Discounting the relativistic future

Tyler Cowen’s new book, “Stubborn Attachments,” contains a quote about why we should use low discount rates. He’s right about the conclusion of wanting low discount rates, but I think the example doesn’t quite make the point. (H/t for pointing out the quote goes to Robert Wiblin.)

…it seems odd, to say the least, to discount the well-being of people as their velocity increases. If, for instance, we sent off a spacecraft at near the velocity of light, the astronauts would return to earth, hardly aged, many millions of years hence. Should we pay less attention to the safety of our spaceship… the faster those vehicles go?

As I responded on Twitter, I’m fairly sure this is conceptually wrong because economists are used to thinking about time in Newtonian terms. If we use a proper spacetime metric, the problem, I argue, goes away — and so do some other things.

Let’s work through Tyler’s example. An astronaut leaves earth and immediately accelerates to 0.99c, crushing him into a pulp in a way that is mathematically conveniently for us. As economically rational agents, assuming his spaceship conveniently resurrects him ,should we care about his safety? [Note: The assumption of economically rational agents is obviously ridiculous, but it’s only slightly more of an exaggeration than the other parts of our story.]

So let’s look forward in time. When it’s a year later on earth, how much do we care about the astronaut? Using a typical discount rate, of say, 5%, we care about him 95% as much.

He, however, has had only about 0.02 years of time pass, and cares a bit more. But when he lets a year pass in his reference frame, he cares 95% as much about future him, but us earthbound people need to wait 50 years for that to happen, and we care about him 50 years from now about 8.7% as much as we did when he launched.

But where is he? About 10¹² kilometers away. Americans can’t be bothered to think about poor people in Africa, so why should they care about this guy who is about 100,000,000 times as far away? But Tyler Cowen agrees with Peter Singer in his moral objections to distance based discounting, so after we’ve spend the next 50 years avoiding existential risks and solving poverty in some economically efficient way, we need to decide how much value we should have initially placed on our astronaut.

Even if we don’t want to discount distance in space, unless using a discount rate of 0%, these post-Einstein sophisticates need to discount distance in space-time. Our astronaut travelling at 0.99c is about already a light year away, and using a handy-dandy space-time distance calculator, that means he’s just about 51 years away, and we think he’s worth about 8% of what he was when we launched him.

Let’s say he turns around, once again suddenly changing velocity, getting crushed to a pulp, and being resurrected by his ship. On the centennial of his launch, he comes back, 2 years older. Unless we’re doing something really complicated with our intergenerational discounting, we should initially have discounted this future by that same 5% yearly, and our future returnee is worth 0.76% of a person. That has nothing to do with space travel, it just means people don’t care about the future. [Note: Yes, high discount rates might be bad if you’re hoping to live to 100, because it means decision-makers now should trash the future for present gain. As if they aren’t already. But we’ll get back to that.]

Our prospective astronaut, however, has a higher self-valuation, and thinks this future is worth about 90% as much as the present. That makes sense — he’s only lived 2 years. [Note: If you’ve got a fast enough spaceship, you’re gonna be able to find a hell of an IRR for your investments. Just make sure you figure out that whole not getting crushed to death thing.] But different people always have different discount rates — we’re just saying that high-speed relativistic astronauts should hope that society cares about the long term future.

So we conclude that the people on earth care about events happening in a century very little, but people who travel really fast care quite a bit more. And we conclude that people who are really far away are absolutely worth less than people nearby, if only because they can’t get back here until the far future. But if we want to put someone on a spaceship, they better realize that they care about their safety a lot more than we do.

The conclusion is inescapable; we need to launch political decision makers away from earth as fast as we can possible make them go. We don’t even need to make sure the spaceship is safe , because in our reference frame, it’ll be a long time until it gets back. This way, they might start to care a little bit more about the far future. [Note: Or at least they’ll care a bit more about engineering standards.] The problem goes away, and so do the politicians.

A Tentative Typology of AI-Foom Scenarios

“If a foom-like explosion can quickly make a once-small system more powerful than the rest of the world put together, the rest of the world might not be able to use law, competition, social norms, or politics to keep it in check.” — Robin Hanson

As Robin Hanson recently discussed, there is a lack of clarity about what an “AI Foom” looks like, or how likely it is. He says “In a prototypical “foom,” or local intelligence explosion, a single AI system…” and proceeds to describe a possibility. I’d like to explore a few more, and discuss what qualifies as a “foom” a bit more. This is not intended as a full exploration, or as a prediction; it merely captures my current thinking.

First, it’s appropriate to briefly mention the assumptions made here;

  • Near Term — Human-intelligence AI is possible in the near term, say 30 years.
  • No Competitive Apocalypse — A single system will be created first, and other groups will not have resources sufficient to quickly build another system with similar capabilities.
  • Unsafe AI — The I launched will not have a well-bounded and safe utility function, and will find something to maximize other than what humanity would like.

These assumptions are not certainties, and are not part of the discussion — but I will condition the rest of the discussion on them, so that debating them is reasonable, elsewhere.

What’s (enough for) a “foom”?

With preliminaries out of the way, what would qualify as a “foom,” an adaptation or change that makes the system “more powerful than the rest of the world put together”?

Non-Foom AI X-Risk

There are a few scenarios which lead more directly to existential risk, without passing through a stage of gathering power. (Beyond listing them, I will not discuss these here. Also, names of scenarios given here do not imply anything about the belief of the namesake.)

a) Accidental Paperclipping — The goals specified allow the AI system to do something destructive, and is irreversible or not noticed. The AI is not sufficiently risk-aware or intelligent to avoid doing so.

b) Purposeful Paperclipping — The goals specified allow the AI system to achieve them, or attempt to do so, by something destructive which the AI can do directly, and is irreversible or not easily noticed in time.

c) Yudkowskian Simplicity-foom — There are relatively simple methods of vastly reducing the complexity of the systems the AI needs to deal with, allowing the system to better perform its goals. At near-human or human intelligence levels, one or more of those methods becomes feasible. (These might include designing viruses, nano-assemblers, or other systems that could wipe out humanity.)

Fooms

There are a few possibilities I would consider for an AI to become immensely powerful;

a) Yudkowskian Intelligence-foom — The AI is sophisticated enough to make further improvements on itself, and quickly moves from human-level intelligence to super-Einstein levels, and beyond. It can now make advances in physics, chemistry, biology, etc. that make it capable of arbitrarily dangerous behaviors.

b) Hansonian-Em foom — The AI can make efficient and small copies of, or variations on itself rapidly and cheaply, and is unboxed (or unboxes itself.) These human-level AI can run on little enough hardware, or run enough faster than humans, that the machines can rapidly amass resources and hack/exploit/buy resources that allow it to quickly gain direct control of financial and then physical resources.

c) Machiavellian Intelligence-foom — The AI can manipulate political systems surreptitiously, and amasses power directly or indirectly via manipulating individual humans. (Perhaps the AI gains resources and control via blackmail of specific individuals, who are unaware on whose behalf the operate.) The resulting control can prevent coordinated action against the AI, and allow it to gather resources to achieve its unstated nefarious true goal.

d) Asimovian Psychohistory-foom — The AI can build predictive models of human reactions well enough to manipulate them over the medium and long term. (This is different than a Machiavellian-foom only because it relies on models of humans and predictive power rather than humanlike manipulation.)

This is almost certainly not a complete or comprehensive list, and I would be grateful for additional suggestions. What it does allow is a discussion of what makes various types of fooms likely, and consider which might be pursued.

AI Complexity and Intelligence Range

The first critical question among these is the complexity of intelligence — I won’t try to estimate this, but others are researching and discussing it. Here, complexity refers to something akin to computational complexity, and refers to the difficulty of running an artificial intelligence of a given capacity. If emulating a small mammal’s brain is possible, but increasing the intelligence of AI from there to human requires an exponential increase in complexity and computing speed, we will say it is very complex, while if it requires only doubling, it is not. (I assume the computational complexity matters here, and there are no breakthroughs in hardware, quantum computing, or computational complexity theory.)

The related question is the range of intelligence. If beyond human-level AI is not possible given the techniques used to achieve human-level intelligence, or requires an exponential or even a large polynomial increase in computing power, we will consider the range small — even if not bounded, there are near-term limits. Moore’s law (if it continues) implies that the speed of AI thought will increase, but not quickly. Alternatively, if the techniques used to achieve human level AI can be extended easily to create even more intelligent systems by adding hardware, the range is large. This gives us a simplified set of possibilities.

Intelligence vs. Range — Cases


Low-Complexity Intelligence within Large Range — If humans are, as Eliezer Yudkowsky has argued, relatively clustered on the scale of intelligence, the difficulty of designing significantly more intelligent reasoning systems may within, or not be far beyond, human capability. Rapid increases in intelligence of AI systems above human levels would be a critical threshold, and an existential risk.

Low-Complexity Intelligence within Small Range — If human minds are near a peak of intelligence, near-human or human-level Hansonian Ems may still be possible to instantiate in relatively little hardware, and their relative lack of complexity make them a potential existential risk.

High-Complexity Intelligence within Small Range — Relatively little existential risk from AI seems to exist, and instead a transition to an “Age of Em” scenario seems likely.

High-Complexity Intelligence within Large Range — A threshold or Foom is unlikely, but incremental AI improvements may still pose existential risks. When a single superintelligent AI is developed, other groups are likely to follow. A singularity may be plausible, where many systems are built with superhuman intelligence, posing different types of existential or other risks.

Human Complexity and Manipulability

The second critical question is human psychology. If human minds can be manipulated more easily by moderately complex AIs than by other humans (which is already significant,) AIs might not need to “foom” in the Yudkowskian sense at all. Instead, the exponential increase in AI power and resources can happen via manipulation at an individual level or at a group level. Humans, individually or en masse, may be convinced that AI should be given this power.

Even if perfect manipulation is impossible, classical blackmail or other typical counterintelligence-type attacks may be possible, leading to a malevolent system to be able to manipulate humans. Alternatively, if human-level cognition can be achieved with much less resources than a human mind, Hansonian-fooms are possible, but so is predictive modeling of individual human minds by a manipulative system.

Alternatively, if very predictive models can be made that approximate human behavior, much like Asimov’s postulated psychohistory. This seems unlikely to be as rapid a threat, but AIs in intelligence, marketing, and other domains may specifically target this ability. If human psychology can be understood more easily than expected, these systems may succeed beyond current expectations, and the AI may be able to manipulate humans en-masse, without controlling individuals. This is similar to an unresolved debate in history about the relative importance of individuals (a la “Great Man Theory”) versus societal trends.

Conclusion

We don’t know when human-level AI will occur, or what form it will take. Focus on AI-safety may depend on the type of AI-foom that we are concerned with, and a better characterization of these uncertainties could be useful for addressing existential risks of AI deployment.

All of this is speculation, and despite my certain-sounding claims above, I am interested in reactions or debate.