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:

Invariant set fractal (blue) for inversion in the red ellipses. Generated using an IFS algorithm.

Invariant set fractal (blue) for inversion in the red ellipses. Generated using an IFS algorithm.
Invariant set fractal (blue) for inversion in the red ellipses. Generated using an IFS algorithm.

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:

Mappings of the ellipses by their inversions: each of the four main ellipses map the other three to their interior but distort the shape of two of them.
Mappings of the ellipses by their inversions: each of the four main ellipses map the other three to their interior but distort the shape of two of them.

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

Nested mappings of the ellipses in the chain, bounding the invariant set. Colors are mixtures of the colors of the generating ellipses, with an increase in saturation.
Nested mappings of the ellipses in the chain, bounding the invariant set. Colors are mixtures of the colors of the generating ellipses, with an increase in saturation.

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:

Invariant set of chain of four outer ellipses and a circle tangent to them on the inside.
Invariant set of chain of four outer ellipses and a circle tangent to them on the inside.

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

Circle of life

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

I found infinity on the stairsAs 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

Infinite ShardI 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.

Bad eternities

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

XXI: Azathoth PleromaMy 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 Hanson n=4 Calabi-Yau manifold projected into 3-space.
The Hanson n=4 Calabi-Yau manifold projected into 3-space.

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 patches making up the Hanson Calabi-Yau surface.
The patches making up the Hanson Calabi-Yau surface.

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:

Boundary of the piece of the Hanson Calabi-Yau manifold displayed.
Boundary of the piece of the Hanson Calabi-Yau manifold displayed.

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”.

Hanson's Calabi-Yau surface for N=2, N=3, N=5 and N=8.
Hanson’s Calabi-Yau surface for N=2, N=3, N=5 and N=8.

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

Knotted surface for n1=4, n2=3.
Knotted surface for n1=4, n2=3.

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

ShadowsThe Future of Life Institute discusses the

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.)

My adventures in demonology

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

Sidewalk pentagramI 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.

Addendum (2017-02-14)

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.

Best problems to work on?

80,000 hours has a lovely overview of “What are the biggest problems in the world?” The best part is that each problem gets its own profile with a description, arguments in favor and against, and what already exists. I couldn’t resist plotting the table in 3D:

Most important problems according to 80,000 Hours, according to scale, neglectedness, and solvability.
Most important problems according to 80,000 Hours, according to scale, neglectedness, and solvability. Color denotes the sum of the values.

There are of course plenty of problems not listed; even if these are truly the most important there will be a cloud of smaller scale problems to the right. They list a few potential ones like cheap green energy, peace, human rights, reducing migration restrictions, etc.

I recently got the same question, and here are my rough answers:

  • Fixing our collective epistemic systems. Societies work as cognitive systems: acquiring information, storing, filtering and transmitting it, synthesising it, making decisions, and implementing actions. This is done through individual minds, media and institutions. Recently we have massively improved some aspects through technology, but it looks like our ability to filter, organise and jointly coordinate has not improved – in fact, many feel it has become worse. Networked media means that information can bounce around multiple times acquiring heavy bias, while filtering mechanisms relying on authority has lost credibility (rightly or wrongly). We are seeing all sorts of problems of coordinating diverse, polarised, globalised or confused societies. Decision-making that is not reality-tracking due to (rational or irrational) ignorance, bias or misaligned incentives is at best useless, at worst deadly. Figuring out how to improve these systems seem to be something with tremendous scale (good coordination and governance helps solve most problems above), it is fairly neglected (people tend to work on small parts rather than figuring out better systems), and looks decently solvable (again, many small pieces may be useful together rather than requiring a total perfect solution).
  • Ageing. Ageing kills 100,000 people per day. It is a massive cause of suffering, from chronic diseases to loss of life quality. It causes loss of human capital at nearly the same rate as all education and individual development together. A reduction in the health toll from ageing would not just save life-years, it would have massive economic benefits. While this would necessitate changes in society most plausible shifts (changing pensions, the concepts of work and life-course, how families are constituted, some fertility reduction and institutional reform) the cost and trouble with such changes is pretty microscopic compared to the ongoing death toll and losses. The solvability is improving: 20 years ago it was possible to claim that there were no anti-ageing interventions, while today there exist enough lab examples to make this untenable. Transferring these results into human clinical practice will however be a lot of hard work. It is also fairly neglected: far more work is being spent on symptoms and age-related illness and infirmity than root causes, partially for cultural reasons.
  • Existential risk reduction: I lumped together all the work to secure humanity’s future into one category. Right now I think reducing nuclear war risk is pretty urgent (not because of the current incumbent of the White House, but simply because the state risk probability seems to dominate the other current risks), followed by biotechnological risks (where we still have some time to invent solutions before the Collingridge dilemma really bites; I think it is also somewhat neglected) and AI risk (I put it as #3 for humanity, but it may be #1 for research groups like FHI that can do something about the neglectedness while we figure out better how much priority it truly deserves). But a lot of the effort might be on the mitigation side: alternative food to make the world food system more resilient and sun-independent, distributed and more robust infrastructure (whether better software security, geomagnetic storm/EMP-safe power grids, local energy production, distributed internet solutions etc.), refuges and backup solutions. The scale is big, most are neglected and many are solvable.

Another interesting set of problems is Robin Hanson’s post about neglected big problems. They are in a sense even more fundamental than mine: they are problems with the human condition.

As a transhumanist I do think the human condition entails some rather severe problems – ageing and stupidity is just two of them – and that we should work to fix them. Robin’s list may not be the easiest to solve, though (although there might be piecemeal solutions worth doing). Many enhancements, like moral capacity and well-being, have great scope and are very neglected but lose out to ageing because of the currently low solvability level and the higher urgency of coordination and risk reduction. As I see it, if we can ensure that we survive (individually and collectively) and are better at solving problems, then we will have better chances at fixing the tougher problems of the human condition.

Survivorship curves and existential risk

In a discussion Dennis Pamlin suggested that one could make a mortality table/survival curve for our species subject to existential risk, just as one can do for individuals. This also allows demonstrations of how changes in risk affect the expected future lifespan. This post is a small internal FHI paper I did just playing around with survivorship curves and other tools of survival analysis to see what they add to considerations of existential risk. The outcome was more qualitative than quantitative: I do not think we know enough to make a sensible mortality table. But it does tell us a few useful things:

  • We should try to reduce ongoing “state risks” as early as possible
  • Discrete “transition risks” that do not affect state risks matters less; we may want to put them off indefinitely.
  • Indefinite survival is possible if we make hazard decrease fast enough.

Simple model

Survivorship curve with constant risk.
Survivorship curve with constant risk.

A first, very simple model: assume a fixed population and power-law sized disasters that randomly kill a number of people proportional to their size every unit of time (if there are survivors, then they repopulate until next timestep). Then the expected survival curve is an exponential decay.

This is in fact independent of the distribution, and just depends on the chance of exceedance. If disasters happen at a rate \lambda and the probability of extinction \Pr(X>\mathrm{population}) = p, then the curve is S(t) = \exp(-p \lambda t).

This can be viewed as a simple model of state risks, the ongoing background of risk to our species from e.g. asteroids and supernovas.

Correlations

Survivorship curve with gradual rebound from disasters.
Survivorship curve with gradual rebound from disasters.

What if the population rebound is slower than the typical inter-disaster interval? During the rebound the population is more vulnerable to smaller disasters. However, if we average over longer time than the rebound time constant we end up with the same situation as before: an adjusted, slightly higher hazard, but still an exponential.

In ecology there has been a fair number of papers analyzing how correlated environmental noise affects extinction probability, generally concluding that correlated (“red”) noise is bad (e.g. (Ripa and Lundberg 1996), (Ovaskainen and Meerson 2010)) since the adverse conditions can be longer than the rebound time.

If events behave in a sufficiently correlated manner, then the basic survival curve may be misleading since it only shows the mean ensemble effect rather than the tail risks. Human societies are also highly path dependent over long timescales: our responses can create long memory effects, both positive and negative, and this can affect the risk autocorrelation.

Population growth

Survivorship curve with population increase.
Survivorship curve with population increase.

If population increases exponentially at a rate G and is reduced by disasters, then initially some instances will be wiped out, but many realizations achieve takeoff where they grow essentially forever. As the population becomes larger, risk declines as \exp(- \alpha G t).

This is somewhat similar to Stuart’s and my paper on indefinite survival using backups: when we grow fast enough there is a finite chance of surviving indefinitely. The growth may be in terms of individuals (making humanity more resilient to larger and larger disasters), or in terms of independent groups (making humanity more resilient to disasters affecting a location). If risks change in size in proportion to population or occur in different locations in a correlated manner this basic analysis may not apply.

General cases

Survivorship curve with increased state risk.
Survivorship curve with increased state risk.

Overall, if there is a constant rate of risk, then we should expect exponential survival curves. If the rate grows or declines as a power t^k of time, we get a Weibull distribution of time to extinction, which has a “stretched exponential” survival curve: \exp(-t/ \lambda)^k.

If we think of risk increasing from some original level to a new higher level, then the survival curve will essentially be piece-wise exponential with a more or less softly interpolating “knee”.

Transition risks

Survivorship curve with transition risk.
Survivorship curve with transition risk.

A transition risk is essentially an impulse of hazard. We can treat it as a Dirac delta function with some weight w at a certain time t, in which case it just reduces the survival curve so \frac{S(\mathrm{after }t)}{S(\mathrm{before }t)}=w. If t is randomly distributed it produces a softer decline, but with the same magnitude.

Rectangular survival curves

Human individual survival curves are rectangularish because of exponentially increasing hazard plus some constant hazard (the Gompertz-Makeham law of mortality). The increasing hazard is due to ageing: old people are more vulnerable than young people.

Do we have any reason to believe a similar increasing hazard for humanity? Considering the invention of new dangerous technologies as adding more state risk we should expect at least enough of an increase to get a more convex shape of the survival curve in the present era, possibly with transition risk steps added in the future. This was counteracted by the exponential growth of human population until recently.

How do species survival curves look in nature?

There is “van Valen’s law of extinction” claiming the normal extinction rate remains constant at least within families, finding exponential survivorship curves (van Valen 1973). It is worth noting that the extinction rate is different for different ecological niches and types of organisms.

However, fits with Weibull distributions seem to work better for Cenozoic foraminifera than exponentials (Arnold, Parker and Hansard 1995), suggesting the probability of extinction increases with species age. The difference in shape is however relatively small (k≈1.2), making the probability increase from 0.08/Myr at 1 Myr to 0.17/Myr at 40 Myr. Other data hint at slightly slowing extinction rates for marine plankton (Cermeno 2011).

In practice there are problems associated with speciation and time-varying extinction rates, not to mention biased data (Pease 1988). In the end, the best we can say at present appears to be that natural species survival is roughly exponentially distributed.

Conclusions for xrisk research

Survival curves contain a lot of useful information. The median lifespan is easy to read off by checking the intersection with the 50% survival line. The life expectancy is the area under the curve.

Survivorship curve with changed constant risk, semilog plot.
Survivorship curve with changed constant risk, semilog plot.

In a semilog-diagram an exponentially declining survival probability is a line with negative slope. The slope is set by the hazard rate. Changes in hazard rate makes the line a series of segments.
An early reduction in hazard (i.e. the line slope becomes flatter) clearly improves the outlook at a later time more than a later equal improvement: to have a better effect the late improvement needs to reduce hazard significantly more.

A transition risk causes a vertical displacement of the line (or curve) downwards: the weight determines the distance. From a given future time, it does not matter when the transition risk occurs as long as the subsequent hazard rate is not dependent on it. If the weight changes depending on when it occurs (hardware overhang, technology ordering, population) then the position does matter. If there is a risky transition that reduces state risk we should want it earlier if it does not become worse.

Acknowledgments

Thanks to Toby Ord for pointing out a mistake in an earlier version.

Appendix: survival analysis

The main object of interest is the survival function S(t)=\Pr(T>t) where T is a random variable denoting the time of death. In engineering it is commonly called reliability function. It is declining over time, and will approach zero unless indefinite survival is possible with a finite probability.

The event density f(t)=\frac{d}{dt}(1-S(t)) denotes the rate of death per unit time.

The hazard function \lambda(t) is the event rate at time t conditional on survival until time t or later. It is \lambda(t) = - S'(t)/S(t). Note that unlike the event density function this does not have to decline as the number of survivors gets low: this is the overall force of mortality at a given time.

The expected future lifetime given survival to time t_0 is \frac{1}{S(t_0)}\int_{t_0}^\infty S(t)dt. Note that for exponential survival curves (i.e. constant hazard) it remains constant.

Review of the cyborg bill of rights 1.0

Cyborg NewtonThe Cyborg Bill of Rights 1.0 is out. Rich MacKinnon suggests the following rights:

FREEDOM FROM DISASSEMBLY
A person shall enjoy the sanctity of bodily integrity and be free from unnecessary search, seizure, suspension or interruption of function, detachment, dismantling, or disassembly without due process.

FREEDOM OF MORPHOLOGY
A person shall be free (speech clause) to express themselves through temporary or permanent adaptions, alterations, modifications, or augmentations to the shape or form of their bodies. Similarly, a person shall be free from coerced or otherwise involuntary morphological changes.

RIGHT TO ORGANIC NATURALIZATION
A person shall be free from exploitive or injurious 3rd party ownerships of vital and supporting bodily systems. A person is entitled to the reasonable accrual of ownership interest in 3rd party properties affixed, attached, embedded, implanted, injected, infused, or otherwise permanently integrated with a person’s body for a long-term purpose.

RIGHT TO BODILY SOVEREIGNTY
A person is entitled to dominion over intelligences and agents, and their activities, whether they are acting as permanent residents, visitors, registered aliens, trespassers, insurgents, or invaders within the person’s body and its domain.

EQUALITY FOR MUTANTS
A legally recognized mutant shall enjoy all the rights, benefits, and responsibilities extended to natural persons.

As a sometime philosopher with a bit of history of talking about rights regarding bodily modification, I of course feel compelled to comment.

What are rights?

Artifical handFirst, what is a right? Clearly anybody can state that we have a right to X, but only some agents and X-rights make sense or have staying power.

One kind of rights are legal rights of various kinds. This can be international law, national law, or even informal national codes (for example the Swedish allemansrätten, which is actually not a moral/human right and actually fairly recent). Here the agent has to be some legitimate law- or rule-maker. The US Bill of Rights is an example: the result of a political  process that produced legal rights, with relatively little if any moral content. Legal rights need to be enforceable somehow.

Then there are normative moral principles such as fundamental rights (applicable to a person since they are a person), natural rights (applicable because of facts of the world) or divine rights (imposed by God). These are universal and egalitarian: applicable everywhere, everywhen, and the same for everybody. Bentham famously dismissed the idea of natural rights as “nonsense on stilts” and there is a general skepticism today about rights being fundamental norms. But insofar they do exist, anybody can discover and state them. Moral rights need to be doable.

While there may be doubts about the metaphysical nature of rights, if a society agrees on a right it will shape action, rules and thinking in an important way. It is like money: it only gets value by the implicit agreement that it has value and can be exchanged for goods. Socially constructed rights can be proposed by anybody, but they only become real if enough people buy into the construction. They might be unenforceable and impossible to perform (which may over time doom them).

What about the cyborg rights? There is no clear reference to moral principles, and only the last one refers to law. In fact, the preamble states:

Our process begins with a draft of proposed rights that are discussed thoroughly, adopted by convention, and then published to serve as model language for adoption and incorporation by NGOs, governments, and rights organizations.

That is, these rights are at present a proposal for social construction (quite literally) that hopefully will be turned into a convention (a weak international treaty) that eventually may become national law. This also fits with the proposal coming from MacKinnon rather than the General Secretary of the UN – we can all propose social constructions and urge the creation of conventions, treaties and laws.

But a key challenge is to come up with something that can become enforceable at some point. Cyborg bodies might be more finely divisible and transparent than human bodies, so that it becomes hard to regulate these rights. How do you enforce sovereignty against spyware?

Justification

Dragon leg 2Why is a right a right? There has to be a reason for a right (typically hinted at in preambles full of “whereas…”)

I have mostly been interested in moral rights. Patrick D. Hopkins wrote an excellent overview “Is enhancement worthy of being a right?” in 2008 where he looks at how you could motivate morphological freedom. He argues that there are three main strategies to show that a right is fundamental or natural:

  1. That the right conforms to human nature. This requires showing that it fits a natural end. That is, there are certain things humans should aim for, and rights help us live such lives. This is also the approach of natural law accounts.
  2. That the right is grounded in interests. Rights help us get the kinds of experiences or states of the world that we (rightly) care about. That is, there are certain things that are good for us (e.g.  “the preservation of life, health, bodily integrity, play, friendship, classic autonomy, religion, aesthetics, and the pursuit of knowledge”) and the right helps us achieve this. Why those things are good for us is another matter of justification, but if we agree on the laundry list then the right follows if it helps achieve them.
  3. That the right is grounded in our autonomy. The key thing is not what we choose but that we get to choose: without freedom of choice we are not moral agents. Much of rights by this account will be about preventing others from restricting our choices and not interfering with their choices. If something can be chosen freely and does not harm others, it has a good chance to be a right. However, this is a pretty shallow approach to autonomy; there are more rigorous and demanding ideas of autonomy in ethics (see SEP and IEP for more). This is typically how many fundamental rights get argued (I have a right to my body since if somebody can interfere with my body, they can essentially control me and prevent my autonomy).

One can do this in many ways. For example, David Miller writes on grounding human rights that one approach is to allow people from different cultures to live together as equals, or basing rights on human needs (very similar to interest accounts), or the instrumental use of them to safeguard other (need-based) rights. Many like to include human dignity, another tricky concept.

Social constructions can have a lot of reasons. Somebody wanted something, and this was recognized by others for some reason. Certain reasons are cultural universals, and that make it more likely that society will recognize a right. For example, property seems to be universal, and hence a right to one’s property is easier to argue than a right to paid holidays (but what property is, and what rules surround it, can be very different).

Legal rights are easier. They exist because there is a law or treaty, and the reasons for that are typically a political agreement on something.

It should be noted that many declarations of rights do not give any reasons. Often because we would disagree on the reasons, even if we agree on the rights. The UN declaration of human rights give no hint of where these rights come from (compare to the US declaration of independence, where it is “self-evident” that the creator has provided certain rights to all men). Still, this is somewhat unsatisfactory and leaves many questions unanswered.

So, how do we justify cyborg rights?

In the liberal rights framework I used for morphological freedom we could derive things rather straightforwardly: we have a fundamental right to life, and from this follows freedom from disassembly. We have a fundamental right to liberty, and together with the right to life this leads to a right to our own bodies, bodily sovereignty, freedom of morphology and the first half of the right to organic naturalization. We have a right to our property (typically derived from fundamental rights to seek our happiness and have liberty), and from this the second half of the organic naturalization right follows (we are literally mixing ourselves rather than our work with the value produced by the implants). Equality for mutants follow from having the same fundamental rights as humans (note that the bill talks about “persons”, and most ethical arguments try to be valid for whatever entities count as persons – this tends to be more than general enough to cover cyborg bodies). We still need some justification of the fundamental rights of life, liberty and happiness, but that is outside the scope of this exercise. Just use your favorite justifications.

The human nature approach would say that cyborg nature is such that these rights fit with it. This might be tricky to use as long as we do not have many cyborgs to study the nature of. In fact, since cyborgs are imagined as self-creating (or at least self-modifying) beings it might be hard to find any shared nature… except maybe the self-creation part. As I often like to argue, this is close to Mirandola’s idea of human dignity deriving from our ability to change ourselves.

The interest approach would ask how the cyborg interests are furthered by these rights. That seems pretty straightforward for most reasonably human-like interests. In fact, the above liberal rights framework is to a large extent an interest-based account.

The autonomy account is also pretty straightforward. All cyborg rights except the last are about autonomy.

Could we skip the ethics and these possibly empty constructions? Perhaps: we could see the cyborg bill of rights as a way of making a cyborg-human society possible to live in. We need to tolerate each other and set boundaries on allowed messing around with each other’s bodies. Universals of property lead to the naturalization right, territoriality the sovereignty right universal that actions under self-control are distinguished from those not under control might be taken as the root for autonomy-like motivations that then support the rest.

Which one is best? That depends. The liberal rights/interest system produces nice modular rules, although there will be much arguments on what has precedence. The human nature approach might be deep and poetic, but potentially easy to disagree on. Autonomy is very straightforward (except when the cyborg starts messing with their brain). Social constructivism allows us to bring in issues of what actually works in a real society, not just what perfect isolated cyborgs (on a frictionless infinite plane) should do.

Parts of rights

Alternative limb projectOne of the cool properties of rights is that they have parts – “the Hohfeldian incidents“, after Wesley Hohfeld (1879–1918) who discovered them. He was thinking of legal rights, but this applies to moral rights too. His system is descriptive – this is how rights work – rather than explaining why the came about or whether this is a good thing. The four parts are:

Privileges (alias liberties): I have a right to eat what I want. Someone with a driver’s licence has the privilege to drive. If you have a duty not do do something, then you have no privilege about it.

Claims: I have a claim on my employer to pay my salary. Children have a claim vis-a-vis every adult not to be abused. My employer is morally and legally dutybound to pay, since they agreed to do so. We are dutybound to refrain from abusing children since it is wrong and illegal.

These two are what most talk about rights deal. In the bill, the freedom from disassembly and freedom of morphology are about privileges and claims. The next two are a bit meta, dealing with rights over the first two:

Powers: My boss has the power to order me to research a certain topic, and then I have a duty to do it. I can invite somebody to my home, and then they have the privilege of being there as long as I give it to them. Powers allow us to change privileges and claims, and sometimes powers (an admiral can relieve a captain of the power to command a ship).

Immunities: My boss cannot order me to eat meat. The US government cannot impose religious duties on citizens. These are immunities: certain people or institutions cannot change other incidents.

These parts are then combined into full rights. For example, my property rights to this computer involve the privilege to use the computer, a claim against others to not use the computer, the power to allow others to use it or to sell it to them (giving them the entire rights bundle), and an immunity of others altering these rights. Sure, in practice the software inside is of doubtful loyalty and there are law-enforcement and emergency situation exceptions, but the basic system is pretty clear. Licence agreements typically give you a far

Sometimes we speak about positive and negative rights: if I have a negative right I am entitled to non-interference from others, while a positive right entitles me to some help or goods. My right to my body is a negative right in the sense that others may not prevent me from using or changing my body as I wish, but I do not have a positive right to demand that they help me with some weird bodymorphing. However, in practice there is a lot of blending going on: public healthcare systems give us positive rights to some (but not all) treatment, policing gives us a positive right of protection (whether we want it or not). If you are a libertarian you will tend to emphasize the negative rights as being the most important, while social democrats tend to emphasize state-supported positive rights.

The cyborg bill of rights starts by talking about privileges and claims. Freedom of morphology clearly expresses an immunity to forced bodily change. The naturalization right is about immunity from unwilling change of the rights of parts, and an expression of a kind of power over parts being integrated into the body. Sovereignty is all about power over entities getting into the body.

The right of bodily sovereignty seems to imply odd things about consensual sex – once there is penetration, there is dominion. And what about entities that are partially inside the body? I think this is because it is trying to reinvent some of the above incidents. The aim is presumably to cover pregnancy/abortion, what doctors may do, and other interventions at the same time. The doctor case is easy, since it is roughly what we agree on today: we have the power to allow doctors to work on our bodies, but we can also withdraw this whenever we want

Some other thoughts

Nigel on the screenThe recent case where the police subpoenad the pacemaker data of a suspected arsonist brings some of these rights into relief. The subpoena occurred with due process, so it was allowed by the freedom from disassembly. In fact, since it is only information and that it is copied one can argue that there was no real “disassembly”. There have been cases where police wanted bullets lodged in people in order to do ballistics on them, but US courts have generally found that bodily integrity trumps the need for evidence. Maybe one could argue for a derived right to bodily privacy, but social needs can presumably trump this just as it trumps normal privacy. Right now views on bodily integrity and privacy are still based on the assumption that bodies are integral and opaque. In a cyborg world this is no longer true, and the law may well move in a more invasive direction.

“Legally recognized mutant”? What about mutants denied legal recognition? Legal recognition makes sense for things that the law must differentiate between, not for things the law is blind to. Legally recognized mutants (whatever they are) would be a group that needs to be treated in some special way. If they are just like natural humans they do not need special recognition. We may have laws making it illegal to discriminate against mutants, but this is a law about a certain kind of behavior rather than the recipient. If I racially discriminate against somebody but happens to be wrong about their race, I am still guilty. So the legal recognition part does not do any work in this right.

And why just mutants? Presumably the aim here is to cover cyborgs, transhumans and other prefix-humans so they are recognized as legal and moral agents with the same standing. The issue is whether this is achieved by arguing that they were human and “mutated”, or are descended from humans, and hence should have the same standing, or whether this is due to them having the right kind of mental states to be persons. The first approach is really problematic: anencephalic infants are mutants but hardly persons, and basing rights on lineage seems ripe for abuse. The second is much simpler, and allows us to generalize to other beings like brain emulations, aliens, hypothetical intelligent moral animals, or the Swampman.

This links to a question that might deserve a section on its own: who are the rightsholders? Normal human rights typically deal with persons, which at least includes adults capable of moral thinking and acting (they are moral agents). Someone who is incapable, for example due to insanity or being a child, have reduced rights but are still a moral patient (someone we have duties towards). A child may not have full privileges and powers, but they do have claims and immunities. I like to argue that once you can comprehend and make use of a right you deserve to have it, since you have capacity relative to the right. Some people also think prepersons like fertilized eggs are persons and have rights; I think this does not make much sense since they lack any form of mind, but others think that having the potential for a future mind is enough to grant immunity. Tricky border cases like persistent vegetative states, cryonics patients, great apes and weird neurological states keep bioethicists busy.

In the cyborg case the issue is what properties make something a potential rightsholder and how to delineate the border of the being. I would argue that if you have a moral agent system it is a rightsholder no matter what it is made of. That is fine, except that cyborgs might have interchangeable parts: if cyborg A gives her arm to cyborg B, have anything changed? I would argue that the arm switched from being a part of/property of A to being a part of/property of B, but the individuals did not change since the parts that make them moral agents are unchanged (this is just how transplants don’t change identity). But what if A gave part of her brain to B? A turns into A’, B turns into B’, and these may be new agents. Or what if A has outsourced a lot of her mind to external systems running in the cloud or in B’s brain? We may still argue that rights adhere to being a moral agent and person rather than being the same person or a person that can easily be separated from other persons or infrastructure. But clearly we can make things really complicated through overlapping bodies and minds.

Summary

I have looked at the cyborg bill of rights and how it fits with rights in law, society and ethics. Overall it is a first stab at establishing social conventions for enhanced, modular people. It likely needs a lot of tightening up to work, and people need to actually understand and care about its contents for it to have any chance of becoming something legally or socially “real”. From an ethical standpoint one can motivate the bill in a lot of ways; for maximum acceptance one needs to use a wide and general set of motivations, but these will lead to trouble when we try to implement things practically since they give no way of trading one off against another one in a principled way. There is a fair bit of work needed to refine the incidences of the rights, not to mention who is a rightsholder (and why). That will be fun.

Infinite Newton

Apropos Newton’s method in the complex plane, what happens when the degree of the polynomial goes to infinity?

Towards infinity

Obviously there will be more zeros, so there will be more attractors and we should expect the boundaries of the basins of attraction to become messier. But it is not entirely clear where the action will be, so it would be useful to compress the entire complex plane into a convenient square.

How do you depict the entire complex plane? While I have always liked the Riemann sphere here I tried mapping x+yi to [\tanh(x),\tanh(y)]. The origin is unchanged, and infinity becomes the edges of the square [-1,1]\times [-1,1]. This is not a conformal map, so things will get squished near the edges.

For color, I used (1/2)+(1/2)[\tanh(|z-1|-1), \tanh(|z+1|-1), \tanh(|z-i|-1)] to map complex coordinates to RGB. This makes the color depend on the distance to 1, -1 and i, making infinity white and zero some drab color (the -1 terms at the end determines the overall color range).

Here is the animated result:

What is going on? As I scale up the size of the leading term from zero, the root created by adding that term moves in from infinity towards the center, making the new basin of attraction grow. This behavior has been described in this post on dancing zeros. The zeros also tend to cluster towards the unit circle, crowding together and distributing themselves evenly. That distribution is the reason for the the colorful “flowers” that surround white spots (poles of the Newton formula, corresponding to zeros of the derivative of the polynomial). The central blob is just the attractor of the most “solid” zero, corresponding to the linear and constant terms of the polynomial.

The jostling is amusing: it looks like the roots do repel each other. This is presumably because close roots require a sharp turn of the function, but the “turning radius” is set by the coefficients that tend to be of order unity. Getting degenerate roots requires coefficients to be in a set of measure zero, so it is rare. Near-degenerate roots exist in a positive measure set surrounding that set, but it is still “small” compared to the general case.

At infinity

So what happens if we let the degree go to infinity? As I previously mentioned, the generic behaviour of \sum_{n=1}^\infty a_n z^n where a_n is independent random numbers is a lacunary function. So we should not expect anything outside the unit circle. Inside the circle there will be poles, so there will be copies of the undefined outside region (because of Great Picard’s Theorem (meromorphic version)). Since the function is analytic these copies will be conformal mappings of the exterior and hence roughly circular. There will also be zeros, and these will have their own basins of attraction. A few of the central ones dominate, but there is an infinite number of attractors as we approach the circular border which is crammed with poles and zeros.

Since we now know we will only deal with the unit disk, we can avoid transforming the entire plane and enjoy the results:

Attractors for random 10,000-degree polynomial.
Attractors for random 10,000-degree polynomial.
Attractors for random 10,000-degree polynomial.
Attractors for random 10,000-degree polynomial.

What happens here is that the white regions represents places where points get mapped onto the undefined outside, while the colored fractal regions are the attraction basins for the zeros. And between them there is a truly wild boundary. In the vanilla z^3+1 fractal every point on the boundary is a meeting point of the three basins, a tri-point. Here there is an infinite number of attractors: the boundary consists of points where an infinite number of different attractors meet.

Checking my predictions for 2016

Last year I made a number of predictions for 2016 to see how well calibrated I am. Here is the results:

Prediction Correct?
No nuclear war: 99% 1
No terrorist attack in the USA will kill > 100 people: 95% 1 (Orlando: 50)
I will be involved in at least one published/accepted-to-publish research paper by the end of 2015: 95% 1
Vesuvius will not have a major eruption: 95% 1
I will remain at my same job through the end of 2015: 90% 1
MAX IV in Lund delivers X-rays: 90% 1
Andart II will remain active: 90% 1
Israel will not get in a large-scale war (ie >100 Israeli deaths) with any Arab state: 90% 1
US will not get involved in any new major war with death toll of > 100 US soldiers: 90% 1
New Zeeland has not decided to change current flag at end of year: 85% 1
No multi-country Ebola outbreak: 80% 1
Assad will remain President of Syria: 80% 1
ISIS will control less territory than it does right now: 80% 1
North Korea’s government will survive the year without large civil war/revolt: 80% 1
The US NSABB will allow gain of function funding: 80% 1 [Their report suggests review before funding, currently it is up to the White House to respond. ]

 

US presidential election: democratic win: 75% 0
A general election will be held in Spain: 75% 1
Syria’s civil war will not end this year: 75% 1
There will be no NEO with Torino Scale >0 on 31 Dec 2016: 75% 0 (2016 XP23 showed up on the scale according to JPL, but NEODyS Risk List gives it a zero.)
The Atlantic basin ACE will be below 96.2: 70% 0 (ACE estimate on Jan 1 is 132)
Sweden does not get a seat on the UN Security Council: 70% 0
Bitcoin will end the year higher than $200: 70% 1
Another major eurozone crisis: 70% 0
Brent crude oil will end the year lower than $60 a barrel: 70% 1
I will actually apply for a UK citizenship: 65% 0
UK referendum votes to stay in EU: 65% 0
China will have a GDP growth above 5%: 65% 1
Evidence for supersymmetry: 60% 0
UK larger GDP than France: 60% 1 (although it is a close call; estimates put France at 2421.68 and UK at 2848.76 – quite possibly this might change)
France GDP growth rate less than 2%: 60% 1
I will have made significant progress (4+ chapters) on my book: 55% 0
Iran nuclear deal holding: 50% 1
Apple buys Tesla: 50% 0
The Nikkei index ends up above 20,000: 50% 0 (nearly; the Dec 20 max was 19,494)

Overall, my Brier score is 0.1521. Which doesn’t feel too bad.

Plotting the results (where I bin together things in [0.5,0.55], [0.5,0.65], [0.7 0.75], [0.8,0.85], [0.9,0.99] bins) give this calibration plot:

Plot of average correctness of my predictions for 2016 as a function of confidence.
Plot of average correctness of my predictions for 2016 as a function of confidence (blue). Red line is perfect calibration.

Overall, I did great on my “sure bets” and fairly weakly on my less certain bets. I did not have enough questions to make this very statistically solid (coming up with good prediction questions is hard!), but the overall shape suggests that I am a bit overconfident, which is not surprising.

Time to come up with good 2017 prediction questions.