# Settling Titan, Schneier’s Law, and scenario thinking

Charles Wohlforth and Amanda R. Hendrix want us to colonize Titan. The essay irritated me in an interesting manner.

Full disclosure: they interviewed me while they were writing their book Beyond Earth: Our Path to a New Home in the Planets, which I have not read yet, and I will only be basing the following on the SciAm essay. It is not really about settling Titan either, but something that bothers me with a lot of scenario-making.

# A weak case for Titan and against Luna and Mars

Basically the essay outlines reasons why other locations in the solar system are not good: Mercury too hot, Venus way too hot, Mars and Luna have too much radiation. Only Titan remains, with a cold environment but not too much radiation.

A lot of course hinges on the assumptions:

We expect human nature to stay the same. Human beings of the future will have the same drives and needs we have now. Practically speaking, their home must have abundant energy, livable temperatures and protection from the rigors of space, including cosmic radiation, which new research suggests is unavoidably dangerous for biological beings like us.

I am not that confident in that we will remain biological or vulnerable to radiation. But even if we decide to accept the assumptions, the case against the Moon and Mars is odd:

Practically, a Moon or Mars settlement would have to be built underground to be safe from this radiation.Underground shelter is hard to build and not flexible or easy to expand. Settlers would need enormous excavations for room to supply all their needs for food, manufacturing and daily life.

So making underground shelters is much harder than settling Titan, where buildings need to be isolated against a -179 C atmosphere and ice ground full with complex and quite likely toxic hydrocarbons. They suggest that there is no point in going to the moon to live in an underground shelter when you can do it on Earth, which is not too unreasonable – but is there a point in going to live inside an insulated environment on Titan either? The actual motivations would likely be less of a desire for outdoor activities and more scientific exploration, reducing existential risk, and maybe industrialization.

Also, while making underground shelters in space may be hard, it does not look like an insurmountable problem. The whole concern is a bit like saying submarines are not practical because the cold of the depths of the ocean will give the crew hypothermia – true, unless you add heating.

I think this is similar to Schneier’s law:

Anyone, from the most clueless amateur to the best cryptographer, can create an algorithm that he himself can’t break.

It is not hard to find a major problem with a possible plan that you cannot see a reasonable way around. That doesn’t mean there isn’t one.

# Settling for scenarios

Maybe Wohlforth and Hendrix spent a lot of time thinking about lunar excavation issues and consistent motivations for settlements to reach a really solid conclusion, but I suspect that they came to the conclusion relatively lightly. It produces an interesting scenario: Titan is not the standard target when we discuss where humanity ought to go, and it is an awesome environment.

Similarly the “humans will be humans” scenario assumptions were presumably chosen not after a careful analysis of relative likelihood of biological and postbiological futures, but just because it is similar to the past and makes an interesting scenario. Plus human readers like reading about humans rather than robots. All together it makes for a good book.

Clearly I have different priors compared to them on the ease and rationality of Lunar/Martian excavation and postbiology. Or even giving us D. radiodurans genes.

In The Age of Em Robin Hanson argues that if we get the brain emulation scenario space settlement will be delayed until things get really weird: while postbiological astronauts are very adaptable, so much of the mainstream of civilization will be turning inward towards a few dense centers (for economics and communications reasons). Eventually resource demand, curiosity or just whatever comes after the Age of Ems may lead to settling the solar system. But that process will be pretty different even if it is done by mentally human-like beings that do need energy and protection. Their ideal environments would be energy-gradient rich, with short communications lags: Mercury, slowly getting disassembled into a hot Dyson shell, might be ideal. So here the story will be no settlement, and then wildly exotic settlement that doesn’t care much about the scenery.

But even with biological humans we can imagine radically different space settlement scenarios, such as the Gerhard O’Neill scenario where planetary surfaces are largely sidestepped for asteroids and space habitats. This is Jeff Bezo’s vision rather than Elon Musk’s and Wohlforth/Hendrix’s. It also doesn’t tell the same kind of story: here our new home is not in the planets but between them.

My gripe is not against settling Titan, or even thinking it is the best target because of some reasons. It is against settling too easily for nice scenarios.

# Beyond the good story

Sometimes we settle for scenarios because they tell a good story. Sometimes because they are amenable to study among other, much less analyzable possibilities. But ideally we should aim at scenarios that inform us in a useful way about options and pathways we have.

That includes making assumptions wide enough to cover relevant options, even the less glamorous or tractable ones.

That requires assuming future people will be just as capable (or more) at solving problems: just because I can’t see a solution to X doesn’t mean it is not trivially solved in the future.

(Maybe we could call it the “Manure Principle” after the canonical example of horse manure being seen as a insoluble urban planning problem at the previous turn of century and then neatly getting resolved by unpredicted trams and cars – and just like Schneier’s law and Stigler’s law the reality is of course more complex than the story.)

In standard scenario literature there are often admonitions not just to select a “best case scenario”, “worst case scenario” and “business as usual scenario” – scenario planning comes into its own when you see nontrivial, mixed value possibilities. In particular, we want decision-relevant scenarios that make us change what we will do when we hear about them (rather than good stories, which entertain but do not change our actions). But scenarios on their own do not tell us how to make these decisions: they need to be built from our rationality and decision theory applied to their contents. Easy scenarios make it trivial to choose (cake or death?), but those choices would have been obvious even without the scenarios: no forethought needed except to bring up the question. Complex scenarios force us to think in new ways about relevant trade-offs.

The likelihood of complex scenarios is of course lower than simple scenarios (the conjunction fallacy makes us believe much more in rich stories). But if they are seen as tools for developing decisions rather than information about the future, then their individual probability is less of an issue.

In the end, good stories are lovely and worth having, but for thinking and deciding carefully we should not settle for just good stories or the scenarios that feel neat.

# The case for Mars

On practical Ethics I post about the goodness of being multi-planetary: is it rational to try to settle Mars as a hedge against existential risk?

The problem is not that it is absurd to care about existential risks or the far future (which was the Economist‘s unfortunate claim), nor that it is morally wrong to have a separate colony, but that there might be better risk reduction strategies with more bang for the buck.

One interesting aspect is that making space more accessible makes space refuges a better option. At some point in the future, even if space refuges are currently not the best choice, they may well become that. There are of course other reasons to do this too (science, business, even technological art).

So while existential risk mitigation right now might rationally aim at putting out the current brushfires and trying to set the long-term strategy right, doing the groundwork for eventual space colonisation seems to be rational.

# The Drake equation and correlations

I have been working on the Fermi paradox for a while, and in particular the mathematical structure of the Drake equation. While it looks innocent, it has some surprising issues.

$N\approx N_* f_p n_e f_l f_i f_c L$

One area I have not seen much addressed is the independence of terms. To a first approximation they were made up to be independent: the fraction of life-bearing Earth-like planets is presumably determined by a very different process than the fraction of planets that are Earth-like, and these factors should have little to do with the longevity of civilizations. But as Häggström and Verendel showed, even a bit of correlation can cause trouble.

If different factors in the Drake equation vary spatially or temporally, we should expect potential clustering of civilizations: the average density may be low, but in areas where the parameters have larger values there would be a higher density of civilizations. A low $N$ may not be the whole story. Hence figuring out the typical size of patches (i.e. the autocorrelation distance) may tell us something relevant.

## Astrophysical correlations

There is a sometimes overlooked spatial correlation in the first terms. In the orthodox formulation we are talking about earth-like planets orbiting stars with planets, which form at some rate in the Milky Way. This means that civilizations must be located in places where there are stars (galaxies), and not anywhere else. The rare earth crowd also argues that there is a spatial structure that makes earth-like worlds exist within a ring-shaped region in the galaxy. This implies an autocorrelation on the order of (tens of) kiloparsecs.

Even if we want to get away from planetocentrism there will be inhomogeneity. The warm intergalactic plasma contains 0.04 of the total mass of the universe, or 85% of the non-dark stuff. Planets account for just 0.00002%, and terrestrials obviously far less. Since condensed things like planets, stars or even galaxy cluster plasma is distributed in a inhomogeneous manner, unless the other factors in the Drake equation produce typical distances between civilizations beyond the End of Greatness scale of hundreds of megaparsec, we should expect a spatially correlated structure of intelligent life following galaxies, clusters and filiaments.

A tangent: different kinds of matter plausibly have different likelihood of originating life. Note that this has an interesting implication: if the probability of life emerging in something like the intergalactic plasma is non-zero, it has to be more than a hundred thousand times smaller than the probability per unit mass of planets, or the universe would be dominated by gas-creatures (and we would be unlikely observers, unless gas-life was unlikely to generate intelligence). Similarly life must be more than 2,000 times more likely on planets than stars (per unit of mass), or we should expect ourselves to be star-dwellers. Our planetary existence does give us some reason to think life or intelligence in the more common substrates (plasma, degenerate matter, neutronium) is significantly less likely than molecular matter.

## Biological correlations

One way of inducing correlations in the $f_l$ factor is panspermia. If life originates at some low rate per unit volume of space (we will now assume a spatially homogeneous universe in terms of places life can originate) and then diffuses from a nucleation site, then intelligence will show up in spatially correlated locations.

It is not clear how much panspermia could be going on, or if all kinds of life do it. A simple model is that panspermias emerge at a density $\rho$ and grow to radius $r$. The rate of intelligence emergence outside panspermias is set to 1 per unit volume (this sets a space scale), and inside a panspermia (since there is more life) it will be $A>1$ per unit volume. The probability that a given point will be outside a panspermia is

$P_{outside} = e^{-(4\pi/3) r^3 \rho}$.

The fraction of civilizations finding themselves outside panspermias will be

$F_{outside} = \frac{P_{outside}}{P_{outside}+A(1-P_{outside})} = \frac{1}{1+A(e^{(4 \pi/3)r^3 \rho}-1)}$.

As A increases, vastly more observers will be in panspermias. If we think it is large, we should expect to be in a panspermia unless we think the panspermia efficiency (and hence r) is very small. Loosely, the transition from going from 1% to 99% probability takes one order of magnitude change in r, three orders of magnitude in $\rho$ and four in A: given that these parameters can a priori range over many, many orders of magnitude, we should not expect to be in the mixed region where there are comparable numbers of observers inside panspermias and outside. It is more likely all or nothing.

There is another relevant distance beside $r$, the expected distance to the next civilization. This is $d \approx 0.55/\sqrt[3]{\lambda}$ where $\lambda$ is the density of civilizations. For the outside panspermia case this is $d_{outside}=0.55$, while inside it is $d_{inside}=0.55/\sqrt[3]{A}$. Note that these distances are not dependent on the panspermia sizes, since they come from an independent process (emergence of intelligence given a life-bearing planet rather than how well life spreads from system to system).

If $r then there will be no panspermia-induced correlation between civilization locations, since there is less than one civilization per panspermia. For $d_{inside} < r < d_{outside}$ there will be clustering with a typical autocorrelation distance corresponding to the panspermia size. For even larger panspermias they tend to dominate space (if $\rho$ is not very small) and there is no spatial structure any more.

So if panspermias have sizes in a certain range, $0.55/\sqrt[3]{A}, the actual distance to the nearest neighbour will be smaller than what one would have predicted from the average values of the parameters of the drake equation.

Running a Monte Carlo simulation shows this effect. Here I use 10,000 possible life sites in a cubical volume, and $\rho=1$ – the number of panspermias will be Poisson(1) distributed. The background rate of civilizations appearing is 1/10,000, but in panspermias it is 1/100. As I make panspermias larger civilizations become more common and the median distance from a civilization to the next closest civilization falls (blue stars). If I re-sample so the number of civilizations are the same but their locations are uncorrelated I get the red crosses: the distances decline, but they can be more than a factor of 2 larger.

## Technological correlations

The technological terms $f_c$ and $L$ can also show spatial patterns, if civilizations spread out from their origin.

The basic colonization argument by Hart and Tipler assumes a civilization will quickly spread out to fill the galaxy; at this point $N\approx 10^{10}$ if we count inhabited systems. If we include intergalactic colonization, then in due time, everything out to a radius of reachability on the order of 4 gigaparsec (for near c probes) and 1.24 gigaparsec (for 50% c probes). Within this domain it is plausible that the civilization could maintain whatever spatio-temporal correlations it wishes, from perfect homogeneity over the zoo hypothesis to arbitrary complexity. However, the reachability limit is due to physics and do impose a pretty powerful limit: any correlation in the Drake equation due to a cause at some point in space-time will be smaller than the reachability horizon (as measured in comoving coordinates) for that point.

Total colonization is still compatible with an empty galaxy if $L$ is short enough. Galaxies could be dominated by a sequence of “empires” that disappear after some time, and if the product between empire emergence rate $\lambda$ and $L$ is small enough most eras will be empty.

A related model is Brin’s resource exhaustion model, where civilizations spread at some velocity but also deplete their environment at some (random rate). The result is a spreading shell with an empty interior. This has some similarities to Hanson’s “burning the cosmic commons scenario”, although Brin is mostly thinking in terms of planetary ecology and Hanson in terms of any available resources: the Hanson scenario may be a single-shot situation. In Brin’s model “nursery worlds” eventually recover and may produce another wave. The width of the wave is proportional to $Lv$ where $v$ is the expansion speed; if there is a recovery parameter $R$ corresponding to the time before new waves can emerge we should hence expect spatial correlation length of order $(L+R)v$. For light-speed expansion and a megayear recovery (typical ecology and fast evolutionary timescale) we would get a length of a million light-years.

Another approach is the percolation theory inspired models first originated by Landis. Here civilizations spread short distances, and “barren” offshoots that do not colonize form a random “bark” around the network of colonization (or civilizations are limited to flights shorter than some distance). If the percolation parameter $p$ is low, civilizations will only spread to a small nearby region. When it increases larger and larger networks are colonized (forming a fractal structure), until a critical parameter value $p_c$ where the network explodes and reaches nearly anywhere. However, even above this transition there are voids of uncolonized worlds. The correlation length famously scales as $\xi \propto|p-p_c|^\nu$, where $\nu \approx -0.89$ for this case. The probability of a random site belonging to the infinite cluster for $p>p_c$ scales as $P(p) \propto |p-p_c|^\beta$ ($\beta \approx 0.472$) and the mean cluster size (excluding the infinite cluster) scales as $\propto |p-p_c|^\gamma$ ($\gamma \approx -1.725$).

So in this group of models, if the probability of a site producing a civilization is $\lambda$ the probability of encountering another civilization in one’s cluster is

$Q(p) = 1-(1-\lambda)^{N|p-p_c|^\gamma}$

for $p. Above the threshold it is essentially 1; there is a small probability $1-P(p)$ of being inside a small cluster, but it tends to be minuscule. Given the silence in the sky, were a percolation model the situation we should conclude either an extremely low $\lambda$ or a low $p$.

## Temporal correlations

Another way the Drake equation can become misleading is if the parameters are time varying. Most obviously, the star formation rate has changed over time. The metallicity of stars have changed, and we should expect any galactic life zones to shift due to this.

One interesting model due to James Annis and Milan Cirkovic is that the rate of gamma ray bursts and other energetic disasters made complex life unlikely in the past, but now the rate has declined enough that it can start the climb towards intelligence – and it was synchronized by this shared background. Such disasters can also produce spatial coherency, although it is very noisy.

In my opinion the most important temporal issue is inherent in the Drake equation itself. It assumes a steady state! At the left we get new stars arriving at a rate $N_*$, and at the right the rate gets multiplied by the longevity term for civilizations $L$, producing a dimensionless number. Technically we can plug in a trillion years for the longevity term and get something that looks like a real estimate of a teeming galaxy, but this actually breaks the model assumptions. If civilizations survived for trillions of years, the number of civilizations would currently be increasing linearly (from zero at the time of the formation of the galaxy) – none would have gone extinct yet. Hence we can know that in order to use the unmodified Drake equation $L$ has to be $< 10^{10}$ years.

Making a temporal Drake equation is not impossible. A simple variant would be something like

$\frac{dN(t)}{dt}=N_*(t)f_p(t)n_e(t)f_l(t)f_i(t)f_c(t)-(1/L)N$

where the first term is just the factors of the vanilla equation regarded as time-varying functions and the second term a decay corresponding to civilizations dropping out at a rate of 1/L (this assumes exponentially distributed survival, a potentially doubtful assumption). The steady state corresponds to the standard Drake level, and is approached with a time constant of 1/L.  One nice thing with this equation is that given a particular civilization birth rate $\beta(t)$ corresponding to the first term, we get an expression for the current state:

$N(t_{now}) = \int_{t_{bigbang}}^{t_{now}} \beta(t) e^{-(1/L) (t_{now}-t)} dt$.

Note how any spike in $\beta(t)$ gets smoothed by the exponential, which sets the temporal correlation length.

If we want to do things even more carefully, we can have several coupled equations corresponding to star formation, planet formation, life formation, biosphere survival, and intelligence emergence. However, at this point we will likely want to make a proper “demographic” model that assumes stars, biospheres and civilization have particular lifetimes rather than random disappearance. At this point it becomes possible to include civilizations with different L, like Sagan’s proposal that the majority of civilizations have short L but some have very long futures.

The overall effect is still a set of correlation timescales set by astrophysics (star and planet formation rates), biology (life emergence and evolution timescales, possibly the appearance of panspermias), and civilization timescales (emergence, spread and decay). The overall effect is dominated by the slowest timescale (presumably star formation or very long-lasting civilizations).

## Conclusions

Overall, the independence of the terms of the Drake equation is likely fairly strong. However, there are relevant size scales to consider.

• Over multiple gigaparsec scales there can not be any correlations, not even artificially induced ones, because of limitations due to the expansion of the universe (unless there are super-early or FTL civilizations).
• Over hundreds of megaparsec scales the universe is fairly uniform, so any natural influences will be randomized beyond this scale.
• Colonization waves in Brin’s model could have scales on the galactic cluster scale, but this is somewhat parameter dependent.
• The nearest civilization can be expected around $d \approx 0.55 [N_* f_p n_e f_l f_i f_c L / V]^{-1/3}$, where $V$ is the galactic volume. If we are considering parameters such that the number of civilizations per galaxy are low V needs to be increased and the density will go down significantly (by a factor of about 100), leading to a modest jump in expected distance.
• Panspermias, if they exist, will have an upper extent limited by escape from galaxies – they will tend to have galactic scales or smaller. The same is true for galactic habitable zones if they exist. Percolation colonization models are limited to galaxies (or even dense parts of galaxies) and would hence have scales in the kiloparsec range.
• “Scars” due to gamma ray bursts and other energetic events are below kiloparsecs.
• The lower limit of panspermias are due to $d$ being smaller than the panspermia, presumably at least in the parsec range. This is also the scale of close clusters of stars in percolation models.
• Time-wise, the temporal correlation length is likely on the gigayear timescale, dominated by stellar processes or advanced civilization survival. The exception may be colonization waves modifying conditions radically.

In the end, none of these factors appear to cause massive correlations in the Drake equation. Personally, I would guess the most likely cause of an observed strong correlation between different terms would be artificial: a space-faring civilization changing the universe in some way (seeding life, wiping out competitors, converting it to something better…)

# What is the natural timescale for making a Dyson shell?

KIC 8462852 (“Tabby’s Star”) continues to confuse. I blogged earlier about why I doubt it is a Dyson sphere. SETI observations in radio and optical has not produced any finds. Now there is evidence that it has dimmed over a century timespan, something hard to square with the comet explanation. Phil Plait over at Bad Astronomy has a nice overview of the headscratching.

However, he said something that I strongly disagree with:

Now, again, let me be clear. I am NOT saying aliens here. But, I’d be remiss if I didn’t note that this general fading is sort of what you’d expect if aliens were building a Dyson swarm. As they construct more of the panels orbiting the star, they block more of its light bit by bit, so a distant observer sees the star fade over time.

However, this doesn’t work well either. … Also, blocking that much of the star over a century would mean they’d have to be cranking out solar panels.

Basically, he is saying that a century timescale construction of a Dyson shell is unlikely. Now, since I have argued that we could make a Dyson shell in about 40 years, I disagree. I got into a Twitter debate with Karim Jebari (@KarimJebari) about this, where he also doubted what the natural timescale for Dyson construction is. So here is a slightly longer than Twitter message exposition of my model.

# Lower bound

There is a strict lower bound set by how long it takes for the star to produce enough energy to overcome the binding energy of the source bodies (assuming one already have more than enough collector area). This is on the order of days for terrestrial planets, as per Robert Bradbury’s original calculations.

# Basic model

Starting with a small system that builds more copies of itself, solar collectors and mining equipment, one can get exponential growth.

A simple way of reasoning: if you have an area $A(t)$ of solar collectors, you will have energy $kA(t)$ to play with, where $k$ is the energy collected per square meter. This will be used to lift and transform matter into more collectors. If we assume this takes $x$ Joules per square meter on average, we get $A'(t) = (k/x)A(t)$, which makes $A(t)$ is an exponential function with time constant $k/x$. If a finished Dyson shell has area $A_D\approx 2.8\cdot 10^{23}$ meters and we start with an initial plant of size $A(0)$ (say on the order of a few hundred square meters), then the total time to completion is $t = (x/k)\ln(A_D/A(0))$ seconds. The logarithmic factor is about 50.

If we assume $k \approx 3\cdot 10^2$ W and $x \approx 40.15$ MJ/kg (see numerics below), then t=78 days.

This is very much in line with Robert’s original calculations. He pointed out that given the sun’s power output Earth could be theoretically disassembled in 22 days. In the above calculations  the time constant (the time it takes to get 2.7 times as much area) is 37 hours. So for most of the 78 days there is just a small system expanding, not making a significant dent in the planet nor being very visible over interstellar distances; only in the later part of the period will it start to have radical impact.

The timescale is robust to the above assumptions: sun-like main sequence stars have luminosities within an order of magnitude of the sun (so $k$ can only change a factor of 10), using asteroid material (no gravitational binding cost) brings down $x$ by a factor of 10; if the material needs to be vaporized $x$ increases by less than a factor of 10; if a sizeable fraction of the matter is needed for mining/transport/building systems $x$ goes down proportionally; much thinner shells (see below) may give three orders of magnitude smaller $x$ (and hence bump into the hard bound above). So the conclusion is that for this model the natural timescale of terrestrial planetary disassembly into Dyson shells is on the order of months.

Digging into the practicalities of course shows that there are some other issues. Material needs to be transported into place (natural timescale about a year for a moving something 1 AU), the heating effects are going to be major on the planet being disassembled (lots of energy flow there, but of course just boiling it into space and capturing the condensing dust is a pretty good lifting method), the time it takes to convert 1 kg of undifferentiated matter into something useful places a limit of the mass flow per converting device, and so on. This is why our conservative estimate was 40 years for a Mercury-based shell: we assumed a pretty slow transport system.

## Numerical values

Estimate for $x$: assuming that each square meter shell has mass 1 kg, that the energy cost comes from the mean gravitational binding energy of Earth per kg of mass (37.5 MJ/kg), plus processing energy (on the order of 2.65 MJ/kg for heating and melting silicon). Note that using Earth slows things significantly.

I had a conversation with Eric Drexler today, where he pointed out that assuming 1 kg/square meter for the shell is arbitrary. There is a particular area density that is special: given that solar gravity and light pressure both decline with the square of the distance, there exists a particular density $\rho=E/(4 \pi c G M_{sun})\approx 0.78$ gram per square meter, which will just hang there neutrally. Heavier shells will need to orbit to remain where they are, lighter shells need cables or extra weight to not blow away. This might hence be a natural density for shells, making $x$ a factor 1282 smaller.

# Linear growth does not work

I think the key implicit assumption in Plait’s thought above is that he imagines some kind of alien factory churning out shell. If it produces it at a constant rate $A'$, then the time until it a has produced a finished Dyson shell with area $A_D\approx 2.8\cdot 10^{23}$ square meters. That will take $A_D/A'$ seconds.

Current solar cell factories produce on the order of a few hundred MW of solar cells per year; assuming each makes about 2 million square meters per year, we need 140 million billion years. Making a million factories merely brings things down to 140 billion years. To get a century scale dimming time, $A' \approx 8.9\cdot 10^{13}$ square meters per second, about the area of the Atlantic ocean.

This feels absurd. Which is no good reason for discounting the possibility.

# Automation makes the absurd normal

As we argued in our paper, the key assumptions are (1) things we can do can be automated, so that if there are more machines doing it (or doing it faster) there will be more done. (2) we have historically been good at doing things already occurring in nature. (3) self-replication and autonomous action occurs in nature. 2+3 suggests exponentially growing technologies are possible where a myriad entities work in parallel, and 1 suggests that this allows functions such as manufacturing to be scaled up as far as the growth goes. As Kardashev pointed out, there is no reason to think there is any particular size scale for the activities of a civilization except as set by resources and communication.

Incidentally, automation is also why cost overruns or lack of will may not matter so much for this kind of megascale projects. The reason Intel and AMD can reliably make billions of processors containing billions of transistors each is that everything is automated. Making the blueprint and fab pipeline is highly complex and requires an impressive degree of skill (this is where most overruns and delays happen), but once it is done production can just go on indefinitely. The same thing is true of Dyson-making replicators. The first one may be a tough problem that takes time to achieve, but once it is up and running it is autonomous and merely requires some degree of watching (make sure it only picks apart the planets you don’t want!) There is no requirement of continued interest in its operations to keep them going.

# Likely growth rates

But is exponential growth limited mostly by energy the natural growth rate? As Karim and others have suggested, maybe the aliens are lazy or taking their time? Or, conversely, that multi century projects are unexpectedly long-term and hence rare.

Obviously projects could occur with any possible speed: if something can construct something in time X, it can in generally be done half as fast. And if you can construct something of size X, you can do half of it. But not every speed or boundary is natural. We do not answer the question of why a forest or the Great Barrier reef have the size they do by cost overruns stopping them, or that they will eventually grow to arbitrary size, but the growth rate is so small that it is imperceptible. The spread of a wildfire is largely set by physical factors, and a static wildfire will soon approach its maximum allowed speed since part of the fire that do not spread will be overtaken by parts that do. The same is true for species colonizing new ecological niches or businesses finding new markets. They can run slow, it is just that typically they seem to move as fast as they can.

Human economic growth has been on the order of 2% per year for very long historical periods. That implies a time constant $\ln(1.02)\approx 50$ years. This is a “stylized fact” that remained roughly true despite very different technologies, cultures, attempts at boosting it, etc. It seems to be “natural” for human economies. So were a Dyson shell built as a part of a human economy, we might expect it to be completed in 250 years.

What about biological reproduction rates? Merkle and Freitas lists the replication time for various organisms and machines. They cover almost 25 orders of magnitude, but seem to roughly scale as $\tau \approx c M^{1/4}$, where $M$ is the mass and $c\approx 10^7$. So if a total mass $M_T$ needs to be converted into replicators of mass $M$, it will take time $t=\tau\ln(M_T)/\ln(2)$. Plugging in the first formula gives $t=c M^{1/4} \ln(M_T)/\ln(2)$. The smallest independent replicators have $M_s=10^{-15} kg$ (this gives $\tau_s=10^{3.25}=29$ minutes) while a big factory-like replicator (or a tree!) would have $M_b=10^5$ ($\tau_b=10^{8.25}=5.6$ years). In turn, if we set $M_T=A_D\rho=2.18\cdot 10^{20}$ (a “light” Dyson shell) the time till construction ranges from 32 hours for the tiny to 378 years for the heavy replicator. Setting $M_T$ to an Earth mass gives a range from 36 hours to 408 years.

The lower end is infeasible, since this model assumes enough input material and energy – the explosive growth of bacteria-like replicators is not possible if there is not enough energy to lift matter out of gravity wells. But it is telling that the upper end of the range is merely multi-century. This makes a century dimming actually reasonable if we think we are seeing the last stages (remember, most of the construction time the star will be looking totally normal); however, as I argued in my previous post, the likelihood of seeing this period in a random star being englobed is rather low. So if you want to claim it takes millennia or more to build a Dyson shell, you need to assume replicators that are very large and heavy.

[Also note that some of the technological systems discussed in Merkle & Freitas are significantly faster than the main branch. Also, this discussion has talked about general replicators able to make all their parts: if subsystems specialize they can become significantly faster than more general constructors. Hence we have reason to think that the upper end is conservative.]

# Conclusion

There is a lower limit on how fast a Dyson shell can be built, which is likely on the order of hours for manufacturing and a year of dispersion. Replicator sizes smaller than a hundred tons imply a construction time at most a few centuries. This range includes the effect of existing biological and economic growth rates. We hence have a good reason to think most Dyson construction is fast compared to astronomical time, and that catching a star being englobed is pretty unlikely.

I think that models involving slowly growing Dyson spheres require more motivation than models where they are closer to the limits of growth.

# Messages on plaques and disks

Representing ourselves

If we wanted to represent humanity most honestly to aliens, we would just give them a constantly updated full documentation of our cultures and knowledge. But that is not possible.

So in METI we may consider sending “a copy of the internet” as a massive snapshot of what we currently are, or as the Voyager recording did, send a sample of what we are. In both cases it is a snapshot at a particular time: had we sent the message at some other time, the contents would have been different. The selection used is also a powerful shaper, with what is chosen as representative telling a particular story.

That we send a snapshot is not just a necessity, it may be a virtue. The full representation of what humanity is, is not so much a message as a gift with potentially tricky moral implications: imagine if we were given the record of an alien species, clearly sent with the intention that we ought to handle it according to some – to us unknowable – preferences. If we want to do some simple communication, essentially sending a postcard-like “here we are! This is what we think we are!” is the best we can do. A thick and complex message would obscure the actual meaning:

The spacecraft will be encountered and the record played only if there are advanced space-faring civilizations in interstellar space. But the launching of this ‘bottle’ into the cosmic ‘ocean’ says something very hopeful about life on this planet.
– Carl Sagan

It is a time capsule we send because we hope to survive and matter. If it becomes an epitaph of our species it is a decent epitaph. Anybody receiving it is a bonus.

Temporal preferences

Clearly we want the message to persist, maybe be detected, and ideally understood. We do not want the message to be distorted by random chance (if it can be avoided) or by independent actors.

This is why I am not too keen on sending an addendum. One can change the meaning of a message with a small addition: “Haha, just kidding!” or “We were such tools in the 1970s!”

Note that we have a present desire for a message (possibly the original) to reach the stars, but the launchers in 1977 clearly wanted their message to reach the stars: their preferences were clearly linked to what they selected. I think we have a moral duty to respect past preferences for information. I have expressed it elsewhere as a temporal golden rule: “treat the past as you want the future to treat you”. We would not want our message or amendments changed, so we better be careful about past messages.

However, adding a careful footnote is not necessarily wrong. But it needs to be in the spirit of the past message, adding to it.

So what kind of update would be useful?

We might want to add something that we have learned since the launch that aliens ought to know. For example, an important discovery. But this needs to be something that advanced aliens are unlikely to already know, which is tricky: they likely know about dark matter, that geopolitical orders can suddenly shift, or a proof of the Poincaré conjecture.

They have to be contingent, unique to humanity, and ideally universally significant. Few things are. Maybe that leaves us with adding the notes for some new catchy melody (“Gangnam style” or “Macarena”?) or a really neat mathematical insight (PCP theorem? Oops, it looks like Andrew Wiles’ Fermat proof is too large for the probe).

In the end, maybe just a “Still here, 38 years later” may be the best addition. Contingent, human, gives some data on the survival of intelligence in the universe.

# Likely not even a microDyson

Right now KIC 8462852 is really hot, and not just because it is a F3 V/IV type star: the light curve, as measured by Kepler, has irregular dips that looks like something (or rather, several somethings) are obscuring the star. The shapes of the dips are odd. The system is too old and IR-clean to have a remaining protoplanetary disk, dust clumps would coalesce, the aftermath of a giant planet impact is very unlikely (and hard to fit with the aperiodicity); maybe there is a storm of comets due to a recent stellar encounter, but comets are not very good at obscuring stars. So a lot of people on the net are quietly or not so quietly thinking that just maybe this is a Dyson sphere under construction.

I doubt it.

My basic argument is this: if a civilization builds a Dyson sphere it is unlikely to remain small for a long period of time. Just as planetary collisions are so rare that we should not expect to see any in the Kepler field, the time it takes to make a Dyson sphere is also very short: seeing it during construction is very unlikely.

# Fast enshrouding

In my and Stuart Armstrong’s paper “Eternity in Six Hours” we calculated that disassembling Mercury to make a partial Dyson shell could be done in 31 years. We did not try to push things here: our aim was to show that using a small fraction of the resources in the solar system it is possible to harness enough energy to launch a massive space colonization effort (literally reaching every reachable galaxy, eventually each solar system). Using energy from already built solar captors more material is mined and launched, producing an exponential feedback loop. This was originally discussed by Robert Bradbury. The time to disassemble terrestrial planets is not much longer than for Mercury, while the gas giants would take a few centuries.

If we imagine the history of a F5 star 1,000 years is not much. Given the estimated mass of KIC 8462852 as 1.46 solar masses, it will have a main sequence lifespan of 4.1 billion years. The chance of seeing it while being enshrouded is one in 4.3 million. This is the same problem as the giant impact theory.

# A ruin?

An abandoned Dyson shell would likely start clumping together; this might at first sound like a promising – if depressing – explanation of the observation. But the timescale is likely faster than planetary formation timescales of $10^5$$10^6$ years – the pieces are in nearly identical orbits – so the probability problem remains.

But it is indeed more likely to see the decay of the shell than the construction by several orders of magnitude. Just like normal ruins hang around far longer than the time it took to build the original building.

# Laid-back aliens?

Maybe the aliens are not pushing things? Obviously one can build a Dyson shell very slowly – in a sense we are doing it (and disassembling Earth to a tiny extent!) by launching satellites one by one. So if an alien civilization wanted to grow at a leisurely rate or just needed a bit of Dyson shell they could of course do it.

However, if you need something like $2.87\cdot 10^{19}$ Watt (a 100,000 km collector at 1 AU around the star) your demands are not modest. Freeman Dyson originally proposed the concept based on the observation that human energy needs were growing exponentially, and this was the logical endpoint. Even at 1% growth rate a civilization quickly – in a few millennia – need most of the star’s energy.

In order to get a reasonably high probability of seeing an incomplete shell we need to assume growth rates that are exceedingly small (on the order of less than a millionth per year). While it is not impossible, given how the trend seems to be towards more intense energy use in many systems and that entities with higher growth rates will tend to dominate a population, it seems rather unlikely. Of course, one can argue that we currently can more easily detect the rare laid-back civilizations than the ones that aggressively enshrouded their stars, but Dyson spheres do look pretty rare.

# Other uses?

Dyson shells are not the only megastructures that could cause intriguing transits.

C. R. McInnes has a suite of fun papers looking at various kinds of light-related megastructures. One can sort asteroid material using light pressure, engineer climate, adjust planetary orbits, and of course travel using solar sails. Most of these are smallish compared to stars (and in many cases dust clouds), but they show some of the utility of obscuring objects.

Duncan Forgan has a paper on detecting stellar engines (Shkadov thrusters) using light curves; unfortunately the calculated curves do not fit KIC8462852 as far as I can tell.

Luc Arnold analysed the light curves produced by various shapes of artificial objectsHe suggested that one could make a weirdly shaped mask for signalling one’s presence using transits. In principle one could make nearly any shape, but for signalling something unusual yet simple enough to be artificial would make most sense: I doubt the KIC transits fit this.

# More research is needed (duh)

In the end, we need more data. I suspect we will find that it is yet another odd natural phenomenon or coincidence. But it makes sense to watch, just in case.

Were we to learn that there is (or was) a technological civilization acting on a grand scale it would be immensely reassuring: we would know intelligent life could survive for at least some sizeable time. This is the opposite side of the Great Filter argument for why we should hope not to see any extraterrestrial life: life without intelligence is evidence for intelligence either being rare or transient, but somewhat non-transient intelligence in our backyard (just 1,500 light-years away!) is evidence that it is neither rare nor transient. Which is good news, unless we fancy ourselves as unique and burdened by being stewards of the entire reachable universe.

But I think we will instead learn that the ordinary processes of astrophysics can produce weird transit curves, perhaps due to weird objects (remember when we thought hot jupiters were exotic?) The universe is full of strange things, which makes me happy I live in it.

[An edited version of this post can be found at The Conversation: What are the odds of an alien megastructure blocking light from a distant star? ]

# ET, phone for you!

I have been in the media recently since I became the accidental spokesperson for UKSRN at the British Science Festival in Bradford:

(As well as BBC 5 Live, BBC Newcastle and BBC Berkshire… so my comments also get sent to space as a side effect).

My main message is that we are going to send in something for the Breakthrough Message initiative: a competition to write a good message to be sent to aliens. The total pot is a million dollars (it seems that was misunderstood in some reporting: it is likely not going to be a huge prize, but rather several). The message will not actually be sent to the stars: this is an intellectual exercise rather than a practical one.

(I also had some comments about the link between Langsec and SETI messages – computer security is actually a bit of an issue for fun reasons. Watch this space.)

# Should we?

One interesting issue is whether there are any good reasons not to signal. Stephen Hawking famously argued against it (but he is a strong advocate of SETI), as does David Brin. A recent declaration argues that we should not signal unless there was a widespread agreement about it. Yet others have made the case that we should signal, perhaps a bit cautiously. In fact, an eminent astronomer just told he could not take concerns about sending a message seriously.

Some of the arguments are (in no particular order):

Pro Con
SETI will not work if nobody speaks. Malign ETI.
ETI is likely to be far more advanced than us and could help us. Past meetings between different civilizations have often ended badly.
Knowing if there is intelligence out there is important. Giving away information about ourselves may expose us to accidental or deliberate hacking.
Hard to prevent transmissions.  Waste of resources.
Radio transmissions are already out there.  If the ETI is quiet, it is for a reason.
Maybe they are waiting for us to make the first move.  We should listen carefully first, then transmit.

It is actually an interesting problem: how do we judge the risks and benefits in a situation like this? Normal decision theory runs into trouble (not that it stops some of my colleagues). The problem here is that the probability and potential gain/loss are badly defined. We may have our own personal views on the likelihood of intelligence within radio reach and its nature, but we should be extremely uncertain given the paucity of evidence.

[ Even the silence in the sky is some evidence, but it is somewhat tricky to interpret given that it is compatible with both no intelligence (because of rarity or danger), intelligence not communicating or looking in spectra we see, cultural convergence towards quietness (the zoo hypothesis, everybody hiding, everybody becoming Jupiter brains), or even the simulation hypothesis. The first category is at least somewhat concise, while the later categories have endless room for speculation. One could argue that since later categories can fit any kind of evidence they are epistemically weak and we should not trust them much.]

Existential risks also tends to take precedence over almost anything. If we can avoid doing something that could cause existential risk the maxiPOK principle tells us not to do it: we can avoid sending and sending might bring down the star wolves on us, so we should avoid it.

There is also a unilateralist curse issue. It is enough that one group somewhere thinks transmitting is a good idea and hence do it to get the consequences, whatever they are. So the more groups that consider transmitting, even if they are all rational, well-meaning and consider the issue at length the more likely it is that somebody will do it even if it is a stupid thing to do. In situations like this we have argued it behoves us to be more conservative individually than we would otherwise have been – we should simply think twice just because sending messages is in the unilateralist curse category. We also argue in that paper that it is even better to share information and make collectively coordinated decisions.

That these arguments strengthen the con side – but largely independently of what the actual anti-message arguments are. They are general arguments that we should be careful, not final arguments.

Conversely, Alan Penny argued that given the high existential risk to humanity we may actually have little to lose: if our risk per century is 12-40% of extinction, then adding a small ETI risk has little effect on the overall risk level, yet a small chance of friendly ETI advice (“By the way, you might want to know about this…”) that decreases existential risk may be an existential hope. Suppose we think it is 50% likely that ETI is friendly, and 1% chance it is out there. If it is friendly it might give us advice that reduces our existential risk by 50%, otherwise it will eat us with 1% probability. So if we do nothing our risk is (say) 12%. If we signal, then the risk is 0.12*0.99 + 0.01*(0.5*0.12*0.5 + 0.5*(0.12*0.99+0.01))=11.9744% – a slight improvement. Like the Drake equation one can of course plug in different numbers and get different effects.

# Truth to the stars

Considering the situation over time, sending a message now may also be irrelevant since we could wipe ourselves out before any response will arrive. That brings to mind a discussion we had at the press conference yesterday about what the point of sending messages far away would be: wouldn’t humanity be gone by then? Also, we were discussing what to present to ETI: an honest or whitewashed version of ourselves? (my co-panelist Dr Jill Stuart made some great points about the diversity issues in past attempts).

My own view is that I’d rather have an honest epitaph for our species than a polished but untrue one. This is both relevant to us, since we may want to be truthful beings even if we cannot experience the consequences of the truth, and relevant to ETI, who may find the truth more useful than whatever our culture currently would like to present.

# The end of the worlds

George Dvorsky has a piece on Io9 about ways we could wreck the solar system, where he cites me in a few places. This is mostly for fun, but I think it links to an important existential risk issue: what conceivable threats have big enough spatial reach to threaten a interplanetary or even star-faring civilization?

This matters, since most existential risks we worry about today (like nuclear war, bioweapons, global ecological/societal crashes) only affect one planet. But if existential risk is the answer to the Fermi question, then the peril has to strike reliably. If it is one of the local ones it has to strike early: a multi-planet civilization is largely immune to the local risks. It will not just be distributed, but it will almost by necessity have fairly self-sufficient habitats that could act as seeds for a new civilization if they survive. Since it is entirely conceivable that we could have invented rockets and spaceflight long before discovering anything odd about uranium or how genetics work it seems unlikely that any of these local risks are “it”. That means that the risks have to be spatially bigger (or, of course, that xrisk is not the answer to the Fermi question).

Of the risks mentioned by George physics disasters are intriguing, since they might irradiate solar systems efficiently. But the reliability of them being triggered before interstellar spread seems problematic. Stellar engineering, stellification and orbit manipulation may be issues, but they hardly happen early – lots of time to escape. Warp drives and wormholes are also likely late activities, and do not seem to be reliable as extinctors. These are all still relatively localized: while able to irradiate a largish volume, they are not fine-tuned to cause damage and does not follow fleeing people. Dangers from self-replicating or self-improving machines seems to be a plausible, spatially unbound risk that could pursue (but also problematic for the Fermi question since now the machines are the aliens). Attracting malevolent aliens may actually be a relevant risk: assuming von Neumann probes one can set up global warning systems or “police probes” that maintain whatever rules the original programmers desire, and it is not too hard to imagine ruthless or uncaring systems that could enforce the great silence. Since early civilizations have the chance to spread to enormous volumes given a certain level of technology, this might matter more than one might a priori believe.

So, in the end, it seems that anything releasing a dangerous energy effect will only affect a fixed volume. If it has energy $E$ and one can survive it below a deposited energy $e$, if it just radiates in all directions the safe range is $r = \sqrt{E/4 \pi e} \propto \sqrt{E}$ – one needs to get into supernova ranges to sterilize interstellar volumes. If it is directional the range goes up, but smaller volumes are affected: if a fraction $f$ of the sky is affected, the range increases as $\propto \sqrt{1/f}$ but the total volume affected scales as $\propto f\sqrt{1/f}=\sqrt{f}$.

Self-sustaining effects are worse, but they need to cross space: if their space range is smaller than interplanetary distances they may destroy a planet but not anything more. For example, a black hole merely absorbs a planet or star (releasing a nasty energy blast) but does not continue sucking up stuff. Vacuum decay on the other hand has indefinite range in space and moves at lightspeed. Accidental self-replication is unlikely to be spaceworthy unless is starts among space-moving machinery; here deliberate design is a more serious problem.

The speed of threat spread also matters. If it is fast enough no escape is possible. However, many of the replicating threats will have sublight speed and could hence be escaped by sufficiently paranoid aliens. The issue here is if lightweight and hence faster replicators can always outrun larger aliens; given the accelerating expansion of the universe it might be possible to outrun them by being early enough, but our calculations do suggest that the margins look very slim.

The more information you have about a target, the better you can in general harm it. If you have no information, merely randomizing it with enough energy/entropy is the only option (and if you have no information of where it is, you need to radiate in all directions). As you learn more, you can focus resources to make more harm per unit expended, up to the extreme limits of solving the optimization problem of finding the informational/environmental inputs that cause desired harm (=hacking). This suggests that mindless threats will nearly always have shorter range and smaller harms than threats designed by (or constituted by) intelligent minds.

In the end, the most likely type of actual civilization-ending threat for an interplanetary civilization looks like it needs to be self-replicating/self-sustaining, able to spread through space, and have at least a tropism towards escaping entities. The smarter, the more effective it can be. This includes both nasty AI and replicators, but also predecessor civilizations that have infrastructure in place. Civilizations cannot be expected to reliably do foolish things with planetary orbits or risky physics.

# A sustainable orbital death ray

I have for many years been a fan of the webcomic Schlock Mercenary. Hardish, humorous military sf with some nice, long-term plotting.

In the current plotline (some spoilers ahead) there is an enormous Chekov’s gun: Earth is surrounded by an equatorial ring of microsatellites that can reflect sunlight. It was intended for climate control, but as the main character immediately points out, it also makes an awesome weapon. You can guess what happens. That leds to an interesting question: just how effective would such a weapon actually be?

From any point on Earth’s surface only part of the ring is visible above the horizon. In fact, at sufficiently high latitudes it is entirely invisible – there you would be safe no matter what. Also, Earth likely casts a shadow across the ring that lowers the efficiency on the nightside.

I guessed, based on the appearance in some strips, that the radius is about two Earth radii (12,000 km), and the thickness about 2000 km. I did a Monte Carlo integration where I generated random ring microsatellites, checking whether they were visible above the horizon for different Earth locations (by looking at the dot product of the local normal and the satellite-location vector; for anything above the horizon this product must be possible) and were in sunlight (by checking that the distance to the Earth-Sun axis was more than 6000 km). The result is the following diagram of how much of the ring can be seen from any given location:

At most, 35% of the ring is visible. Even on the nightside where the shadow cuts through the ring about 25% is visible. In practice, there would be a notch cut along the equator where the ring cannot fire through itself; just how wide it would be depends on the microsatellite size and properties.

Overlaying the data on a world map gives the following footprint:

The ring is strongly visible up to 40 degrees of latitude, where it starts to disappear below the southern or northern horizon. Antarctica, northern Canada, Scandinavia and Siberia are totally safe.

This corresponds to the summer solstice, where the ring is maximally tilted relative to the Earth-Sun axis. This is when it has maximal power: at the equinoxes it is largely parallel to the sunlight and cannot reflect much at all.

The total amount of energy the ring receives is $E_0 = \pi (r_o^2-r_i^2)|\sin(\theta)|S$ where $r_o$ is the outer radius, $r_i$ the inner radius, $\theta$ the tilt (between 23 degrees for the summer/winter solstice and 0 for equinoxes) and $S$ is the solar constant, 1.361 kW/square meter. This ignores the Earth shadow. So putting in $\theta=20^{\circ}$ for a New Years Eve firing, I get $E_0 \approx 7.6\cdot 10^{16}$ Watt.

If we then multiply by 0.3 for visibility, we get 23 petawatts – is nothing to sneeze at! Of course, there will be losses, both in reflection (likely a few percent at most) and more importantly through light scattering (about 25%, assuming it behaves like normal sunlight). Now, a 17 PW beam is still pretty decent. And if you are on the nightside the shadowed ring surface can still give about 8 PW. That is about six times the energy flow in the Gulf Stream.

How destructive would such a beam be? A megaton of TNT is 4.18 PJ. So in about a second the beam could produce a comparable amount of heat.  It would be far redder than a nuclear fireball (since it is essentially 6000K blackbody radiation) and the IR energy would presumably bounce around and be re-radiated, spreading far in the transparent IR bands. I suspect the fireball would quickly affect the absorption in a complicated manner and there would be defocusing effects due to thermal blooming: keeping it on target might be very hard, since energy would both scatter and reflect. Unlike a nuclear weapon there would not be much of a shockwave (I suspect there would still be one, but less of the energy would go into it).

The awesome thing about the ring is that it can just keep on firing. It is a sustainable weapon powered by renewable energy. The only drawback is that it would not have an ommminous hummmm….

Addendum 14 December: I just realized an important limitation. Sunlight comes from an extended source, so if you reflect it using plane mirrors you will get a divergent beam – which means that the spot it hits on the ground will be broad. The sun has diameter 1,391,684 km and is 149,597,871 km away, so the light spot 8000 km below the reflector will be 74 km across. This is independent of the reflector size (down to the diffraction limit and up to a mirror that is as large as the sun in the sky).

At first this sounds like it kills the ring beam. But one can achieve a better focus by clever alignment. Consider three circular footprints arranged like a standard Venn diagram. The center area gets three times the solar input as the large circles. By using more mirrors one can make a peak intensity that is much higher than the side intensity. The vicinity will still be lit up very brightly, but you can focus your devastation better than with individual mirrors – and you can afford to waste sunlight anyway. Still, it looks like this is more of a wide footprint weapon of devastation rather than a surgical knife.

# Galactic duck and cover

How much does gamma ray bursts (GRBs) produce a “galactic habitable zone”? Recently the preprint “On the role of GRBs on life extinction in the Universe” by Piran and Jimenez has made the rounds, arguing that we are near (in fact, inside) the inner edge of the zone due to plentiful GRBs causing mass extinctions too often for intelligence to arise.

This is somewhat similar to James Annis and Milan Cirkovic’s phase transition argument, where a declining rate of supernovae and GRBs causes global temporal synchronization of the emergence of intelligence. However, that argument has a problem: energetic explosions are random, and the difference in extinctions between lucky and unlucky parts of the galaxy can be large – intelligence might well erupt in a lucky corner long before the rest of the galaxy is ready.

I suspect the same problem is true for the Piran and Jimenez paper, but spatially. GRBs are believed to be highly directional, with beams typically a few degrees across. If we have random GRBs with narrow beams, how much of the center of the galaxy do they miss?

I made a simple model of the galaxy, with a thin disk, thick disk and bar population. The model used cubical cells 250 parsec long; somewhat crude, but likely good enough. Sampling random points based on star density, I generated GRBs. Based on Frail et al. 2001 I gave them lognormal energies and power-law distributed jet angles, directed randomly. Like Piran and Jimenez I assumed that if the fluence was above 100 kJ/m^2 it would be extinction level. The rate of GRBs in the Milky Way is uncertain, but a high estimate seems to be one every 100,000 years. Running 1000 GRBs would hence correspond to 100 million years.

If we look at the galactic plane we find that the variability close to the galactic centre is big: there are plenty of lucky regions with many stars.

When integrating around the entire galaxy to get a measure of risk at different radii and altitudes shows a rather messy structure:

One interesting finding is that the most dangerous place may be above the galactic plane along the axis: while few GRBs happen there, those in the disk and bar can reach there (the chance of being inside a double cone is independent of distance to the center, but along the axis one is within reach for the maximum number of GRBs).

Integrating the density of stars that are not affected as a function of radius and altitude shows that there is a mild galactic habitable zone hole within 4 kpc. That we are close to the peak is neat, but there is a significant number of stars very close to the center.

This is of course not a professional model; it is a slapdash Matlab script done in an evening to respond to some online debate. But I think it shows that directionality may matter a lot by increasing the variance of star fates. Nearby systems may be irradiated very differently, and merely averaging them will miss this.

If I understood Piran and Jimenez right they do not use directionality; instead they employ a scaled rate of observed GRBs, so they do not have to deal with the iffy issue of jet widths. This might be sound, but I suspect one should check the spatial statistics: correlations are tricky things (and were GRB axes even mildly aligned with the galactic axis the risk reduction would be huge). Another way of getting closer to their result is of course to bump up the number of GRBs: with enough, the centre of the galaxy will naturally be inhospitable. I did not do the same careful modelling of the link between metallicity and GRBs, nor the different sizes.

In any case, I suspect that GRBs are weak constraints on where life can persist and too erratic to act as a good answer to the Fermi question – even a mass extinction is forgotten within 10 million years.