General Purpose Intelligence: Arguing The Orthogonality Thesis

1

 Analysis and Metaphysics

GENERAL PURPOSE I NTELLIGENCE : ARGUING THE ORTHOGONALITY THESIS

STUART ARMSTRONG
stuart.armstrong@philosophy.ox.ac.uk
Future of Humanity Institute, Oxford Martin School
Philosophy Department, University of Oxford

In his paper “The Superintelligent Will”, Nick Bostrom formalised the
Orthogonality thesis: the idea that the final goals and intelligence levels of artificial
agents are independent of each othe r. This paper presents arguments for a (narrower)
version of the thesis . It proceed s through three steps. First it shows that
superintelligent agents with essentially arbitrary goals can exist in our universe –
both as theoretical impractical agents such a s AIXI and as physically possible real -
world agents . Then it argues that if humans are capable of building human -level
artificial intelligences, we can build them with an extremely broad spectrum of
goals. Finally it shows that the same result holds for any superintelligent agent we
could directly or indirectly build. This result is relevant for arguments about the
potenti al motivations of future agents: knowing an artificial agent is of high
intelligence d oes not allow us t o presume that it will be moral, we will need to figure
out its goals directly.

Keywords: AI ; Artificial Intelligence; efficiency; intelligence ; goals;
orthogonality

1 The Orthogonality thesis
Scientists and mathematicians are the stereotypical examples of high
intelligence humans. But the ir morality and ethics have been all over the
map. On modern political scales, they can be left - (Oppenheimer) or right -
wing (von Neumann) and historically they have slotted into most of the
politi cal groupings of their period ( Galois , Lavoisier). Ethically, they have
ranged from very humanitarian (Darwin, Einstein outside of his private

2
 life), through amoral (von Braun) to commercially belligerent (Edison) and
vindictive (Newton). Few scientists ha ve been put in a position where they
could demonstrate genuine ly evil behaviour, but there have been a few of
those (Teichmüller, Philipp Lenard, Ted Kaczynski, Shirō Ishii).
Of course, m any scientists have been absolutely conventional in their
views and a ttitudes given the society of their time. But the above examples
hint that their ethics are not strongly impacted by their high intelligence;
intelligence and ethics seem ‘orthogonal’ (varying independently of each
other, to some extent). If we turn to the case of (potential) artificial
intelligences we can ask whether that relation continues: would high
intelligence go along with certain motivations and goals , or are they
unrelated ?
To avoid the implicit anthropomorphisation in terms such as ‘ethics’, we
will be looking at agents ‘final goals’ – the ultimate objectives they are
aiming for. Then t he Orthogonality thesis , due to Nick Bostrom (Bostrom,
2012) , states that:

Intelligence and final goals are orthogonal axes along which
possible agents can freely vary. In other words, more or less any
level of intelligence could in principle be combined with more or less
any final goal.

It is analogous to Hume’s thesis about the independence of reason and
morality (Hume, 1739) , but applied more narrowly, using the normatively
thinner concept s ‘intelligence’ and ‘final goals’ rather than ‘reason’ and
‘morality’ .
But even ‘intelligence’, as generally used, has too many connotations. A
better term would be efficiency, or instrumental rationality, or the ability to
effectively solve problems given limited knowledge and resources (Wang,
2011) . Nevertheless , we will be sticking with terminology such as
‘intelligent agent’, ‘artificial intelligence’ or ‘superintelligence’, as they are
well established, but using them synonymously with ‘efficient agent’,
artificial efficiency’ and ‘superefficient algorithm’. The relevant criteria is
whether the agent can effectively ac hieve its goals in general situations, not
whether its inner process matches up with a particular definition of what
intelligence is.
3
 Thus an artificial intelligence (AI) is an artificial algorithm,
deterministic or probabilistic , implemented on some device , that
demonstrates an ability to achieve goals in varied and general situations1.
We don’t assume that it need be a computer program, or a well laid -out
algorithm with clear loops and structures – artificial neural networks or
evolved genetic algori thms certainly qualify.
A human level AI is defined to be an AI that can successfully
accomplish any task at least as well as an average human would (to avoid
worrying about robot bodies and such -like, we may restrict the list of tasks
to those accomplisha ble over the internet). Thus we would expect the AI to
hold conversation s about Paris Hilton’s sex life, to compose ironic
limericks, to shop for the best deal on Halloween costumes and to debate
the proper role of religion in politics, at least as well as an average human
would.
A superhuman AI is similarly defined as an AI that would exceed the
ability of the best human in all (or almost all) tasks. It would do the best
research, write the most successful novels, run companies and motivate
employees bette r than anyone else. In areas where there may not be clear
scales (what’s the world’s best artwork?) we would expect a majority of the
human population to agree the AI’s work is among the very best.
Nick Bostrom’s paper argued that the Orthogonality thesis does not
depend on the Humean theory of motivation , but could still be true under
other philosophical theories . It should be immediately apparent that the
Orthogonality thesis is related to arguments about moral realism. Despite
this, we will not address t he fertile and extensive literature on this subject.
Firstly, because it is contentious: different schools of philosophical thought
have different interpretations of the truth and meaning of moral realism,
disputes that cannot be currently resolved empiric ally. Since we are looking
to resolve a mainly empirical question – what systems of motivations could

1 We need to assume it has goals, of course. Determining whether
something qualifies as a goal -based agent is very tricky (researcher Owain
Evans is trying to establish a rigorous definition), but this paper will adopt
the somewhat informal definition that an agent has goals if it achieves
similar outcomes from very different starting positions. If the agent ends
up making ice cream in any circumstances, we can assume ice creams are
in its goals.
4
 we actually code into a putative AI – this theoretical disagreement is highly
problematic.
Secondly, we hope that by approaching the issue from the computational
perspective, we can help shed new light on these issues. After all, we do not
expect that the trigger mechanism of a cruise missile to block detonation
simply because people will die – but would an “ultra -smart bomb” behave
the same way? By e xploring the goals of artificial systems up to higher
level of efficiency, we may contribute to seeing which kinds of agents are
susceptible to moral realism arguments, and which are not.
Thus t his paper will content itself with present ing direct arguments for
the Orthogonality thesis . We will assume throughout that human level AIs
(or at least human comparable AIs) are possible (if not, the thesis is void of
useful content). We will also take the position that humans the mselves can
be viewed as non -determi nistic algorithms2: this is not vital to the paper, but
is useful for comparison of goals between various types of agents. We will
do the same with entities such as committees of humans, institutions or
corporations, if these can be considered to be acting in an agent -like way.
The thesis itself might be critiqued for over -obviousness or triviality – a
moral anti -realist, for instance, could find it too evident to need defending.
Nevertheless, t he argument that AIs – or indeed, any sufficiently intelligent
being – would necessarily behave morally is a surprisingly common one. A.
Kornai, for instance, considers it as a worthwhile starting point for
investigations into AI morality (Kornai, 2013) . He bases his argument on A.
Gewith’s approach in his book, Reason and Morality (Gewirth, 1978) (the
book’s argument can be found in a summarised form in one of E. M.
Adams ’s papers (Adams, 1980) ) in which it is argued that all agents must
follow a “Principle of Generic Consistency” that causes them to behave in
accordance with all other agent’s generic rights to freedom and well -being.
Others have argued that certain specific moralities are attractors in the space
of moral systems, towards which any AI will tend if they start off with
certain mild constraints (Waser, 2008) . Because of these and other examples

2 Since every law of nature is algorithmic (with some probabil istic process
of known odds), and no exceptions to these laws are known, neither for
human nor non -human processes.
5
 (and some online c riticism of the Orthogonality thesis3), we thought the
thesis was worth defending explicitly, and that the argument brought out in
its favour would be of general interest to the general discussion.

1.1 Qualifying the Orthogonality thesis
The Orthogonality thesis, taken literally, is false. Some motivations are
mathematically incompatible with changes in intelligence (“I want to prove
the Gödel statement for the being I would be if I were more intelligent” ).
Some goals specifically refer to the intelligence of the agent, directly (“I
want to be much less efficient !”) or indirectly (“I want to impress people
who want me to be much less efficient !”). Though we could make a case
that an agent wanting to be less efficient could initially be of any
intelligence le vel, it won’t stay there long, and it’s hard to see how an agent
with that goal could have become intelligent in the first place. So we will
exclude from consideration those goals that intrinsically refer to the
intelligence level of the agent.
We will als o exclude goals that are so complex or hard to describe that
the complexity of the goal becomes crippling for the agent. If the agent’s
goal takes five planets worth of material to describe, or if it takes the agent
twenty years each time it checks what it s goal is, then it’s obvious that that
agent can’t function as an intelligent being on any reasonable scale.
Many have made the point that there is likely to be convergence in
instrumental goals (Omohundro, 2008) . Whatever their final goals, it would
generally be in any agent’s interest to accumulate more power, to become
more intelligence and to be able to cooperate with other agents of similar
ability (and to have all the negotiation, threatening and cajoling ski lls that
go along with that cooperation). Note the similarity with what John Rawls
called ‘primary goods’ (Rawls, 1971) . We will however be focusing

3 See for example
http://philosophicaldisquisitions.blogspot.co.uk/2012/04/bostrom -on-
superintelligence -and.html , which criticise the thesis specifically.
6
 exclusively on final goals, as the instrumental goals are merely tools to
accomplish these4.
Further we will not try to show that intelligence and final goals can vary
freely, in any dynamical sense (it could be quite hard to define this). Instead
we will look at the thesis as talking about possible states: that there exist
agents of all levels of intelligence with any given goals. Since it’s always
possible to make an agent stupider or less efficient, what we are really
claiming is t hat there could exist possible high-intelligence agents with any
given goal. Thus the restricted Orthogonality thesis that we will be
discussing is:

High -intelligence agents can exist having more or less any final
goals (as long as these goals are of feas ible complexity, and do not
refer intrinsically to the agent’s intelligence )5.

We will be looking at two variations of the “can exist” clause: whether
the agent can exist in theory, and whether we could build such an agent
(given that we could build an AI at all). Though evidence will be presented
directly for this thesis in the theoretic agent case, the resu lts of this paper
cannot be considered to “prove” the thesis for agents we could build
(though they certainly raise its likelihood). In that case, we will be looking
at proving a still weaker thesis:

The fact of being of high intelligence p rovides extreme ly little
constraint on what final g oals an agent could have (as long as these
goals are of feasible complexity, and do not refer intrinsically to the
agent’s intelligence).

4 An AI skilled in cooperation would drop this if cooperation no longer
served its purpose; similarly, an AI accumulati ng power and resources
would stop doing this if it found better ways of achieving its goals.
5 Even logically impossible goals can exist: “construct a disproof of Modus
Ponens (within classical logic)” is a perfectly fine goal for an intelligence to
have – it will quickly realise that this translates to “prove classical logic is
inconsistent”, a task mathematicians have occasionally attempted.
7
 That thesis still has nearly all the relevant practical implications that the
strong Orthogonality thesis does.

1.2 Orthogonality in practice for AI designers
The arguments presented in this paper are all theoretical. They posit that
AIs with certain goals either ‘can exist’, or that ‘if we could build an AI, we
could build one with any g oal’. In practice, the first AIs, if and when they
are created, will be assembled by a specific team, using specific methods,
and with specific goals in mind. They may be more or less successful at
inculcating the goals into the AI (or, as is common in com puter
programming, they may inculcate the goals exactly, only to realise later that
these weren’t the goals they really wanted). The AI may be trained by
interacting with certain humans in certain situations, or by understanding
certain ethical principles, or by a myriad of other possible methods, which
will likely focus on a narrow target in the space of goals. The relevance of
the Orthogonality thesis for AI designers is therefore mainly limited to a
warning: that high intelligence and efficiency are not enough to guarantee
positive goals, and that they thus need to work carefully to inculcate the
goals they value into the AI.

2 Orthogonality for theoretic agents
If we were to step back for a moment and consider, in our mind’s eyes,
the sp ace of every possi ble algorithm, peering into their goal systems and
teasing out some measure of their relative intelligence s, would we expect
the Orthogonality thesis to hold? Since we are not worrying about
practicality or constructability, all that we would require is th at for any
given goal system (within the few constraints enumerated above) , there
exists a theoretically implementable algorithm of high intelligence.
Any measurable6 goal can be paired up with a reward signal: an agent
gets a reward for achieving states of the world desired by the goal, and
denied these rewards for actions that fail to do so. Among reward signal

6 Measuring a goal brings up subtle issues with the symbol grounding
problem and similar problems. We’ll ignore the se issues in the present
paper .
8
 maximisers, the AIXI is the theoretically best agent the re is, more
successful at reaching its goals (up to a finite constant) than any other agent
(Hutter, 2005) . AIXI itself is incomputable, but there are computable
variants such as AIXItl or G ödel machines (Schmidhuber, 2007) that
approximate AIXI’s efficiency . These methods work for whatever reward
signal plugged into them. Or we could simply imagine a supercomputer
with arbitrarily large amounts of computing power and a decent
understanding of the laws of physics ( a ‘Laplace demon’ (Laplace, 1814)
capable of probabilistic reasoning ), placed ‘outside the universe’ and
computing the future course of events. Paired with an obedient active agent
inside the universe with a me asurable goal , for which it would act as an
advisor , this would also constitute an ‘ultimate agent’. Thus i n the extreme
theoretical case, the Orthogonality thesis seems true.
There is only one problem with these agents: they are either impossible
in pract ice (AIXI or Laplace’s demon), or require incredibly large amounts
of computing resources to work. Let us step down from the theoretical
pinnacle and require that these agents could actually exist in our world (still
not requiring that we be able or likely to build them ).
An interesting thought experiment occurs here. We could imagine an
AIXI -like super -agent, with all its impractical resources, that is tasked to
design and train an AI that could exist in our world, and that would
accomplish the super -agent’s goals. Using its own vast intelligence, the
super -agent would therefore design a constrained agent maximally effective
at accomp lishing those goals in our world. Then this agent would be the
high-intelligence real -world agent we are looking for. It doesn’t matter than
the designer is impossible in practice – if the super -agent can succeed in the
theoretical thought experiment, then the trained AI can exist in our world.
This argument generalises to other ways of producing the AI. Thus to
deny the Orthogonality thesis is to assert that there is a goal system G, such
that, among other things:
1. There cannot exist an y efficient real -world algorithm with goal G.
2. If a being with arbitrari ly high resources, intelligence, time and
goal G, were to try design an efficient real -world algorithm with the same
goal, it must fail.
9
 3. If a human society were highly motivated7 to design an efficient
real-world algorithm with goal G, and were given a million years to do so
along with huge amounts of resources , training and knowledge about AI, it
must fail.
4. If a high -resource human society were highly motivated to achieve
the goal G, then it could not do so (here the human society itself is seen as
the algorithm).
5. Same as above, for any hypothetical alien societies.
6. There cannot exist any pattern of reinforcement learning that
would train a highly efficient real-world intelligence to follow the goal G.
7. There cannot exist any evolutionary or environmental pressures
that would evolve a highly efficient real world intelligences follow ing goal
G.
All of these seem extraordinarily strong claims to make! The last claims
all derive from t he first, and merely serve to illustrate how strong the first
claim actually is. Claim 4, in particular, seems to run counter to everything
we know about human nature.

3 Orthogonality for human -level AIs

Of course, even if effici ent agents could exist for all these goals, that
doesn’t mean that we could ever build them, even if we could build AIs. In
this section, we’ll look at the ground for assuming the Orthogonality thesis
holds for human -level agents. Since intelligence isn’t varying much, the
thesis be comes simply:
If we could construct human -level AIs at all, then there is
extremely little constraint on the final goals that such AIs could have
(as long as these goals are of feasible complexity, and do not refer
intrinsically to the agent’s intelligence ).
So, is this true? The arguments in this section are generally independent
of each other, and can be summarised as:

7 A motivation might simply be a threat: some truthful powerful being
saying “Design an algorithm with goal G. If you succeed, I will give you
great goods; if you fail, I will destroy you all. The algorithm will never be
used in practice, so there are no moral objections to it being designed.”
10
 1. Some possible AI designs have orthogonality built right into them.
2. AI goals can reach the span of human goals, which is large.
3. Algorithms can be combined to generate an AI with any easily
measurable goal.
4. Various algorithmic modifications can be used to further expand
the space of possible goals, if needed.

3.1 Utility functions
One classical picture of a rational agent is of an agent with a specific
utility function, which it will then act to maximise in expectation. This
picture encapsulates the Orthogonality thesis: whatever the utility function,
the rational agent will then attempt to maxi mise it, using the approaches in
all cases (planning, analysing input data, computing expected results) . If an
AI is built according to this model , with the utility function being
prescriptive (given to the AI in a program) rather than descriptive (an
abstract formalisation of an agent’s other preferences) , then the thesis would
be trivially true: we could simply substitute the utility function for
whichever one we desired.
However, many putative agent designs are not utility function based,
such a s neural networks , genetic algorithms, or humans. So from now on we
will consider that our agents are not expected utility maximiser s with clear
and separate utility function s, and look at proving Orthogonality in these
harder circumstances.

3.2 The span of h uman motivations
It seems a reasonable assumption that if there exists a human being with
particular goals, and we can program an AI, then we can construct a human -
level AI with similar goals. This is immediately the case if the AI was a
whole brain emulat ion/upload (Sandberg & Bostrom, 2008) , a digital copy
of a specific human mind. Even for more general agents, such as evolved
agents, this remains a reasonable thesis. For a start, we know that real-world
evolution has produced us, so constructing human -like agents that way is
certainly possible. Human minds remain our only real model of general
intelligence, and this strongly direct s and informs our AI designs, which are
likely to be as human -similar as we can make them. Simila rly, human goals
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 are the easiest goals for us to understand, hence the easiest to try and
implement in AI. Hence it seems likely that we could implement most
human goals in the first generation of human -level AIs.
So how wide is the space of human motivati ons8? Our race spans foot -
fetishists, religious saints, serial killers, instinctive accountants, role-
players, self-cannibals, firefighters and conceptual artists. The autistic, those
with exceptional social skills, the obsessive compulsive and some with
split-brains . Being s of great empathy and the many who used to enjoy
torture and executions as public spectacles9. It is evident that the space of
possible human motivations is vast10. For any desire, any particular goal, no
matter how niche11, pathological, bizarre or extreme, as long as there is a
single human who ever had it, we could build and run an AI with the same
goal.
But with AIs we can go even further. We could take any of these goals
as a starting point , make them malleable (as goals are in humans) , and push
them further out. We could provide the AIs with specific reinforcements to
push their goals in extreme directions (reward the saint for ever -more
saintly behaviour) . If the agents are fast enough, we could run whole
societies of them with huge v arieties of evolutionary or social pressures, to
further explore the goal -space.

8 One could argue that we should consider the space of general animal
intelligences – octopuses, supercolonies of social insects, etc... But the
methods described can already produce th ese animal’s types of
behaviours.
9 Even today, many people have had great fun torturing and abusing their
characters in games like “the Sims”
(http://meodia.com/article /281/sadistic -ways -people -torture -their -sims/ ).
The same urges are present, albeit diverted to fictionalised settings.
Indeed games offer a wide variety of different goals that could conceivably
be imported into an AI if it were possible to erase the reali ty/fiction
distinction in its motivation.
10 As can be shown by a glance through a biography of famous people –
and famous means they were generally allowed to rise to prominence in
their own society, so the space of possible motivations was already cut
dow n.
11 Of course, if we built an AI with that goal and copied it millions of times,
it would no longer be niche.
12
 We may also be able to do surgery directly on their goals, to introduce
more yet variety. For example, we could take a dedicated utilitarian charity
worker obsessed with savin g lives in poorer countries (but who doesn’t
interact, or want to interact, directly with those saved), and replace ‘saving
lives’ with ‘maximising the number of paperclips in the universe ’ or any
similar abstract goal. This is more speculative, of course – but there are
other ways of getting similar results.
3.3 Instrumental goals as final goals
If someone were to hold a gun to your head, they could make you do
almost anything. Certainly there are people who, with a gun at their head,
would be willing to do al most anything. A distinction is generally made
between instrumental goals and final goals, with the former being seen as
simply paths to the latter, and interchangeable with other plausible paths .
The gun to your head disrupts the balance: your final goal is simply not to
get shot, while your instrumental goals become what the gun holder wants
them to be, and you put a great amount of effort into accomplishing the
minute details of these instrumental goals. Note that the gun has not
changed your level of intelligence or ability.
This is relevant because instrumental goals seem to be far more varied in
humans than final goals. One can have instrumental goals of filling papers,
solving equations, walking dogs, making money, pushing buttons in various
sequences, opening doors, enhancing shareholder value, assembling cars,
bombing villages or putting sharks into tanks. Or simply doing whatever the
guy with gun at our head orders us to do. If we could accept human
instrumental goals as AI final goals, we wou ld extend the space of goals
quite dramatically.
To do so we would want to put the threatened agent, and the gun
wielder, together into the same AI. Algorithmically there is nothing
extraordinary about this : certain subroutines have certain behaviours
depending on the outputs of other subroutines. The ‘gun wielder ’ need not
be particularly intelligent: it simply needs to be able to establish whether its
goals are being met. If for instance those goals are given by a utility
function then all that is req uired in an automated system that measure
progress toward increasing utility and punishes (or erases) the rest of the AI
if not. The ‘rest of AI’ is just required to be a human -level AI which would
be susceptible to this kind of pressure. Note that we do n ot require that it
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 even be close to human in any way, simply that it place a highest value on
self-preservation (or on some similar small goal that the ‘gun wielder’
would have power over).
For humans, another similar model is that of a job in a corporatio n or
bureaucracy: in order to achieve the money required for their final goals,
some human are willing to perform extreme tasks (organising the logistics
of genocides, weapon design, writing long emotional press releases they
don’t agree with at all). Agai n, if the corporation -employee relationship can
be captured in a single algorithm, this would generate an intelligent AI
whose goal is anything measurable by the ‘corporation’. The ‘money’ could
simply be an internal reward channel, perfectly aligning the incentives.
If the subagent is anything like a human, they would quickly integrate
the other goals into their own motivation12, removing the need for the gun
wielder/corporation part of the algorithm.

3.4 Noise, anti -agents and goal combination
There are further ways of extending the space of goals we could
implement in human -level AIs. One simple way is simply to introduce
noise: fl ip a few bits and subroutines , add bugs and get a new agent. Of
course, this is likely to cause the agent’s intelligence to d ecrease somewhat,
but we have generated new goals. Then, if appropriate, we could use
evolution or other improvements to raise the agent’s intelligence again; this
will likely undo some, but not all of effect of the noise. Or we could use
some of the trick s above to make a smarter agent implement the goals of the
noise -modified agent.
A more extreme example would be to create an anti -agent: an agent
whose single goal is to stymie the plans and goals of single given agent.
This alrea dy happens with vengeful humans, and we would just need to dial
it up: have an anti -agent that would do all it can to counter the goals of a
given agent, even if that agent doesn’t exist (“I don’t care that you’re dead,
I’m still going to despoil your country, because that’s what you’d wanted
me to not do”). This further extends the space of possible goals.

12 Such as the hostages suffering from Stockholm syndrome (de Fabrique,
Romano, Vecchi, & van Hasselt, 2007) .
14
 Different agents with different goals can also be combined into a single
algorithm. With some algorithmic method for the AIs to negotiate their
combined objective and balance th e relative importance of their goals, this
procedure would construct a single AI with a combined goal system. There
would likely be no drop in intelligence/efficiency: committees of two can
work very well towards their common goals, especially if there is some
automatic penalty for disagreements.

3.5 Further tricks up the sleeve
This section started by emphasising the wide space of human goals, and
then introduced tricks to push goal systems further beyond these
boundaries. The list isn’t exhaustive: there are surely more devices and
ideas one can use to continue to extend the space of possible goals for
human -level AIs. Though this might not be enough to get every goal, we
can nearly certainly use these procedures to construct a human -level AI
with any human -comprehensible goal . But would the same be true for
superhuman AIs?

4 Orthogonality for superhuman AIs
We now come to the area where the Orthogonality thesis seems the most
vulnerable. It is one thing to have human -level AIs, or abstract
superintelligent algorithms created ex nihilo, with certain goals. But if ever
the human race were to design a superintelligent AI, there would be some
sort of process involved – directed evolution, recursive self -improvement13,
design by a committee of AIs, or similar – and it seems at least possible that
such a process could fail to fully explore the goal -space. The Orthogo nality
thesis in this context is :
If we could construct superintelligent AIs at all, then there is
extremely little constraint on the final goals that such AIs could have
(as long as these goals are of feasible complexity, and do not refer
intrinsically to the agent’s intelligence).
There are two counter -theses. The weakest claim is:

13 See f or instance E. Yudkowsky ’s design “General Intelligence and Seed AI
2.3” http://singinst.org/ourresearch/publications/GISAI/
15
 Incompleteness: there are large categories of goals tha t no
superintelligence designed by us could have.
A stronger claim is:
Convergence: all human -designed superintelligences would have
one of a small set of goals.
Here ‘small’ means ‘smaller than the space of current human
motivations’, thus very small in compar ison with the space of possible AI
goals. They should be distinguished; Incompleteness is all that is needed to
contradict Orthogonality, but Convergence is often the issue being
discussed. Often C onvergence is stated in terms of a particular model of
meta ethics , to which it is assumed all agents will converge (see some of the
references in the introduction, or various online texts and argument14).

4.1 No convergence
The plausibility of the convergence thesis is highly connected with the
connotations of the terms used in it. “All human -designed rational beings
would follow the same morality (or one of small sets of moralities)” sound s
plausible; in contra st “all human -designed superefficient algorithms would
accomplish the same task” seems ridiculous . To quote an online
commentator, how good at playing chess would a chess computer have to
be before it started feeding the hungry?
Similarly, if there were such a convergen ce, then all self -improving or
constructed superintelligence must fall prey to it, even if it were actively
seeking to avoid it. After all, the self-improving lower -level AIs or the
designers have certain goals in mind (as we’ve seen in the previous sectio n,
if the designers are AIs themselves, they could have potentially any goals in
mind). Obviously, t hey would be less likely to achieve the ir goals if the se
goals were to change as they got more intelligent (Omohundro, 2008) (see
also N. Bostrom’s forthcoming book Superintelligence: Groundwork to a
Strategic Analysis of the Machine Intelligence Revolution ). The same goes
if the superintelligent AI they de signed didn’t share these goals . Hence the
AI designers will be actively trying to prevent such a convergence, if they
suspected that one was likely to happen. If for instance their goals were

14 Such as J. Müller’s “Ethics, risks and opportunities of superintelligences ”
http://www.jonatasmuller.com/superintelligences.pdf
16
 immoral, they would program their AI not to care about morality ; they
would use every trick up their sleeves to prevent the AI’s goals from
drifting from their own.
So the convergence thesis requires that for the vast majority of goals G:
1. It is possible for a superintelligence to exist with goal G (by
section 2).
2. There exists an entity with goal G (by section 3), capable of
building a superintelligent AI.
3. Yet any attempt of that entity to build a superintel ligent A I with
goal G will be a failure, and the superintelligence’s goals will converge on
some other goal.
4. This is true even if the entity is aware of the convergence and
explicitly attempts to avoid it.
5. If the superintelligence were to be constructed by successive self -
improvement, then an entity with goal G operating on itself to boost its
intelligence is unable to do so in a way that would preserve goal G.
This makes the convergence thesis very unlikely. The argument also
works against the incompletene ss thesis, but in a weaker fashion: it seems
more plausible that some types of goals would be unreachable, despite
being theoretically possible.
There is another interesting aspec t of the convergence thesis: these goals
G are to emerge , somehow , without them being aimed for or desired. If one
accepts that goals aimed for will not be reached, one has to ask why
convergence is assumed: why not divergence? Why not assume that though
G is aimed for, random accidents o r faulty implementation will lead to the
AI ending up with one of a muc h wider array of possible goals, rather than a
much narrower one? We won’t delve deeper into this, and simply make the
point that “superintelligent AIs won’t have the goals we want them to have”
is therefore not an ar gument in favour of the convergence thesis.

4.2 Oracles show the way
If the Orthogonality thesis is wrong, then it implies that Oracles are
impossible to build. An Oracle is a superintelligent AI that accurately
answers human questions about the world , such as the likely consequences
of certain policies and decisions (Armstrong, Sandberg, & Bostrom,
17
 2012)15. If such an Oracle could be built, then we could attach it to a
human -level AI with goal G. The human -level AI could then ask the Oracle
what the results of different decisions actions could be, and choose the
action that best accomplishes G. In this way, the combined system would be
a superintelligent AI with goal G.
What makes the “no Oracle” implication even more counterintuit ive is
that any superintelligence must be able to look ahead, design actions,
predict the consequences of its actions, and choose the best one available.
But the convergence and indifference theses imply that this general skill is
one that we can make avai lable only to AIs with certain specific goals.
Though agents with those specific goals are capable of doing effective
predictions, they automatically lose this ability if their goals were to change.

4.3 Tricking the controller
Just as with human -level AIs, one could construct a superintelligent AI
by wedding together a superintelligence with a large motivated committee
of human -level AIs dedicated to implementing a goal G, and checking the
superintelligence’s actions. Thus to de ny the Orthogonality thesis requires
that one believes that the superintelligence is always capable of tricking this
committee, no matter how detaile d and thorough their oversight.
This argument extend s the Orthogonality thesis to moderately
superintellige nt AIs, or to any situation where there ’s a diminishing return
to intelligence. It only fails if we take AI to be fantastically superhuman:
capable of tricking or seducing any collection of human -level beings.

4.4 Temporary f ragments of algorithms , fictional
worlds and extra tricks
These are other tricks that can be used to create an AI with any goals.
For any superintelligent AI, there are certain inputs that will make it behave
in certain ways. For instance, a human -loving moral AI could be compel led

15 Not to be confused with the concept of Oracle in computer science,
which is either an abstract machine capable of instantaneous
computation s in various complexity classes, or mechanism in software
testing.
18
 to follow most goals G for a day, if they were rewarded with something
sufficiently positive afterwards. But its actions for that one day are the
result of a series of inputs to a particular algorithm; if we turned off the AI
after that day, we would h ave accomplished moves towards goal G without
having to reward its “true” goals at all. And then we could continue th e trick
the next day with another copy.
For this to fail, it has to be the case that we can create an algorithm
which will perform certain actions on certain inputs as long as it isn’t turned
off afterwards , but that we cannot create an algorithm that does the same
thing if it was to be turned off.
Another alternative is to create a superintelligent AI that has goals in a
fictional world (suc h as a game or a reward channel) over which we have
control. Then we could trade interventions in the fictional world against
advice in the real world towards whichever goals we desire16.
These two arguments may f eel weaker than the ones before: they are
tricks that may or may not work, depending on the details of the AI ’s setup.
But to deny the Orthogonality thesis requires not only denying that these
tricks w ould ever work, but denying that any tricks or methods that we (or
any human -level AIs) could think up, would ever work at controlling the
AIs. We need to assume superintelligent AIs cannot be controlled in any
way that anyone could think of.

4.5 In summary
Denying the Orthogonality thesis thus requires that:
1. There are goals G, such that an entity an entity with goal G cannot
build a superintelligence with the same goal. This despite the fact that the
entity can build a superintelligence, and that a superintelligence wi th goal G
can exist.

16 Another possibility, for those who believe AIs above a certain level of
intelligence must converge in their motivations , is to hav e a society of AIs
below this level . If the AIs are closely linked, this could be referred to as a
superorganism . Then the whole superorganism could be setup to have a ny
particular goal and yet have high intelligence/efficiency. See
http://lesswrong.com/r/discussion/lw/gzl/amending\_the\_general\_pupose
\_intelligence\_arguing/ for more details.
19
 2. Goal G cannot arise accidentally from some other origin, and
errors and ambiguities do not significantly broaden the space of possible
goals.
3. Oracles and general purpose planners cannot be built .
Superintelligent AIs cannot have their planning abilities repurposed.
4. A superintelligence will always be able to trick its overseers , no
matter how careful and cunning they are.
5. Though we can create an algorithm that does certain actions if it
was not to be turned off after, we cannot create an algorithm that does the
same thing if it was to be turned off after.
6. An AI will always come to care intrinsically about things in the
real world.
7. No tricks can be thought up to successfully constrain the AI’ s
goals: superintelligent AIs simply cannot be controlled.

5 Conclusion
It is not enough to know that an agent is intelligent (or superintelligent).
If we want to know something about its final goals, about the actions it will
be willing to undertake to achieve them, and hence its ultimate impact on
the world, there are n o shortcuts. We have to directly figure out what these
goals are (or figure out a way of programming them in) , and cannot rely on
the agent being moral just because it is superintelligent/superef ficient.

6 Acknowledgements
It gives me great pleasure to acknowledge the help and support of
Anders Sandberg, Nick Bostrom, Toby Ord, Diego Caleiro, Owain Evans,
Daniel Dewey, Eliezer Yudkowsky, Vladimir Slepnev, Viliam Bur, Matt
Freeman, Wei Dai, Will Newsome, Paul Crowley, Mao Shan, Alexander
Kruel, Steve Rayhawk, Tim Tyler, John Nicholas, Ben Hoskin and Rasmus
Eide, as well as those members of the Less Wrong online community going
by the names shminux, and Dmytry. The work was funded by the Future of
Humanity Institute (FHI), in the Department of Philosophy of Oxford
University. The FHI is part of the Oxford Martin School.
20
 7 Notes and References
Adams, E. M. (1980). Gewirth on Reason and Morality. The Review of
Metaphysics, 33 (3), 579 -592.
Armstrong, S., Sandberg, A., & Bostrom, N. (2012). Thinking Inside the Box:
Controlling and Using an Oracle AI. Minds and Machines, 22 (4).
Bostrom, N. (2012). The Superintelligent Will: Motivation and Instrumental
Rationality in Advance Artificial Agents. Minds and Machines, 22 (2), 71 -85.
de Fabrique, N., Romano, S. J., Vecchi, G. M., & van Hasselt, V. B. (2007).
Understanding Stockholm Syndrome. FBI Law Enforcement Bulletin (Law
Enforcement Communication Unit), 76 (7), 10-15.
Gewirth, A. (1978). Reason and Morality. University of Chicago Press.
Hume, D. (1739). A Treatise of Human Nature.
Hutter, M. (2005). Universal algorithmic intelligence: A mathematical top -down
approach. In B. Goertzel, & C. Pennachin (Eds.), Artiﬁ cial General Intelligence.
Springer -Verlag.
Kornai, A. (2013). Bounding the impact of AGI. Oxford 2012 Winter
Intelligence conference on AGI. Oxford.
Laplace, P. -S. (1814). Essai philosophique sur les probabilités.
Omohundro, S. M. (2008). The Basic AI Dri ves. In P. Wang, B. Goertzel, & S.
Franklin (Eds.), Artificial General Intelligence: Proceedings of the First AGI
Conference (Vol. 171).
Rawls, J. (1971). A Theory of Justice . Harvard University Press.
Sandberg, A., & Bostrom, N. (2008). Whole brain emula tion: A roadmap.
Future of Humanity Institute Technical report, 2008 -3.
Schmidhuber, J. (2007). Gödel machines: Fully self -referential optimal universal
self-improvers. In Artificial General Intelligence. Springer.
Wang, P. (2011). The assumptions on knowl edge and resources in models of
rationality. International Journal of Machine Consciousness, 3 (1), 193 -218.
Waser, M. R. (2008). Discovering the foundations of a universal system of
ethics as a road to safe artificial intelligence. Biologically inspired co gnitive
architectures: Papers from the AAAI fall symposium , (pp. 195 -200).