Class Project

[Eliezer Yudkowsky]

“Do as well as Einstein?” Jeffreyssai said, incredulously. “Just as well as Einstein? Albert Einstein was a great scientist of his era, but that was his era, not this one! Einstein did not comprehend the Bayesian methods; he lived before the cognitive biases were discovered; he had no scientific grasp of his own thought processes. Einstein spoke nonsense of an impersonal God—which tells you how well he understood the rhythm of reason, to discard it outside his own field! He was too caught up in the drama of rejecting his era’s quantum mechanics to actually fix it. And while I grant that Einstein reasoned cleanly in the matter of General Relativity—barring that matter of the cosmological constant—he took ten years to do it. Too slow!”

“Too slow?” repeated Taji incredulously.

“Too slow! If Einstein were in this classroom now, rather than Earth of the negative first century, I would rap his knuckles! You will not try to do as well as Einstein! You will aspire to do BETTER than Einstein or you may as well not bother!”

Jeffreyssai shook his head. “Well, I’ve given you enough hints. It is time to test your skills. Now, I know that the other beisutsukai don’t think much of my class projects...” Jeffreyssai paused significantly.

Brennan inwardly sighed. He’d heard this line many times before, in the Bardic Conspiracy, the Competitive Conspiracy: The other teachers think my assignments are too easy, you should be grateful, followed by some ridiculously difficult task—

“They say,” Jeffreyssai said, “that my projects are too hard; insanely hard; that they pass from the realm of madness into the realm of Sparta; that Laplace himself would catch on fire; they accuse me of trying to tear apart my students’ souls—”

Oh, crap.

“But there is a reason,” Jeffreyssai said, “why many of my students have achieved great things; and by that I do not mean high rank in the Bayesian Conspiracy. I expected much of them, and they came to expect much of themselves. So...”

Jeffreyssai took a moment to look over his increasingly disturbed students, “Here is your assignment. Of quantum mechanics, and General Relativity, you have been told. This is the limit of Eld science, and hence, the limit of public knowledge. The five of you, working on your own, are to produce the correct theory of quantum gravity. Your time limit is one month.”

“What?” said Brennan, Taji, Styrlyn, and Yin. Hiriwa gave them a puzzled look.

“Should you succeed,” Jeffreyssai continued, “you will be promoted to beisutsukai of the second dan and sixth level. We will see if you have learned speed. Your clock starts—now.”

And Jeffreyssai strode out of the room, slamming the door behind him.

“This is crazy!” Taji cried.

Hiriwa looked at Taji, bemused. “The solution is not known to us. How can you know it is so difficult?”

“Because we knew about this problem back in the Eld days! Eld scientists worked on this problem for a lot longer than one month.”

Hiriwa shrugged. “They were still arguing about many-worlds too, weren’t they?”

“Enough! There’s no time!”

The other four students looked to Styrlyn, remembering that he was said to rank high in the Cooperative Conspiracy. There was a brief moment of weighing, of assessing, and then Styrlyn was their leader.

Styrlyn took a great breath. “We need a list of approaches. Write down all the angles you can think of. Independently—we need your individual components before we start combining. In five minutes, I’ll ask each of you for your best idea first. No wasted thoughts! Go!”

Brennan grabbed a sheet and his tracer, set the tip to the surface, and then paused. He couldn’t think of anything clever to say about unifying general relativity and quantum mechanics...

The other students were already writing.

Brennan tapped the tip, once, twice, thrice. General relativity and quantum mechanics...

Taji put his first sheet aside, grabbed another.

Finally, Brennan, for lack of anything clever to say, wrote down the obvious.

Minutes later, when Styrlyn called time, it was still all he had written.

“All right,” Styrlyn said, “your best idea. Or the idea you most want the rest of us to take into account in our second components. Taji, go!”

Taji looked over his sheets. “Okay, I think we’ve got to assume that every avenue that Eld science was trying is a blind alley, or they would have found it. And if this is possible to do in one month, the answer must be, in some sense, elegant. So no multiple dimensions. If we start doing anything that looks like we should call it ‘string theory’, we’d better stop. Maybe begin by considering how failure to understand decoherence could have led Eld science astray in quantizing gravity.”

“The opposite of folly is folly,” Hiriwa said. “Let us pretend that Eld science never existed.”

“No criticisms yet!” said Styrlyn. “Hiriwa, your suggestion?”

“Get rid of the infinities,” said Hiriwa, “extirpate that which permits them. It should not be a matter of cleverness with integrals. A representation that allows infinity must be false-to-fact.”

“Yin.”

“We know from common sense,” Yin said, “that if we stepped outside the universe, we would see time laid out all at once, reality like a crystal. But I once encountered a hint that physics is timeless in a deeper sense than that.” Yin’s eyes were distant, remembering. “Years ago, I found an abandoned city; it had been uninhabited for eras, I think. And behind a door whose locks were broken, carved into one wall: quote .ua sai .ei mi vimcu ty bu le mekso unquote.”

Brennan translated: Eureka! Eliminate t from the equations. And written in Lojban, the sacred language of science, which meant the unknown writer had thought it to be true.

“The ‘timeless physics’ of which we’ve all heard rumors,” Yin said, “may be timeless in a very literal sense.”

“My own contribution,” Styrlyn said. “The quantum physics we’ve learned is over joint positional configurations. It seems like we should be able to take that apart into a spatially local representation, in terms of invariant distant entanglements. Finding that representation might help us integrate with general relativity, whose curvature is local.”

“A strangely individualist perspective,” Taji murmured, “for one of the Cooperative Conspiracy.”

Styrlyn shook his head. “You misunderstand us, then. The first lesson we learn is that groups are made of people… no, there is no time for politics. Brennan!”

Brennan shrugged. “Not much, I’m afraid, only the obvious. Inertial mass-energy was always observed to equal gravitational mass-energy, and Einstein showed that they were necessarily the same. So why is the ‘energy’ that is an eigenvalue of the quantum Hamiltonian, necessarily the same as the ‘energy’ quantity that appears in the equations of General Relativity? Why should spacetime curve at the same rate that the little arrows rotate?”

There was a brief pause.

Yin frowned. “That seems too obvious. Wouldn’t Eld science have figured it out already?”

“Forget Eld science existed,” Hiriwa said. “The question stands: we need the answer, whether it was known in ancient times or not. It cannot possibly be coincidence.”

Taji’s eyes were abstracted. “Perhaps it would be possible to show that an exception to the equality would violate some conservation law...”

“That is not where Brennan pointed,” Hiriwa interrupted. “He did not ask for a proof that they must be set equal, given some appealing principle; he asked for a view in which the two are one and cannot be divided even conceptually, as was accomplished for inertial mass-energy and gravitational mass-energy. For we must assume that the beauty of the whole arises from the fundamental laws, and not the other way around. Fair-rephrasing?”

“Fair-rephrasing,” Brennan replied.

Silence reigned for thirty-seven seconds, as the five pondered the five suggestions.

“I have an idea...”

[Eliezer Yudkowsky]

Disclaimer: I am not a physicist, but, hey, neither is Brennan.

Thanks to Robin Lee Powell for translating the inscription that Yin found.

[Leah]

Specifically, Brennan’s error is assuming that you need a new theory to account for this. In fact, there is only one possible spin-2 particle in quantum field theory and it is the graviton. Physicists actually accidentally rediscovered GR in the 50′s because of this.

[Peter3]

I love these quasi-futuristic exchanges you’ve come up with. They’re really helpful for putting your other posts into perspective—not just facts, but what facts mean for the way we should look at the world.

[steven]

This is the limit of Eld science, and hence, the limit of public knowledge.

Wait, so these people are doing this only for recreation?

So no multiple dimensions.

You want to make physics heightless and depthless? I suppose it would be a logical next step.

I don’t see what’s inelegant about more than three space dimensions. It’s not like three is a special number (as far as I know).

[bogdanb]

I imagine what’s described as inelegant is hidden dimensions.

Especially if they need to be hidden just so for the thing to work, and if they’re hidden for no obvious reason.

[Meta_and_Meta]

Make it zero dimensions and call it a “day.” All else is Maya.

[Robin_Z]

This is the limit of Eld science, and hence, the limit of public knowledge. Wait, so these people are doing this only for recreation?

No—this is Eliezer’s alternate universe storyline in which the science-equivalent is treated as a secret the same way the Pythagoreans did. The initiates—the people with access to the secret knowledge—use it for technology, just as we do, except because the general public doesn’t know the science, the tech looks amazing.

The idea, I believe, is to reduce the attraction of bogus secret societies. In Brennan’s world, anyone who made one would be challenged to accomplish as great or greater feats than the Bayesians—a task that a mere mystery cult would fail at.

[billswift]

There are actually multiple reasons, some stories stress different ones. The one I like is that by keeping the results secret, they can train students in discovery by encouraging/​forcing them to rediscover the laws as part of their training.

[lessdazed]

The societies I have been told about are limited in scope. Only a rationalistic conspiracy would be in direct competition with the Bayesians. The Cooperative Conspiracy and Bayesian Conspiracy apparently allow open membership in both, while the Cooperative Conspiracy would probably be in competition with an Individualist Conspiracy or Competitive Conspiracy.

Of course, even the Model Airplane Conspiracy could restrict members to only their conspiracy, preventing them from being Bayesian Conspirators despite the conspiracies’ dissimilar subjects, particularly if the Bayesians forbade hiding one’s identity.

Insofar as one ought to speak and think cleanly, secret societies would not be challenged to show results—this is to talk as if under the sway of their mystery. They would be assumed to be worse than useless until they demonstrated results—useless at first thought because mystery has no value, less than that at second thought because not showing value is evidence of not being able to show it, which is evidence of not having it.

[Doug_S.]

Joke solution:

We’re living in a simulation, and the reason GR and QM don’t mix is because we’re living in a buggy simulation. ;)

[Polymeron]

Or rather, QM displays the behavior of rounding, because “there’s no need to simulate past that level of precision”, resulting in all the funky behaviors of quantum tunneling and the likes. This carries into GR as rounding errors.

I’m sure if I knew the science better I’d see the flaws in this hypothesis, but for now I don’t even see why it would be particularly implausible. It’s actually something of an elegant answer...

[DanielLC]

Quantum physics is precise, pretty, and hard to calculate. This is the exact opposite of what you’d expect from a computer simulation.

For example, the uncertainty principle is not due to the universe keeping track of less than expected and thus some of the position and momentum being lost in rounding. It’s due to the universe keeping track of much, much more than expected, with an entire waveform rather than just two vectors.

In other words, it’s not doing with six floating point numbers what would classically take six real numbers. It’s doing with infinity real numbers what would classically take six real numbers.

I don’t see what about GR even resembles rounding errors.

[Brandon_Reinhart]

Sorry if I’m getting myself derailed, but is there any particular purpose to metaphor of the “Cooperative Conspiracy”? It seems to be smuggling in some kind of critique of group-think, although because this particular conspiracy isn’t fully defined the nature of the critique isn’t clear. (Although the team claims he is “rumored” to be a member of this conspiracy, they do not seem to be largely alarmed, indicating some measure of philosophical tolerance.) Is the cooperative conspiracy a metaphor for some behavioral phenomenon well known or apparent among researchers?

[Eliezer Yudkowsky]

This is a pre-existing world I built, where the Cooperative Conspiracy is one of many conspiracies struggling in the shadows for control of humankind’s destiny.

As for whether the Cooperative Conspiracy is a metaphor for anything, I don’t believe the Bardic Conspiracy would want me to answer that question: they hold that people should be free to put their own interpretations on stories.

[VAuroch]

How many Conspiracies have you conceived of specifically, in this world? We know of Competitive, Cooperative, Bardic, and Bayesian. Are there dozens more? Hundreds? Two?

[hyporational]

Most of them are secret.

[mitchell_porter2]

And on Day 26 they rediscovered string theory, and saw that it was good.

[Robin_Brandt]

What is the argument behind the confident negative attitude towards string theory/​M-theory? I am not a physicist, but in layman’s eyes it seems elegant. Is there any special argument or is it just general skepticism towards big unproven theoretical models?

[Alsadius]

At risk of necromancy, I’ll reply.

It’s hideously inelegant, and it makes no testable predictions. That means it gets low marks from both Bayes and Science. It might conceivably be excusable to argue that most of the structure of the universe is hidden if you can actually produce elegant math or come up with some new predictions from that basis, but after thirty years the string theorists can’t even agree on how many dimensions to do the math in. A massive investment of effort has gone precisely nowhere, and there’s no reason to believe it’ll do better in future. I’ll pass.

[mitchell_porter2]

Robin B., I can’t speak for Eliezer’s characters, but I believe the fashionability of skepticism about string theory has come from the lack of falsifiable predictions, after so many years. No-one has been able to say “this is the ground state”. Instead string theorists have studied a large number of possible ground states (distinguished by background geometry), most of them looking nothing like what we see, as they try to get a grip on the theory. The hope used to be that all but one would prove on further study to be unstable. Now there’s an interest in anthropic predictions, though that’s just one school of thought.

I have read that no-one has ever exhibited a string-theory ground state exactly reproducing the Standard Model, though you can get close. That has to be significant. If such a place can be found in the space of ground states (“moduli space”), you could then try to reason out why it was dynamically favored. And we’ll get more information within a few years from the Large Hadron Collider, which will establish whether there’s a Higgs boson or something else (I bet on something else; the Higgs was just the simplest way to make a tractable theory and lingers by default).

In string theory’s favor is that it generically has spin-1/​2 particles (fermions), spin-1 particles (gauge bosons), and spin-2 particles (gravitons). That’s a neat trick. So I tend to think either that it is the answer, or that it is just a beast of so many parts that anything you might look for is in there somewhere. In the latter case, it could be compared to the Monster group, the “largest sporadic simple finite group”. There are infinitely many finite simple groups, just as there are infinitely many possible field theories, and most of those groups resemble some subgroup of the Monster, just as string theory has spin-1/​2, spin-1, and spin-2 fields, just like the real world. It could be that string theory is just the “maximally complicated field theory” (and in fact, mathematically, it has a relationship to the Monster) and that it derives this generic pseudo-predictiveness solely from that. It has a little bit of everything, so anything looks a little bit like it. It would certainly be a mistake to take some real object, like Rubik’s cube, discover a few facts about its symmetry group, and then announce that its symmetry group must be the Monster, just because the Monster has subgroups with those properties. It could be that string theorists are making a mistake like that.

On the other hand, what’s the alternative? The phenomenological approach to particle physics is just to postulate enough fields with enough properties to explain what you see. You can treat gravity as just another field, contingently present, but then your theory becomes mathematically intractable. Part of string theory’s appeal is that you can calculate graviton-graviton scattering, etc., unlike any previous theory of quantum gravity. But the price is that you buy into the unification philosophy. Recently, there have been claims that “contingent” theories of quantum gravity—according to which reality is just a bunch of fields plus gravity, and there’s no deeper reason as to why it’s that combination of fields—can be made to work; this is the “loop quantum gravity” research program. It’s my judgement that string theory is mathematically much more solid. The loop quantum gravity researchers have had to backtrack several times, after making ambitious claims about the construction of consistent “gravity-plus-anything” quantum theories. Right now the evidence (in my semi-lay opinion) points in the other direction, that gravity needs to be part of a larger ensemble of fields with special properties if it is to be quantizable. Which suggests string theory.

[steven]

How would this Bardic Conspiracy have any real power? Clearly these are storytelling hobbyists in some post-Singularity world, and the others are Bayes hobbyists, wisdom-of-crowds hobbyists, and moral virtue hobbyists.

the two are one and cannot be divided even conceptually, as was accomplished for inertial mass-energy and gravitational mass-energy

Only partly true; it’s still a mystery why resistance-to-acceleration-caused-by-electromagnetic-forces has anything to do with propensity-to-curve-spacetime. (You can distinguish between “active” and “passive” gravitational mass.)

[Czynski]

How would this Bardic Conspiracy have any real power?

12 years later, Steven, I have an answer for you. Narratives are very, very good at translating into motivation. In some sense they are the native language of motivation. If you want to keep your motivation fueled while you attack a problem, having a story to tell about how it’s important is incredibly valuable.

And unskilled narrativemancy is quite dangerous; the same things that make it valuable to have a properly-aimed narrative make it very harmful to have a misaimed narrative. It will feel true and important and point you off in the wrong direction and it will take you a long while to recover from the error (and indeed you may never recover).

The initiation ceremony is an example of really good Bardic technique at work; they are presenting the message of ‘speak the truth even if your voice trembles’ in a way that the initiates will never, ever forget. That is a story which will never leave them and permanently remind them of the dangers of succumbing to social pressure.

This is particularly important when trying to harness the power of large groups; I suspect if Conspiracies were joined purely based on the standpoint of how best to optimize the world, the Cooperative and Bardic Conspiracies would have long-since merged.

But also,

Bayes hobbyists, wisdom-of-crowds hobbyists, and moral virtue hobbyists.

These are bad characterizations of the conspiracies. Bayesian Conspiracy is obvious, but is it Cooperative or Competitive which is supposed to be the wisdom-of-crowds faction? And how could either of those be construed as ‘moral virtue hobbyists’?

I’d characterize the four as “Bayes’s Theorem, wielded correctly, is extremely powerful”, “Narrative, wielded correctly, is extremely powerful”, “The human urge to excel, wielded correctly, is extremely powerful”, and “A large group of people working together, wielded correctly, is extremely powerful”. They are each offering, to their initiates, a “Big Secret” of “Learn to master this tool and you will become masters of the world”. Bardic actually has the strongest argument, because the system of Conspiracies is in fact a direct application of Bardic techniques to the world.

[Tom_McCabe2]

I really, really hope that you aren’t going to try and publish a theory of quantum gravity, for practical reasons; even if it’s more elegant than every other theory yet proposed, the lack of experimental evidence and your lack of credentials will make you seem like a crackpot.

[steven]

resistance-to-acceleration-caused-by-electromagnetic-forces

Actually never mind that part, this ends up in the Hamiltonian you were talking about via potential energy so you already mentioned this mystery. Still, saying “passive gravitational mass is conceptually the same thing as inertial mass” is more accurate than saying “gravitational mass is conceptually the same thing as inertial mass”.

[Eliezer Yudkowsky]

You assume too much about this world, steven.

[Richard_Hollerith2]

many conspiracies struggling in the shadows for control of humankind’s destiny.

It is Eliezer’s fictional world, but I would enjoy it more if one of the conspiracies—perhaps called the Nonhumanist Conspiracy—did not particularly care about the destiny of humankind except to the extent that humankind is instrumental to the destiny of something bigger like the universe or the all-there-is.

[stevo]

“Sacred language of science” is a contradiction. I like the story so far, and the inclusion of Lojban.

stevo

[TGGP4]

Perhaps, Richard, such a group does exist, but its members are not humans.

[Psy-Kosh]

Hrm… I have several thoughts in relation to this… One perhaps being that we need to perhaps look for a way to replace the energy term with a stress energy tensor...

But, perhaps a more specific interesting thought that I have here relates to almost an “opposite” thought I once had:

Can the space in which the quantum amplitude vectors (forget that they can be decomposed as complex numbers for a moment) move around itself be curved?

Well, this post got me thinking of that again… What would it look like for the “complex plane” to be curved? Well, one form that could take would be to allow an angle other than 2*Pi to be the angle which corresponds to the angle “spinning all the way around”

So, what’s that look like? Well, in some form of units, the arrow’s state can be represented as something like this:

e^iAx

where x is some measure of distance in configuration space and A is some coefficient...

Wait… does not energy itself show up somewhere in that A?

and if initially x was proportional in some fixed way to angle, would not that A somehow correspond to then a curvature of the complex plane, a change in the angle needed to go all the way around?

So it does look like, at least from one perspective, what energy is doing in QM directly corresponds to something sortakinda like curvature.

Except… you can always locally redefine your distance-in-configuration-space units to make A = 1 or whatever, at least locally… so maybe something along the lines of the change in A, or what A “looks like” given different subspaces factored out of the configuration space.

I have one or two mathematical “toy” ideas I want to play around with regards to that, but it’s late, and still I need to think about it a bit more, but, well.… That’s the basic notions I’ve got from the above suggested question.

Anyone else want to go somewhere with that, or smash it? :)

[Dihymo]

I am here to report that the reasons QM and GR don’t like each other are: Short answer: they are competing with each other

Long answer: There is a term that appears in perhaps different forms in both sets of equations that is counted twice. This possibly involves a factor that one of them is multiplied by. That factor may be as Psy-Kosh said a question of flat space versus curved space.

The existence of that factor prevents cancellation or some other thing which gives us infinities.

First find that term and the factor and eliminate them from the equations. Recalculate the constants so that it is no longer necessary. Next make sure the constants are the same over both theories. Combine the final shape of both theories. The next step is critical:

If you still get infinities, make them go away. Relate the way you made them go away to that term and factor.

[Skatche]

You seem very confident about this, so I assume you have some kind of evidence to back it up?

[Perplexed]

I assume you have some kind of evidence …

What do you base that assumption on? :)

Before issuing a challenge, it is sometimes wise to check dates to see whether a poster is still active. Click on his name here, then to the upper right, and get a list of his comments.

[Skatche]

Oh, wow, whoops! I sometimes get lost in the maze of links here and forget that I’m not on the front page anymore.

Anyway, my post was mostly sarcastic. His post and Psy-Kosh’s are barely coherent, let alone well-defended, or so they appear to me. On the other hand, I figured I might as well ask, in case he was just explaining something legitimate really poorly.

[Czynski]

extirpate that which permits them

link is broken, should point to http://​​citeseer.ist.psu.edu/​​viewdoc/​​summary?doi=10.1.1.41.3367

[Raemon]

Fixed, thanks.

[rnollet]

The current link seems to be nonworking. Does anyone know the title of what is supposed to be linked here?

[Jake_NB]

Actually Brennan’s idea is common knowledge in physics—energy is derived as the generator of time translation, both in GR and in QFT, so there is nothing new here.

[Ulisse Mini]

Taji looked over his sheets. “Okay, I think we’ve got to assume that every avenue that LessWrong was trying is a blind alley, or they would have found it. And if this is possible to do in one month, the answer must be, in some sense, elegant. So no multiple agents. If we start doing anything that looks like we should call it ‘HcH’, we’d better stop. Maybe begin by considering how failure to understand pre-coherent minds could have led LessWrong astray in formalizing corrigibility.”

“The opposite of folly is folly,” Hiriwa said. “Let us pretend that LessWrong never existed.”

(This could be turned into a longer post but I don’t have time...)