The Hyperbolic Time Chamber as Brain Emulation Analogy

A time dilation chamber as thought experiment on the power of pure thought, with comparison to computer AGI advantages/disadvantages (transhumanism, anime, AI)
created: 29 Aug 2012; modified: 12 Jul 2017; status: finished; confidence: likely; importance: 9

A time dilation tool from an anime is discussed for its practical use on Earth; there seem surprisingly few uses and none that will change the world, due to the severe penalties humans would incur while using it, and basic constraints like Amdahl’s law limit the scientific uses. A comparison with the position of an Artificial Intelligence such as an emulated human brain seems fair, except most of the time dilation disadvantages do not apply or can be ameliorated and hence any speedups could be quite effectively exploited. I suggest that skeptics of the idea that speedups give advantages are implicitly working off the crippled time dilation tool and not making allowance for the disanalogies.

Dragon Ball Z, a popular (but mediocre) shonen fighting anime, includes a cute bit of SF in it - the Hyperbolic Time Chamber (HTC), which can be thought of a reverse twin paradox in which time speeds up for 2 people: the HTC opens and closes once a day realtime, but inside its little pocket universe, a full year passes for 2 people, giving a 365x speedup. There’s no such thing as a HTC-within-a-HTC, so uses are limited to just that one 365x speedup - no 3652 speedups.

Ignoring the DBZ-specific aspects of the HTC like the person limit or increased gravity or air and temperature changes, one wonders: what one would do with a HTC in the real world?

Uses for time acceleration

In DBZ, the only use seems to be for training montages to let characters power up to fight a new alien or martial artist, but world-destroying martial artists seem to be rare in the real world, so we couldn’t use it for that.

Could we use it for regular martial arts training? The DBZ article for the HTC mentions no non-emergency use, and a little thought leads us to conclude that, probably not: inside the HTC, time passes as normal, which means that you don’t save any time. All the HTC is doing is rearranging relative time between groups. If you step in, you still age a full year before stepping out, and you will now die a year early by the realtime calendar. So what’s the point? We can think of a few uses - imagine someone who gets injured just before the Olympics - but let’s face it, that may be convenient for a few people, but it’s hardly changing the world. A whole time-accelerated pocket universe… Surely we can think of something less pointless than tweaking athletics?

Downsides

Actually, it’s worse than pointless - the HTC is a super-supermax prison: you cannot leave at any point before the year is up, you cannot communicate in any way, nothing goes in or out, and you have only what you brought with you (and always what you brought with you).

Autarchy

Under such conditions, a year in the HTC could well be considered cruel and unusual punishment; no doctor would volunteer for it, so any prisoners in the HTC face a serious risk of death from any cause unless a fellow prisoner that day/year had medical training. The food will also suck, as any food will have to be storable for a year (it wouldn’t do to starve to death a day before the door opens back to the real world); you can’t grow your own because there is no apparent sun, soil, or seasons inside the HTC, and while you could probably bring in a greenhouse & soil and fertilize with recycled food, how are you going to power the lights in your greenhouse? Drag in a miniature nuclear power plant or a radioisotope thermoelectric generator? And we haven’t even considered how much time one would spend (waste) on this small-scale agriculture; maintaining Biosphere 2 was a full-time job for many highly-skilled people, and if that was true for the HTC, there would hardly be any point in it.

If one punted on the problems of maintaining a high quality of life and posited a dedicated researcher, well, the HTC is still not useful. They will find it hard to take with them an entire library or laboratory, many ingredients are too expensive or perishable to buy in advance just because the researcher might need them, but if they don’t have access to pretty much everything, they’ll quickly hit some sort of barrier where one email or order would let them finish a project but that email can’t be sent for up to a year. (Imagine a researcher who enters the HTC - and his laptop’s hard-drive dies. Oops. Hope he had backups or spares, of his data and his laptop and everything else for that matter.) Omitting these concerns, research is a social process in the sense that one is often discussing or explaining or defending the research, and without these interactions it is easy to go down blind alleys, make minor-seeming but fatal mistakes1, wind up reinventing something standard in another field, etc. One can easily waste a month this way, and so a year. A group would help, but groups are susceptible to groupthink and will still go down blind alleys or simply lack relevant expertise. (In this respect, the Millennial Maths in Neal Stephenson’s Anathem are highly unrealistic; any group of academics which closeted themselves for a millennium would overwhelmingly likely be a sheer waste of human capital.)

One might wonder about other kinds of education in the HTC like mathematics, but all the above points apply to any reason to live in the HTC: why would you accept all those burdens to spend a year learning something… when you could just live that same year in the real world at much less cost and a far higher standard of living? It certainly would be nice to go into the HTC for a few weeks and come back with a dozen PhDs - but not if you emerge aged 40, having lived the best years of your life in a prison cell and probably deep in debt too!

Aging

Speaking of a few years in the HTC, what about biological aging? People don’t ordinarily spend half their lives acquiring multiple degrees outside the prison of an HTC, why would they voluntarily do so inside it? It’s the same trade, after all: half your life for multiple degrees. This point has been made in fictional treatments of time-acceleration R.A. Lafferty’s classic short story The Six Fingers of Time where the protagonist is given the ability to slow down time by a mysterious ancient conspiracy, and while he tries to uncover their secrets, he dies of old age - they had let him slow down time, but not his inherent natural aging. Or William Sleator’s YA novel Singularity, where the original discoverer of the HTC dies before his family expects it, looking suspiciously like an old man; the implication is that he spent so much time in the HTC investigating it that the normal aging while inside it used up a good chunk of his lifespan. Ironically, if he had been able to survive another month, he would have seen the resolution of the mystery. The protagonist benefits somewhat from his own year in the HTC, but for idiosyncratic reasons. Similarly in Greg Egan’s The Clockwork Rocket the protagonist discovers a method of time acceleration which she resolves to use to save her world from certain doom by launching a generationship to be accelerated and discover some salvation; but she and the first generation (a good chunk of their world’s scientific community) fully expect to perish of age long before the generationship returns just years later in realtime. In a more conventional example, we may admire how prison & revenge give the Count in The Count of Monte Cristo a great deal of focus during his educational prison stay but how many of us would agree to be imprisoned the same way if there were no hidden fortune waiting for us at the end?

This is a fundamental issue and probably why time-acceleration is a underused trope in science fiction compared to time dilation or time travel: the downside is simply too apparent.

Some uses

Zero-sum competition

The point about the HTC rearranging relative time for athletes and the original use in DBZ - training to save the world when every minute counts - suggests one class of problems: things which are extremely time-sensitive with multiple competing groups and zero-sum or winner-take-all dynamics.

With large sums of money at stake, we can hand-wave the super-supermax prison points: oil companies only have to pay oil rig workers a few score or hundreds of thousands of dollars for working several weeks at a time on oil rigs, and scientists and astronauts compete for position in isolated facilities as Antarctic bases or the International Space Station. All of these are far less isolated or burdensome than the HTC, but by more than a few factors? Seems unlikely. So a few million dollars may suffice to cover the costs of a small group, especially if they can reuse infrastructure from previous days/years.

Are there business problems where a year’s headstart is worth at least a few million dollars? Sure! Many programming tasks come to mind: would Google pay a few million to lock up the core Android coders to take care of a years’ worth of outstanding bugs and to-do items? Would Apple do something similar? What about any hedge fund? It seems plausible that every day of a HTC could be booked or even auctioned off.

The negatives here include the lack of communication and iteration: when the group heads through the door, that’s the last they’ll hear from the world for a year. They can’t release a prototype at the 6 month mark and see how it does after a month. If they fall to groupthink and take the wrong approach, there are no outsiders who will say that their approach is crazy and elaborate and why don’t they just do the standard thing? Worse, if they discover they forgot a key piece of documentation or hardware or they run out of chips or they need a particular expert or something, the next time they can get it is… a year later. Oops. Hope that wasn’t a fatal error. (Even if they had communication, it’d only bound the losses: if it takes a second to load a webpage in realtime, then it will take them >365 seconds or >6 minutes.) This lack of iteration runs counter to many business styles and is entirely antithetical to modern tech businesses which prize constant feedback and ability to change ideas & approaches on a dime.

Still, with multi-terabyte hard drives, one could just take a copy of all documentation and source code (or perhaps bring along a few Internet Archive-style petaboxes and store a copy of a small fraction of the Internet), and for some tasks like stock-market research, it’s plausible one could bring everything one needs. Hedge funds would probably benefit from being able to send in their quants for a year of concentrated research and scoop the competition.

Non-zero-sum uses

The more concrete a field, the less the benefit. Most commercial services would be impossible: you can’t cut someone’s hair in the real world from the HTC, although with loads of equipment you could work on a robot which cuts hair. You can’t run clinical drug experiments on a group of patients from inside a HTC either; for that matter, you’ll have a hard time bringing along rats or monkeys. But you could read a lot of papers on rats. (But not necessarily do much; for example, meta-analyses will be hard because frequently authors do not include the exact numbers one needs, and so one has to contact them - exactly what can’t be done in the HTC.) Pure mathematicians might benefit, but by and large, mathematics is not so competitive & time-sensitive that sticking some mathematicians into the HTC would be worth the premium.

Which is not to say there are no concrete uses. One cute example would be storage of goods: instead of an art & wine free port, just stick your wine & cheese & other goods in the HTC and let them age a year every day until ripened to perfection. More valuably, one could bypass accelerated aging tests and just age a product directly; want to know if the Clock of the Long Now will work or the Rosetta disk be readable for 10,000 years under ideal conditions? That’s just 10,000 days or 28 years away. (We could also expect an efflorescence of counterfeit art, documents, and goods for the same reasons.) Better yet, want to run fast primate aging experiments? If you can front the money and either automate the care & feeding of the subjects or find lab technicians willing to spend their lives in prison, you can run as many as you please.

These wouldn’t be revolutionary improvements, though (with the exception of aging research which might revolutionize human society if the results were useful).

Self-contained vs not

More generally, we could say that Amdahl’s law applies to use of HTC: any task has serial and parallel elements, but if some elements are made cheaper or even free, the time to accomplish the task still depends on the other bottleneck elements. Elements which can be done in complete isolation and which benefit from relative speedups correspond to parallel elements, and elements which must be done in the real world correspond to the serial elements. With a HTC, the HTC-elements will quickly speed up, but tasks will now bottleneck on real-world tasks. (Imagine Google sends its Android programmers into the HTC and they return a day later bearing a repository groaning with new patches; the features still have to be tested in a real world context, reviewed, infrastructure updated, and finally actually transmitted to the customers who may begin using them.)

One opportunity is to look at Amdahl’s law as a positive, and look at the computer version of an isolated team in the HTC beavering away on a project: a bunch of servers working on an extremely hard serial problem. For example, simulating a long evolution of protein folding. Many problems in scientific computation or operations research where there is more than a day’s margin might also benefit from what is effectively a super-fast processor with 1-day latency. Further, such a supercomputing facility in an HTC faces problems with replacement parts and getting the electricity such computations will consume (and how much would you have to pay the sysadmins & technicians to be imprisoned for a year?), and so its capacity will come at a premium compared to the equivalent real-world problem; a problem like hash cracking which is trivially parallelizable would not benefit from such a facility. Electricity is the dominant cost of computing power these days, so a HTC must save on electricity or justify its cost premium. Instead of throwing one really expensive HTC server at the problem for a year, throw 365 cheap power-efficient servers at it for a day as many tech companies are able to do, or just run it on a cloud computing platform.

These points do not apply to any computation which is inherently serial and cannot be run on more than a few computers. One such category of non-parallelizable problems (assuming NC≠P) is the complexity class P-complete, which includes such economically important tasks as linear programming optimization. However, the important unparallelizable problems (at least linear programming) typically have very fast approximate or heuristic solvers, and optimization problems tend to asymptote and experience severely diminishing returns. Is there a problem where the time-limit is so tight and the additional optimization so valuable that it would pay for a year of premium power consumption & computation? I don’t know. Maybe there is.

So, many business applications would not benefit, many research tasks would not benefit, and I haven’t thought of any important areas of life which would benefit from a HTC. Some people would find it convenient to re-arrange their lives even at some cost, arranging big blocks of time for some self-contained things (for example, working on one’s own projects), but the benefit would be limited; I would analogize to modafinil, which can be employed to free up a block of 8 hours (skipping a night of sleep) but at a cost (money). If one believes that modafinil use comes with no health penalties or recovery sleep, it arguably is better than a HTC because it can be used in more convenient chunks and you remain in the real world while using it, running at realtime. Yet, while modafinil is popular among a few groups, it has not revolutionized the world.

In general, a world with one or many HTCs would look a great deal like our own, although in some areas, there will be sudden bursts of progress as HTC groups return from their expeditions with their prizes and likely a one-time economic boost as HTC-specific applications are discovered.

Real HTCs

Well, cute and interesting, but why do we care about this SF trope from DBZ?

Because the HTC can be analogized to an emulated brain or an upload! The 365x speedup of people in the HTC could be the speedup of a brain on a supercomputer after considerable optimization2. (One could argue that early uploads will run at far less than real-time as they will be created as soon as hardware is just powerful enough to run them at all, and be completely uncompetitive & research projects; but then again, their creation could come long after the hardware exists, waiting on bottlenecks like scanning of brains - the hardware overhang question.) A computer, like a HTC, cannot be nested to give a speedup; a virtual computer will usually rule slower relative to realtime. A brain on a computer without any peripherals like a robot will be isolated from the real world, just like the people in the chamber, and so on.

We found the HTC not useful in practice; does this conclusion also follow for uploads? Should we expect uploads to struggle in the marketplace, finding valued niches but not causing increases in world GDP growth rates or any sort of Singularity?

Emulations are not HTCs

While the similarities are striking, so are the dissimilarities:

  1. a computer can have communications with the Internet & world; a 365x slowdown may be painful, but it is better than a fixed delay of 0-365 days.

    Even when the slowdown hits, there is the option - much reduced in the HTC - of switching to an entirely different task. (Similar to the computing world’s reaction to clock speed stagnation and the rise of multi-cores, with the attendant pressure on Amdahl’s law3: process-level parallelism. You can’t do just one thing faster, so you might as well do many things slower.) This eliminates many of the objections. If it really can’t find anything to do with its time, an emulation can always slow itself down to real-time.
  2. the overhead of living in the Hyperbolic Time Chamber is reduced; a computer in the real world benefits from all the real world infrastructure like power plants or semiconductor chip fabs. There are some power savings from underclocking, but there’s not much reason to otherwise run as fast as possible. (This permits many more minds to run sped-up as compared to humans living in the HTC, reducing further the disadvantage of #1 and also increasing the value of being sped-up.)
  3. A person in the HTC is a relatively fixed quantity, especially since many resources will be unavailable; an emulated brain has access to those resources per #1, but also has many options different from a regular human. (A much-discussed topic; see eg. Sotala 2012.)
  4. An emulated brain is free of a major time limit for regular humans: aging. While a human could not afford to get 12 PhDs even if a HTC existed - because that would consume the most productive decades of his life - an emulated brain could. This breaks the symmetry further.

Between these 4 disanalogic points, an upload avoids some of the disadvantages that renders the HTC noncompetitive and gains some advantages which may make it more competitive, and make the sudden improvements a much more general phenomenon.

Expecting any dramatic changes from uploads or AGIs in general has been mocked by critics as an over-valuing of brains in a box or, pace Gene Wolfe, magical thinking (The would-be sorcerer alone has faith in the efficacy of pure knowledge). If we look at such criticism, do the arguments seem to assume a model of thinking in which the upload/AI is trapped in the HTC, or does it resemble an upload/AI outside the HTC?

See also


  1. The inability to critique your own results or ideas as capably as someone else can seems to have deep roots in psychology and support evolutionary accounts of reasoning as evolved primarily for arguing and convincing other people, not truth-seeking. See also rubber-ducking.

  2. Although it’s unlikely that the exact speedup would be near 365x, as power & heating constraints dominate the problem; GeraldMonroe points out that a straightforward comparison of transistor vs neuron switching speed leads to factors like 25 million, and modern CPUs are limited in speed mostly by heat dissipation issues - the standard 2/4GHz CPU could run at 5Ghz+ if one had powerful cooling. Heat concerns led Keith Henson to argue that datacenters of uploaded brains would eventually relocate to the deep sea for maximal cooling (and hence, speed).

  3. Amdahl’s law is also relevant to the economics of uploaded brains: suppose one believed that specialized or tool AIs will always outperform any uploaded brain or AGI at a specific task, and every improvement that speeds up the uploads/AGIs improves the tool AIs just as much, such that the uploads/AGIs never surpass the tool AI; does this imply that there will be no uploads/AGIs outside niches like research, as humans using tool AIs are more profitable? Holden Karnofsky seems to think something similar when he doesn’t think that competitive pressure will force people running tool AIs to eventually switch to running AGIs; Nick Szabo explicitly believes uploads/AGIs can never be profitable given tool AI competition:

    Even if there was such a thing as a general intelligence the specialized machines would soundly beat it in the marketplace. It would be far from a close contest.

    I disagree. The market is not purely tool AI vs AGI. Humans do not increase their speed even if tool AIs are increasing their speed arbitrarily. Therefore, a human+tool-AI system’s performance asymptotically approaches the limit where the tool-AI part takes zero time and the human part takes 100% of the time. Time pressures may force a shift to ever more tool AI systems and eventually tool-AI+AGI systems when that becomes possible. (Greater use of highly adaptable and flexibly autonomous systems and processes can provide [substantial] time-domain operational advantages over adversaries who are limited to human planning and decision speeds…) The moment that algorithmic progress or Moore’s law means that an AGI even slightly outperforms a human at using the tool-AI, the same economic reasons you were counting on as your salvation suddenly turn on you and drive the replacement of any humans in the loop. Since humans are a known fixed quantity, if an AGI can be improved - even if at all times it is strictly inferior to a tool AI at the latter’s specialization - then eventually an AGI+tool-AI system will outperform a human+tool-AI system (barring exotic unproven assumptions about asymptotic limits).

    Attempts to evade this by splitting up or combining tool AIs either don’t avoid this logic or wind up accepting the conclusion: if every human skill has been transferred to tool-AIs, then a complex of tool-AIs now forms an AGI which outperforms all humans by definition; if not every human skill has been transferred, such as employing tool-AIs as most appropriate for the moment, then there is the large economic niche for AGIs which I have identified with my Amdahl’s law argument. So either there exist AGI which outperform all humans, or there exists economic pressure to use AGI. For example, if one argued that a complex of tool-AIs would not share worldviews or data appropriately and need a human to coordinate them, well, why can’t an AGI do this and be superior to the humans per Amdahl’s law?

    What human is in the loop on high frequency trading? Who was in the loop when Knight Capital’s market maker was losing hundreds of millions of dollars? The answer is that no one was in the loop because humans in the loop would not have been economically competitive. That’s fine when it’s just billions of dollars at stake and companies can decide to take the risk for themselves or not - but the stakes can change, externalities can increase.

    Here’s another near-future test/example: how do we humans deal with drones? Drones are exploding in popularity, are increasing their capabilities constantly, and are coveted by countless security agencies and private groups for their tremendous use in all sorts of roles both benign and disturbing. Just like AIs would be. The tool vs general AI distinction maps nicely onto drones as well: a tool AI corresponds to a drone being manually flown by a human pilot somewhere, while a general AI would correspond to an autonomous drone which is carrying out some mission (blast insurgents?). So, here is a near-future test of the question are people likely to let tool AIs ’drive themselves for greater efficiency?’ - simply ask whether in, say, a decade there are autonomous drones carrying tasks that now would only be carried out by piloted drones. If in a decade we learn that autonomous drones are killing people, then we have an answer to our tool AI question: it doesn’t matter because given a tool AI, people will just turn it into a general AI.