Imagine a group of 100 world-renowned scientists and military strategists. Could such a group easily wipe away the Roman empire when beamed back in time?
Imagine a group of 530 Spaniards...
At the risk of confirming every negative stereotype RationalWiki and the like have of us...have you read the Sequences? I'm reluctant to write a full response to this, but I think large parts of the Sequences were written to address some of these ideas.
I'm afraid I had the same reaction. XiXiDu's post seems to take the "shotgun" approach of listing every thought that popped into XiXiDu's head, without applying much of a filter. It's exhausting to read. Or, as one person I know put it, "XiXiDu says a lot of random shit."
P1 Fast, and therefore dangerous, recursive self-improvement is logically possible.
All your counter-arguments are enthymematic; as far as I can tell, you are actually arguing against a proposition which looks more like
P1 Recursive self-improvement of arbitrary programs towards unalterable goals is possible with very small constant factors and P or better general asymptotic complexity
I would find your enthymematic far more convincing if you explained why things like Goedel machines are either fallacious or irrelevant.
P1.b The fast computation of a simple algorithm is sufficient to outsmart and overpower humanity.
Your argument is basically an argument from fiction; it's funny that you chose that example of the Roman Empire when recently Reddit spawned a novel arguing that a Marine Corps (surely less dangerous than your 100) could do just that. I will note in passing that black powder's formulation is so simple and famous that even I, who prefers archery, knows it: saltpeter, charcoal, and sulfur. I know for certain that the latter two are available in the Roman empire and suspect the former would not be hard to get. EDIT: and this same day, a Mafia-related paper I was read...
It would be helpful if you summarised the premises in a short list. At the moment one has to do a lot of scrolling.
Edit: Actually, I think it would be a very good idea; their not being writen out together makes it easy to miss the fact that they're not all necessary, some imply others, and that they basically don't cut reality at its joints. You assert that these are all necessary and logically separate premises. Yet P4 is clearly not necessary for FOOM - something not being the default outcome does not mean it will not happen. P3 implies P2, and P2 implies P1. And P5 is clearly not necessary either - FOOM could occur in a thousand years time.
And again with the second set of premises - they are clearly not distinct, and not all necessary. For example,
is not necessary; they might succeed by preventing anyone else from developing GAI.
If you mean net, then yes. But otherwise, it's perfectly possible that they might speed up UFAI and AI, and yet still be a good thing, if the latter outweighs the former.
and
is the conclusion of the argument! This premise alone is suf...
Reading this made my brain hurt. It's a pile of false analogies that ignores the best arguments disagreeing with it, which is particularly ironic in light of the epigraph. (I'm thinking of Chalmers specifically, but really you can take your pick.)
I'm tempted to go through and point out every problem with this post, but I noticed at least a dozen on my first read-through and I just don't have the time.
Posts arguing against the LW orthodoxy deserve disproportional attention and consideration to combat groupthink, but this is just too wrong for me to tolerate.
But since nobody else seems to be willing to take a critical look at the overall topic
What I take a critical look at and what I write about in public are two very, very different things. Your audience is more heterogeneous than you might think.
You (XiXiDu) don't seem to think that intelligent machines are likely to be that big a deal. The switch to an engineered world is likely to be the biggest transformation of the planet since around the evolution of sex - or the last genetic takeover. It probably won't crash civilisation - or kill all humans - but it's going to be an enormous change, and the deatils of how it goes down could make a big difference to everyone. I do sometimes wonder whether you get that.
Good post.
You seem to excessively focus on recursive self-improvement to the exclusion of other hard takeoff scenarios, however. As Eliezer noted,
RSI is the biggest, most interesting, hardest-to-analyze, sharpest break-with-the-past contributing to the notion of a "hard takeoff" aka "AI go FOOM", but it's nowhere near being the only such factor. The advent of human intelligence was a discontinuity with the past even without RSI...
That post mentions several other hard takeoff scenarios, e.g.:
I upvoted for the anecdote, but remember that you're referring to von Neumann, who invented both the basic architecture of computers and the self-replicating machine. I am not qualified to judge whether or not those are as original as relativity, but they are certainly big.
Thanks for working this up.
However, it leads me to thinking about a modest FOOM. What's the least level of intelligence needed for a UFAI to be an existential risk? What's the least needed for it to be extremely deadly, even if not an existential risk?
Thanks - I've read the bullet points and it looks like a really good summary (apologies for skimming - I'll read it in more detail when I have time).
Just a few minor points:
If I understand you correctly, you are saying this: "Don't bother with this superintelligence risk, for it is incredibly tiny."
A bold statement. Too bold for a potentially disastrous chain of events, which you assure us it's just impossible.
P(FOOM) = P(P1∧P2∧P3∧P4∧P5)
This is wrong because the premises aren't independent. It's actually this:
P(P1) P(P2|P1) P(P3|P2∧P1) P(P4|P3∧P2∧P1) P(P5|P4∧P3∧P2∧P1)
Not only there has to be UFAI risk, the FAI development must reduce the risk, which to me looks like the most shaky of the propositions. A buggy FAI that doesn't break itself somehow is for certain unfriendly (e.g. it can want to euthanize you to end your suffering, or to cut apart your brain into 2 hemispheres to satisfy each hemisphere's different desires, or something much more bizarre), while some random AI out of AI design space may e.g. typically wirehead everything except curiosity, and then it'd just keep us in a sort of wildlife preserve.
Note: tr...
Fantastic post. This sets a new standard for "SIAI skepticism". Dialectically it should be very useful as people try to rebut it at the same level of detail. I think you shouldn't mess with it too much now, as it may become a reference point.
If you’re interested in being on the right side of disputes, you will refute your opponents' arguments. But if you're interested in producing truth, you will fix your opponents' arguments for them. To win, you must fight not only the creature you encounter; you [also] must fight the most horrible thing that can be constructed from its corpse.
This is an informal post meant as a reply to a post by user:utilitymonster, 'What is the best compact formalization of the argument for AI risk from fast takeoff?'
I hope to find the mental strength to put more effort into it in future to improve it. But since nobody else seems to be willing to take a critical look at the overall topic I feel that doing what I can is better than doing nothing.
Please review the categories 'Further Reading' and 'Notes and References'.
Contents
In this post I just want to take a look at a few premises (P#) that need to be true simultaneously to make the SIAI a wortwhile charity from the point of view of someone trying to do as much good as possible by contributing money. I am going to show that the case of risks from AI is strongly conjunctive, that without a concrete and grounded understanding of AGI an abstract analysis of the issues is going to be very shaky, and that therefore SIAI is likely to be a bad choice as a charity. In other words, that which speaks in favor of SIAI does mainly consist of highly specific, conjunctive, non-evidence-backed speculations on possible bad outcomes.
P1 Fast, and therefore dangerous, recursive self-improvement is logically possible.
It took almost four hundred years to prove Fermat’s Last Theorem. The final proof is over a hundred pages long. Over a hundred pages! And we are not talking about something like an artificial general intelligence that can magically make itself smart enough to prove such theorems and many more that no human being would be capable of proving. Fermat’s Last Theorem simply states “no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two.”
Even artificial intelligence researchers admit that "there could be non-linear complexity constrains meaning that even theoretically optimal algorithms experience strongly diminishing intelligence returns for additional compute power." [1] We just don't know.
Other possible problems include the impossibility of a stable utility function and a reflective decision theory, the intractability of real world expected utility maximization or that expected utility maximizers stumble over Pascal's mugging, among other things [2].
For an AI to be capable of recursive self-improvement it also has to guarantee that its goals will be preserved when it improves itself. It is still questionable if it is possible to conclusively prove that improvements to an agent's intelligence or decision procedures maximize expected utility. If this isn't possible it won't be rational or possible to undergo explosive self-improvement.
P1.b The fast computation of a simple algorithm is sufficient to outsmart and overpower humanity.
Imagine a group of 100 world-renowned scientists and military strategists.
Could such a group easily wipe away the Roman empire when beamed back in time?
Even if you gave all of them a machine gun, the Romans would quickly adapt and the people from the future would run out of ammunition.
Consider that it takes a whole technological civilization to produce a modern smartphone.
You can't just say "with more processing power you can do more different things", that would be analogous to saying that "100 people" from today could just build more "machine guns". But they can't! They can't use all their knowledge and magic from the future to defeat the Roman empire.
A lot of assumptions have to turn out to be correct to make humans discover simple algorithms over night that can then be improved to self-improve explosively.
You can also compare this to the idea of a Babylonian mathematician discovering modern science and physics given that he would be uploaded into a supercomputer (a possibility that is in and of itself already highly speculative). It assumes that he could brute-force conceptual revolutions.
Even if he was given a detailed explanation of how his mind works and the resources to understand it, self-improving to achieve superhuman intelligence assumes that throwing resources at the problem of intelligence will magically allow him to pull improved algorithms from solution space as if they were signposted.
But unknown unknowns are not signposted. It's rather like finding a needle in a haystack. Evolution is great at doing that and assuming that one could speed up evolution considerably is another assumption about technological feasibility and real-world resources.
That conceptual revolutions are just a matter of computational resources is pure speculation.
If one were to speed up the whole Babylonian world and accelerate cultural evolution, obviously one would arrive quicker at some insights. But how much quicker? How much are many insights dependent on experiments, to yield empirical evidence, that can't be speed-up considerably? And what is the return? Is the payoff proportionally to the resources that are necessary?
If you were going to speed up a chimp brain a million times, would it quickly reach human-level intelligence? If not, why then would it be different for a human-level intelligence trying to reach transhuman intelligence? It seems like a nice idea when formulated in English, but would it work?
Being able to state that an AI could use some magic to take over the earth does not make it a serious possibility.
Magic has to be discovered, adapted and manufactured first. It doesn't just emerge out of nowhere from the computation of certain algorithms. It emerges from a society of agents with various different goals and heuristics like "Treating Rare Diseases in Cute Kittens". It is an evolutionary process that relies on massive amounts of real-world feedback and empirical experimentation. Assuming that all that can happen because some simple algorithm is being computed is like believing it will emerge 'out of nowhere', it is magical thinking.
Unknown unknowns are not sign-posted. [3]
If people like Benoît B. Mandelbrot would have never decided to research Fractals then many modern movies wouldn't be possible, as they rely on fractal landscape algorithms. Yet, at the time Benoît B. Mandelbrot conducted his research it was not foreseeable that his work would have any real-world applications.
Important discoveries are made because many routes with low or no expected utility are explored at the same time [4]. And to do so efficiently it takes random mutation, a whole society of minds, a lot of feedback and empirical experimentation.
"Treating rare diseases in cute kittens" might or might not provide genuine insights and open up new avenues for further research. As long as you don't try it you won't know.
The idea that a rigid consequentialist with simple values can think up insights and conceptual revolutions simply because it is instrumentally useful to do so is implausible.
Complex values are the cornerstone of diversity, which in turn enables creativity and drives the exploration of various conflicting routes. A singleton with a stable utility-function lacks the feedback provided by a society of minds and its cultural evolution.
You need to have various different agents with different utility-functions around to get the necessary diversity that can give rise to enough selection pressure. A "singleton" won't be able to predict the actions of new and improved versions of itself by just running sandboxed simulations. Not just because of logical uncertainty but also because it is computationally intractable to predict the real-world payoff of changes to its decision procedures.
You need complex values to give rise to the necessary drives to function in a complex world. You can't just tell an AI to protect itself. What would that even mean? What changes are illegitimate? What constitutes "self"? That are all unsolved problems that are just assumed to be solvable when talking about risks from AI.
An AI with simple values will simply lack the creativity, due to a lack of drives, to pursue the huge spectrum of research that a society of humans does pursue. Which will allow an AI to solve some well-defined narrow problems, but it will be unable to make use of the broad range of synergetic effects of cultural evolution. Cultural evolution is a result of the interaction of a wide range of utility-functions.
Yet even if we assume that there is one complete theory of general intelligence, once discovered, one just has to throw more resources at it. It might be able to incorporate all human knowledge, adapt it and find new patterns. But would it really be vastly superior to human society and their expert systems?
Can intelligence itself be improved apart from solving well-defined problems and making more accurate predictions on well-defined classes of problems? The discovery of unknown unknowns does not seem to be subject to other heuristics than natural selection. Without goals, well-defined goals, terms like "optimization" have no meaning.
P2 Fast, and therefore dangerous, recursive self-improvement is physically possible.
Even if it could be proven that explosive recursive self-improvement is logically possible, e.g. that there are no complexity constraints, the question remains if it is physically possible.
Our best theories about intelligence are highly abstract and their relation to real world human-level general intelligence is often wildly speculative [5][6].
P3 Fast, and therefore dangerous, recursive self-improvement is economically feasible.
To exemplify the problem take the science fictional idea of using antimatter as explosive for weapons. It is physically possible to produce antimatter and use it for large scale destruction. An equivalent of the Hiroshima atomic bomb will only take half a gram of antimatter. But it will take 2 billion years to produce that amount of antimatter [7].
We simply don’t know if intelligence is instrumental or quickly hits diminishing returns [8].
P3.b AGI is able to create (or acquire) resources, empowering technologies or civilisatory support [9].
We are already at a point where we have to build billion dollar chip manufacturing facilities to run our mobile phones. We need to build huge particle accelerators to obtain new insights into the nature of reality.
An AI would either have to rely on the help of a whole technological civilization or be in control of advanced nanotech assemblers.
And if an AI was to acquire the necessary resources on its own, its plan for world-domination would have to go unnoticed. This would require the workings of the AI to be opaque to its creators yet comprehensible to itself.
But an AI capable of efficient recursive self improvement must be able to
So if the AI can do that, why wouldn't humans be able to use the same algorithms to predict what the initial AI is going to do? And if the AI can't do that, how is it going to maximize expected utility if it is unable to predict what it is going to do?
Any AI capable of efficient self-modification must be able to grasp its own workings and make predictions about improvements to various algorithms and its overall decision procedure. If an AI can do that, why would the humans who build it be unable to notice any malicious intentions? Why wouldn't the humans who created it not be able to use the same algorithms that the AI uses to predict what it will do? If humans are unable to predict what the AI will do, how is the AI able to predict what improved versions of itself will do?
And even if an AI was able to somehow acquire large amounts of money. It is not easy to use the money. You can't "just" build huge companies with fake identities, or a straw man, to create revolutionary technologies easily. Running companies with real people takes a lot of real-world knowledge, interactions and feedback. But most importantly, it takes a lot of time. An AI could not simply create a new Intel or Apple over a few years without its creators noticing anything.
The goals of an AI will be under scrutiny at any time. It seems very implausible that scientists, a company or the military are going to create an AI and then just let it run without bothering about its plans. An artificial agent is not a black box, like humans are, where one is only able to guess its real intentions.
A plan for world domination seems like something that can't be concealed from its creators. Lying is no option if your algorithms are open to inspection.
P4 Dangerous recursive self-improvement is the default outcome of the creation of artificial general intelligence.
Complex goals need complex optimization parameters (the design specifications of the subject of the optimization process against which it will measure its success of self-improvement).
Even the creation of paperclips is a much more complex goal than telling an AI to compute as many decimal digits of Pi as possible.
For an AGI, that was designed to design paperclips, to pose an existential risk, its creators would have to be capable enough to enable it to take over the universe on its own, yet forget, or fail to, define time, space and energy bounds as part of its optimization parameters. Therefore, given the large amount of restrictions that are inevitably part of any advanced general intelligence (AGI), the nonhazardous subset of all possible outcomes might be much larger than that where the AGI works perfectly yet fails to hold before it could wreak havoc.
And even given a rational utility maximizer. It is possible to maximize paperclips in a lot of different ways. How it does it is fundamentally dependent on its utility-function and how precisely it was defined.
If there are no constraints in the form of design and goal parameters then it can maximize paperclips in all sorts of ways that don't demand recursive self-improvement.
"Utility" does only become well-defined if we precisely define what it means to maximize it. Just maximizing paperclips doesn't define how quickly and how economically it is supposed to happen.
The problem is that "utility" has to be defined. To maximize expected utility does not imply certain actions, efficiency and economic behavior, or the drive to protect yourself. You can also rationally maximize paperclips without protecting yourself if it is not part of your goal parameters.
You can also assign utility to maximize paperclips as long as nothing turns you off but don't care about being turned off. If an AI is not explicitly programmed to care about it, then it won't.
Without well-defined goals in form of a precise utility-function, it might be impossible to maximize expected "utility". Concepts like "efficient", "economic" or "self-protection" all have a meaning that is inseparable with an agent's terminal goals. If you just tell it to maximize paperclips then this can be realized in an infinite number of ways that would all be rational given imprecise design and goal parameters. Undergoing to explosive recursive self-improvement, taking over the universe and filling it with paperclips, is just one outcome. Why would an arbitrary mind pulled from mind-design space care to do that? Why not just wait for paperclips to arise due to random fluctuations out of a state of chaos? That wouldn't be irrational. To have an AI take over the universe as fast as possible you would have to explicitly design it to do so.
But for the sake of a thought experiment assume that the default case was recursive self-improvement. Now imagine that a company like Apple wanted to build an AI that could answer every question (an Oracle).
If Apple was going to build an Oracle it would anticipate that other people would also want to ask it questions. Therefore it can't just waste all resources on looking for an inconsistency arising from the Peano axioms when asked to solve 1+1. It would not devote additional resources on answering those questions that are already known to be correct with a high probability. It wouldn't be economically useful to take over the universe to answer simple questions.
It would neither be rational to look for an inconsistency arising from the Peano axioms while solving 1+1. To answer questions an Oracle needs a good amount of general intelligence. And concluding that asking it to solve 1+1 implies to look for an inconsistency arising from the Peano axioms does not seem reasonable. It also does not seem reasonable to suspect that humans desire an answer to their questions to approach infinite certainty. Why would someone build such an Oracle in the first place?
A reasonable Oracle would quickly yield good solutions by trying to find answers within a reasonable time which are with a high probability just 2–3% away from the optimal solution. I don't think anyone would build an answering machine that throws the whole universe at the first sub-problem it encounters.
P5 The human development of artificial general intelligence will take place quickly.
What evidence do we have that there is some principle that, once discovered, allows us to grow superhuman intelligence overnight?
If the development of AGI takes place slowly, a gradual and controllable development, we might be able to learn from small-scale mistakes, or have enough time to develop friendly AI, while having to face other existential risks.
This might for example be the case if intelligence can not be captured by a discrete algorithm, or is modular, and therefore never allow us to reach a point where we can suddenly build the smartest thing ever that does just extend itself indefinitely.
Therefore the probability of an AI to undergo explosive recursive self-improvement (P(FOOM)) is the probability of the conjunction (P#∧P#) of its premises:
P(FOOM) = P(P1∧P2∧P3∧P4∧P5)
Of course, there are many more premises that need to be true in order to enable an AI to go FOOM, e.g. that each level of intelligence can effectively handle its own complexity, or that most AGI designs can somehow self-modify their way up to massive superhuman intelligence. But I believe that the above points are enough to show that the case for a hard takeoff is not disjunctive, but rather strongly conjunctive.
In this section I will assume the truth of all premises in the previous section.
P6 SIAI can solve friendly AI.
Say you believe that unfriendly AI will wipe us out with a probability of 60% and that there is another existential risk that will wipe us out with a probability of 10% even if unfriendly AI turns out to be no risk or in all possible worlds where it comes later. Both risks have the same utility x (if we don't assume that an unfriendly AI could also wipe out aliens etc.). Thus .6x > .1x. But if the probability of solving friendly AI = A to the probability of solving the second risk = B is A ≤ (1/6)B then the expected utility of mitigating friendly AI is at best equal to the other existential risk because .6Ax ≤ .1Bx.
Consider that one order of magnitude more utility could easily be outweighed or trumped by an underestimation of the complexity of friendly AI.
So how hard is it to solve friendly AI?
Take for example Pascal's mugging, if you can't solve it then you need to implement a hack that is largely based on human intuition. Therefore, in order to estimate the possibility of solving friendly AI one needs to account for the difficulty in solving all sub-problems.
Consider that we don't even know "how one would start to research the problem of getting a hypothetical AGI to recognize humans as distinguished beings." [10]
P7 SIAI does not increase risks from AI.
By trying to solve friendly AI, SIAI has to think about a lot of issues related to AI in general and might have to solve problems that will make it easier to create artificial general intelligence.
It is far from being clear that SIAI is able to protect its findings against intrusion, betrayal, industrial or espionage.
P8 SIAI does not increase negative utility.
There are several possibilities by which SIAI could actually cause a direct increase in negative utility.
1) Friendly AI is incredible hard and complex. Complex systems can fail in complex ways. Agents that are an effect of evolution have complex values. To satisfy complex values you need to meet complex circumstances. Therefore any attempt at friendly AI, which is incredible complex, is likely to fail in unforeseeable ways. A half-baked, not quite friendly, AI might create a living hell for the rest of time, increasing negative utility dramatically [11].
2) Humans are not provably friendly. Given the power to shape the universe the SIAI might fail to act altruistic and deliberately implement an AI with selfish motives or horrible strategies [12].
P9 It makes sense to support SIAI at this time [13].
Therefore the probability of SIAI to be a worthwhile charity (P(CHARITY)) is the probability of the conjunction (P#∧P#) of its premises:
P(CHARITY) = P(P6∧P7∧P8∧P9)
As before, there are many more premises that need to be true in order for SIAI to be the best choice for someone who wants to maximize doing good by contributing money to a charity.
The following posts and resources elaborate on many of the above points and hint at a lot of additional problems.
[1] Q&A with Shane Legg on risks from AI
[2] http://lukeprog.com/SaveTheWorld.html
[3] "In many ways, this is a book about hindsight. Pythagoras could not have imagined the uses to which his equation would be put (if, indeed, he ever came up with the equation himself in the first place). The same applies to almost all of the equations in this book. They were studied/discovered/developed by mathematicians and mathematical physicists who were investigating subjects that fascinated them deeply, not because they imagined that two hundred years later the work would lead to electric light bulbs or GPS or the internet, but rather because they were genuinely curious."
17 Equations that changed the world
[4] Here is my list of "really stupid, frivolous academic pursuits" that have lead to major scientific breakthroughs.
http://blog.ketyov.com/2012/02/basic-science-is-about-creating.html
[5] "AIXI is often quoted as a proof of concept that it is possible for a simple algorithm to improve itself to such an extent that it could in principle reach superhuman intelligence. AIXI proves that there is a general theory of intelligence. But there is a minor problem, AIXI is as far from real world human-level general intelligence as an abstract notion of a Turing machine with an infinite tape is from a supercomputer with the computational capacity of the human brain. An abstract notion of intelligence doesn’t get you anywhere in terms of real-world general intelligence. Just as you won’t be able to upload yourself to a non-biological substrate because you showed that in some abstract sense you can simulate every physical process."
Alexander Kruel, Why an Intelligence Explosion might be a Low-Priority Global Risk
[6] "…please bear in mind that the relation of Solomonoff induction and “Universal AI” to real-world general intelligence of any kind is also rather wildly speculative… This stuff is beautiful math, but does it really have anything to do with real-world intelligence? These theories have little to say about human intelligence, and they’re not directly useful as foundations for building AGI systems (though, admittedly, a handful of scientists are working on “scaling them down” to make them realistic; so far this only works for very simple toy problems, and it’s hard to see how to extend the approach broadly to yield anything near human-level AGI). And it’s not clear they will be applicable to future superintelligent minds either, as these minds may be best conceived using radically different concepts."
Ben Goertzel, 'Are Prediction and Reward Relevant to Superintelligences?'
[7] http://public.web.cern.ch/public/en/spotlight/SpotlightAandD-en.html
[8] "If any increase in intelligence is vastly outweighed by its computational cost and the expenditure of time needed to discover it then it might not be instrumental for a perfectly rational agent (such as an artificial general intelligence), as imagined by game theorists, to increase its intelligence as opposed to using its existing intelligence to pursue its terminal goals directly or to invest its given resources to acquire other means of self-improvement, e.g. more efficient sensors."
Alexander Kruel, Why an Intelligence Explosion might be a Low-Priority Global Risk
[9] Section 'Necessary resources for an intelligence explosion', Why an Intelligence Explosion might be a Low-Priority Global Risk, Alexander Kruel
[10] http://lesswrong.com/lw/3aa/friendly_ai_research_and_taskification/
[11] http://lesswrong.com/r/discussion/lw/ajm/ai_risk_and_opportunity_a_strategic_analysis/5ylx
[12] http://lesswrong.com/lw/8c3/qa_with_new_executive_director_of_singularity/5y77
[13] "I think that if you're aiming to develop knowledge that won't be useful until very very far in the future, you're probably wasting your time, if for no other reason than this: by the time your knowledge is relevant, someone will probably have developed a tool (such as a narrow AI) so much more efficient in generating this knowledge that it renders your work moot."
Holden Karnofsky in a conversation with Jaan Tallinn