Throwing balls on torus-earth

A question came up on Physics Stack Exchange: how does thrown object trajectories look on a toroidal planet?

Locally we should expect them to be like on Earth: there is constant gravitational acceleration orthogonal to the ground, so they will just look like parabolas.

But if the trajectory is longer the rapid rotation ought to twist it, since there is a fair Coriolis effect. So the differential equation will be $\mathbf{x}''=\mathbf{g}+2\mathbf{x}'\times\mathbf{\Omega}.$ If we just look at the velocity vector we get $\mathbf{v}'=\mathbf{g}+2\mathbf{v}\times\mathbf{\Omega}.$

That is, the forcefield will twist the velocity around if it is large and orthogonal to the angular velocity vector. If the velocity is parallel it will just be affected by gravity. For a trajectory near the pole it will become twisted and tilted:

Trajectories of a ball thrown from the surface with the angular velocity vector parallel to the gravity vector.

For a starting point on the equator the twisting gets a bit more complex:

Trajectories of a ball thrown from the surface with the angular velocity vector orthogonal to the gravity vector.

One can also recognise the analogy to an electron in an electromagnetic field: $latex \mathbf{v}’ = (q/m)(\mathbf{E}+\mathbf{v}\times \mathbf{B})$. Without gravity we should hence expect thrown balls to just follow helices around the omega-vector direction just like charged particles follow magnetic field-lines. One can eliminate the electric field from the equation by using a different velocity coordinate $latex \mathbf{v_2}=\mathbf{v}-\mathbf{E}\times\mathbf{B}/B^2$. Hence we can treat ball trajectories like helices plus a drift velocity in the $\mathbf{g}\times\mathbf{\Omega}$ direction. The helix radius will be $v/2\Omega$ .

How large is the Coriolis effect? On Earth $\Omega=2\pi/86400\approx 0.0000727$ . On Donut it is 0.000614 and on Hoop 0.000494, several times higher. Still, the correction is not going to be enormous: for a ball moving 10 meters per second the helix radius will be 69 km on Earth (at the pole), 8.1 km on Donut, and 10 km on Hoop. We hence need to throw the ball a suborbital distance before the twists become really visible. At these distances the curvature of the planet and the non-linearity of the gravitational field also begins to bite.

I have not simulated such trajectories since I need a proper mass distribution model of the worlds, and it is messy. However, for an infinitely thin ring one can solve orbits numerically relatively easily (you “just” have to integrate elliptic integrals):

Beside the “normal” equatorial orbits and torus-like orbits winding themselves around the ring, there are internal halo-orbits and chaotic tangles.

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:

Supposing 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.

What kinds of grand futures are there?

I have been working for about a year on a book on “Grand Futures” – the future of humanity, starting to sketch a picture of what we could eventually achieve were we to survive, get our act together, and reach our full potential. Part of this is an attempt to outline what we know is and isn’t physically possible to achieve, part of it is an exploration of what makes a future good.

Here are some things that appear to be physically possible (not necessarily easy, but doable):

Societies of very high standards of sustainable material wealth. At least as rich (and likely far above) current rich nation level in terms of what objects, services, entertainment and other lifestyle ordinary people can access.
Human enhancement allowing far greater health, longevity, well-being and mental capacity, again at least up to current optimal levels and likely far, far beyond evolved limits.
Sustainable existence on Earth with a relatively unchanged biosphere indefinitely.
Expansion into space:
- Settling habitats in the solar system, enabling populations of at least 10 trillion (and likely many orders of magnitude more)
- Settling other stars in the milky way, enabling populations of at least 10²⁹ people
- Settling over intergalactic distances, enabling populations of at least 10³⁸people.
Survival of human civilisation and the species for a long time.
- As long as other mammalian species – on the order of a million years.
- As long as Earth’s biosphere remains – on the order of a billion years.
- Settling the solar system – on the order of 5 billion years
- Settling the Milky Way or elsewhere – on the order of trillions of years if dependent on sunlight
- Using artificial energy sources – up to proton decay, somewhere beyond 10³² years.
Constructing Dyson spheres around stars, gaining energy resources corresponding to the entire stellar output, habitable space millions of times Earth’s surface, telescope, signalling and energy projection abilities that can reach over intergalactic distances.
Moving matter and objects up to galactic size, using their material resources for meaningful projects.
Performing more than a google (10¹⁰⁰) computations, likely far more thanks to reversible and quantum computing.

While this might read as a fairly overwhelming list, it is worth noticing that it does not include gaining access to an infinite amount of matter, energy, or computation. Nor indefinite survival. I also think faster than light travel is unlikely to become possible. If we do not try to settle remote galaxies within 100 billion years accelerating expansion will move them beyond our reach. This is a finite but very large possible future.

What kinds of really good futures may be possible? Here are some (not mutually exclusive):

Survival: humanity survives as long as it can, in some form.
“Modest futures”: humanity survives for as long as is appropriate without doing anything really weird. People have idyllic lives with meaningful social relations. This may include achieving close to perfect justice, sustainability, or other social goals.
Gardening: humanity maintains the biosphere of Earth (and possibly other planets), preventing them from crashing or going extinct. This might include artificially protecting them from a brightening sun and astrophysical disasters, as well as spreading life across the universe.
Happiness: humanity finds ways of achieving extreme states of bliss or other positive emotions. This might include local enjoyment, or actively spreading minds enjoying happiness far and wide.
Abolishing suffering: humanity finds ways of curing negative emotions and suffering without precluding good states. This might include merely saving humanity, or actively helping all suffering beings in the universe.
Posthumanity: humanity deliberately evolves or upgrades itself into forms that are better, more diverse or otherwise useful, gaining access to modes of existence currently not possible to humans but equally or more valuable.
Deep thought: humanity develops cognitive abilities or artificial intelligence able to pursue intellectual pursuits far beyond what we can conceive of in science, philosophy, culture, spirituality and similar but as yet uninvented domains.
Creativity: humanity plays creatively with the universe, making new things and changing the world for its own sake.

I have no doubt I have missed many plausible good futures.

Note that there might be moral trades, where stay-at-homes agree with expansionists to keep Earth an idyllic world for modest futures and gardening while the others go off to do other things, or long-term oriented groups agreeing to give short-term oriented groups the universe during the stelliferous era in exchange for getting it during the cold degenerate era trillions of years in the future. Real civilisations may also have mixtures of motivations and sub-groups.

Note that the goals and the physical possibilities play out very differently: modest futures do not reach very far, while gardener civilisations may seek to engage in megascale engineering to support the biosphere but not settle space. Meanwhile the happiness-maximizers may want to race to convert as much matter as possible to hedonium, while the deep thought-maximizers may want to move galaxies together to create permanent hyperclusters filled with computation to pursue their cultural goals.

I don’t know what goals are right, but we can examine what they entail. If we see a remote civilization doing certain things we can make some inferences on what is compatible with the behaviour. And we can examine what we need to do today to have the best chances of getting to a trajectory towards some of these goals: avoiding getting extinct, improve our coordination ability, and figure out if we need to perform some global coordination in the long run that we need to agree on before spreading to the stars.

Dissolving the Fermi Paradox

The Universe Today wrote an article about a paper by me, Toby and Eric about the Fermi Paradox. The preprint can be found on Arxiv (see also our supplements: 1,2,3 and 4). Here is a quick popular overview/FAQ.

TL;DR

The Fermi question is not a paradox: it just looks like one if one is overconfident in how well we know the Drake equation parameters.
Our distribution model shows that there is a large probability of little-to-no alien life, even if we use the optimistic estimates of the existing literature (and even more if we use more defensible estimates).
The Fermi observation makes the most uncertain priors move strongly, reinforcing the rare life guess and an early great filter.
Getting even a little bit more information can update our belief state a lot!

So, do you claim we are alone in the universe?
What is the paper about?
Dissolving the Fermi paradox: there is not much tension
The Great Filter: lack of obvious aliens is not strong evidence for our doom
Isn’t this armchair astrobiology?
Probability?
Correlations?
You can’t resample guesses from the literature!
But doesn’t resampling from admittedly overconfident literature constitute “garbage in, garbage out”?
What did the literature resampling show?
What are our assumed uncertainties?
Abiogenesis
Doesn’t creationists argue stuff like this?
Complex life
How much can we rule out aliens?
So what? What is the use of this?
Ah, but I already knew this!

So, do you claim we are alone in the universe?

No. We claim we could be alone, and the probability is non-negligible given what we know… even if we are very optimistic about alien intelligence.

What is the paper about?

The Fermi Paradox – or rather the Fermi Question – is “where are the aliens?” The universe is immense and old and intelligent life ought to be able to spread or signal over vast distances, so if it has some modest probability we ought to see some signs of intelligence. Yet we do not. What is going on? The reason it is called a paradox is that is there is a tension between one plausible theory ([lots of sites]x[some probability]=[aliens]) and an observation ([no aliens]).

Dissolving the Fermi paradox: there is not much tension

We argue that people have been accidentally misled to feel there is a problem by being overconfident about the probability.

$N=R_*\cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot L$

The problem lies in how we estimate probabilities from a product of uncertain parameters (as the Drake equation above). The typical way people informally do this with the equation is to admit that some guesses are very uncertain, give a “representative value” and end up with some estimated number of alien civilisations in the galaxy – which is admitted to be uncertain, yet there is a single number.

Obviously, some authors have argued for very low probabilities, typically concluding that there is just one civilisation per galaxy (“the $N\approx 1$ school”). This may actually still be too much, since that means we should expect signs of activity from nearly any galaxy. Others give slightly higher guesstimates and end up with many civilisations, typically as many as one expects civilisations to last (“the $N\approx L$ school”). But the proper thing to do is to give a range of estimates, based on how uncertain we actually are, and get an output that shows the implied probability distribution of the number of alien civilisations.

If one combines either published estimates or ranges compatible with current scientific uncertainty we get a distribution that makes observing an empty sky unsurprising – yet is also compatible with us not being alone.

The reason is that even if one takes a pretty optimistic view (the published estimates are after all biased towards SETI optimism since the sceptics do not write as many papers on the topic) it is impossible to rule out a very sparsely inhabited universe, yet the mean value may be a pretty full galaxy. And current scientific uncertainties of the rates of life and intelligence emergence are more than enough to create a long tail of uncertainty that puts a fair credence on extremely low probability – probabilities much smaller than what one normally likes to state in papers. We get a model where there is 30% chance we are alone in the visible universe, 53% chance in the Milky Way… and yet the mean number is 27 million and the median about 1! (see figure below)

This is a statement about knowledge and priors, not a measurement: armchair astrobiology.

(A) A probability density function for N, the number of civilisations in the Milky Way, generated by Monte Carlo simulation based on the authors’ best estimates of our current uncertainty for each parameter. (B) The corresponding cumulative density function. (C) A cumulative density function for the distance to the nearest detectable civilisation.

The Great Filter: lack of obvious aliens is not strong evidence for our doom

After this result, we look at the Great Filter. We have reason to think at least one term in the Drake equation is small – either one of the early ones indicating how much life or intelligence emerges, or one of the last one that indicate how long technological civilisations survive. The small term is “the Filter”. If the Filter is early, that means we are rare or unique but have a potentially unbounded future. If it is a late term, in our future, we are doomed – just like all the other civilisations whose remains would litter the universe. This is worrying. Nick Bostrom argued that we should hope we do not find any alien life.

Our paper gets a somewhat surprising result: when updating our uncertainties in the light of no visible aliens, it reduces our estimate of the rate of life and intelligence emergence (the early filters) much more than the longevity factor (the future filter).

The reason is that if we exclude the cases where our galaxy is crammed with alien civilisations – something like the Star Wars galaxy where every planet has its own aliens – then that leads to an update of the parameters of the Drake equation. All of them become smaller, since we will have a more empty universe. But the early filter ones – life and intelligence emergence – change much more downwards than the expected lifespan of civilisations since they are much more uncertain (at least 100 orders of magnitude!) than the merely uncertain future lifespan (just 7 orders of magnitude!).

So this is good news: the stars are not foretelling our doom!

Note that a past great filter does not imply our safety.

The conclusion can be changed if we reduce the uncertainty of the past terms to less than 7 orders of magnitude, or the involved probability distributions have weird shapes. (The mathematical proof is in supplement IV, which applies to uniform and normal distributions. It is possible to add tails and other features that breaks this effect – yet believing such distributions of uncertainty requires believing rather strange things. )

Isn’t this armchair astrobiology?

Yes. We are after all from the philosophy department.

The point of the paper is how to handle uncertainties, especially when you multiply them together or combine them in different ways. It is also about how to take lack of knowledge into account. Our point is that we need to make knowledge claims explicit – if you claim you know a parameter to have the value 0.1 you better show a confidence interval or an argument about why it must have exactly that value (and in the latter case, better take your own fallibility into account). Combining overconfident knowledge claims can produce biased results since they do not include the full uncertainty range: multiplying point estimates together produces a very different result than when looking at the full distribution.

All of this is epistemology and statistics rather than astrobiology or SETI proper. But SETI makes a great example since it is a field where people have been learning more and more about (some) of the factors.

The same approach as we used in this paper can be used in other fields. For example, when estimating risk chains in systems (like the risk of a pathogen escaping a biosafety lab) taking uncertainties in knowledge will sometimes produce important heavy tails that are irreducible even when you think the likely risk is acceptable. This is one reason risk estimates tend to be overconfident.

Probability?

What kind of distributions are we talking about here? Surely we cannot speak of the probability of alien intelligence given the lack of data?

There is a classic debate in probability between frequentists, claiming probability is the frequency of events that we converge to when an experiment is repeated indefinitely often, and Bayesians, claiming probability represents states of knowledge that get updated when we get evidence. We are pretty Bayesian.

The distributions we are talking about are distributions of “credences”: how much you believe certain things. We start out with a prior credence based on current uncertainty, and then discuss how this gets updated if new evidence arrives. While the original prior beliefs may come from shaky guesses they have to be updated rigorously according to evidence, and typically this washes out the guesswork pretty quickly when there is actual data. However, even before getting data we can analyse how conclusions must look if different kinds of information arrives and updates our uncertainty; see supplement II for a bunch of scenarios like “what if we find alien ruins?”, “what if we find a dark biosphere on Earth?” or “what if we actually see aliens at some distance?”

Correlations?

Our use of the Drake equation assumes the terms are independent of each other. This of course is a result of how Drake sliced things into naturally independent factors. But there could be correlations between them. Häggström and Verendel showed that in worlds where the priors are strongly correlated updates about the Great Filter can get non-intuitive.

We deal with this in supplement II, and see also this blog post. Basically, it doesn’t look like correlations are likely showstoppers.

You can’t resample guesses from the literature!

Sure can. As long as we agree that this is not so much a statement about what is actually true out there, but rather the range of opinions among people who have studied the question a bit. If people give answers to a question in the range from ten to a hundred, that tells you something about their beliefs, at least.

What the resampling does is break up the possibly unconscious correlation between answers (“the $N\approx 1$ school” and “the $N\approx L$ school” come to mind). We use the ranges of answers as a crude approximation to what people of good will think are reasonable numbers.

You may say “yeah, but nobody is really an expert on these things anyway”. We think that is wrong. People have improved their estimates as new data arrives, there are reasons for the estimates and sometimes vigorous debate about them. We warmly recommend Vakoch, D. A., Dowd, M. F., & Drake, F. (2015). The Drake Equation. The Drake Equation, Cambridge, UK: Cambridge University Press, 2015 for a historical overview. But at the same time these estimates are wildly uncertain, and this is what we really care about. Good experts qualify the certainty of their predictions.

But doesn’t resampling from admittedly overconfident literature constitute “garbage in, garbage out”?

Were we trying to get the true uncertainties (or even more hubristically, the true values) this would not work: we have after all good reasons to suspect these ranges are both biased and overconfidently narrow. But our point is not that the literature is right, but that even if one were to use the overly narrow and likely overly optimistic estimates as estimates of actual uncertainty the broad distribution will lead to our conclusions. Using the literature is the most conservative case.

Note that we do not base our later estimates on the literature estimate but our own estimates of scientific uncertainty. If they are GIGO it is at least our own garbage, not recycled garbage. (This reading mistake seems to have been made on Starts With a Bang).

What did the literature resampling show?

An overview can be found in Supplement III. The most important point is just that even estimates of super-uncertain things like the probability of life lies in a surprisingly narrow range of values, far more narrow than is scientifically defensible. For example, $f_l$ has five estimates ranging from $10^{-30}$ to $10^{-5}$ , and all the rest are in the range $10^{-3}$ to 1. $f_i$ is even worse, with one microscopic and nearly all the rest between one in a thousand to one.

(A) The uncertainty in the research community represented via a synthetic probability density function over N — the expected number of detectable civilizations in our galaxy. The curve is generated by random sampling from the literature estimates of each parameter. Direct literature estimates of the number of detectable civilisations are marked with red rings. (B) The corresponding synthetic cumulative density function. (C) A cumulative density function for the distance to the nearest detectable civilisation, estimated via a mixture model of the nearest neighbour functions. — (A) The uncertainty in the research community represented via a synthetic probability density function over N — the expected number of detectable civilisations in our galaxy. The curve is generated by random sampling from the literature estimates of each parameter. Direct literature estimates of the number of detectable civilisations are marked with red rings. (B) The corresponding
*synthetic cumulative density function. (C) A cumulative density function for the distance to the nearest detectable civilisation, estimated via a mixture model of the nearest neighbour functions.*

It also shows that estimates that are likely biased towards optimism (because of publication bias) can be used to get a credence distribution that dissolves the paradox once they are interpreted as ranges. See the above figure, were we get about 30% chance of being alone in the Milky Way and 8% chance of being alone in the visible universe… but a mean corresponding to 27 million civilisations in the galaxy and a median of about a hundred.

There are interesting patterns in the data. When plotting the expected number of civilisations in the Milky Way based on estimates from different eras the number goes down with time: the community has clearly gradually become more pessimistic. There are some very pessimistic estimates, but even removing them doesn’t change the overall structure.

What are our assumed uncertainties?

A key point in the paper is trying to quantify our uncertainties somewhat rigorously. Here is a quick overview of where I think we are, with the values we used in our synthetic model:

$N_*$ : the star formation rate in the Milky Way per year is fairly well constrained. The actual current uncertainty is likely less than 1 order of magnitude (it can vary over 5 orders of magnitude in other galaxies). In our synthetic model we put this parameter as log-uniform from 1 to 100.
$f_p$ : the fraction of systems with planets is increasingly clear ≈1. We used log-uniform from 0.1 to 1.
: number of Earth-like in systems with planets.
- This ranges from rare earth arguments ( $<10^{-12}$ ) to >1. We used log-uniform from 0.1 to 1 since recent arguments have shifted away from rare Earths, but we checked that adding it did not change the conclusions much.
: Fraction of Earthlike planets with life.
- This is very uncertain; see below for our arguments that the uncertainty ranges over perhaps 100 orders of magnitude.
- There is an absolute lower limit due to ergodic repetition: $f_l >10^{-10^{115}}$ – in an infinite universe there will eventually be randomly generated copies of Earth and even the entire galaxy (at huge distances from each other). Observer selection effects make using the earliness of life on Earth problematic.
- We used a log-normal rate of abiogenesis that was transformed to a fraction distribution.
: Fraction of lifebearing planets with intelligence/complex life.
- This is very uncertain; see below for our arguments that the uncertainty ranges over perhaps 100 orders of magnitude.
- One could argue there has been 5 billion species so far and only 1 intelligent, so we know $f_i>2\cdot 10^{-10}$ . But one could argue that we should count assemblages of 10 million species, which gives a fraction 1/500 per assemblage. Observer selection effects may be distorting this kind of argument.
- We could have used a log-normal rate of complex life emergence that was transformed to a fraction distribution or a broad log-linear distribution. Since this would have made many graphs hard to interpret we used log-uniform from 0.001 to 1, not because we think this likely but just as a simple illustration (the effect of the full uncertainty is shown in Supplement II).
: Fraction of time when it is communicating.
- Very uncertain; humanity is 0.000615 so far. We used log-uniform from 0.01 to 1.
: Average lifespan of a civilisation.
- Fairly uncertain; $50?<L< 10^9-10^{10}$ years (upper limit because of the Drake equation applicability: it assumes the galaxy is in a steady state, and if civilisations are long-lived enough they will still be accumulating since the universe is too young.)
- We used log-uniform from 100 to 10,000,000,000.

Note that this is to some degree a caricature of current knowledge, rather than an attempt to represent it perfectly. Fortunately our argument and conclusions are pretty insensitive to the details – it is the vast ranges of uncertainty that are doing the heavy lifting.

Abiogenesis

Why do we think the fraction of planets with life parameters could have a huge range?

First, instead of thinking in terms of the fraction of planets having life, consider a rate of life formation in suitable environments: what is the induced probability distribution? The emergence is a physical/chemical transition of some kind of primordial soup, and transition events occur in this medium at some rate per unit volume: $f_L\approx \lambda V t$ where $V$ is the available volume and $t$ is the available time. High rates would imply that almost all suitable planets originate life, while low rates would imply that almost no suitable planets originate life.

The uncertainty regarding the length of time when it is possible is at least 3 orders of magnitude ( $10^7-10^{10}$ years).

The uncertainty regarding volumes spans 20+ orders of magnitude – from entire oceans to brine pockets on ice floes.

Uncertainty regarding transition rates can span 100+ orders of magnitude! The reason is that this might involve combinatoric flukes (you need to get a fairly longish sequence of parts into the right sequence to get the right kind of replicator), or that it is like the protein folding problem where Levinthal’s paradox shows that it takes literally astronomical time to get entire oceans of copies of a protein to randomly find the correctly folded position (actual biological proteins “cheat” by being evolved to fold neatly and fast). Even chemical reaction rates span 100 orders of magnitude. On the other hand, spontaneous generation could conceivably be common and fast! So we should conclude that $\lambda$ has an uncertainty range of at least 100 orders of magnitude.

Actual abiogenesis will involve several steps. Some are easy, like generating simple organic compounds (plentiful in asteroids, comets and Miller-Urey experiment). Some are likely tough. People often overlook that even how to get proteins and nucleic acids in a watery environment is somewhat of a mystery since these chains tend to hydrolyze; the standard explanation is to look for environments that have a wet-dry cycle allowing complexity to grow. But this means $V$ is much smaller than an ocean.

That we have tremendous uncertainty about abiogenesis does not mean we do not know anything. We know a lot. But at present we have no good scientific reasons to believe we know the rate of life formation per liter-second. That will hopefully change.

Doesn’t creationists argue stuff like this?

There is a fair number of examples of creationists arguing that the origin of life must be super-unlikely and hence we must believe in their particular god.

The problem(s) with this kind of argument is that it presupposes that there is only one planet, and somehow we got a one-in-a-zillion chance on that one. That is pretty unlikely. But the reality is that there is a zillion planets, so even if there is a one-in-a-zillion chance for each of them we should expect to see life somewhere… especially since being a living observer is a precondition for “seeing life”! Observer selection effects really matter.

We are also not arguing that life has to be super-unlikely. In the paper our distribution of life emergence rate actually makes it nearly universal 50% of the time – it includes the possibility that life will spontaneously emerge in any primordial soup puddle left alone for a few minutes. This is a possibility I doubt anybody believes in, but it could be that would-be new life is emerging right under our noses all the time, only to be outcompeted by the advanced life that already exists.

Creationists make a strong claim that they know $f_l \ll 1$ ; this is not really supported by what we know. But $f_l \ll 1$ is totally within possibility.

Complex life

Even if you have life, it might not be particularly good at evolving. The reasoning is that it needs to have a genetic encoding system that is both rigid enough to function efficiently and fluid enough to allow evolutionary exploration.

All life on Earth shares almost exactly the same genetic systems, showing that only rare and minor changes have occurred in $\approx 10^{40}$ cell divisions. That is tremendously stable as a system. Nonetheless, it is fairly commonly believed that other genetic systems preceded the modern form. The transition to the modern form required major changes (think of upgrading an old computer from DOS to Windows… or worse, from CP/M to DOS!). It would be unsurprising if the rate was < 1 per $10^{100}$ cell divisions given the stability of our current genetic system – but of course, the previous system might have been super-easy to upgrade.

Modern genetics required >1/5 of the age of the universe to evolve intelligence. A genetic system like the one that preceded ours might both be stable over a google cell divisions and evolve more slowly by a factor of 10, and run out the clock. Hence some genetic systems may be incapable of ever evolving intelligence.

This related to a point made by Brandon Carter much earlier, where he pointed out that the timescales of getting life, evolving intelligence and how long biospheres last are independent and could be tremendously different – that life emerged early on Earth may have been a fluke due to the extreme difficulty of also getting intelligence within this narrow interval (on all the more likely worlds there are no observers to notice). If there are more difficult transitions, you get an even stronger observer selection effect.

Evolution goes down branches without looking ahead, and we can imagine that it could have an easier time finding inflexible coding systems (“B life”) unlike our own nice one (“A life”). If the rate of discovering B-life is $\lambda_B$ and the rate of discovering capable A-life is $\lambda_A$ , then the fraction of A-life in the universe is just $\lambda_A/\lambda_B$ – and rates can differ many orders of magnitude, producing a life-rich but evolution/intelligence-poor universe. Multiple step models add integer exponents to rates: these the multiply order of magnitude differences.

So we have good reasons to think there could be a hundred orders of magnitude uncertainty on the intelligence parameter, even without trying to say something about evolution of nervous systems.

How much can we rule out aliens?

Humanity has not scanned that many stars, so obviously we have checked even a tiny part of the galaxy – and could have missed them even if we looked at the right spot. Still, we can model how this weak data updates our beliefs (see Supplement II).

The strongest argument against aliens is the Tipler-Hart argument that settling the Milky Way, even when you are expanding at low speed, will only take a fraction of its age. And once a civilisation is everywhere it is hard to have it go extinct everywhere – it will tend to persist even if local pieces crash. Since we do not seem to be in a galaxy paved over by an alien supercivilisation we have a very strong argument to assume a low rate of intelligence emergence. Yes, even if if 99% of civilisations stay home or we could be in an alien zoo, you still get a massive update against a really settled galaxy. In our model the probability of less than one civilisation per galaxy went from 52% to 99.6% if one include the basic settlement argument.

The G-hat survey of galaxies, looking for signs of K3 civilisations, did not find any. Again, maybe we missed something or most civilisations don’t want to re-engineer galaxies, but if we assume about half of them want to and have 1% chance of succeeding we get an update from 52% chance of less than one civilisation per galaxy to 66%.

Using models of us looking at about 1,000 stars or that we do not think there is any civilisation within 18 pc gives a milder update, from 52% to 53 and 57% respectively. These just rule out super-densely inhabited scenarios.

So what? What is the use of this?

People like to invent explanations for the Fermi paradox that all would have huge implications for humanity if they were true – maybe we are in a cosmic zoo, maybe there are interstellar killing machines out there, maybe singularity is inevitable, maybe we are the first civilisation ever, maybe intelligence is a passing stage, maybe the aliens are sleeping… But if you are serious about thinking about the future of humanity you want to be rigorous about this. This paper shows that current uncertainties actually force us to be very humble about these possible explanations – we can’t draw strong conclusions from the empty sky yet.

But uncertainty can be reduced! We can learn more, and that will change our knowledge.

From a SETI perspective, this doesn’t say that SETI is unimportant or doomed to failure, but rather that if we ever see even the slightest hint of intelligence out there many parameters will move strongly. Including the all-important $L$ .

From an astrobiology perspective, we hope we have pointed at some annoyingly uncertain factors and that this paper can get more people to work on reducing the uncertainty. Most astrobiologists we have talked with are aware of the uncertainty but do not see the weird knock-on-effects from it. Especially figuring out how we got our fairly good coding system and what the competing options are seems very promising.

Even if we are not sure we can also update our plans in the light of this. For example, in my tech report about settling the universe fast I pointed out that if one is uncertain about how much competition there might be for the universe one can use one’s probability estimates to decide on the range to aim for.

Uncertainty matters

Perhaps the most useful insight is that uncertainty matters and we should learn to embrace it carefully rather than assume that apparently specific numbers are better.

Perhaps never in the history of science has an equation been devised yielding values differing by eight orders of magnitude. . . . each scientist seems to bring his own prejudices and assumptions to the problem.
– History of Astronomy: An Encyclopedia, ed. by John Lankford, s.v. “SETI,” by Steven J. Dick, p. 458.

When Dick complained about the wide range of results from the Drake equation he likely felt it was too uncertain to give any useful result. But 8 orders of magnitude differences is in this case just a sign of downplaying our uncertainty and overestimating our knowledge! Things gets much better when we look at what we know and don’t know, figuring out the implications from both.

Jill Tarter said the Drake equation was “a wonderful way to organize our ignorance”, which we think is closer to the truth than demanding a single number as an answer.

Ah, but I already knew this!

We have encountered claims that “nobody” really is naive about using the Drake equation. Or at least not any “real” SETI and astrobiology people. Strangely enough people never seem to make this common knowledge visible, and a fair number of papers make very confident statements about “minimum” values for life probabilities that we think are far, far above the actual scientific support.

Sometimes we need to point out the obvious explicitly.

[Edit 2018-06-30: added the GIGO section]

Arguing against killer robot janissaries

Military robot being shown to families at New Scientist Live 2017.

I have a piece in Dagens Samhälle with Olle Häggström, Carin Ism, Max Tegmark and Markus Anderljung urging the Swedish parliament to consider banning lethal autonomous weapons.

This is of course mostly symbolic; the real debate is happening right now over in Geneva at the CCW. I also participated in a round-table with the Red Cross that led to their report on the issue, which is one of the working papers presented there.

I am not particularly optimistic that we will get a ban – nor that a ban would actually achieve much. However, I am much more optimistic that this debate may force a general agreement about the importance of getting meaningful human control. This is actually an area where most military and peace groups would agree: nobody wants systems that are unaccountable and impossible to control. Making sure there are international agreements that using such systems is irresponsible and maybe even a war crime would be a big win. But there are lots of devils in the details.

When it comes to arguments for why LAWs are morally bad I am personally not so convinced that the bad comes from a machine making the decision to kill a person. Clearly some machine possible decisionmaking does improve proportionality and reduce arbitrariness. Similarly arguments about whether they would increase or reduce the risk of military action and how this would play out in terms of human suffering and death are interesting empirical arguments but we should not be overconfident in that we know the answers. Given that once LAWs are in use it will be hard to roll them back if the answers are bad, we might find it prudent to try to avoid them (but consider the opposing scenario where since time immemorial robots have fought our wars and somebody now suggests using humans too – there is a status quo bias here).

My main reason for being opposed to LAWs is not that they would be inherently immoral, nor that they would necessarily or even likely make war worse or more likely. My view is that the problem is that they give states too much power. Basically they make their monopoly on violence independent of the wishes of the citizens. Once a sufficiently potent LAW military (or police force) exist it will be able to exert coercive and lethal power as ordered without any mediation through citizens. While having humans in the army certainly doesn’t guarantee moral behavior, if ordered to turn against the citizenry or act in a grossly immoral way they can exert moral agency and resist (with varying levels of overtness). The LAW army will instead implement the orders as long as they are formally lawful (assuming there is at least a constraint against unlawful commands). States know that if they mistreat their population too much their army might side with the population, a reason why some of the nastier governments make use of mercenaries or a special separate class of soldier to reduce the risk. If LAWs become powerful enough they might make dictatorships far more stable by removing a potentially risky key component of state power from the internal politics.

Bans and moral arguments are unlikely to work against despots. But building broad moral consensuses on what is acceptable in war does have effects. If R&D emphasis is directed towards finding solutions to how to manage responsibility for autonomous device decisions that will develop a lot of useful technologies for making such systems at least safer – and one can well imagine similar legal and political R&D into finding better solutions to citizen-independent state power.

In fact, far more important than LAWs is what to do about Lethal Autonomous States. Bad governance kills, many institutions/corporations/states behave just as badly as the worst AI risk visions and have a serious value alignment problem, and we do not have great mechanisms for handling responsibility in inter-state conflicts. The UN system is a first stab at the problem but obviously much, much more can be done. In the meantime, we can try avoiding going too quickly down a risky path while we try to find safe-making technologies and agreements.

Admitting blog infidelity with StackExchange

I have neglected Andart II for some time, partly for the good reason of work (The Book is growing!), partly because I got a new addiction: answering (and asking) questions on Physics and Astronomy StackExchange. Very addictive, but also very educational. Here are links to some of the stuff I have been adding, which might be of interest to some readers.

What are the limiting abundances of the elements at the end of the stelliferous era?
Could life survive on a planet orbiting a neutron star?
Are there places in space completely devoid of light? (I was surprised by this result, I thought there would always be galaxies visible to the naked eye)
What will the last day of humanity look like?
What is the radiative cooling rate at extremely low temperatures?
Dielectric film statite: optimal mirroring for blackbody spectrum? (I think one can do better than my sketch)
What is the theoretical efficiency of fusion? (Still, given the mass-energy conversion in accretion disks maybe we can skip it)
Does accelerating cosmological expansion increase beam spread? (A problem for remote supercivilisations)
What is the simplest way of measuring the thickness of a soap bubble? (It was very fun making the graph, but my attempts at making a more spectrally true one failed in Matlab)
Isoperimetric inequality and mass
Temperature of an object placed half way between sun and earth
How were atoms able to form after the Big Bang?
Why must Debye cooling eventually slow down? (Cooling of ultra-cold objects is weird)
Is there an entropy cost for moving an object?
Is the average temperature of a big accretion disk colder than a small one?
Have we found all stable nuclear isomers? (Do you have a favourite nuclear isomer?)
Why are there no ellipsoidal drums?
Electric lamp and City electricity frequency
Can one determine the speed of the rain from the shape of the rainbow? (Surprisingly, almost yes)
How does the Venus flytrap count?
Putting grams of antimatter in the atmosphere
What angle gives the longest path for a projectile? (Simple question, tricky answer)
Painting with a Pendulum: Would it be possible to graph the pattern?
Where will the Goldilocks zone be when the Sun becomes a red giant?
Position of neutral points (Modelling the field of a bar magnet is more complex than expected)
Ways to make a star go supernova?
When must an alien civilization send off a signal that can reach us today?
Determining the value of Pi empirically
Possible for bacteria to burst container?
How would kinetic bombardment look like on impact to an observer on Earth’s surface? (I am so much going to use this in some roleplaying game scenario, despite my critique of the scheme)
Why does the moon appear fairly flat to a naked eye?
Is it possible to evaporate a gram of a transuranic element and if so how much energy would it take? (A bit of overview of strong heating)
Why doesn’t paper tear into 3 pieces?
How many times should an experiment be repeated?
Asteroid hopping (It takes a lot of skill)
Strange ice found in my garden (this one and the next one gave me a surprising number of points and badges)
Frost bubble formation
How were atoms able to form after the big bang? (I was surprised by my equilibration time estimate being about two weeks)

Can you be a death positive transhumanist?

I recently came across the concept of “death positivity”, expressed as the idea that we should accept the inevitability of death and embrace the diversity of attitudes and customs surrounding it. Looking a bit deeper, I found the Order of the Good Death and their statement.

That got me thinking about transhumanist attitudes to death and how they are perceived.

While the brief Kotaku description makes it sound that death positivity is perhaps about celebrating death, the Order of the Good Death mainly is about acknowledging death and dying. That we hide it behind closed doors and avoid public discussion (or even thinking about it) is doing harm to society and arguably our own emotions. Fear and denial are not good approaches. Perhaps the best slogan-description is “Accepting that death itself is natural, but the death anxiety of modern culture is not.”

The Order aims at promoting more honest public discussion, curiosity, innovation and gatherings to discuss death-related topic. Much of this relates to the practices in the “death industry”, some of which definitely should be discussed in terms of economic costs, environmental impact, ethics and legal rights.

Denying death as a bad thing?

There is an odd paradox here. Transhumanism is often described as death denying, and this description is not meant as a compliment in the public debate. Wanting to live forever is presented as immature, selfish or immoral. Yet we have an overall death denying society, so how can this be held to be bad?

Part of it is that the typical frame of the critique is from a “purveyor of wisdom” (a philosopher, a public intellectual, the local preacher) who no doubt might scold society too had not the transhumanist been a more convenient target.

This critique is rarely applied to established religions that are even more radically death denying – Christianity after all teaches the immortality of the soul, and in Hinduism and Buddhism ending the self is a nearly impossible struggle through countless reincarnations: talk about denying death! You rarely hear people asking how life could have a meaning if there is an ever-lasting hereafter. (In fact, some have like Tolstoy argued that it is only because such ever-lasting states that anything could have meaning). Some of the lack of critique is due to social capital: major religions hold much of it, transhumanism less, so criticising tends to focus on those groups that have less impact. Not just because the “purveyor of wisdom” fears a response but because they are themselves consciously or not embedded inside the norms and myths of these influential groups.

Another reason for criticising the immortalist position is death denial. Immortalism, and its more plausible sibling longevism, directly breaks the taboo against discussing death honestly. It questions core ideas about what human existence is like, and it by necessity delves into the processes of ageing and death. It tries to bring up uncomfortable subjects and does not accept the standard homilies about why life should be like it is, and why we need to accept it. This second reason actually makes transhumanism and death positivity unlikely allies.

Naïve transhumanists sometimes try to recruit people by offering the hope of immortality. Often they are surprised and shocked by the negative reactions. Leaving the appearance of a Faustian bargain aside, people typically respond by shoring up their conventional beliefs and defending their existential views. Few transhumanist ideas cause stronger reactions than life extension – I have lectured about starting new human species, uploading minds, remaking the universe, enhancing love, and many extreme topics, but I rarely get as negative comments as when discussing the feasibility and ethics of longevity.

The reason for this is in my opinion very much fear of death (with a hefty dose of status quo bias mixed in). As we grow up we have to handle our mortality and we build a defensive framework telling us how to handle it – typically by downplaying the problem of death by ignoring it, explaining or hoping via a religious framework, or finding some form of existential acceptance. But since most people rarely are exposed to dissenting views or alternatives they react very badly when this framework is challenged. This is where death positivity would be very useful.

Why strict immortalism is a non-starter

Given our current scientific understanding death is unavoidable. The issue is not whether life extension is possible or not, just the basic properties of our universe. Given the accelerating expansion of the universe we can only gain access to a finite amount of material resources. Using these resources is subject to thermodynamic inefficiencies that cannot be avoided. Basically the third law of thermodynamics and Landauer’s principle imply that there is a finite number of information processing steps that can be undertaken in our future. Eventually the second law of thermodynamics wins (helped by proton decay and black hole evaporation) and nothing that can store information or perform the operations needed for any kind of life will remain. This means that no matter what strange means any being undertakes as far as we understand physics it will eventually dissolve.

One should also not discount plain bad luck: finite beings in a universe where quantum randomness happens will sooner or later be subjected to a life-ending coincidence.

The Heat Death of the Universe and Quantum Murphy’s Law are a very high upper bounds. They are important because they force any transhumanist who doesn’t want to dump rationality overboard and insist that the laws of physics must allow true immortality because it is desired to acknowledge that they will eventually die – perhaps aeons hence and in a vastly changed state, but at some point it will have happened (perhaps so subtly that nobody even noticed: shifts in identity also count).

To this the reasonable transhumanist responds with a shrug: we have more pressing mortality concerns today, when ageing, disease, accidents and existential risk are so likely that we can hardly expect to survive a century. We endlessly try to explain to interviewers that transhumanism is not really seeking capital “I” Immortality but merely indefinitely long lifespans, and actually we are interested in years of health and activity rather than just watching the clock tick as desiccated mummies. The point is, a reasonable transhumanistic view will be focused on getting more and better life.

Running from death or running towards life?

One can strive to extend life because one is scared of drying – death as something deeply negative – or because life is worth living – remaining alive has a high value.

But if one can never avoid having death at some point in one’s lifespan then the disvalue of death will always be present. It will not affect whether living one life is better than another.

An exception may be if one believes that the disvalue can be discounted by being delayed, but this merely affects the local situation in time: at any point one prefers the longest possible life, but the overall utility as seen from the outside when evaluating a life will always suffer the total disvalue.

I believe the death-apologist thinkers have made some good points about why death is not intensely negative (e.g. the Lucretian arguments). I do not think they are convincing in that it is a positive property of the world. If “death gives life meaning” then presumably divorce is what makes love meaningful. If it is a good thing that old people retire from positions of power, why not have mandatory retirement rather than the equivalent of random death-squads? In fact, defences of death as a positive tend to use remarkably weak reasons for motivations, reasons that would never be taken seriously if motivating complacency about a chronic or epidemic disease.

Life-affirming transhumanism on the other hand is not too worried about the inevitability of death. The question is rather how much and what kind of good life is possible. One can view it as a game of seeking to maximise a “score” of meaningfulness and value under risk. Some try to minimise the risk, others to get high points, still others want to figure the rules or structure their life projects to make a meaningful structure across time.

Ending the game properly

This also includes ending life when it is no longer meaningful. Were one to regard death as extremely negative, then one should hang on even if there was nothing but pain and misery in the future. If death merely has zero value, then one can be in bad states where it is better to be dead than alive.

As we have argued in a recent paper many of the anti-euthanasia arguments turn on their head when applied to cryonics: if one regards life as a too precious gift to be thrown away and that the honourable thing is to continue to struggle on, then undergoing cryothanasia (being cryonically suspended well before one would otherwise have died) when suffering a terminal disease in the rational hope that this improves ones chances clearly seems better than to not take the chance or allow disease to reduce one’s chances.

This also shows an important point where one kind of death positivity and transhumanism may part ways. One can frame accepting death as accept that death exists and deal with it. Another frame, equally compatible with the statement, is not struggling too much against it. The second frame is often what philosophers suggest as a means for equanimity. While possibly psychologically beneficial it clearly has limits: the person not going to the doctor with a treatable disease when they know it will develop into something untreatable (or not stepping out of the way of an approaching truck) is not just “not struggling” but being actively unreasonable. One can and should set some limit where struggle and interventions become unreasonable, but this is always going to be both individual and technology dependent. With modern medicine many previously lethal conditions (e.g. bacterial meningitis, many cancers) have become treatable to such an extent that it is not reasonable to avail oneself to treatment.

Transhumanism puts a greater value in longevity than is usual, partially because of its optimistic outlook (the future is likely to be good, technology is likely to advance), and this leads to a greater willingness to struggle on even when conventional wisdom says it is a good time to give up and become fatalistic. This is a reason transhumanists are far more OK with radical attempts to stave off death than most people, including cryonics.

Cryonics

Cryonics is another surprisingly death-positive aspect of transhumanism. It forces you to confront your mortality head on, and it does not offer very strong reassurance. Quite the opposite: it requires planning for ones (hopefully temporary) demise, consider the various treatment/burial options, likely causes of death, and the risks and uncertainties involved in medicine. I have friends who seriously struggled with their dread of death when trying to sign up.

Talking about the cryonics choice with family is one of the hardest parts of the practice and has caused significant heartbreak, yet keeping silent and springing it as a surprise guarantees even more grief (and lawsuits). This is one area where better openness about death would be extremely helpful.

It is telling that members of the cryonics community seeks out each other, since it is one of the few environments where these things can be discussed openly and without stigma. It seems likely that the death-positive and the cryonics community have more in common than they might think.

Cryonics also has to deal with the bureaucracy and logistics of death, with the added complication that it aims at something slightly different than conventional burial. To a cryonicist the patients are still patients even when they have undergone cardiac arrest, are legally declared dead, solid and immersed in liquid nitrogen: they need care and protection since they may only be temporarily dead. Or deanimated, if we want to reserve “death” as a word for irreversibly non-living. (As a philosopher, I must say I find the cryosuspended state delightfully like a thought-experiment in a philosophy paper).

Final words

I have argued that transhumanism should be death-positive, at least in the sense that discussing death and accepting its long-term inevitability is both healthy and realistic. Transhumanists will not generally support a positive value of death and will tend to react badly to that kind of statement. But assigning it a vastly negative value produces a timid outlook that is unlikely to work well with the other parts of the transhumanist idea complex. Rather, death is bad because life is good but that doesn’t mean we should not think about it.

Indeed, transhumanists may want to become better at talking about death. Respected and liked people who have been part of the movement for a long time have died and we are often awkward about how to handle it. Transhumanists need to handle grief too. Even if the subject may be only temporarily dead in a cryonic tank.

Conversely, transhumanism and cryonics may represent an interesting challenge for the death positive movement in that they certainly represent an unusual take on attitudes and customs towards death. Seeing death as an engineering problem is rather different from how most people see it. Questioning the human condition is risky when dealing with fragile situations. And were transhumanism to be successful in some of its aims there may be new and confusing forms of death.

Existential risk in Gothenburg

This fall I have been chairing a programme at the Gothenburg Centre for Advanced Studies on existential risk, thanks to Olle Häggström. Visiting researchers come and participate in seminars and discussions on existential risk, ranging from the very theoretical (how do future people count?) to the very applied (should we put existential risk on the school curriculum? How?). I gave a Petrov Day talk about how to calculate risks of nuclear war and how observer selection might mess this up, beside seminars on everything from the Fermi paradox to differential technology development. In short, I have been very busy.

To open the programme we had a workshop on existential risk September 7-8 2017. Now we have the videos up of our talks:

Anders Sandberg: Tipping points, uncertainty and systemic risks: what to do when the whole is worse than its parts? (I was mistaken about my time allotment, so the talk runs at breakneck speed.)
Karin Kuhlemann: Complexity, creeping normalcy, and conceit: Why certain catastrophic risks are sexier than others
Phil Torres: Agential risks: Implications for existential risk reduction
Karim Jebari: Resetting the tape of history
Due to a technical mishap, we have no video for David Denkenberger‘s talk on Cost of non-sunlight dependent food for agricultural catastrophes. Try instead watching his talk Feeding everyone no matter what given at CSER in Cambridge last year, which covers much of the same ground.
Thore Husfeldt: Plausibility and utility of apocalyptic AI scenarios
Roman Yampolskiy: Artificial intelligence as an existential risk to humanity
Stuart Armstrong: Practical methods to make safe AI
Robin Hanson: Disasters in the Age of Em and after
Katja Grace: Empirical evidence on the future of AI
James Miller: Hints from the Fermi paradox for surviving existential risks
Catherine Rhodes: International governance of existential risk
Seth Baum: In search of the biggest risk reduction opportunities

I think so far a few key realisations and themes have in my opinion been

(1) the pronatalist/maximiser assumptions underlying some of the motivations for existential risk reduction were challenged; there is an interesting issue of how “modest futures” rather than “grand futures” play a role and non-maximising goals imply existential risk reduction.

(2) the importance of figuring out how “suffering risks”, potential states of astronomical amounts of suffering, relate to existential risks. Allocating effort between them rationally touches on some profound problems.

(3) The under-determination problem of inferring human values from observed behaviour (a talk by Stuart) resonated with the under-determination of AI goals in Olle’s critique of the convergent instrumental goal thesis and other discussions. Basically, complex agent-like systems might be harder to succinctly describe than we often think.

(4) Stability of complex adaptive systems – brains, economies, trajectories of human history, AI. Why are some systems so resilient in a reliable way, and can we copy it?

(5) The importance of estimating force projection abilities in space and as the limits of physics are approached. I am starting to suspect there is a deep physics answer to the question of attacker advantage, and a trade-off between information and energy in attacks.

We will produce an edited journal issue with papers inspired by our programme, stay tuned. Avancez!

Fractals and Steiner chains

I recently came across this nice animated gif of a fractal based on a Steiner chain, due to Eric Martin Willén. I immediately wanted to replicate it.

Make Steiner chains easily

First, how do you make a Steiner chain? It is easy using inversion geometry. Just decide on the number of circles tangent to the inner circle ( $n$ ). Then the ratio of the radii of the inner and outer circle will be $r/R = (1-\sin(\pi/n))/(1+\sin(\pi/n))$ . The radii of the circles in the ring will be $(R-r)/2$ and their centres are located at distance $(R+r)/2$ from the origin. This produces a staid concentric arrangement. Now invert with relation to an arbitrary circle: all the circles are mapped to other circles, their tangencies preserved. Voila! A suitably eccentric Steiner chain to play with.

Since the original concentric chain obviously can be rotated continuously without losing touch with the inner and outer circle, this also generates a continuous family of circles after the inversion. This is why Steiner’s porism is true: if you can make the initial chain, you get an infinite number of other chains with the same number of circles.

Iterated function systems with circle maps

The fractal works by putting copies of the whole set of circles in the chain into each circle, recursively. I remap the circles so that the outer circle becomes the unit circle, and then it is easy to see that for a given small circle with (complex) centre $z$ and radius $r$ the map $f(w)=(w+z)r$ maps the interior of the unit circle to it. Use the ease of rotating the original concentric ring to produce an animation, and we can reconstruct the fractal.

Done.

Except… it feels a bit dry.

Ever since I first encountered iterated function systems in the 1980s I have felt they tend towards a geometric aesthetics that is not me, ferns notwithstanding. A lot has to do with the linearity of the transformations. One can of course add rotations, which cheers up the fractal a bit.

But still, I love the nonlinearity and harmony of conformal mappings.

Inversion makes things better!

Enter the circle inversion fractals. They are the sets of the plane that map to themselves when being inverted in any and all of a set of generating circles (or, equivalently, the limit set of points under these inversions). As a rule of thumb, when the circles do not touch the fractal will be Cantor/Fatou-style fractal dust. When the circles are tangent the fractal will pass through the point of tangency. If three circles are tangent the fractal will contain a circle passing through these points. Since Steiner chains have lots of tangencies, we should get a lot of delicious fractals by using them as generators.

I use nearly the same code I used for the elliptic inversion fractals, mostly because I like the colours. The “real” fractal is hidden inside the nested circles, composed of an infinite Apollonian gasket of circles.

Note how the fractal extends outside the generators, forming a web of circles. Convergence is slow near tangent points, making it “fuzzy”. While it is easy to see the circles that belong to the invariant set that are empty, there are also circles going through the foci inside the coloured disks, touching the more obvious circles near those fuzzy tangent points. There is a lot going on here.

But we can complicate things by allowing the chain to slide and see how the fractal changes.

This is pretty neat.

Overcoming inertia

The tremendous accelerations involved in the kind of spaceflight seen on Star Trek would instantly turn the crew to chunky salsa unless there was some kind of heavy-duty protection. Hence, the inertial damping field.
— Star Trek: The Next Generation Technical Manual, page 24.

For a space opera RPG setting I am considering adding inertia manipulation technology. But can one make a self-consistent inertia dampener without breaking conservation laws? What are the physical consequences? How many cool explosions, superweapons, and other tropes can we squeeze out of it? How to avoid the worst problems brought up by the SF community?

What inertia is

As Newton put it, inertia is the resistance of an object to a change in its state of motion. Newton’s force law $F=ma$ is a consequence of the definition of momentum, $p=mv$ (which in a way is more fundamental since it directly ties in with conservation laws). The mass in the formula is the inertial mass. Mass is a measure of how much there is of matter, and we normally multiply it with a hidden constant of 1 to get the inertial mass – this constant is what we will want to mess with.

There are relativistic versions of the laws of motion that handles momentum and inertia for high velocities, where the kinetic energy becomes so large that it starts to add mass to the whole system. This makes the total inertia go up, as seen by an outside observer, and looks like a nice case for inertia-manipulating tech being vaguely possible.

However, Einstein threw a spanner into this: gravity also acts on mass and conveniently does so exactly as much as inertia: gravitational mass (the masses in $F=Gm_1m_2/r^2$ ) and inertial mass appear to be equal. At least in my old school physics textbook (early 1980s!) this was presented as a cool unsolved mystery, but it is a consequence of the equivalence principle in general relativity (1907): all test particles accelerate the same way in a gravitational field, and this is only possible if their gravitational mass and inertial mass are proportional to one another.

So, an inertia manipulation technology will have to imply some form of gravity manipulation technology. Which may be fine from my standpoint, since what space opera is complete without antigravity? (In fact, I already had decided to have Alcubierre warp bubble FTL anyway, so gravity manipulation is in.)

Playing with inertia

OK, let’s leave relativity to the side for the time being and just consider the classical mechanics of inertia manipulation. Let us posit that there is a magical field that allows us to dial up or down the proportionality constant for inertial mass: the momentum of a particle will be $p=\mu m v$ , the force law $F=\mu m a$ and the formula for kinetic energy $K=(1/2) \mu m v^2$ . $\mu$ is the effect of the magic field, running from $0<\mu<\infty$ , with 1 corresponding to it being absent.

I throw a 1 g ping-pong ball at 1 m/s into my inertics device and turn on the field. What happens? Let us assume the field is $\mu=1000$ . Now the momentum and kinetic energy jumps by a factor of 1000 if the velocity remains unchanged. Were I to catch the ball I would have gained 999 times its original kinetic energy: this looks like an excellent perpetual motion machine. Since we do not want that to be possible (a space empire powered by throwing ping-pong balls sounds silly) we must demand that energy is conserved.

Velocity shifting to preserve kinetic energy

One way of doing energy conservation is for the velocity to go down for my heavy ping-pong ball. This means that the new velocity will be $v/\sqrt{\mu}$ . Inertia-increasing fields slow down objects, while inertia-decreasing fields speed them up.

Forcefields/armour

One could have a force-field made of super-high inertia that would slow down incoming projectiles. At first this seems pointless, since once they get through to the other side they speed up and will do the same damage. But we could of course put in a bunch of armour in this field, and have it resist the projectile. The kinetic energy will be the same but it will be a lower velocity collision which means that the strength of the armour has a better chance of stopping it (in fact, as we will see below, we can use superdense armour here too). Consider the difference between being shot with a rifle bullet or being slowly but strongly stabbed by it: in the later case the force can be distributed by a good armour to a vast surface. Definitely a good thing for a space opera.

Spacecraft

A spacecraft that wants to get somewhere fast could just project a low $\mu$ field around itself and boost its speed by a huge $1/\sqrt{\mu}$ factor. Sounds very useful. But now an impacting meteorite will both have an high relative speed, and when it enters the field get that boosted by the same factor again: impacts will happen at velocities increased by a factor of $1/\mu$ as measured by the ship. So boosting your speed with a factor of a 1000 will give you dust hitting you at speeds a million times higher. Since typical interplanetary dust already moves a few km/s, we are talking about hyperrelativistic impactors. The armour above sounds like a good thing to have…

Note that any inertia-reducing technology is going to improve rockets even if there is no reactionless drive or other shenanigans: you just reduce the inertia of the reaction mass. The rocket equation no longer bites: sure, your ship is mostly massive reaction mass in storage, but to accelerate the ship you just take a measure of that mass, restore its inertia, expel it, and enjoy the huge acceleration as the big engine pushes the overall very low-inertia ship. There is just a snag in this particular case: when restoring the inertia you somehow need to give the mass enough kinetic energy to be at rest in relation to the ship…

Cannons

This kind of inertics does not make for a great cannon. I can certainly make my projectile speed up a lot in the bore by lowering its inertia, but as soon as it leaves it will slow down. If we assume a given amount of force $F$ accelerating it along the length $L$ bore, it will pick up $FL$ Joules of kinetic energy from the work the cannon does – independent of mass or inertia! The difference may be power: if you can only supply a certain energy per second like in a coilgun, having a slower projectile in the bore is better.

Physics

Note that entering and leaving an inertics field will induce stresses. A metal rod entering an inertia-increasing field will have the part in the field moving more slowly, pushing back against the not slowed part (yet another plus for the armour!). When leaving the field the lighter part outside will pull away strongly.

Another effect of shifting velocities is that gases behave differently. At first it looks like changing speeds would change temperature (since we tend to think of the temperature of a gas as how fast the molecules are bouncing around), but actually the kinetic temperature of a gas depends on (you guessed it) the average kinetic energy. So that doesn’t change at all. However, the speed of sound should scale as $\propto 1/\sqrt{\mu}$ : it becomes far higher in the inertia-dampening field, producing helium-voice like effects. Air molecules inside an inertia-decreasing field would tend to leave more quickly than outside air would enter, producing a pressure difference.

Momentum conservation is a headache

Changing the velocity so that energy is conserved unfortunately has a drawback: momentum is not conserved! I throw a heavy object at my inertics machine at velocity $v$ , momentum $mv$ and energy $(1/2)mv^2$ , it reduces is inertia and increases the speed to $v/\sqrt{\mu}$ , keeps the kinetic energy at $(1/2)mv^2$ , and the momentum is now $mv/\sqrt{\mu}$ .

What if we assume the momentum change comes from the field or machine? When I hit the mass $M$ machine with an object it experiences a force enough to change its velocity by $w=mv(1-1/\sqrt{\mu})/M$ . When set to increase inertia it is pushed back a bit, potentially moving up to speed $(m/M)v$ . When set to decrease inertia it is pushed forward, starting to move towards the direction the object impacted from. In fact, it can get arbitrarily large velocities by reducing $\mu$ close to 0.

This sounds odd. Demanding momentum and energy conservation requires $mv = mv/\sqrt{\mu} + Mw$ (giving the above formula) and $mv^2 = \mu m(v/\sqrt{\mu})^2 + Mw^2$ , which insists that $w=0$ . Clearly we cannot have both.

I don’t know about you, but I’d rather keep energy conserved. It is more obvious when you cheat about energy conservation.

Still, as Einstein pointed out using 4-vectors, momentum and energy conservation are deeply entangled – one reason inertics isn’t terribly likely in the real world is that they cannot be separated. We could of course try to conserve 4-momentum ( $(E/c,\gamma \mu m v_x, \gamma \mu m v_y, \gamma \mu m v_z)$ ), which would look like changing both energy and normal momentum at the same time.

Energy gain/loss to preserve momentum

What about just retaining the normal momentum rather than the kinetic energy? The new velocity would be $v/\mu$ , the new kinetic energy would be $K_1=(1/2) \mu m (v/\mu)^2 = (1/2) mv^2 / \mu = K_0/\mu$ . Just like in the kinetic energy preserving case the object slows down (or speeds up), but more strongly. And there is an energy debt of $K_0 (1-1/\mu)$ that needs to be fixed.

One way of resolving energy conservation is to demand that the change in energy is supplied by the inertia-manipulation device. My ping-pong ball does not change momentum, but requires 0.999 Joule to gain the new kinetic energy. The device has to provide that. When the ball leaves the field there will be a surge of energy the device needs to absorb back. Some nice potential here for things blowing up in dramatic ways, a requirement for any self-respecting space opera.

Spacecraft

If I want to accelerate my spaceship in this setting, I would point my momentum vector towards the target, reduce my inertia a lot, and then have to provide a lot of kinetic energy from my inertics devices and power supply (actually, store a lot – the energy is a surplus). At first this sounds like it is just as bad as normal rocketry, but in fact it is awesome: I can convert my electricity directly into velocity without having to lug around a lot of reaction mass! I will even get it back when slowing down, a bit like electric brake regeneration systems. The rocket equation does not apply beyond getting some initial momentum. In fact, the less velocity I have from the start, the better.

At least in this scheme inertia-reduced reaction mass can be restored to full inertia within the conceptual framework of energy addition/subtraction.

One drawback is that now when I run into interplanetary dust it will drain my batteries as the inertics system needs to give it a lot of kinetic energy (which will then go on harming me!)

Another big problem (pointed out by Erik Max Francis) is that turning energy into kinetic energy gives an energy requirement $latex dK/dt=mva$, which depends on an absolute speed. This requires a privileged reference frame, throwing out relativity theory. Oops (but not unexpected).