/g_{BE}\rho_{berries} = 11.4188 m. So while the surface will be free blueberries they will start pulping within a few meters of the surface.

This pulping has an important effect: the pulp separates from the air, coalescing into a smaller sphere. If we assume pulp to be an incompressible fluid, then a sphere of pulp with the same mass as the initial berries will be \rho_{pulp} r_{pulp}^3 = \rho_{berries}r_{earth}^3, or r_{pulp} = (\rho_{berries}/ \rho_{pulp} )^{1/3}r_{earth}. In this case we end up with a planet with 0.8879 times smaller radius (5,657 km), surrounded by a vast atmosphere.

The freefall timescale for the planet is initially 41 minutes, but relatively shortly the pulping interactions, the air convection etc will slow things down in a complicated way. I expect that the the actual coalescence will take hours, with some late bubbles from the deep interior erupting fairly late.

The gravity on the pulp surface is just 1.5833 m/s2, 16% of normal gravity – almost exactly lunar gravity. This weakens convection currents and the speed with which bubbles move up. The scale height of the atmosphere, assuming the same composition and temperature as on Earth, will be 6.2 times higher. This means that pressure will decline much less with altitude, allowing far thicker clouds and weather systems. As we will see, the atmosphere will puff up more.

The separation has big consequences. Enormous amounts of air will be pushing out from the pulp as bubbles and jets, producing spectacular geysers (especially since the gravity is low). Even more dramatic is the heating: a lot of gravitational energy is released as the mass is compacted. The total gravitational energy of a constant density sphere of radius R is

\int_0^R G [4\pi r^2 \rho] [4 \pi r^3 \rho/3] / r dr  = (16\pi^2 G\rho^2/3) \int_0^R r^4 dr
=(16\pi^2 G/15)\rho^2 R^5

(the first factor in the integral is the mass of a spherical shell of radius r, the second the mass of the stuff inside, and the third the 1/r gravitational potential). If we ignore the mass of the air since it is small and we just want an order of magnitude estimate,  the compression of the berry mass gives energy

E=(16\pi^2 G/15)(\rho_{berries}^2 r_{earth}^5 - \rho_{pulp}^2R_{pulp}^5) \approx 4.3594\times 10^{29} J.

This is the energy output of the sun over half an hour, nothing to sneeze at: blueberry earth will become hot. There is about 573,000 J per kg, enough to heat the blueberries from freezing to boiling.

The result is that blueberry earth will turn into a roaring ocean of boiling jam, with the geysers of released air and steam likely ejecting at least a few berries into orbit (escape velocity is just 4.234 km/s, and berries at the initial surface will be even higher up in the potential). As the planet evolves a thick atmosphere of released steam will add to the already considerable air from the berries. It is not inconceivable that the planet may heat up further due to a water vapour greenhouse effect, turning into a very odd Venusian world.

Meanwhile the jam ocean is very deep, and the pressure at depth will be enough to cause the formation of high pressure ice even if it is warm. If the formation process is slow there will be some separation of water into ice and a concentration of other chemicals in the jam ocean, but I suspect the rapid collapse will instead make some kind of composite pulp ice. Ice VII forms above 9 GPa, so if we just use constant gravity this happens at a depth z_{ice}=P_{VII}/g_{BE}\rho_{pulp}\approx 1,909 km, about two-thirds of the radius. This would make up most of the interior. However, gravity is a bit weaker in the interior, so we need to take that into account. The pressure from all the matter above radius r is P(r) =(3GM^2/8\pi R^4)(1-(r/R)^2), and the ice core will have radius r_{ice}=\sqrt{1-P_{VII}/P(0)}  \approx 3,258 km. This is smaller, about 57% of the radius, and just 20% of the total volume.

The coalescence will also speed up rotation. The original blueberry earth would of course make one rotation every 24 hours, but the smaller result would have a smaller moment of inertia. The angular momentum conservation gives (2/5)MR_1^2(2\pi/T_1) = (2/5)MR_2^2(2\pi/T_2), or T_2 = (R_2/R_1)^2 T_1, in this case 18.9210 hours. This in turn will increase the oblateness a bit, to approximately 0.038 – an 8.8 times increase over Earth.

Another effect is the orbit of the Moon. Now the two bodies have about equal mass. Is the Moon bound to blueberry earth? A kilogram of lunar material has potential energy GM_{BE}/r_{moon} \approx 1.6925 \times 10^{5} J, while the kinetic energy is 2.6442\times 10^5 J – more than enough to escape. Had it remained the jam ocean would have made an excellent tidal dissipation mechanism that would have slowed down rotation and moved blueberry earth towards tidal lock with the moon much earlier than the 50 billion years it would otherwise have taken.

So, to sum up, to a person standing on the surface of the Earth when it turns into blueberries, the first effect would be a drastic reduction of gravity. Standing on the blueberries might be possible in theory, except that almost immediately they begin to compress rapidly and air starts erupting everywhere. The effect is basically the worst earthquake ever, and it keeps on going until everything has fallen 714 km. While this is going on everything heats up drastically until the entire environment is boiling jam and steam. The end result is a world that has a steam atmosphere covering an ocean of jam on top of warm blueberry granita.

Why Cherry 2000 should not be banned, Terminator should, and what this has to do with Oscar Wilde

Binary curious[This is what happens when I blog after two glasses of wine. Trigger warning for possibly stupid cultural criticism and misuse of Oscar Wilde.]

From robots to artificiality

On practical ethics I discuss what kind of robots we ought to campaign against. I have signed up against autonomous military robots, but I think sex robots are fine. The dividing line is that the harm done (if any) is indirect and victimless, and best handled through sociocultural means rather than legislation.

I think the campaign against sex robots has a point in that there are some pretty creepy ideas floating around in the world of current sex bots. But I also think it assumes these ideas are the only possible motivations. As I pointed out in my comments on another practical ethics post, there are likely people turned on by pure artificiality – human sexuality can be far queerer than most think.

Going off on a tangent, I am reminded of Oscar Wilde’s epigram

“The first duty in life is to be as artificial as possible. What the second duty is no one has as yet discovered.”

Being artificial is not the same thing as being an object. As noted by Barris, Wilde’s artificiality actually fits in with pluralism and liberalism. Things could be different. Yes, in the artificial world nothing is absolutely given, everything is the result of some design choices. But assuming some eternal Essence/Law/God is necessary for meaning or moral exposes one to a fruitless search for that Thing (or worse, a premature assumption one has found It, typically when looking in the mirror). Indeed, as Dorian Gray muses, “Is insincerity such a terrible thing? I think not. It is merely a method by which we can multiply our personalities.” We are not single personas with unitary identities and well defined destinies, and this is most clearly visible in our social plays.

Sex, power and robots

Continuing on my Wildean binge, I encountered another epigram:

“Everything in the world is about sex except sex. Sex is about power.”

I think this cuts close to the Terminator vs. Cherry 2000 debate. Most modern theorists of gender and sex are of course power-obsessed (let’s blame Foucault). The campaign against sex robots clearly see the problem as the robots embodying and perpetuating a problematic unequal power structure. I detect a whiff of paternalism there, where women and children – rather than people – seem to be assumed to be the victims and in the need of being saved from this new technology (at least it is not going as far as some other campaigns that fully assume they are also suffering from false consciousness and must be saved from themselves, the poor things). But sometimes a cigar is just a cigar… I mean sex is sex: it is important to recognize that one of the reasons for sex robots (and indeed prostitution) is the desire for sex and the sometimes awkward social or biological constraints of experiencing it.

The problem with autonomous weapons is that power really comes out of a gun. (Must resist making a Zardoz reference…) It might be wielded arbitrarily by an autonomous system with unclear or bad orders, or it might wielded far too efficiently by an automated armed force perfectly obedient to its commanders – removing the constraint that soldiers might turn against their rulers if being aimed against their citizenry. Terminator is far more about unequal and dangerous power than sex (although I still have fond memories of seeing a naked Arnie back in 1984). The cultural critic may argue that the power games in the bedroom are more insidious and affect more of our lives than some remote gleaming gun-metal threat, but I think I’d rather have sexism than killing and automated totalitarianism. The uniforms of the killer robots are not even going to look sexy.

It is for your own good

Trying to ban sex robots is about trying to shape society into an appealing way – the goal of the campaign is to support “development of ethical technologies that reflect human principles of dignity, mutuality and freedom” and the right for everybody to have their subjectivity recognized without coercion. But while these are liberal principles when stated like this, I suspect the campaign or groups like it will have a hard time keeping out of our bedrooms. After all, they need to ensure that there is no lack of mutuality or creepy sex robots there. The liberal respect for mutuality can become a very non-liberal worship of Mutuality, embodied in requiring partners to sign consent forms, demanding trigger warnings, and treating everybody who is not responding right to its keywords as suspects of future crimes. The fact that this absolutism comes from a very well-meaning impulse to protect something fine makes it even more vicious, since any criticism is easily mistaken as an attack on the very core Dignity/Mutuality/Autonomy of humanity (and hence any means of defence are OK). And now we have all the ingredients for a nicely self-indulgent power trip.

This is why Wilde’s pluralism is healthy. Superficiality, accepting the contrived and artificial nature of our created relationships, means that we become humble in asserting their truth and value. Yes, absolute relativism is stupid and self defeating. Yes, we need to treat each other decently, but I think it is better to start from the Lockean liberalism that allows people to have independent projects rather than assume that society and its technology must be designed to embody the Good Values. Replacing “human dignity” with the word “respect” usually makes ethics clearer.

Instead of assuming we can a priori figure out how technology will change us and then select the right technology, we try and learn. We can make some predictions with reasonable accuracy, which is why trying to rein in autonomous weapons makes sense (the probability that they lead to a world of stability and peace seems remote). But predicting cultural responses to technology is not something we have any good track record of: most deliberate improvements of our culture have come from social means and institutions, not banning technology.

“The fact is, that civilisation requires slaves. The Greeks were quite right there. Unless there are slaves to do the ugly, horrible, uninteresting work, culture and contemplation become almost impossible. Human slavery is wrong, insecure, and demoralising. On mechanical slavery, on the slavery of the machine, the future of the world depends.”

Awesome blogs

I recently discovered Alex Wellerstein’s excellent blog Restricted data: the nuclear secrecy blog. I found it while looking for nuclear stockpiles data, but was drawn in by a post on the evolution of nuclear yield to mass. Then I started reading the rest of it. And finally, when reading this post about the logo of the IAEA I realized I needed to mention to the world how good it is. Be sure to test the critical assembly simulator to learn just why critical mass is not the right concept.

Another awesome blog is Almost looks like work by Jasmcole. I originally found it through a wonderfully over the top approach to positioning a wifi router (solving Maxwell’s equations turns out to be easier than the Helmholz equation!). But there are many other fascinating blog essays on physics, mathematics, data visualisation, and how to figure out propeller speeds from camera distortion.