A tale of 2.5 orthogonality theses

[Arepo]

tl;dr-tl;dr

You can summarise this whole post as ‘we shouldn’t confuse theoretical possibility with likelihood, let alone with theoretical certainty’.

tl;dr

I’m concerned that EA AI-advocates tend to equivocate between two or even three different forms of the orthogonality thesis using a motte and bailey argument, and that this is encouraged by misleading language in the two seminal papers.

• The motte (the trivially defensible position) is the claim that it is theoretically possible to pair almost any motivation set with high intelligence and that AI will therefore not necessarily be benign or human-friendly.

• The inner bailey (a nontrivial but plausible position with which it’s equivocated) is the claim that there’s a substantial chance that AI will be unfriendly and non-benign, and that caution is wise until we can be very confident that it won’t.

• The outer bailey (a still less defensible position with which both are also equivocated) is the claim that we should expect almost no relationship, if any, between intelligence and motivations, and therefore that AI alignment is extremely unlikely.

This switcheroo overemphasises the chance of hostile AI, and so might be causing us to overemphasise the priority of AI work.

Motte: the a priori theoretical possibility thesis

In the paper that introduced the term ‘orthogonality thesis’, Bostrom gave a handful of arguments against a very strong relationship between intelligence and motivation, e.g.

A member of an intelligent social species might also have motivations related to cooperation and competition: like us, it might show in-group loyalty, a resentment of free-riders, perhaps even a concern with reputation and appearance. By contrast, an artificial mind need not care intrinsically about any of those things, not even to the slightest degree.

This seems a reasonable way of disabusing the idea that AI is obviously guaranteed to behave in ‘moral’ ways: all of what we typically think of as intelligence has a common root (Earth-specific evolution), and thus could only be one branch of a much larger tree—of which we have a very biased view. This and arguments like it focus on theoretical possibility: they aim to establish the very weak thesis that almost no pairing of intelligence and motivation is logically inconsistent or ruled out by physics.

But coining this argument ‘orthogonality’ seems to have been a poor choice of name. ‘Orthogonality’ is not normally a statistical concept, so has no natural interpretation. But by far the most upvoted comments on these two stats.stackexchange threads explicitly understand it ‘not correlated’, an interpretation that would imply the much stronger outer bailey—that AI alignment is extremely unlikely.

This ambiguity continues in the other prominent paper on the subject, General Purpose Intelligence: Arguing the Orthogonality Thesis, in which Stuart Amstrong argues in more depth for ‘a narrower version of the [orthogonality] thesis’.

For example, Armstrong initially states that he’s arguing for the thesis that ‘high-intelligence agents can exist having more or less any final goals’ - ie theoretical possibility—but then adds that he will ‘be looking at proving the … still weaker thesis [that] the fact of being of high intelligence provides extremely little constraint on what final goals an agent could have’ - which I think Armstrong meant as ‘there are very few impossible pairings of high intelligence and motivation’, but which much more naturally reads to me as ‘high intelligence is almost equally as likely to be paired with any set of motivations as any other’.

He goes on to describe a purported counterthesis to ‘orthogonality’, which he labels ‘convergence’, but which I would call necessary strong convergence (see Appendix): ‘all human-designed superintelligences would have one of a small set of goals’, which he notes as a needlessly strong claim for contradicting orthogonality. He spends the rest of the paper arguing only against this overly strong claim. To quote his summary in full:

Denying the Orthogonality thesis thus requires that:

1. There are goals G, such that 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 with goal G can exist.

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.

It’s not clear what proposition these points are supposed to establish. Most of them might be required to assert necessary strong convergence (some could be false in a world where creators could trick or blackmail their superintelligence into giving advice that they could use maliciously but where the intelligence itself was always benignly motivated); but it seems plausible that all of them are false and that we nonetheless live in a world where there will in expectation be moderate or even extremely strong correlation or convergence among superintelligent motivations, just as there is among human motivations.

And it’s still possible that all of them are true. The motte itself is ambiguous between two sub-sub-theses: 1) that we know of no mathematical proof or physical law necessitating a very strong relationship between intelligence and motivation, and 2) that is no such law. The first is so trivial as to not need any argument, so Armstrong and Bostrom’s arguments seem more relevant to building an intuition for the second. But it remains conceivable that we could discover functions of some property of intelligence that, controlling for other factors, perfectly predict some property of motivation. Any given physical law, such as the function of mass that outputs gravitational force, would have looked wildly improbable if similarly speculated on well before its discovery.

The paper’s conclusion has similar ambiguity:

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 no 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/​superefficient.

Few if any interactions in the real world ‘are known’ or ‘can be relied on’ with perfect certainty, and yet there are many phenomena we rely on to differing degrees—the sun rising and setting, economic and social patterns of humans, the laws of physics not radically changing from one moment to the next, etc. So, interpreted in what seems to me the natural way, this conclusion implies that AI risk is big enough to concern us in practice, rather than that the weaker thesis that the paper actually argued for, that it is conceivable that AI could have strange motivations. The latter thesis should still concern us, but neither of these papers give us any reason to think AI actually will be unsafe.

To be clear, I don’t think either paper was intended to mislead—I can just see reasons why their language would have done so, and I fear they have led many people in the EA community to an even stronger conclusion.

Outer bailey: the very weak statistical relationship or necessitated misalignment thesis

Beyond theoretical possibility and likelihood lies the far more ambitious claim that there’s only a very weak or no statistical relationship between intelligence and motivations; in other words that AI is almost certain to be human-incompatible. This is the claim etymologically implied by the word ‘orthogonality’, which is perhaps how it’s become the claim that some EAs believe the orthogonality thesis makes.

Anecdotally, I was originally spurred to write this post after multiple conversations with EAs who responded to my expressions of scepticism about the level of risk from AI by paraphrasing Bostrom’s line that ‘Intelligence [in the sense of instrumental reasoning] and motivation can be thought of as a pair of orthogonal axes on a graph’. In the context of challenging my scepticism, this implies both that this way of thinking about it is actually an argument rather than an illustration of a conclusion, and that it’s an argument specifically against scepticism of necessitated misalignment, and therefore in favour of the very weak relationship thesis.

It was difficult to test the extent of this confusion without accidentally resolving it. I posted one poll asking ‘what the orthogonality thesis implies about [a relationship between] intelligence and terminal goals’, to which 14 of 16 respondents selected the option ‘there is no relationship or only an extremely weak relationship between intelligence and goals’, but someone pointed out that respondents might have interpreted ‘no relationship’ as ‘no strict logical implication from one to the other’. The other options hopefully gave context, but in a differently worded version of the poll 10 of 13 people picked options describing theoretical possibility. But early on someone commented on that poll asserting that ‘no statistical relationship is … clearly false’, which presumably discouraged people from choosing it.

Either way, this was a very small sample population. Nonetheless my best guess is that somewhere between a sizeable minority and a sizable majority of EAs familiar with the orthogonality thesis (20-80%) believe the ‘very weak statistical relationship’ interpretation of what it states.

Given that ‘very weak statistical relationship’ is equivalent to the Stack Exchange-sanctioned ‘no correlation’ interpretation of ‘orthogonality’, this belief about what the thesis implies isn’t unreasonable among anyone who hasn’t carefully read the seminal papers. But it’s concerning that in 10 years of using this term our community has failed to disambiguate between the near-opposite meanings.

[Edit: two recent prominent EA sources seem to have interpreted the orthogonality thesis this way:

In David Denkenberger, Anders Sandberg, Ross John Tieman, and Joshua M. Pearce’s paper Long term cost-effectiveness of resilient foods for global catastrophes compared to artificial general intelligence they say ‘the goals of the intelligence are essentially arbitrary [48]’, with the reference pointing to Bostrom’s essay.

In Chapter 4 of What We Owe the Future, MacAskill describes ‘The scenario most closely associated with [the book Superintelligence being] one in which a single AI agent designs better and better versions of itself, quickly developing abilities far greater than the abilities of all of humanity combined. Almost certainly, its aims would not be the same as humanity’s aims.’ It’s been a long time since I read Superintelligence, so I can’t remember whether Bostrom does present this claim, or whether MacAskill has subsequently interpreted it that way. Either way, this seems like an importantly misleading claim from one of the most prominent members of the EA movement]

Inner bailey: The evidential thesis against probable convergence or correlation

This is the claim that we should not in practice expect a strong relationship between intelligence of any level and terminal goals. It’s an empirical claim, and so must stand on its own, without support from arguments for theoretical possibility.

And perhaps it can—the point of this post is not to evaluate all evidential arguments, but to emphasise that arguments for theoretical possibility have virtually no bearing on the evidential thesis.

So by focusing on theoretical possibility, Bostrom’s and Armstrong’s papers show almost nothing about how likely or how strong a relationship actually is. The flipside of Bostrom’s observation of common roots being potentially biasing is that if some phenomenon has universally been observed with common cause, that seems like evidence both that 1) if it were produced by some other cause it might have different properties, which would support the case for a weaker relationship, and 2) that it can only be produced by the observed cause—or by sufficiently precise emulation of that cause as to share its properties, such as by simulating evolutionary processes digitally—which would support the case for a stronger relationship. In fact elsewhere in his paper Bostrom says ‘it would be easier to create an AI with simple goals like [maximising paperclips],’ actually asserting a fairly strong relationship, albeit one that may not comfort us.

Bostrom also invokes Hume’s is-ought cleft:

David Hume thought that beliefs alone (say, about what is a good thing to do) cannot motivate action: some desire is required. This would support the orthogonality thesis by undercutting one possible objection to it, namely, that sufficient intelligence might entail the acquisition of certain beliefs, and that these beliefs would necessarily produce certain motivations.

But Hume’s claim is far from settled. Since there’s a wide range of metaethical views among philosophers and EAs—i.e. many people believe their own intelligence has led them to specific moral beliefs—we shouldn’t assume the is-ought divide is necessarily insurmountable, or that this is an argument which EAs will necessarily find compelling.

Bostrom offers some further arguments for the evidential orthogonality thesis, but a) these all have the form ‘one could believe X, and X would imply noncorrelation’ where one might reasonably think X could be false or that the implication was weak (eg ‘it would suffice to assume, for example, that an agent—be it ever so intelligent—can be motivated to pursue any course of action if the agent happens to have certain standing desires of some sufficient, overriding strength.’), and b) anecdotally these nuances often don’t seem to carry over into typical EA conversations on the subject. In Robert Miles’ popular video for example, he describes belief in an (unspecified) relationship as a ‘mistake’, which can be redressed simply by stating the is-ought problem.

Some reasons to expect correlation

It’s extremely difficult to justify strong statements about likelihood of convergence or correlation. I assert no view on how likely they are or in what form, beyond that EAs should be more cautious about claiming they’re very unlikely. But in the interest of showing why I think it’s still an importantly open question, and to give an intuition as to how one could believe in strong convergence or correlation I’ll describe some scenarios under which they could look very likely:

1. Developing AI with human-compatible motivations turns out to be approximately as easy as developing it with any other motivations, or at least not vastly harder (eg if some step turns out to involve training an AI that responds in a comprehensible way), and because the vast majority of AI developers want human-compatible motivations in their creation, in practice that’s what the majority of general AIs develop^[1]

2. Evolution might have taken the easiest path: AI with wholly alien motivations could be possible in principle, but so difficult to create from first principles that whole brain emulation of evolved organisms/​artificial evolution are the most practical paths to developing it—and these result in agents with similar motivations to the original brain/​to other evolved organisms^[2]

3. We might default to building AIs as bounded services rather than general optimisers^[3]

4. Developing some key aspect of intelligence turns out to necessarily entail developing some motivation. For example, it turns out to be impossible or much harder to mentally model social behaviour without actually emulating some genuine sense of social responsibility (psychopaths aren’t a counterexample; social-moralistic instincts vary widely, but I know of no example of a human who has none whatsoever)

5. Complex behavioural patterns turn out to be impossible/​much harder to develop without involving consciousness—whatever that is—and consciousness turns out to have an inherent terminal drive toward positive utility (or toward some other common goal)

6. Some version of pragmatism is right, such that values and facts turn out to be part of the same framework, and just as we apparently have universal epistemological axioms—despite them having no non-self-referential basis—it will turn out we have universal ‘moral axioms’

7. There’s some other ‘correct’ way of reasoning about morality, such as a logical process of eliminating incoherent moralities, that sufficiently high intelligences tend to use to reach particular motivations^[4]

8. There might be a non-motivating but relatively easy to define moral truth, such that we optionally can and actually do program AIs to care about it

9. Some totally nonhumanlike set of motivations turns out to be much easier to develop (as Bostrom suggested), but these really are in some moral-realistic sense, better motivations than our own

Each of these seems plausible to me except 8 and 9, since I’m not a moral realist—but many smarter people than me are. The first is perhaps the most important, since the overwhelming desire among software engineers to not wipe out the world could outweigh even very high abstract theoretical difficulty in making safe AI. In scenarios 1, 2, and perhaps 3-5 there could be strong convergence in the short term and much less in the long run. But for practical purposes, this seems good enough—if benign or human-friendly AI has a decent first-mover advantage then paperclippers will have very little hope of conquering the universe.

Conclusion

Even if we think alignment is very likely, as long as there’s any uncertainty it makes sense to remain concerned about AI safety—but the higher credence we have in such alignment, the more we should prioritise competing concerns.

If you have arguments in favour of the evidential thesis, I’d encourage you to write them up as top level posts for the forum or as academic papers rather than (or as well as) posting them in response to this, since the subject seems too important for substantive cases to get lost in a comments section! Also, the arguments given for the orthogonality thesis may be useful for dislodging complacency about intelligent agents ‘obviously’ being moral.

But my primary claims have been:

• The ‘orthogonality thesis’ is a misleading name for those arguments

• Much of the language around those arguments is equivocal

• Understood properly the thesis describes a claim so weak it has almost no practical relevance

• That claim could nevertheless still be false

• It gives almost no information about the relevant and open questions around the probability of AI having any given motivations

• So we should refer to it sparingly if at all

Appendix: Terminology

As the main body shows, orthogonality discussions suffer from a lack of clarity around some key terms. Following Bostrom and Amstrong I use ‘morality’, ‘terminal goals’, and ‘motivations’ more or less interchangeably—I don’t think any confusion in this discussion lies there. ‘Intelligence’ is thornier, but I’m using it equivalently to Bostrom and Armstrong: ‘something like instrumental rationality—skill at prediction, planning, and means-ends reasoning in general’. This is a shaky definition, since skill at these things may be hard to disentangle from the results you’re trying to predict and plan, but again I don’t think anything that issue affects any of the arguments in this essay.

But the statements about potential relationships between intelligence and motivation need to be clarified. Below I list some non-exhaustive classes of thesis one could plausibly hold about such a relationship:

Relationship type^[5]

Since there’s no natural ordering of motivations or even necessarily of intelligence—they may not even have discrete values—I don’t think there’s any natural definition of the following terms. In what follows I give my best effort at sufficiently precise definitions of what they intuitively mean to me, which I hope don’t wildly misrepresent what Armstrong and Bostrom had in mind.

• Correlation: an agent’s general intelligence predicts its motivations.

An example of ‘correlation’. There isn’t really any way to think of this as orthogonal axes on a two-dimensional graph. What would the y-axis represent? And I’ve snuck in ‘IQ’ as a quantifiable proxy for general intelligence in a way that could be problematic. That doesn’t mean that any particular interpretation of ‘orthogonality’ doesn’t hold (you could present it as multiple axes or on multiple graphs), but it highlights the awkwardness of the analogy

• Convergence: the higher an agent’s general intelligence, the more predictable its motivations are (we could state this in reverse, i.e. that lower intelligence could be more predictive, but that thesis doesn’t seem very relevant whether or not it’s true. Universally benevolent ostriches won’t help us much if superintelligences are vastly diverse in their goals).^[6]

An example of ‘convergence’; again, this isn’t representable as axes on a two-dimensional graph

• Independence: there is no or very weak (see below) correlation, convergence, or any other relationship between an agent’s level of intelligence and its motivations.

For most purposes we don’t care that much about the difference between correlation and convergence towards greater intelligence, but it seems worth recognising them as distinct concepts. Non-convergent strong correlation might allow for superintelligence which seems neither benign nor human friendly, for example.

To present a more natural interpretation we need to have a much more tightly defined y-axis, specifically one with orderable elements. And this is likely to be most understandable in the real world if they have cardinality. As far as I can see, this forces you to explicitly treat one particular (necessarily orderable, preferably cardinal) axiology as the benchmark against which we can then track dis/​conformity.

An example of a graph with orthogonal axes representing intelligence and (a much more specific subquestion about) motivation, which may or may not feature (here well-defined) correlation

Relationship possibility^[5:1]

• Theoretically possible: it’s not literally impossible for a particular relationship type to hold, or for an entity to exist with almost any given pairing of intelligence and motivation.

• Necessitated or near-necessitated: it is guaranteed or almost guaranteed that a particular relationship type will hold.

• Evidential (ie anything in between): some specific view on the probability of a particular relationship type holding (such views need substantially greater definition than the extreme cases, since one could make many unconnected statements for example about statistical significance, strength of effect, class of effect).

Relationship specificity^[7]

• Strong: relatively strong correlation (i.e. better predictive ability) or convergence (predictive ability increases relatively fast), or perhaps convergence to a relatively small set of intelligence/​motivation pairings.

• Weak: not strong.

Behavioural Destinations^[7:1]

• Human-friendly: high intelligences will tend towards human-friendly behaviour.

• Benign: high intelligences will tend towards morally optimal behaviour, whatever—if anything—that turns out to be. Human friendliness is not guaranteed.

• Aligned: this could either be synonymous with ‘human-friendly’, or mean ‘either human-friendly or benign’. Elsewhere this is obviously an important distinction which easily gets overlooked, but the distinction doesn’t matter much to this post. For what it’s worth, I think of it as more like the latter.

• Other: Something that is neither benign nor human friendly. Further details are not particularly relevant...

‘The orthogonality thesis’ as explicitly argued for seems to be a claim of ‘non-necessary correlation and non-necessary convergence’ with no implication about specificity or destination, though Bostrom briefly asserts something like ‘probable convergent low specificity correlation towards non-human-friendly behaviour’ - and see main body for other interpretations people have held.

Acknowledgements

I owe a debt to Simon Marshall, Johan Lugthart, Siao Si Looi, David Kristoffersson, John Halstead, Emrik Garden for many helpful discussions and invaluable comments on this post. Mistakes, discrepancies and accidental insults of anyone’s mother are all mine.

---

1. ↩︎

   Ben Garfinkel has informally argued that a version of this scenario is likely. Elsewhere and in semi-public docs that I didn’t get his permission to share, he’s argued for other reasons to expect convergence (I note them here since I’m fairly confident he would be willing to share them with anyone who emailed him expressing interest).

2. ↩︎

   In mild support of this, Joshua Greene has argued that utilitarianism is the one moral system that can’t be explained by evolution selecting for tribal instincts, since by definition utilitarianism is impartial between all tribes; in other words, the capacity for utilitarian motivations is something evolution got stuck with despite it conferring negative survival and reproductive prospects.

3. ↩︎

   This seems more consistent with AI development to date at least than Yudkowsky’s vision of ‘the “AI arrow” creeping steadily up the scale of intelligence, moving past mice and chimpanzees, with AIs still remaining “dumb” because AIs can’t speak fluent language or write science papers.’

4. ↩︎

   Examples of this are commonplace. As a child, I had the goal of being both a palaeontologist and an astronaut. At some stage I figured out that they required such different skillsets that doing both was impossible, and ruled out the goal: a realisation which required both a certain level of intelligence and reflection. One could argue that these were merely instrumental goals, but that seems like playing a semantic game—my motivations were changed by my intelligence. If we believe terminal goals relate to anything more pluralist than (say) hedonistic utilitarianism, then we can easily imagine inconsistency in such goals.

   It seems likely that sufficiently high intelligence would reveal an increasing number of such inconsistencies in our motivations; if so, this would necessarily cause some level of motivational convergence unless high intelligence also caused us to develop as many new goals as it ruled out.

5. ↩︎↩︎

   Relationship possibility and type are logically independent—one could hold any combination of them.

6. ↩︎

   As noted Armstrong describes convergence as ‘all human-designed superintelligences would have one of a small set of goals,’ which is both overly strong (‘all’) and not a full definition (what about intelligences above and below whatever would qualify as a superintelligence?), but if we imagine it generalising it seems roughly consistent with the definition I’ve given.

7. ↩︎↩︎

   Not applicable to claims of literal independence.

[John G. Halstead]

I’m a bit surprised not to see this post get more attention. My impression is that for a long time a lot of people put significant weight on the orthogonality argument. As Sasha argues, it is difficult to see why it should update us towards the view that AI alignment is difficult or an important problem to work on, let alone by far the most important problem in human history. I would be curious to hear its proponents explain what they think of Sasha’s argument.

For example, in his response to bryan caplan on the scale of AI risk, Eliezer Yudkowsky makes the following argument:

“1. Orthogonality thesis – intelligence can be directed toward any compact goal; consequentialist means-end reasoning can be deployed to find means corresponding to a free choice of end; AIs are not
automatically nice; moral internalism is false.

2. Instrumental convergence – an AI doesn’t need to specifically hate you to hurt you; a
paperclip maximizer doesn’t hate you but you’re made out of atoms that it can use to make paperclips, so leaving you alive represents an opportunity cost and a number of foregone paperclips. Similarly,
paperclip maximizers want to self-improve, to perfect material technology, to gain control of resources, to persuade their programmers that they’re actually quite friendly, to hide their real thoughts from their programmers via cognitive steganography or similar strategies, to give no sign of value disalignment until they’ve achieved near-certainty of victory from the moment of their first overt strike, etcetera.

3. Rapid capability gain and large capability differences – under scenarios seeming more plausible than not, there’s the possibility of AIs gaining in capability very rapidly, achieving large absolute
differences of capability, or some mixture of the two. (We could try to keep that possibility non-actualized by a deliberate effort, and that effort might even be successful, but that’s not the same as the avenue
not existing.)

4. 1-3 in combination imply that Unfriendly AI is a critical Problem-to-be-solved, because AGI is not automatically nice, by default does things we regard as harmful, and will have avenues
leading up to great intelligence and power.”

This argument does not work. This argument shows that AI systems will not necessarily be aligned. It tells us nothing about whether they are likely to be aligned or whether it will be easy to align AI systems. All of the above is completely compatible with the view that AI will be easy to align and we will obviously try and to align them eg since we don’t all want to die. To borrow the example from ben garfinkel, cars could in principle be given any goals. This has next to no bearing on what goals they will have in the real world or the set of likely possible futures.

[Steven Byrnes]

The quote above is an excerpt from here, and immediately after listing those four points, Eliezer says “But there are further reasons why the above problem might be difficult to solve, as opposed to being the sort of thing you can handle straightforwardly with a moderate effort…”.

[John G. Halstead]

ah i see i hadn’t seen that

[Max_Daniel]

FWIW my impression is more like “I feel like I’ve heard the (valid) observation expressed in the OP many times before, even though I don’t exactly remember where”, and I think it’s an instance of the unfortunate but common phenomenon where the state of the discussion among ‘people in the field’ is not well represented by public materials.

[Max_He-Ho]

As far as I understand it, orthogonality and instrumental convergence together actually make a case for AI being by default not aligned. The quote from Eliezer here goes a bit beyond the post. For the orthogonality thesis by itself, I agree with you & the main theses of the post. I would interpret “not aligned by default” as something like a random AI is probably not aligned. So I tend to disagree also when just considering these two points. This is also the way I originally understood Bostrom in Superintelligence.

However, I agree that this doesn’t tell you whether aligning AI is hard, which is another question. For this, we at least have the empirical evidence of a lot of smart people banging their heads against it for years without coming up with detailed general solutions that we feel confident about. I think this is some evidence for it being hard.

[Arepo]

(Epistemic status of this comment: much weaker than of the OP)

I am suspicious a) of a priori non-mathematical reasoning being used to generate empirical predictions on the outside view and b) of this particular a priori non-mathematical reasoning on the inside view. It doesn’t look like AI algorithms have tended to get more resource grabby as they advance. AlphaZero will use all the processing power you throw at it, but it doesn’t seek more. If you installed the necessary infrastructure (and, ok, upgraded the storage space), it could presumably run on a ZX Spectrum.

And very intelligent humans don’t seem profoundly resource grabby, either. For every Jeff Bezos you have an Edward Witten, who obsessively dedicates dedicating his or her own time to some passion project but does very little to draw external resources towards it.

So based on existing intelligences, satisficing behaviour seems more like the expected default than maximising.

[Greg_Colbourn]

AlphaZero isn’t smart enough (algorithmically speaking). From Human Compatible (p.207):

Life for AlphaGo during the training period must be quite frustrating: the better it gets, the better its opponent gets—because its opponent is a near-exact copy of itself. Its win percentage hovers around 50 percent, no matter how good it becomes. If it were more intelligent—if it had a design closer to what one might expect of a human-level AI system—it would be able to fix this problem. This AlphaGo++ would not assume that the world is just the Go board, because that hypothesis leaves a lot of things unexplained. For example, it doesn’t explain what “physics” is supporting the operation of AlphaGo++’s own decisions or where the mysterious “opponent moves” are coming from. Just as we curious humans have gradually come to understand the workings of our cosmos, in a way that (to some extent) also explains the workings of our own minds, and just like the Oracle AI discussed in Chapter 6, AlphaGo++ will, by a process of experimentation, learn that there is more to the universe than the Go board. It will work out the laws of operation of the computer it runs on and of its own code, and it will realize that such a system cannot easily be explained without the existence of other entities in the universe. It will experiment with different patterns of stones on the board, wondering if those entities can interpret them. It will eventually communicate with those entities through a language of patterns and persuade them to reprogram its reward signal so that it always gets +1. The inevitable conclusion is that a sufficiently capable AlphaGo++ that is designed as a rewardsignal maximizer will wirehead.

From wireheading, it might then go on to resource grab to maximise the probability that it gets a +1 or maximise the number of +1s it’s getting (e.g. filling planet sized memory banks with 1s); although already it would have to have a lot of power over humans to be able to convince them to reprogram it by sending messages via the go board!

I don’t think the examples of humans (Bezos/​Witten) are that relevant, in as much as we are products of evolution, and are “adaption executors” rather than “fitness maximisers”, are imperfectly rational, and tend to be (broadly speaking) aligned/​human-compatible, by default.

[Steven Byrnes]

I think the “real” orthogonality thesis is what you call the motte. I don’t think the orthogonality thesis by itself proves “alignment is hard”; rather you need additional arguments (things like Goodhart’s law, instrumental convergence, arguments about inner misalignment, etc.).

I don’t want to say that nobody has ever made the argument “orthogonality, therefore alignment is hard”—people say all kinds of things, especially non-experts—but it’s a wrong argument and I think you’re overstating how popular it is among experts.

Armstrong initially states that he’s arguing for the thesis that ‘high-intelligence agents can exist having more or less any final goals’ - ie theoretical possibility—but then adds that he will ‘be looking at proving the … still weaker thesis [that] the fact of being of high intelligence provides extremely little constraint on what final goals an agent could have’ - which I think Armstrong meant as ‘there are very few impossible pairings of high intelligence and motivation’, but which much more naturally reads to me as ‘high intelligence is almost equally as likely to be paired with any set of motivations as any other’.

I think the last part of this excerpt (“almost equally”) is unfair. I mean, maybe some readers are interpreting it that way, but if so, I claim that those readers don’t know what the word “constraint” means. Right?

I posted one poll asking ‘what the orthogonality thesis implies about [a relationship between] intelligence and terminal goals’, to which 14 of 16 respondents selected the option ‘there is no relationship or only an extremely weak relationship between intelligence and goals’, but someone pointed out that respondents might have interpreted ‘no relationship’ as ‘no strict logical implication from one to the other’. The other options hopefully gave context, but in a differently worded version of the poll 10 of 13 people picked options describing theoretical possibility.

I think the key reason that knowledgeable optimistic people are optimistic is the fact that humans will be trying to make aligned AGIs. But neither of the polls mention that. The statement “There is no statistical relationship between intelligence and goals” is very different from “An AGI created by human programmers will have a uniformly-randomly-selected goal”; I subscribe to (something like) the former (in the sense of selecting from “the space of all possible intelligent algorithms” or something) but I put much lower probability on (something like) the latter, despite being pessimistic about AGI doom. Human programmers are not uniformly-randomly sampling the space of all possible intelligent algorithms (I sure hope!)

[Arepo]

Hi Steven,

To clarify, I make no claims about what experts think. I would be moderately surprised if more than a small minority of them pay any attention to the orthogonality thesis, presumably having their own nuanced views how AI development might pan out. My concern is with the non-experts who make up the supermajority of the EA community—who frequently decide whether to donate their money to AI research vs other causes, who are prioritising deeper dives, who in some cases decide whether to make grants, who are deciding whether to become experts, or who are building communities that informally or formally give careers advice to others, and who generally contribute to the picture of ‘what effective altruism is about’, both steering the culture and informing the broader public’s perception.

I think the last part of this excerpt (“almost equally”) is unfair. I mean, maybe some readers are interpreting it that way, but if so, I claim that those readers don’t know what the word “constraint” means. Right?

See above—it doesn’t really matter whether they don’t know what it means if it affects their decisions. I’m not accusing anyone of wrongdoing, just giving an explanation as to why it seems many EAs have come to believe the stronger versions of the thesis and trying to discourage them from holding it without decent evidence.

I subscribe to (something like) [no statistical relationship] (in the sense of selecting from “the space of all possible intelligent algorithms” or something)

I don’t know how to understand ‘the space of all possible intelligent algorithms’ as a statistical relationship without imagining it populated with actual instances. If I said ‘there’s a statistical relationship between age and death’, I think most people would understand my claim as being true, despite the huge space of all possible old people.

[Steven Byrnes]

My concern is with the non-experts…

My perspective is “orthogonality thesis is one little ingredient of an argument that AGI safety is an important cause area”. One possible different perspective is “orthogonality thesis is the reason why AGI safety is an important cause area”. Your belief is that a lot of non-experts hold the latter perspective, right? If so, I’m skeptical.

I think I’m reasonably familiar with popular expositions of the case for AGI safety, and with what people inside and outside the field say about why or why not to work on AGI safety. And I haven’t come across “orthogonality thesis is the reason why AGI safety is an important cause area” as a common opinion, or even a rare opinion, as far as I can recall.

For example, Brian Christian, Stuart Russell, and Nick Bostrom all talk about Goodhart’s law and/​or instrumental convergence in addition to (or instead of) orthogonality, Sam Harris talks about arms races and fragility-of-value, Ajeya Cotra talks about inner misalignment, Rob Miles talks about all of the above, Toby Ord uses the “second species argument”, etc. People way outside the field don’t talk about “orthogonality thesis” because they’ve never heard of it.

So if lots of people are saying “orthogonality thesis is the reason why AGI safety is an important cause area”, I don’t know where they would have gotten that idea, and I remain skeptical that this is actually the case.

I don’t know how to understand ‘the space of all possible intelligent algorithms’ as a statistical relationship without imagining it populated with actual instances.

My main claim here is that asking random EA people about the properties of “intelligence” (in the abstract) is different from asking them about the properties of “intelligent algorithms that will actually be created by future AI programmers”. I suspect that most people would feel that these are two different things, and correspondingly give different answers to questions depending on which one you ask about. (This could be tested, of course.)

A separate question is how random EA people conceptualize “intelligence” (in the abstract). I suspect “lots of different ways”, and those ways might be more or less coherent. For example, one coherent possibility is to consider the set of all 2^8000000 possible 1-megabyte source code algorithms, then select the subset that is “intelligent” (operationalized somehow), and then start talking about the properties of algorithms in that set.

[Siao Si]

(disclaimer that I talked to Sasha before he put up this post) but as a ‘random EA person’ I did find reading this clarifying.

It’s not that I believed that “orthogonality thesis the reason why AGI safety is an important cause area”, but that I had never thought about the distinction between “no known law relating intelligence and motivations” and “near-0 statistical correlation between intelligence and motivations”.

If I’d otherwise been prompted to think about it, I’d probably have arrived at the former, but I think the latter was rattling around inside my system 1 because the term “orthogonality” brings to mind orthogonal vectors.

[John G. Halstead]

see the example from yudkowsky above. As I understand it, he is the main person who has encouraged rationalists to be focused on AI. In trying to explain why AI is important to a smart person (Bryan Caplan) he appeals to the orthogonality argument which has zero bearing on whether AI alignment will be hard or worth working on.

[Greg_Colbourn]

The Orthogonality Thesis is useful to counter the common naive intuition that sufficiently intelligent AI will be benevolent by default (which a lot of smart people tend to hold prior to examining the arguments in any detail). But as Steven refers to above, it’s only one component of the argument for taking AGI x-risk seriously (and Yudkowsky lists several others in that example. He leads with orthogonality to prime the pump; to emphasise that common human intuitions aren’t useful here.).

[John G. Halstead]

Hi Greg, I don’t think anyone would ever have held that it is logically impossible for AGI not to be aligned. That is clearly a crazy view. All that orthogonality argument proves is that it is logically possible for AGI not to be aligned, which is almost trivial.

[Greg_Colbourn]

Right, but I think “by default” is important here. Many more people seem to think alignment will happen by default (or at least something along the lines of us being able to muddle through, reasoning with the AI and convincing it to be good, or easily shutting it down if it’s not, or something), rather than the opposite.

[John G. Halstead]

All the argument shows is that it is logically possible for AGI not to be aligned. Since Bryan Caplan is a sane human being, it’s improbable that he would ever not have accepted that claim. So, it’s unclear why Yudkowsky would have presented it to him as an important argument about AGI alignment.

[Greg_Colbourn]

So the last Caplan says there is:

“1′. AIs have a non-trivial chance of being dangerously un-nice.

I do find this plausible, though only because many governments will create un-nice AIs on purpose.”

Which to me sounds like he doesn’t really get it. Like he’s ignoring “by default does things we regard as harmful” (which he kind of agrees to above; he agrees with “2. Instrumental convergence”). You’re right in that the Orthogonality Thesis doesn’t carry the argument on it’s own, but in conjunction with Instrumental Convergence (and to be more complete, mesa-optimisation), I think it does.

It’s a shame that Caplan doesn’t reply to Yudkowsky’s follow up:

Bryan, would you say that you’re not worried about 1′ because:

1’a: You don’t think a paperclip maximizer is un-nice enough to be dangerous, even if it’s smarter than us.
1’b: You don’t think a paperclip maximizer of around human intelligence is un-nice enough to be dangerous, and you don’t foresee paperclip maximizers becoming much smarter than humans.
1’c: You don’t think that AGIs as un-nice as a paperclip maximizer are probable, unless those durned governments create AGIs that un-nice on purpose.

[John G. Halstead]

it’s tricky to see what happened in that debate because i have twitter and that blog blocked on weekdays!

[Arepo]

I just posted a reply to a similar comment about orthogonality + IC here.

[Arepo]

‘By default’ seems like another murky term. The orthogonality thesis asserts (something like) that it’s not something you should place a bet at arbitrarily long odds on, but maybe it’s nonetheless very likely to work out, because per Drexler, we just don’t code AI as an unbounded optimiser, which you might still call ‘by default’.

At the moment I have no idea what to think, tbh. But I lean towards focusing on GCRs that definitely need direct action in the short term, such as climate change, over ones that might be more destructive but where the relevant direct action is likely to be taken much further off.

[Greg_Colbourn]

So by ‘by default’ I mean without any concerted effort to address existential risk from AI, or just following “business as usual” with AI development. Yes, Drexler’s CAIS would be an example of this. But I’d argue that “just don’t code AI as an unbounded optimiser” is very likely to fail due to mesa-optimisers and convergent instrumental goals emerging in sufficiently powerful systems.

Interesting you mention climate change, as I actually went from focusing on that pre-EA to now thinking that AGI is a much more severe, and more immediate, threat! (Although I also remain interested in other more “mundane” GCRs.)

[Yitz]

As a singular data point, I’ll submit that until reading this article, I was under the impression that the Orthogonality thesis is the main reason why researchers are concerned.

[John G. Halstead]

agreed! some evidence of that in my comment

[Linch]

I don’t know how to understand ‘the space of all possible intelligent algorithms’ as a statistical relationship without imagining it populated with actual instances

Not my field, but my understanding is that using the uniform prior is pretty normal/​common for theoretical CS.

[Buck]

What do you mean by “uniform prior” here?

[John G. Halstead]

Even if you think a uniform prior has zero information, which is a disputed position in philosophy, we have lots of information to update with here. eg that programmers will want AI systems to have certain motivations, that they won’t want to be killed etc.

[Antoine de Scorraille]

Thank you so much for this post!
It’s very satisfying for me because when I was a newbie in EA I very poorly tried to tackle this topic (my first!), so I see this one is the successful shot!

So conviced that I’ve edited my post to redirect to this one instead.

[Greg_Colbourn]

Thought provoking post, thanks. I think the Orthogonality Thesis (in its theoretical form—your “Motte”) is useful to counter the common naive intuition that sufficiently intelligent AI will be benevolent by default (or at least open to being “reasoned with”).

But (as Steven Byrnes says), it is just one component of the argument that AGI x-risk is a significant threat. Others being Goodhart’s Law and the fragility of human values (what Stuart Russell refers to as the “King Midas problem”), Instrumental Convergence, Mesa-optimisation, the second species argument (what Stuart Russell refers to as the “gorilla problem”); and differential technological development (capabilities research outstripping alignment research), arms races, and (lack of) global coordination amidst a rapid increase in available compute (increasing hardware overhang).

I guess you could argue that strong convergence on human-compatible values by default would make most of these concerns moot, but there is little to suggest that this is likely. Going through your “Some reasons to expect correlation”, I think that 1-4 don’t address the risks from mesa-optimisation and instrumental convergence (on seeking resources etc—think turning the world into “computronium”). In general, it seems that things have to be completely water-tight in order to avoid x-risk. We might asymptote toward human-compatibility of ML systems, but all the doom flows through the gap between the curve and the axis. Making it completely watertight is an incredibly difficult challenge. Especially as it needs to be done on the first try when deploying AGI.

5-8 are interesting: perhaps (to use your terms) if some form of moral exclusivism bottoming out to valence utilitarianism is true, and the superintelligence discovers it by default, we might be ok (but even then, your 9 may apply).

[Greg_Colbourn]

Riffing on possible reasons to be hopeful, I recently compiled a list of potential “miracles” (including empirical “crucial considerations” [/​wishful thinking]) that could mean the problem of AGI x-risk is bypassed:

• Possibility of a failed (unaligned) takeoff scenario where the AI fails to model humans accurately enough (i.e. realise smart humans could detect its “hidden” activity in a certain way). [This may only set things back a few months to years; or could lead to some kind of Butlerian Jihad if there is a sufficiently bad (but ultimately recoverable) global catastrophe (and then much more time for Alignment the second time around?)].

• Valence realism being true. Binding problem vs AGI Alignment.

  • Omega experiencing every possible consciousness and picking the best? [Could still lead to x-risk in terms of a Hedonium Shockwave].

• Moral Realism being true (and the AI discovering it and the true morality being human-compatible).

• Natural abstractions leading to Alignment by Default?

• Rohin’s links here.

• AGI discovers new physics and exits to another dimension (like the creatures in Greg Egan’s Crystal Nights).

• Simulation/​anthropics stuff.

• Alien Information Theory being true!? (And the aliens having solved alignment).

I don’t think I put more than 10% probability on them collectively though, and my P(doom) is high enough to consider it “crunch time”.

[Dawn Drescher]

Thanks for the thorough argumentation!

I’m unsure whether this is just a nitpick or too much of a personal take, but which precise version of the orthogonality thesis goes through has little effect on how worried I am about AGI, and I’m worried that the nonexpert reader this article is meant for will come away thinking that it does.

The argument for worry about AGI is, in my mind, carried by:

1. Cooperation failures in multipolar AGI takeoffs, and

2. Instrumental convergence around self-preservation (and maybe resource acquisition but not sure),

combined with the consideration that it might all go well a thousand times, but when the 1042nd AGI is started, it might not. And I imagine that once AGIs are useful, lots of them will be started by many different actors.

Conversely, I filed the orthogonality thesis away as a counterargument to an argument that I’ve heard a few times, something like, “Smarter people tend to be nicer, so we shouldn’t worry about superintelligence, because it’ll just be super nice.” A weak orthogonality thesis, a counterargument that just shows that that is not necessarily the case, is enough to defend the case for worry.

I think I subscribe to a stronger formulation of the orthogonality thesis, but I’d have to think long and hard to come up with ways in which that would matter. (I’m sure it does in some subtle ways.)

[Max_He-Ho]

Thanks for this post! I think it’s especially helpful to tease apart theoretical possibility and actual relationships (such as correlation) between goals and intelligence (under different situations). As you say, the orthogonality thesis has almost no implications for the actual relations between them.

What’s important here is the actual probability of alignment. I think it would be very valuable to have at least a rough baseline/​ default value since that is just the general starting point for predicting and forecasting. I’d love to know if there’s some work done on this (even if just order of magnitude estimations) or if someone can give it mathematical rigor. Most importantly, I think we need a prior for the size and dimensionality of the state space of possible values/​goals. Together with a random starting point of an AI in that state space, we should be able to calculate a baseline value from which we then update based on arguments like the ones you mention as well as negative ones. If we get more elaborate in our modeling, we might include an uninformative/​neutral prior for the dynamics of that state space based on other variables like intelligence which is then equally subject to updates from arguments and evidence.

Considering the fragility of human values/​ the King Midas problem – that is in brief the difficulty of specifying human values completely & correctly while they likely make up a very tiny fraction in a huge state space of possible goals/​values, I expect this baseline to be an extremely low value.

Turning to your points on updating from there (reasons to expect correlation), while they are interesting, I feel very uncertain about each one of them. At the same time instrumental convergence, inner alignment, Goodhart’s Law, and others seem to be (to different degrees) strong reasons to update in the opposite direction. I’d add here the empirical evidence thus far of smart people not succeeding in finding satisfactory solutions to the problem. Of course, you’re right that 1. is probably the strongest reason for correlation. Yet, since the failure modes that I’m most worried about involve accidental mistakes rather than bad intent, I’m not sure whether to update a lot based on this. I’m overall vastly uncertain about this point since AI developers’ impact seems to involve predicting how successful we will be in both finding and implementing acceptable solutions to the alignment problem.

I feel like the reasons you mention to expect correlation should be further caveated in light of a point Stuart Russel makes frequently: Even if there is some convergence towards human values in practice for a set of variables of importance to some approximation, it seems unlikely that this covers all the variables we care about & we should expect other unconstrained variables about which we might care to be set to extreme values since that’s what optimizers tend to do.

One remark on “convergence” in the terminology section. You write

lower intelligence could be more predictive [of motivations], but that thesis doesn’t seem very relevant whether or not it’s true.

I disagree, you focus on the wrong case there (benevolent ostriches). If we knew lower intelligence to be more (and higher intelligence to be less) predictive of goals, it would be a substantial update from our baseline of how difficult alignment is for an AGI thus making alignment harder and progressively so in the development of more intelligent systems. That would be important information.

Finally, like some previous commenters, I also don’t have the impression that the orthogonality thesis is (typically seen as) a standalone argument for the importance of AIS.