# How much for that neutron in the window?

That is a great question. I once came up with the answer “50 tons of neutrons are needed” to a serious problem (you don’t want to know). How cheaply could you get that?

Figuring out roughly how many neutrons there are per kilogram of pure elements is pretty easy. Get their standard atomic weights, $A$, and subtract the atomic number $Z$ since that is the number of protons: $N=A-Z$. Now we know how many neutrons there are per atom on average (standard atomic weights include the different isotope weights, weighted by their abundance).

[ Since nucleons (protons and neutrons) are about 1830 times heavier than electrons, we can ignore the electrons for an error on order of 0.05%. There is also a binding energy error, since some of the total atomic mass is because of binding energy between nucleons, which is 0.94% or less. These errors are nothing compared to price uncertainties.]

We know that one nucleon weighs about $u=1.660539040\cdot 10^{-27}$ kg, so the number of nucleons per kilogram is $N_{\mathrm{nucl}} \approx 1/(Au)$ and the number of neutrons per kilo is $N_n \approx N_{\mathrm{nucl}}(N/A)$. This ranges from $7.5\cdot 10^{25}$ for helium down to $1.2\cdot 10^{24}$ for Oganesson. Hydrogen just has $4.7\cdot 10^{24}$ neutrons per kilogram, despite having $5.97\cdot 10^{26}$ nucleons per kilogram – there isn’t that much deuterium and tritium around to contribute neutrons.

Now, the price of elements is badly defined. I can get a kilogram of coal much cheaper than a kilogram of diamond, and ultra-pure elements are very expensive even if the everyday element is cheap. Plus, prices vary. And it is hard to buy plutonium on the open market. Ignoring all that and taking the numbers from Wikipedia (and ignoring the that some values look odd, and some are for compounds, and that the prices are unadjusted for inflation, and that they are lacking for many elements…) we can actually calculate the number of neutrons per dollar:

And the winner is… aluminium! You can get $8.8\cdot 10^{24}$ neutrons per dollar from aluminium.

In second place, nitrogen ($7.1\cdot 10^{24}$) and in third, hydrogen ($6.8\cdot 10^{24}$)! Hydrogen may be very neutron-poor, but since it is rather cheap and you get lots of nucleons per kilo, this balances the lack.

Given that these prices are dodgy, I would expect an uncertainty on the order of a magnitude (at least). So the true winner, given the cheapest actual source of the element, might be hard to find without excruciating price comparisons. But we can be fairly certain it is going to be something with an atomic number less than 25. Uranium is unlikely to be a cheap neutron source in this sense (and just look at poor plutonium!)

So, given that aluminium is 51.8% neutrons by weight I need 96.5 tons. The current aluminium price is $1,650.00 per ton, so I would have to pay$159,225 for the neutrons in my doomsday weapon – I mean, totally innocuous thought experiment!

# The Aestivation hypothesis: popular outline and FAQ

Anders Sandberg & Milan Ćirković

Since putting up a preprint for our paper “That is not dead which can eternal lie: the aestivation hypothesis for resolving Fermi’s paradox” (Journal of the British Interplanetary Society, in press) we have heard some comments and confusion that suggest to us that it would be useful to try to outline and clarify what our idea is, what we think about it, and some of the implications.

# The super-short version of the paper

Maybe we are not seeing alien civilizations because they are all rationally “sleeping” in the current early cosmological era, waiting for a remote future when it is more favourable to exploit the resources of the universe. We show that given current observations we can rule out a big chunk of possibilities like this, but not all.

# A bit more unpacked explanation

Information processing requires physical resources, not just computers or brains, but energy to run them. There is a thermodynamic cost to perform information processing that is temperature dependent: in principle, running processing become 10 times more efficient if your computer is 10 times colder (measured in Kelvins). Right now the cosmic background radiation makes nearly everything in the universe hotter than 3 Kelvin, but as the universe expands this background temperature will decline exponentially. So if you want to do as much information processing as possible with the energy you have it makes sense to wait. It becomes exponentially better. Eventually the background temperature bottoms out because of horizon radiation in a few trillion years: at this point it no longer makes sense to wait with the computation.

Hence, an advanced civilization may have explored a big chunk of the universe, done what is doable with existing nature, and now mostly have internal “cultural” things to do. These things can be regarded as information processing. If they want to maximize processing they should not do it today but wait until the cold future when they will get tremendously more done (1030 times more!). They should hence aestivate, leaving their domain protected by some automation until they wake up.

If this is correct, there might be old and powerful civilizations around that are hard to observe, not because they are deliberately hiding but because they are inactive for the time being.

However, were this hypothesis true, they would not want to lose their stuff. We should expect to see fewer processes that reduce resources  that could be useful in the far future. In the paper we look at processes that look like they might waste resources: stars converting mass into energy that is lost, stars imploding into black holes, galactic winds losing gas into intergalactic space, galaxy collisions, and galaxy clusters getting separated by the expansion of the universe. Current observations do not seem to indicate anything preventing these processes (and most interventions would be very visible).

Hence, either:

1. the answer to the Fermi question “where are they?!” is something else (like there being no aliens),
2. advanced civilizations aestivate but do so with only modest hoards of resources rather than entire superclusters,
3. they are mostly interested in spreading far and wide since this gives a lot of stuff with a much smaller effort than retaining it.

## Necessary assumptions

The aestivation hypothesis makes the following assumptions:

1. There are civilizations that mature much earlier than humanity. (not too implausible, given that Earth is somewhat late compared to other planets)
2. These civilizations can expand over sizeable volumes, gaining power over their contents. (we have argued that this is doable)
3. These civilizations have solved their coordination problems. (otherwise it would be hard to jointly aestivate; assumption likelihood hard to judge)
4. A civilization can retain control over its volume against other civilizations. (otherwise it would need to actively defend its turf in the present era and cannot aestivate; likelihood hard to judge)
5. The fraction of mature civilizations that aestivate is non-zero. (if it is rational at least some will try)
6. Aestivation is largely invisible. (seems likely, since there would be nearly no energy release)

# Have you solved the Fermi question?

We are not claiming we now know the answer to the Fermi question. Rather, we have a way of ruling out some possibilities and a few new possibilities worth looking for (like galaxies with inhibited heavy star formation).

# Do you really believe in it?

I (Anders) personally think the likeliest reason we are not seeing aliens is not that they are aestivating, but just that they do not exist or are very far away.

We have an upcoming paper giving some reasons for this belief. The short of it is that we are very uncertain about the probability of life and intelligence given the current state of scientific knowledge. They could be exceedingly low, and this means we have to assign a fairly high credence to the empty universe hypothesis. If that hypothesis is not true, then aestivation is a pretty plausible answer in my personal opinion.

Why write about a hypothesis you do not think is the most likely one? Because we need to cover as much of possibility space as possible, and the aestivation hypothesis is neatly suggested by considerations of the thermodynamics of computation and physical eschatology. We have been looking at other unlikely Fermi hypotheses like the berserker hypothesis to see if we can give good constraints on them (in that case, our existence plus some ecological instability problems make berzerkers unlikely).

# What is the point?

Understanding the potential and limits of intelligence in the universe tells us things about our own chances and potential future.

At the very least, this paper shows what a future advanced human-derived civilization may try to achieve, and some of the ultimate limits on far-future information processing. It gives some new numbers to feed into Nick Bostrom’s astronomical waste argument for working very hard on reducing existential risk in the present: the potential future is huge.

In regards to alien civilizations, the paper maps a part of possibility space, showing what is required for this Fermi paradox explanation to work as an explanation. It helps cut down on the possibilities a fair bit.

## What about the Great Filter?

We know there has to be at least one the unlikely step between non-living matter and easily observable technological civilizations (“the Great Filter”), otherwise the sky would be full of them. If it is an early filter (life or intelligence is rare) we may be fairly alone but our future is open; were the filter a later step, we should expect to be doomed.

The aestivation hypothesis doesn’t tell us much about the filter. It allows explaining away the quiet sky as evidence for absence of aliens, so without knowing if it is true or not we do not learn anything from the silence. The lack of megascale engineering is evidence against certain kinds of alien goals and activities, but rather weak evidence.

## Meaning of life

Depending on what you are trying to achieve, different long-term strategies make sense. This is another way SETI may tell us something interesting about the Big Questions by showing what advanced species are doing (or not):

If the ultimate value you aim for is local such as having as many happy minds as possible, then you want to spread very far and wide, even though the galaxy clusters you have settled will eventually drift apart and be forever separated. The total value doesn’t depend on all those happy minds talking to each other. Here the total amount of value is presumably proportional to the amount of stuff you have gathered times how long it can produce valuable thoughts. Aestivation makes sense, and you want to spread far and wide before doing it.

If the ultimate value you aim for is nonlocal, such as having your civilization produce the deepest possible philosophy, then all parts need to stay in touch with each other. This means that expanding outside a gravitationally bound supercluster is pointless: your expansion will halt at this point. We can be fairly certain there are no advanced civilizations trying to scrape together larger superclusters since it would be very visible.

If the ultimate value you aim for is finite, then at some point you may be done: you have made the perfect artwork or played all the possible chess games. Such a civilization only needs resources enough to achieve the goal, and then presumably will shut down. If the goal is small it might do this without aestivating, while if it is large it may aestivate with a finite hoard.

If the ultimate goal is modest, like enjoying your planetary utopia, then you will not affect the large-scale universe (although launching intergalactic colonization may still be good for security, leading to a nonlocal instrumental goal). Modest civilizations do not affect the overall fate of the universe.

# Can we test it?

Yes! The obvious way is to carefully look for odd processes keeping the universe from losing potentially useful raw materials. The suggestions in the paper give some ideas, but there are doubtless other things to look for.

Also, aestivators would protect themselves from late-evolving species that could steal their stuff. If we were to start building self-replicating von Neumann probes in the future, if there are aestivations around they better stop us. This hypothesis test may of course be rather dangerous…

# Isn’t there more to life than information processing?

Information is “a difference that makes a difference”: information processing is just going from one distinguishable state to another in a meaningful way. This covers not just computing with numbers and text, but having one brain state follow another, doing economic transactions, and creating art. Falling in love means that a mind goes from one state to another in a very complex way. Maybe the important subjective aspect is something very different from states of brain, but unless you think that it is possible to fall in love without having the brain change state there will be an information processing element to it. And that information processing is bound by the laws of thermodynamics.

Some theories of value place importance on how or that something is done rather than the consequences or intentions (which can be viewed as information states): maybe a perfect Zen action holds value on its own. If the start and end state are the same, then an infinite amount of such actions can be done and an equal amount of value achieved – yet there is no way of telling if they have ever happened, since there will not be a memory of them occurring.

In short, information processing is something we instrumentally need for the mental or practical activities that truly matter.

# “Aestivate”?

Like hibernate, but through summer (latin aestus=heat, aestivate=spend the summer). Hibernate (latin hibernus=wintry) is more common, but since this is about avoiding heat we choose the slightly rarer term.

# Can’t you put your computer in a fridge?

Yes, it is possible to cool below 3 K. But you need to do work to achieve it, spending precious energy on the cooling. If you want your computing done *now* and do not care about the total amount of computing, this is fine. But if you want as much computing as possible, then fridges are going to waste some of your energy.

There are some cool (sorry) possibilities by using very large black holes as heat sinks, since their temperature would be lower than the background radiation. But this will only last for a few hundred billion years, then the background will be cooler.

# Does computation costs have to be temperature dependent?

The short answer is no, but we do not think this matters for our conclusion.

The irreducible energy cost of computation is due to the Landauer limit (this limit or principle has also been ascribed to Brillouin, Shannon, von Neumann and many others): to erase one bit of information you need to pay an energy cost equal to $kT\ln(2)$ or more. Otherwise you could cheat the second law of thermodynamics.

However, logically reversible computation can work without paying this by never erasing information. The problem is of course that eventually memory runs out, but Bennett showed that one can then “un-compute” the computation by running it backwards, removing the garbage. The problem is that reversible computation needs to run very close to the average energy of the system (taking a long time) and that error correction is irreversible and temperature dependent. Same thing is true for quantum computation.

If one has a pool of negentropy, that is, something ordered that can be randomized, then one can “pay” for bit erasure using this pool until it runs out. This is potentially temperature independent! One can imagine having access to a huge memory full of zero bits. By swapping your garbage bit for a zero, you can potentially run computations without paying an energy cost (if the swapping is free): it has essentially zero temperature.

If there are natural negentropy pools aestivation is pointless: advanced civilizations would be dumping their entropy there in the present. But as far as we know, there are no such pools. We can make them by ordering matter or energy, but that has a work cost that depends on temperature (or using yet another pool of negentropy).

### Space-time as a resource?

Maybe the flatness of space-time is the ultimate negentropy pool, and by wrinkling it up we can get rid of entropy: this is in a sense how the universe has become so complex thanks to matter lumping together. The total entropy due to black holes dwarfs the entropy of normal matter by several orders of magnitude.

Were space-time lumpiness a useful resource we should expect advanced civilizations to dump matter into black holes on a vast scale; this does not seem to be going on.

# Lovecraft, wasn’t he, you know… a bit racist?

Yup. Very racist. And fearful of essentially everything in the modern world: globalisation, large societies, changing traditions, technology, and how insights from science make humans look like a small part of the universe rather than the centre of creation. Part of what make his horror stories interesting is that they are horror stories about modernity and the modern world-view. From a modernist perspective these things are not evil in themselves.

His vision of a vast universe inhabited by incomprehensible alien entities far outside the range of current humanity does fit in with Dysonian SETI and transhumanism: we should not assume we are at the pinnacle of power and understanding, we can look for signs that there are far more advanced civilizations out there (and if there is, we better figure out how to relate to this fact), and we can aspire to become something like them – which of course would have horrified Lovecraft to no end. Poor man.

# Håkan’s surface

Here is a minimal surface based on the Weierstrass-Enneper representation $f(z)=1, g(z)=\tanh^2(z)$. Written explicitly as a function from the complex number z to 3-space it is $\Re([-\tanh(z)(\mathrm{sech}^2(z)-4)/6,i(6z+\tanh(z)(\mathrm{sech}^2(z)-4))/6,z-\tanh(z)])$.

It is based on my old tanh surface, but has a wilder style. It gets helped by the fact that my triangulation in the picture is pretty jagged. On one hand it has two flat ends, but also a infinite number of catenoid openings (only two shown here).

I call it Håkan’s surface, since I came up with it on my dear husband’s birthday. Happy birthday, Håkan!

# Why fears of supersizing are misplaced

I am a co-author of the paper “On the Impossibility of Supersized Machines” (together with Ben Garfinkel, Miles Brundage, Daniel Filan, Carrick Flynn, Jelena Luketina, Michael Page, Andrew Snyder-Beattie, and Max Tegmark):

In recent years, a number of prominent computer scientists, along with academics in fields such as philosophy and physics, have lent credence to the notion that machines may one day become as large as humans. Many have further argued that machines could even come to exceed human size by a significant margin. However, there are at least seven distinct arguments that preclude this outcome. We show that it is not only implausible that machines will ever exceed human size, but in fact impossible.

In the spirit of using multiple arguments to bound a risk (so that the failure of single arguments do not decrease the power of the joint argument strongly) we show that there are philosophical reasons (the meaninglessness of “human-level largeness”, the universality of human largeness, the hard problem of largeness), psychological reasons (acting as an error theory based on motivated cognition), conceptual reasons (humans plus machines will be larger) and scientific/mathematical reasons (irreducible complexity, the quantum-Gödel issue) to not believe the possibility of machines larger than humans.

While it is cool to do exploratory engineering to demonstrate what can in principle be built, it is also very reassuring to show there are boundaries of what is possible. That allows us to focus on the (large) space within.

# Catastrophizing for not-so-fun and non-profit

Oren Cass has an article in Foreign Affairs about the problem of climate catastrophizing. It is basically how it becomes driven by motivated reasoning but also drives motivated reasoning in a vicious circle. Regardless of whether he himself has motivated reasoning too, I think the text is relevant beyond the climate domain.

Some of FHI research and reports are mentioned in passing. Their role is mainly in showing that there could be very bright futures or other existential risks, which undercuts the climate catastrophists that he is really criticising:

Several factors may help to explain why catastrophists sometimes view extreme climate change as more likely than other worst cases. Catastrophists confuse expected and extreme forecasts and thus view climate catastrophe as something we know will happen. But while the expected scenarios of manageable climate change derive from an accumulation of scientific evidence, the extreme ones do not. Catastrophists likewise interpret the present-day effects of climate change as the onset of their worst fears, but those effects are no more proof of existential catastrophes to come than is the 2015 Ebola epidemic a sign of a future civilization-destroying pandemic, or Siri of a coming Singularity

I think this is an important point for the existential risk community to be aware of. We are mostly interested in existential risks and global catastrophes that look possible but could be impossible (or avoided), rather than trying to predict risks that are going to happen. We deal in extreme cases that are intrinsically uncertain, and leave the more certain things to others (unless maybe they happen to be very under-researched). Siri gives us some singularity-evidence, but we think it is weak evidence, not proof (a hypothetical AI catastrophist would instead say “so, it begins”).

Confirmation bias is easy to fall for. If you are looking for signs of your favourite disaster emerging you will see them, and presumably loudly point at them in order to forestall the disaster. That suggests extra value in checking what might not be xrisks and shouldn’t be emphasised too much.

## Catastrophizing is not very effective

The nuclear disarmament movement also used a lot of catastrophizing, with plenty of archetypal cartoons showing Earth blowing up as a result of nuclear war or commonly claiming it would end humanity. The fact that the likely outcome merely would be mega- or gigadeath and untold suffering was apparently not regarded as rhetorically punchy enough. Ironically, Threads, The Day After or the Charlottesville scenario in Effects of Nuclear War may have been far more effective in driving home the horror and undesirability of nuclear war better, largely by giving a smaller-scale more relateable scenarios. Scope insensitivity, psychic numbing, compassion fade and related effects make catastrophizing a weak, perhaps even counterproductive, tool.

Another take-home message: when arguing for the importance of xrisk we should make sure we do not end up in the stupid loop he describes. If something is the most important thing ever, we better argue for it well and backed up with as much evidence and reason as can possibly be mustered. Turning it all into a game of overcoming cognitive bias through marketing or attributing psychological explanations to opposing views is risky.

The catastrophizing problem for very important risks is related to Janet Radcliffe-Richards’ analysis of what is wrong with political correctness (in an extended sense). A community argues for some high-minded ideal X using some arguments or facts Y. Someone points out a problem with Y. The rational response would be to drop Y and replace it with better arguments or facts Z (or, if it is really bad, drop X). The typical human response is to (implicitly or explicitly) assume that since Y is used to argue for X, then criticising Y is intended to reduce support for X. Since X is good (or at least of central tribal importance) the critic must be evil or at least a tribal enemy – get him! This way bad arguments or unlikely scenarios get embedded in a discourse.

Standard groupthink where people with doubts figure out that they better keep their heads down if they want to remain in the group strengthens the effect, and makes criticism even less common (and hence more salient and out-groupish when it happens).

## Reasons to be cheerful?

An interesting detail about the opening: the GCR/Xrisk community seems to be way more optimistic than the climate community as described. I mentioned Warren Ellis little novel Normal earlier on this blog, which is about a mental asylum for futurists affected by looking into the abyss. I suspect he was maybe modelling them on the moody climate people but adding an overlay of other futurist ideas/tropes for the story.

Assuming climate people really are that moody.

# An elliptic remark

I recently returned to toying around with circle and sphere inversion fractals, that is, fractal sets that are invariant under inversion in a given set of circles or spheres.

That got me thinking: can you invert points in other things than circles? Of course you can! José L. Ramírez has written a nice overview of inversion in ellipses. Basically a point $P$ is projected to another point $P'$ so that $||P-O||\cdot ||P'-O||=||Q-O||^2$ where $O$ is the centre of the ellipse and $Q$ is the point where the ray between $O, P', P$ intersects the ellipse.

In Cartesian coordinates, for an ellipse centered on the origin and with semimajor and minor axes $a,b$, the inverse point of $P=(u,v)$ is $P'=(x,y)$ where $x=\frac{a^2b^2u}{b^2u^2+a^2v^2}$ and $y=\frac{a^2b^2v}{b^2u^2+a^2v^2}$. Basically this is a squashed version of the circle formula.

Many of the properties remain the same. Lines passing through the centre of the ellipse are unchanged. Other lines get mapped to ellipses; if they intersect the inversion ellipse the new ellipse also intersect it at those points. Hence tangent lines are mapped to tangent ellipses. Ellipses with parallel axes and equal eccentricities map onto other ellipses (or lines if they intersect the centre of the inversion ellipse). Other conics get turned into cubics; for example a hyperbola gets mapped to a lemniscate. (See also this paper for more examples).

Now, from a fractal standpoint this means that if you have a set of ellipses that are tangent you should expect a fractal passing through their points of tangency. Basically all of the standard circle inversion fractals hence have elliptic counterparts. Here is the result for a ring of 4 or 6 mutually tangent ellipses:

These pictures were generated by taking points in the plane and inverting them with randomly selected ellipses; as the process continues they get attracted to the invariant set (this is basically a standard iterated function system). It also has the known problem of finding the points at the tangencies, since the iteration has to loop consistently between inverting in the two ellipses to get there, but it is likely that a third will be selected at some point.

One approach is to deliberately recurse downward to find the points using a depth first search. We can take look at where each ellipse is mapped by each of the inversions, and since the fractal is inside each of the mapped ellipses we can then continue mapping the chain of mapped ellipses, getting nice bounds on where it is going (as long as everything is shrinking: this is guaranteed as long as it is mappings from the outside to the inside of the generating ellipses, but if they were to overlap things can explode). Doing this for just one step reveals one reason for the quirky shapes above: some of the ellipses get mapped into crescents or pears, adding a lot of bends:

Now, continuing this process makes a nested structure where the invariant set is hidden inside all the other mapped ellipses.

It is still hard to reach the tangent points, but at least now they are easier to detect. They are also numerically tough: most points on the ellipse circumferences are mapped away from them towards the interior of the generating ellipse. Still, if we view the mapped ellipses as uncertainties and shade them in we can get a very pleasing map of the invariant set:

Here are a few other nice fractals based on these ideas:

Using a mix of circles and ellipses produces a nice mix of the regularity of the circle-based Apollonian gaskets and the swooshy, Hénon fractal shape the ellipses induce.

# Appendix: Matlab code

% center=[-1 -1 2 1; -1 1 1 2; 1 -1 1 2; 1 1 2 1];
% center(:,3:4)=center(:,3:4)*(2/3);
%
%center=[-1 -1 2 1; -1 1 1 2; 1 -1 1 2; 1 1 2 1; 3 1 1 2; 3 -1 2 1];
%center(:,3:4)=center(:,3:4)*(2/3);
%center(:,1)=center(:,1)-1;
%
% center=[-1 -1 2 1; -1 1 1 2; 1 -1 1 2; 1 1 2 1];
% center(:,3:4)=center(:,3:4)*(2/3);
% center=[center; 0 0 .51 .51];
%
% egg
% center=[0 0 0.6666 1; 2 2 2 2; -2 2 2 2; -2 -2 2 2; 2 -2 2 2];
%
% double
%r=0.5;
%center=[-r 0 r r; r 0 r r; 2 2 2 2; -2 2 2 2; -2 -2 2 2; 2 -2 2 2];
%
% Double egg
center=[0.3 0 0.3 0.845; -0.3 0 0.3 0.845; 2 2 2 2; -2 2 2 2; -2 -2 2 2; 2 -2 2 2];
%
M=size(center,1); % number of ellipses
N=100; % points on fill curves
X=randn(N+1,2);
clf
hold on
tt=2*pi*(0:N)/N;
alpha 0.2
for i=1:M
X(:,1)=center(i,1)+center(i,3)*cos(tt);
X(:,2)=center(i,2)+center(i,4)*sin(tt);
plot(X(:,1),X(:,2),'k');
for j=1:M
if (i~=j)
recurseDown(X,[i j],10,center)
drawnow
end
end
end


## Recursedown.m

function recurseDown(X,ellword,maxlevel,center)
i=ellword(end); % invert in latest ellipse
%
% Perform inversion
C=center(i,1:2);
A2=center(i,3).^2;
B2=center(i,4).^2;
Y(:,1)=X(:,1)-C(:,1);
Y(:,2)=X(:,2)-C(:,2);
X(:,1)=C(:,1)+A2.*B2.*Y(:,1)./(B2.*Y(:,1).^2+A2.*Y(:,2).^2);
X(:,2)=C(:,2)+A2.*B2.*Y(:,2)./(B2.*Y(:,1).^2+A2.*Y(:,2).^2);
%
if (norm(max(X)-min(X))<0.005) return; end
%
co=hsv(size(center,1));
coco=mean([1 1 1; 1 1 1; co(ellword,:)]);
%
%    plot(X(:,1),X(:,2),'Color',coco)
fill(X(:,1),X(:,2),coco,'FaceAlpha',.2,'EdgeAlpha',0)
%
if (length(ellword)<maxlevel)
for j=1:size(center,1)
if (j~=i)
recurseDown(X,[ellword j],maxlevel,center)
end
end
end


# The frightening infinite spaces: apeirophobia

Bobby Azarian writes in The Atlantic about Apeirophobia: The Fear of Eternity. This is the existential vertigo experienced by some when considering everlasting life (typically in a religious context), or just the infinite. Pascal’s Pensées famously touches on the same feeling: “The eternal silence of these infinite spaces frightens me.” For some this is upsetting enough that it actually count as a specific phobia, although in most cases it seems to be more a general unease.

# Fearing immortality

I found the concept relevant since yesterday I had a conversation with a philosopher arguing against life extension. Many of her arguments were familiar: they come up again and again if you express a positive view of longevity. It is interesting to notice that many other views do not elicit the same critical response. Suggest a future in space and some think it might be wasteful or impossible, but rarely with the same tenaciousness as life extension. As soon as one rational argument is disproven another one takes its place.

In the past I have usually attributed this to ego defence and maybe terror management. We learn about our mortality when we are young and have to come up with a way of handling it: ignoring it, denying it by assuming eternal hereafters, that we can live on through works or children, various philosophical solutions, concepts of the appropriate shape of our lives, etc. When life extension comes up, this terror management or self image is threatened and people try to defend it – their emotional equilibrium is risked by challenges to the coping strategy (and yes, this is also true for transhumanists who resolve mortality by hoping for radical life extension: there is a lot of motivated thinking going on in defending the imminent breakthroughs against death, too). While “longevity is disturbing to me” is not a good argument it is the motivator for finding arguments that can work in the social context. This is also why no amount of knocking down these arguments actually leads anywhere: the source is a coping strategy, not a rationally consistent position.

However, the apeirophobia essay suggests a different reason some people argue against life extension. They are actually unsettled by indefinite or infinite lives. I do not think everybody who argues has apeirophobia, it is probably a minority fear (and might even be a different take on the fear of death). But it is a somewhat more respectable origin than ego defence.

When I encounter arguments for the greatness of finite and perhaps short spans of life, I often rhetorically ask – especially if the interlocutor is from a religious worldview – if they think people will die in Heaven. It is basically Sappho’s argument (“to die is an evil; for the gods have thus decided. For otherwise they would be dying.”) Of course, this rarely succeeds in convincing anybody but it tends to throw a spanner in the works. However, the apeirophobia essay actually shows that some religious people may have a somewhat consistent fear that eternal life in Heaven isn’t a good thing. I respect that. Of course, I might still ask why God in their worldview insists on being eternal, but even I can see a few easy ways out of that issue (e.g. it is a non-human being not affected by eternity in the same way).

# Arbitrariness

As I often have to point out, I do not believe immortality is a thing. We are finite beings in a random universe, and sooner or later our luck runs out. What to aim for is indefinitely long lives, lives that go on (with high probability) until we no longer find them meaningful. But even this tends to trigger apeirophobia. Maybe one reason is the indeterminacy: there is nothing pre-set at all.

Pascal’s worry seem to be not just the infinity of the spaces but also their arbitrariness and how insignificant we are relative to them. The full section of the Pensées:

205: When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill, and even can see, engulfed in the infinite immensity of spaces of which I am ignorant, and which know me not, I am frightened, and am astonished at being here rather than there; for there is no reason why here rather than there, why now rather than then. Who has put me here? By whose order and direction have this place and time been allotted to me? Memoria hospitis unius diei prætereuntis.

206: The eternal silence of these infinite spaces frightens me.

207: How many kingdoms know us not!

208: Why is my knowledge limited? Why my stature? Why my life to one hundred years rather than to a thousand? What reason has nature had for giving me such, and for choosing this number rather than another in the infinity of those from which there is no more reason to choose one than another, trying nothing else?

Pascal is clearly unsettled by infinity and eternity, but in the Pensées he tries to resolve this psychologically: since he trusts God, then eternity must be a good thing even if it is hard to bear. This is a very different position from my interlocutor yesterday, who insisted that it was the warm finitude of a human life that gave life meaning (a view somewhat echoed in Mark O’Connell’s To Be a Machine). To Pascal apeirophobia was just another challenge to become a good Christian, to the mortalist it is actually a correct, value-tracking intuition.

# Apeirophobia as a moral intuition

I have always been sceptical of psychologizing why people hold views. It is sometimes useful for emphatizing with them and for recognising the futility of knocking down arguments that are actually secondary to a core worldview (which it may or may not be appropriate to challenge). But it is easy to make mistaken guesses. Plus, one often ends up in the “sociological fallacy”: thinking that since one can see non-rational reasons people hold a belief then that belief is unjustified or even untrue. As Yudkowsky pointed out, forecasting empirical facts by psychoanalyzing people never works. I also think this applies to values, insofar they are not only about internal mental states: that people with certain characteristics are more likely to think something has a certain value than people without the characteristic only gives us information about the value if that characteristic somehow correlates with being right about that kind of values.

Feeling apeirophobia does not tell us that infinity is bad, just as feeling xenophobia does not tell us that foreigners are bad. Feeling suffering on the other hand does give us direct knowledge that it is intrinsically aversive (it takes a lot of philosophical footwork to construct an argument that suffering is actually OK). Moral or emotional intuitions certainly can motivate us to investigate a topic with better intellectual tools than the vague unease, conservatism or blind hope that started the process. The validity of the results should not depend on the trigger since there is no necessary relation between the feeling and the ethical state of the thing triggering it: much of the debate about “the wisdom of repugnance” is clarifying when we should expect the intuition to overwhelm the actual thinking and when they are actually reliable. I always get very sceptical when somebody claims their intuition comes from a innate sense of what the good is – at least when it differs from mine.

Would people with apeirophobia have a better understanding of the value of infinity than somebody else? I suspect apeirophobes are on average smarter and/or have a higher need for cognition, but this does not imply that they get things right, just that they think more and more deeply about concepts many people are happy to gloss over. There are many smart nonapeirophobes too.

A strong reason to be sceptical of apeirophobic intuitions is that intuitions tend to work well when we have plenty of experience to build them from, either evolutionarily or individually. Human practical physics intuitions are great for everyday objects and speeds, and progressively worsens as we reach relativistic or quantum scales. We do not encounter eternal life at all, and hence we should be very suspicious about the validity of aperirophobia as a truth-tracking innate signal. Rather, it is triggered when we become overwhelmed by the lack of references to infinity in our lived experience or we discover the arbitrarily extreme nature of “infinite issues” (anybody who has not experienced vertigo when they understood uncountable sets?) It is a correct signal that our minds are swimming above an abyss we do not know but it does not tell us what is in this abyss. Maybe it is nice down there? Given our human tendency to look more strongly for downsides and losses than positives we will tend to respond to this uncertainty by imagining diffuse worst case scenario monsters anyway.

I do not think I have apeirophobia, but I can still see how chilling belief in eternal lives can be. Unsong’s disutility-maximizing Hell is very nasty, but I do not think it exists. I am not worried about Eternal Returns: if you chronologically live forever but actually just experience a finite length loop of experiences again and again then it makes sense to say that your life just that long.

My real worry is quantum immortality: from a subjective point of view one should expect to survive whatever happen in a multiverse situation, since one cannot be aware in those branches where one died. The problem is that the set of nice states to be in is far smaller than the set of possible states, so over time we should expect to end up horribly crippled and damaged yet unable to die. But here the main problem is the suffering and reduction of circumstances, not the endlessness.

There is a problem with endlessness here though: since random events play a decisive role in our experienced life paths it seems that we have little control over where we end up and that whatever we experience in the long run is going to be wholly determined by chance (after all, beyond 10100 years or more we will all have to be a succession of Boltzmann brains). But the problem seems to be more  the pointlessness that emerges from this chance than that it goes on forever: a finite randomised life seems to hold little value, and as Tolstoy put it, maybe we need infinite subjective lives where past acts matter to actually have meaning. I wonder what apeirophobes make of Tolstoy?

# Embracing the abyss

My recommendation to apeirophobes is not to take Azarian’s advice and put eternity out of mind, but instead to embrace it in a controllable way. Learn set theory and the paradoxes of infinity. And then look at the time interval $t=[0, \infty)$ and realise it can be mapped into the interval $[0,1)$ (e.g. by $f(t)=1/(t+1)$). From the infinite perspective any finite length of life is equal. But infinite spans can be manipulated too: in a sense they are also all the same. The infinities hide within what we normally think of as finite.

I suspect Pascal would have been delighted if he knew this math. However, to him the essential part was how we turn intellectual meditation into emotional or existential equilibrium:

Let us therefore not look for certainty and stability. Our reason is always deceived by fickle shadows; nothing can fix the finite between the two Infinites, which both enclose and fly from it.

If this be well understood, I think that we shall remain at rest, each in the state wherein nature has placed him. As this sphere which has fallen to us as our lot is always distant from either extreme, what matters it that man should have a little more knowledge of the universe? If he has it, he but gets a little higher. Is he not always infinitely removed from the end, and is not the duration of our life equally removed from eternity, even if it lasts ten years longer?

In comparison with these Infinites all finites are equal, and I see no reason for fixing our imagination on one more than on another. The only
comparison which we make of ourselves to the finite is painful to us.

In the end it is we who make the infinite frightening or the finite painful. We can train ourselves to stop it. We may need very long lives in order to grow to do it well, though.

# Calabi-Yau and Hanson’s surfaces

I have a glass cube on my office windowsill containing a slice of a Calabi-Yau manifold, one of Bathsheba Grossman’s wonderful creations. It is an intricate, self-intersecting surface with lots of unexpected symmetries. A visiting friend got me into trying to make my own version of the surface.

First, what is the equation for it? Grossman-Hanson’s explanation is somewhat involved, but basically what we are seeing is a 2D slice through a 6-dimensional manifold in a projective space expressed as the 4D manifold $z_1^5+z_2^5=1$, where the variables are complex. Hanson shows that this is a kind of complex superquadric in this paper. This leads to the formulae:

$z_1(\theta,\xi,k_1)=e^{2\pi i k_1 / n}\cosh(\theta+\xi i)^{2/n}$

$z_2(\theta,\xi,k_2)=e^{2 \pi i k_2 / n}\sinh(\theta+\xi i)^{2/n}/i$

where the k’s run through $0 \leq k \leq (n-1)$. Each pair $k_1,k_2$ corresponds to one patch of what is essentially a complex catenoid. This is still a 4D object. To plot it, we plot the points

$(\Re(z_1),\Re(z_2),\cos(\alpha)\Im(z_1)+\sin(\alpha)\Im(z_2))$

where $\alpha$ is some suitable angle to tilt the projection into 3-space. Hanson’s explanation is very clear; I originally reverse-engineered the same formula from the code at Ziyi Zhang’s site.

The result is pretty nifty. It is tricky to see how it hangs together in 2D; rotating it in 3D helps a bit. It is composed of 16 identical patches:

The boundary of the patches meet other patches except along two open borders (corresponding to large or small values of $\theta$): these form the edges of the manifold and strictly speaking I ought to have rendered them to infinity. That would have made it unbounded and somewhat boring to look at: four disks meeting at an angle, with the interesting part hidden inside. By marking the edges we can see that the boundary are four linked wobbly circles:

A surface bounded by a knot or a link is called a Seifert surface. While these surfaces look a lot like minimal surfaces they are not exactly minimal when I estimate the mean curvature (it should be exactly zero); while this could be because of lack of numerical precision I think it is real: while minimal surfaces are Ricci-flat, the converse is not necessarily true.

Changing N produces other surfaces. N=2 is basically a catenoid (tilted and self-intersecting). As N increases it becomes more like a barrel or a pufferfish, with one direction dominated by circular saddle regions, one showing a meshwork of spaces reminiscent of spacefilling minimal surfaces, and one a lot of overlapping “barbs”.

Note that just like for minimal surfaces one can multiply $z_1, z_2$ by $e^{i\omega}$ to get another surface in an associate family. In this case it circulates the patches along their circles without changing the surface much.

Hanson also notes that by changing the formula to $z_1^{n_1}+z_2^{n_2}=1$ we can get boundaries that are torus-knot-like. This leads to the formulae:

$z_1(\theta,\xi,k_1)=e^{2\pi i k_1 / n_1}\cosh(\theta+\xi i)^{2/n_1}$

$z_2(\theta,\xi,k_2)=e^{2 \pi i k_2 / n_2}\sinh(\theta+\xi i)^{2/n_2}/i$

## Appendix: Matlab code

%% Initialization edge=0; % Mark edge? coloring=1; % Patch coloring type n=4; s=0.1; % Gridsize alp=1; ca=cos(alp); sa=sin(alp); % Projection [theta,xi]=meshgrid(-1.5:s:1.5,1*(pi/2)*(0:1:16)/16); z=theta+xi*i; % Color scheme tt=2*pi*(1:200)'/200; co=.5+.5*[cos(tt) cos(tt+1) cos(tt+2)]; colormap(co) %% Plot clf hold on for k1=0:(n-1) for k2=0:(n-1) z1=exp(k1*2*pi*i/n)*cosh(z).^(2/n); z2=exp(k2*2*pi*i/n)*(1/i)*sinh(z).^(2/n); X=real(z1); Y=real(z2); Z=ca*imag(z1)+sa*imag(z2); if (coloring==0) surf(X,Y,Z); else switch (coloring) case 1 C=z1*0+(k1+k2*n); % Color by patch case 2 C=abs(z1); case 3 C=theta; case 4 C=xi; case 5 C=angle(z1); case 6 C=z1*0+1; end h=surf(X,Y,Z,C); set(h,'EdgeAlpha',0.4) end if (edge>0) plot3(X(:,end),Y(:,end),Z(:,end),'r','LineWidth',2) plot3(X(:,1),Y(:,1),Z(:,1),'r','LineWidth',2) end end end view([2 3 1]) camlight h=camlight('left'); set(h,'Color',[1 1 1]*.5) axis equal axis vis3d axis off 

# The capability caution principle and the principle of maximal awkwardness

Capability Caution Principle: There being no consensus, we should avoid strong assumptions regarding upper limits on future AI capabilities.

It is an important meta-principle in careful design to avoid assuming the most reassuring possibility and instead design based on the most awkward possibility.

When inventing a cryptosystem, do not assume that the adversary is stupid and has limited resources: try to make something that can withstand a computationally and intellectually superior adversary. When testing a new explosive, do not assume it will be weak – stand as far away as possible. When trying to improve AI safety, do not assume AI will be stupid or weak, or that whoever implements it will be sane.

Often we think that the conservative choice is the pessimistic choice where nothing works. This is because “not working” is usually the most awkward possibility when building something. If I plan a project I should ensure that I can handle unforeseen delays and that my original plans and pathways have to be scrapped and replaced with something else. But from a safety or social impact perspective the most awkward situation is if something succeeds radically, in the near future, and we have to deal with the consequences.

Assuming the principle of maximal awkwardness is a form of steelmanning and the least convenient possible world.

This is an approach based on potential loss rather than probability. Most AI history tells us that wild dreams rarely, if ever, come true. But were we to get very powerful AI tools tomorrow it is not too hard to foresee a lot of damage and disruption. Even if you do not think the risk is existential you can probably imagine that autonomous hedge funds smarter than human traders, automated engineering in the hands of anybody and scalable automated identity theft could mess up the world system rather strongly. The fact that it might be unlikely is not as important as that the damage would be unacceptable. It is often easy to think that in uncertain cases the burden of proof is on the other party, rather than on the side where a mistaken belief would be dangerous.

As FLI stated it the principle goes both ways: do not assume the limits are super-high either. Maybe there is a complexity scaling making problem-solving systems unable to handle more than 7 things in “working memory” at the same time, limiting how deep their insights could be. Maybe social manipulation is not a tractable task. But this mainly means we should not count on the super-smart AI as a solution to problems (e.g. using one smart system to monitor another smart system). It is not an argument to be complacent.

People often misunderstand uncertainty:

• Some think that uncertainty implies that non-action is reasonable, or at least action should wait till we know more. This is actually where the precautionary principle is sane: if there is a risk of something bad happening but you are not certain it will happen, you should still try to prevent it from happening or at least monitor what is going on.
• Obviously some uncertain risks are unlikely enough that they can be ignored by rational people, but you need to have good reasons to think that the risk is actually that unlikely – uncertainty alone does not help.
• Gaining more information sometimes reduces uncertainty in valuable ways, but the price of information can sometimes be too high, especially when there are intrinsically unknowable factors and noise clouding the situation.
• Looking at the mean or expected case can be a mistake if there is a long tail of relatively unlikely but terrible possibilities: on the average day your house does not have a fire, but having insurance, a fire alarm and a fire extinguisher is a rational response.
• Combinations of uncertain factors do not become less uncertain as they are combined (even if you describe them carefully and with scenarios): typically you get broader and heavier-tailed distributions, and should act on the tail risk.

FLI asks the intriguing question of how smart AI can get. I really want to know that too. But it is relatively unimportant for designing AI safety unless the ceiling is shockingly low; it is safer to assume it can be as smart as it wants to. Some AI safety schemes involve smart systems monitoring each other or performing very complex counterfactuals: these do hinge on an assumption of high intelligence (or whatever it takes to accurately model counterfactual worlds). But then the design criteria should be to assume that these things are hard to do well.

Under high uncertainty, assume Murphy’s law holds.

(But remember that good engineering and reasoning can bind Murphy – it is just that you cannot assume somebody else will do it for you.)

Wired has an article about the CSER Existential Risk Conference in December 2016, rather flatteringly comparing us to superheroes. Plus a list of more or less likely risks we discussed. Calling them the “10 biggest threats” is perhaps exaggerating a fair bit: nobody is seriously worried about simulation shutdowns. But some of the others are worth working a lot more on.

## High-energy demons

I am cited as talking about existential risk from demon summoning. Since this is bound to be misunderstood, here is the full story:

As noted in the Wired list, we wrote a paper looking at the risk from the LHC, finding that there is a problem with analysing very unlikely (but high impact) risks: the probability of a mistake in the analysis overshadows the risk itself, making the analysis bad at bounding the risk. This can be handled by doing multiple independent risk bounds, which is a hassle, but it is the only (?) way to reliably conclude that things are safe.

I blogged a bit about the LHC issue before we wrote the paper, bringing up the problem of estimating probabilities for unprecedented experiments through the case of Taleb’s demon (which properly should be Taylor’s demon, but Stigler’s law of eponymy strikes again). That probably got me to have a demon association to the wider physics risk issues.

The issue of how to think about unprecedented risks without succumbing to precautionary paralysis is important: we cannot avoid doing new things, yet we should not be stupid about it. This is extra tricky when considering experiments that create things or conditions that are not found in nature.

## Not so serious?

A closely related issue is when it is reasonable to regard a proposed risk as non-serious. Predictions of risk from strangelets, black holes, vacuum decay and other “theoretical noise” caused by theoretical physics theories at least is triggered by some serious physics thinking, even if it is far out. Physicists have generally tended to ignore such risks, but when forced by anxious acceleratorphobes the arguments had to be nontrivial: the initial dismissal was not really well founded. Yet it seems totally reasonable to dismiss some risks. If somebody worries that the alien spacegods will take exception to the accelerator we generally look for a psychiatrist rather than take them seriously. Some theories have so low prior probability that it seems rational to ignore them.

But what is the proper de minimis boundary here? One crude way of estimating it is to say that risks of destroying the world with lower probability than one in 10 billion can safely be ignored – they correspond to a risk of less than one person in expectation. But we would not accept that for an individual chemistry experiment: if the chance of being blown up if someone did it was “less than 100%” but still far above some tiny number, they would presumably want to avoid risking their neck. And in the physics risk case the same risk is borne by every living human. Worse, by Bostrom’s astronomical waste argument, existential risks risks more than 1046 possible future lives. So maybe we should put the boundary at less than 10-46: any risk more likely must be investigated in detail. That will be a lot of work. Still, there are risks far below this level: the probability that all humans were to die from natural causes within a year is around 10-7.2e11, which is OK.

One can argue that the boundary does not really exist: Martin Peterson argues that setting it at some fixed low probability, that realisations of the risk cannot be ascertained, or that it is below natural risks do not truly work: the boundary will be vague.

## Demons lurking in the priors

Be as it may with the boundary, the real problem is that estimating prior probabilities is not always easy. They can vault over the vague boundary.

Hence my demon summoning example (from a blog post near Halloween I cannot find right now): what about the risk of somebody summoning a demon army? It might cause the end of the world. The theory “Demons are real and threatening” is not a hugely likely theory: atheists and modern Christians may assign it zero probability. But that breaks Cromwell’s rule: once you assign 0% to a probability no amount of evidence – including a demon army parading in front of you – will make you change your mind (or you are not applying probability theory correctly). The proper response is to assume some tiny probability $\epsilon$, conveniently below the boundary.

…except that there are a lot of old-fashioned believers who do think the theory “Demons are real and threatening” is a totally fine theory. Sure, most academic readers of this blog will not belong to this group and instead to the $\epsilon$ probability group. But knowing that there are people out there that think something different from your view should make you want to update your view in their direction a bit – after all, you could be wrong and they might know something you don’t. (Yes, they ought to move a bit in your direction too.) But now suppose you move 1% in the direction of the believers from your $\epsilon$ belief. You will now believe in the theory to $\epsilon + 1\% \approx 1\%$. That is, now you have a fairly good reason not to disregard the demon theory automatically. At least you should spend effort on checking it out. And once you are done with that you better start with the next crazy New Age theory, and the next conspiracy theory…

## Reverend Bayes doesn’t help the unbeliever (or believer)

One way out is to argue that the probability of believers being right is so low that it can be disregarded. If they have probability $\epsilon$ of being right, then the actual demon risk is of size $\epsilon$ and we can ignore it – updates due to the others do not move us. But that is a pretty bold statement about human beliefs about anything: humans can surely be wrong about things, but being that certain that a common belief is wrong seems to require better evidence.

The believer will doubtlessly claim seeing a lot of evidence for the divine, giving some big update $\Pr[belief|evidence]=\Pr[evidence|belief]\Pr[belief]/\Pr[evidence]$, but the non-believer will notice that the evidence is also pretty compatible with non-belief: $\frac{\Pr[evidence|belief]}{\Pr[evidence|nonbelief]}\approx 1$ – most believers seem to have strong priors for their belief that they then strengthen by selective evidence or interpretation without taking into account the more relevant ratio $\Pr[belief|evidence] / \Pr[nonbelief|evidence]$. And the believers counter that the same is true for the non-believers…

Insofar we are just messing around with our own evidence-free priors we should just assume that others might know something we don’t know (maybe even in a way that we do not even recognise epistemically) and update in their direction. Which again forces us to spend time investigating demon risk.

## OK, let’s give in…

Another way of reasoning is to say that maybe we should investigate all risks somebody can make us guess a non-negligible prior for. It is just that we should allocate our efforts proportional to our current probability guesstimates. Start with the big risks, and work our way down towards the crazier ones. This is a bit like the post about the best problems to work on: setting priorities is important, and we want to go for the ones where we chew off most uninvestigated risk.

If we work our way down the list this way it seems that demon risk will be analysed relatively early, but also dismissed quickly: within the religious framework it is not a likely existential risk in most religions. In reality few if any religious people hold the view that demon summoning is an existential risk, since they tend to think that the end of the world is a religious drama and hence not intended to be triggered by humans – only divine powers or fate gets to start it, not curious demonologists.

## That wasn’t too painful?

Have we defeated the demon summoning problem? Not quite. There is no reason for all those priors to sum to 1 – they are suggested by people with very different and even crazy views – and even if we normalise them we get a very long and heavy tail of weird small risks. We can easily use up any amount of effort on this, effort we might want to spend on doing other useful things like actually reducing real risks or doing fun particle physics.

There might be solutions to this issue by reasoning backwards: instead of looking at how X could cause Y that could cause Z that destroys the world we ask “If the world would be destroyed by Z, what would need to have happened to cause it?” Working backwards to Y, Y’, Y” and other possibilities covers a larger space than our initial chain from X. If we are successful we can now state what conditions are needed to get to dangerous Y-like states and how likely they are. This is a way of removing entire chunks of the risk landscape in efficient ways.

This is how I think we can actually handle these small, awkward and likely non-existent risks. We develop mental tools to efficiently get rid of lots of them in one fell sweep, leaving the stuff that needs to be investigated further. But doing this right… well, the devil lurks in the details. Especially the thicket of totally idiosyncratic risks that cannot be handled in a general way. Which is no reason not to push forward, armed with epsilons and Bayes’ rule.

That the unbeliever may have to update a bit in the believer direction may look like a win for the believers. But they, if they are rational, should do a small update into the unbeliever direction. The most important consequence is that now they need to consider existential risks due to non-supernatural causes like nuclear war, AI or particle physics. They would assign them a lower credence than the unbeliever, but as per the usual arguments for the super-importance of existential risk this still means they may have to spend effort on thinking about and mitigating these risks that they otherwise would have dismissed as something God would have prevented. This may be far more annoying to them than unbelievers having to think a bit about demonology.

Emlyn O’Regan makes some great points over at Google+, which I think are worth analyzing:

1. “Should you somehow incorporate the fact that the world has avoided destruction until now into your probabilities?”
2. “Ideas without a tech angle might be shelved by saying there is no reason to expect them to happen soon.” (since they depend on world properties that have remained unchanged.)
3. ” Ideas like demon summoning might be limited also by being shown to be likely to be the product of cognitive biases, rather than being coherent free-standing ideas about the universe.”

In the case of (1), observer selection effects can come into play. If there are no observers on a post demon-world (demons maybe don’t count) then we cannot expect to see instances of demon apocalypses in the past. This is why the cosmic ray argument for the safety of the LHC need to point to the survival of the Moon or other remote objects rather than the Earth to argue that being hit by cosmic rays over long periods prove that it is safe. Also, as noted by Emlyn, the Doomsday argument might imply that we should expect a relatively near-term end, given the length of our past: whether this matters or not depends a lot on how one handles observer selection theory.

In the case of (2), there might be development in summoning methods. Maybe medieval methods could not work, but modern computer-aided chaos magick is up to it. Or there could be rare “the stars are right” situations that made past disasters impossible. Still, if you understand the risk domain you may be able to show that the risk is constant and hence must have been low (or that we are otherwise living in a very unlikely world). Traditions that do not believe in a growth of esoteric knowledge would presumably accept that past failures are evidence of future inability.

(3) is an error theory: believers in the risk are believers not because of proper evidence but from faulty reasoning of some kind, so they are not our epistemic peers and we do not need to update in their direction. If somebody is trying to blow up a building with a bomb we call the police, but if they try to do it by cursing we may just watch with amusement: past evidence of the efficacy of magic at causing big effects is nonexistent. So we have one set of evidence-supported theories (physics) and another set lacking evidence (magic), and we make the judgement that people believing in magic are just deluded and can be ignored.

(Real practitioners may argue that there sure is evidence for magic, it is just that magic is subtle and might act through convenient coincidences that look like they could have happened naturally but occur too often or too meaningfully to be just chance. However, the skeptic will want to actually see some statistics for this, and in any case demon apocalypses look like they are way out of the league for this kind of coincidental magic).

Emlyn suggests that maybe we could scoop all the non-physics like human ideas due to brain architecture into one bundle, and assign them one epsilon of probability as a group. But now we have the problem of assigning an idea to this group or not: if we are a bit uncertain about whether it should have $\epsilon$ probability or a big one, then it will get at least some fraction of the big probability and be outside the group. We can only do this if we are really certain that we can assign ideas accurately, and looking at how many people psychoanalyse, sociologise or historicise topics in engineering and physics to “debunk” them without looking at actual empirical content, we should be wary of our own ability to do it.

So, in short, (1) and (2) do not reduce our credence in the risk enough to make it irrelevant unless we get a lot of extra information. (3) is decent at making us sceptical, but our own fallibility at judging cognitive bias and mistakes (which follows from claiming others are making mistakes!) makes error theories weaker than they look. Still, the really consistent lack of evidence of anything resembling the risk being real and that claims internal to the systems of ideas that accept the possibility imply that there should be smaller, non-existential, instances that should be observable (e.g. individual Fausts getting caught on camera visibly succeeding in summoning demons), and hence we can discount these systems strongly in favor of more boring but safe physics or hard-to-disprove but safe coincidental magic.