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# 53

This post has been recorded as part of the LessWrong Curated Podcast, and can be listened to on Spotify, Apple Podcasts, and Libsyn.

TL;DR: To even consciously consider an alignment research direction, you should have evidence to locate it as a promising lead. As best I can tell, many directions seem interesting but do not have strong evidence of being “entangled” with the alignment problem such that I expect them to yield significant insights.

For example, “we can solve an easier version of the alignment problem by first figuring out how to build an AI which maximizes the number of real-world diamonds” has intuitive appeal and plausibility, but this claim doesn’t have to be true and this problem does not necessarily have a natural, compact solution. In contrast, there do in fact exist humans who care about diamonds. Therefore, there are guaranteed-to-exist alignment insights concerning the way people come to care about e.g. real-world diamonds.

“Consider how humans navigate the alignment subproblem you’re worried about” is a habit which I (TurnTrout) picked up from Quintin Pope. I wrote the post, he originated the tactic.

A simplified but still very difficult open problem in AI alignment is to state an unbounded program implementing a diamond maximizer that will turn as much of the physical universe into diamond as possible. The goal of "making diamonds" was chosen to have a crisp-seeming definition for our universe (the amount of diamond is the number of carbon atoms covalently bound to four other carbon atoms). If we can crisply define exactly what a 'diamond' is, we can avert issues of trying to convey complex values into the agent.

Ontology identification problem, Arbital

I find this problem interesting, both in terms of wanting to know how to solve a reframed version of it, and in terms of what I used to think about the problem. I used to[1] think, “yeah, ‘diamond’ is relatively easy to define. Nice problem relaxation.” It felt like the diamond maximizer problem let us focus on the challenge of making the AI’s values bind to something at all which we actually intended (e.g. diamonds), in a way that’s robust to ontological shifts and that doesn’t collapse into wireheading or tampering with e.g. the sensors used to estimate the number of diamonds.

Although the details are mostly irrelevant to the point of this blog post, the Arbital article suggests some solution ideas and directions for future research, including:

1. Scan AIXI-tl’s Turing machines and locate diamonds within their implicit state representations.
2. Given how inaccessible we expect AIXI-tl’s representations to be by default, have AIXI-tl just consider a Turing-complete hypothesis space which uses more interpretable representations.
3. “Being able to describe, in purely theoretical principle, a prior over epistemic models that have at least two levels and can switch between them in some meaningful sense”

Do you notice anything strange about these three ideas? Sure, the ideas don’t seem workable, but they’re good initial thoughts, right?

The problem isn’t that the ideas aren’t clever enough. Eliezer is pretty dang clever, and these ideas are reasonable stabs given the premise of “get some AIXI variant to maximize diamond instead of reward.”

The problem isn’t that it’s impossible to specify a mind which cares about diamonds. We already know that there are intelligent minds who value diamonds. You might be dating one of them, or you might even be one of them! Clearly, the genome + environment jointly specify certain human beings who end up caring about diamonds.

One problem is where is the evidence required to locate these ideas? Why should I even find myself thinking about diamond maximization and AIXI and Turing machines and utility functions in this situation? It’s not that there’s no evidence. For example, utility functions ensure the agent can’t be exploited in some dumb ways. But I think that the supporting evidence is not commensurate with the specificity of these three ideas or with the specificity of the “ontology identification” problem framing.

Here’s an exaggeration of how these ideas feel to me when I read them:

“I lost my phone”, you tell your friend.

They ask, “Have you checked Latitude: -34.44006, Longitude: -64.61333?”

Uneasily, you respond: “Why would I check there?”

Your friend shrugs: “Just seemed promising. And it’s on land, it’s not in the ocean. Don’t worry, I incorporated evidence about where you probably lost it.”

Against CIRL as a special case of against quickly jumping into highly specific speculation while ignoring empirical embodiments-of-the-desired-properties.

In the context of "how do we build AIs which help people?", asking "does CIRL solve corrigibility?" is hilariously unjustified. By what evidence have we located such a specific question? We have assumed there is an achievable "corrigibility"-like property; we have assumed it is good to have in an AI; we have assumed it is good in a similar way as "helping people"; we have elevated CIRL in particular as a formalism worth inquiring after.

But this is not the first question to askwhen considering "sometimes people want to help each other, and it'd be great to build an AI which helps us in some way." Much better to start with existing generally intelligent systems (humans) which already sometimes act in the way you want (they help each other) and ask after the guaranteed-to-exist reason why this empirical phenomenon happens.

Now, if you are confused about a problem, it can be better to explore some guesses than no guesses—perhaps it’s better to think about Turing machines than to stare helplessly at the wall (but perhaps not). Your best guess may be wrong (e.g. write a utility function which scans Turing machines for atomic representations of diamonds), but you sometimes still learn something by spelling out the implications of your best guess (e.g. the ontology identifier stops working when AIXI Bayes-updates to non-atomic physical theories). This can be productive, as long as you keep in mind the wrongness of the concrete guess, so as to not become anchored on that guess or on the framing which originated it (e.g. build a diamond maximizer).

However, in this situation, I want to look elsewhere. When I confront a confusing, difficult problem (e.g. how do you create a mind which cares about diamonds?), I often first look at reality (e.g. are there any existing minds which care about diamonds?). Even if I have no idea how to solve the problem, if I can find an existing mind which cares about diamonds, then since that mind is real, that mind has a guaranteed-to-exist causal mechanistic play-by-play origin story for why it cares about diamonds. I thereby anchor my thinking to reality; reality is sturdier than “what if” and “maybe this will work”; many human minds do care about diamonds.

In addition to “there’s a guaranteed causal story for humans valuing diamonds, and not one for AIXI valuing diamonds”, there’s a second benefit to understanding how human values bind to the human’s beliefs about real-world diamonds. This second benefit is practical: I’m pretty sure the way that humans come to care about diamonds has nearly nothing to do with the ways AIXI-tl might be motivated to maximize diamonds. This matters, because I expect that the first AGI’s value formation will be far more mechanistically similar to within-lifetime human value formation, than to AIXI-tl’s value alignment dynamics.

Next, it can be true that the existing minds are too hard for us to understand in ways relevant to alignment. One way this could be true is that human values are a "mess", that "our brains are kludges slapped together by natural selection." If human value formation were sufficiently complex, with sufficiently many load-bearing parts such that each part drastically affects human alignment properties, then we might instead want to design simpler human-comprehensible agents and study their alignment properties.

While I think that human values are complex, I think the evidence for human value formation’s essential complexity is surprisingly weak, all things reconsidered in light of modern, post-deep learning understanding. Still... maybe humans are too hard to understand in alignment-relevant ways!

But, I mean, come on. Imagine an alien[2] visited and told you:

Oh yeah, the AI alignment problem. We knocked that one out a while back. Information inaccessibility of the learned world model? No, I’m pretty sure we didn’t solve that, but we didn’t have to. We built this protein computer and trained it with, I forget actually, was it just what you would call “deep reinforcement learning”? Hm. Maybe it was more complicated, maybe not, I wasn’t involved.

We might have hardcoded relatively crude reward signals that are basically defined over sensory observables, like a circuit which activates when their sensors detect a certain kind of carbohydrate. Scanning you, it looks like some of the protein computers ended up with your values, even. Small universe, huh?

Actually, I forgot how we did it, sorry. And I can’t make guarantees that our approach scales beyond your intelligence level or across architectures, but maybe it does. I have to go, but here are a few billion of the trained protein computers if you want to check them out!

Ignoring the weird implications of the aliens existing and talking to you like this, and considering only the alignment implications—The absolute top priority of many alignment researchers should be figuring out how the hell the aliens got as far as they did.[3] Whether or not you know if their approach scales to further intelligence levels, whether or not their approach seems easy to understand, you have learned that these computers are physically possible, practically trainable entities. These computers have definite existence and guaranteed explanations. Next to these actually existent computers, speculation like “maybe attainable utility preservation leads to cautious behavior in AGIs” is dreamlike, unfounded, and untethered.

If it turns out to be currently too hard to understand the aligned protein computers, then I want to keep coming back to the problem with each major new insight I gain. When I learned about scaling laws, I should have rethought my picture of human value formation—Did the new insight knock anything loose? I should have checked back in when I heard about mesa optimizers, about the Bitter Lesson, about the feature universality hypothesis for neural networks, about natural abstractions.

Because, given my life’s present ambition (solve AI alignment), that’s what it makes sense for me to do—at each major new insight, to reconsider my models[4] of the single known empirical example of general intelligences with values, to scour the Earth for every possible scrap of evidence that humans provide about alignment. We may not get much time with human-level AI before we get to superhuman AI. But we get plenty of time with human-level humans, and we get plenty of time being a human-level intelligence.

The way I presently see it, the godshatter of human values—the rainbow of desires, from friendship to food—is only unpredictable relative to a class of hypotheses which fail to predict the shattering.[5] But confusion is in the map, not the territory. I do not consider human values to be “unpredictable” or “weird”, I do not view them as a “hack” or a “kludge.” Human value formation may or may not be messy (although I presently think not). Either way, human values are, of course, part of our lawful reality. Human values are reliably produced by within-lifetime processes within the brain. This has an explanation, though I may be ignorant of it. Humans usually bind their values to certain objects in reality, like dogs. This, too, has an explanation.

And, to be clear, I don’t want to black-box outside-view extrapolate from the “human datapoint”; I don’t want to focus on thoughts like “Since alignment ‘works well’ for dogs and people, maybe it will work well for slightly superhuman entities.” I aspire for the kind of alignment mastery which lets me build a diamond-producing AI, or if that didn’t suit my fancy, I’d turn around and tweak the process and the AI would press green buttons forever instead, or—if I were playing for real—I’d align that system of mere circuitry with humane purposes.

For that ambition, the inner workings of those generally intelligent apes is invaluable evidence about the mechanistic within-lifetime process by which those apes form their values, and, more generally, about how intelligent minds can form values at all. What factors matter for the learned values, what factors don’t, and what we should do for AI. Maybe humans have special inductive biases or architectural features, and without those, they’d grow totally different kinds of values. But if that were true, wouldn’t that be important to know?

If I knew how to interpret the available evidence, I probably would understand how I came to weakly care about diamonds, and what factors were important to that process (which reward circuitry had to fire at which frequencies, what concepts I had to have learned in order to grow a value around “diamonds”, how precisely activated the reward circuitry had to be in order for me to end up caring about diamonds).

Humans provide huge amounts of evidence, properly interpreted—and therein lies the grand challenge upon which I am presently fixated. In an upcoming post, I’ll discuss one particularly rich vein of evidence provided by humans. (EDIT 1/1/23: See this shortform comment.)

Thanks to Logan Smith and Charles Foster for feedback. Spiritually related to but technically distinct from The First Sample Gives the Most Information.

EDIT: In this post, I wrote about the Arbital article's unsupported jump from "Build an AI which cares about a simple object like diamonds" to "Let's think about ontology identification for AIXI-tl." The point is not that there is no valid reason to consider the latter, but that the jump, as written, seemed evidence-starved. For separate reasons, I currently think that ontology identification is unattractive in some ways, but this post isn't meant to argue against that framing in general. The main point of the post is that humans provide tons of evidence about alignment, by virtue of containing guaranteed -to-exist mechanisms which produce e.g. their values around diamonds.

# Appendix: One time I didn’t look for the human mechanism

Back in 2018, I had a clever-seeming idea. We don’t know how to build an aligned AI; we want multiple tries; it would be great if we could build an AI which “knows it may have been incorrectly designed”; so why not have the AI simulate its probable design environment over many misspecifications, and then not do plans which tend to be horrible for most initial conditions. While I drew some inspiration from how I would want to reason in the AI’s place, I ultimately did not think thoughts like:

We know of a single group of intelligent minds who have ever wanted to be corrigible and helpful to each other. I wonder how that, in fact, happens?

Instead, I was trying out clever, off-the-cuff ideas in order to solve e.g. Eliezer’s formulation of the hard problem of corrigibility. However, my idea and his formulation suffered a few disadvantages, including:

1. The formulation is not guaranteed to describe a probable or “natural” kind of mind,
2. These kinds of “corrigible” AIs are not guaranteed to produce desirable behavior, but only imagined to produce good behavior,
3. My clever-seeming idea was not at all constrained by reality to actually work in practice, as opposed to just sounding clever to me, and
4. I didn’t have a concrete use case in mind for what to do with a “corrigible” AI.

I wrote this post as someone who previously needed to read it.

1. ^

I now think that diamond’s physically crisp definition is a red herring. More on that in future posts.

2. ^

This alien is written to communicate my current belief state about how human value formation works, so as to make it clear why, given my beliefs, this value formation process is so obviously important to understand.

3. ^

There is an additional implication present in the alien story, but not present in the evolutionary production of humans. The aliens are implied to have purposefully aligned some of their protein computers with human values, while evolution is not similarly “purposeful.” This implication is noncentral to the key point, which is that the human-values-having protein computers exist in reality.

4. ^

Well, I didn’t even have a detailed picture of human value formation back in 2021. I thought humans were hopelessly dumb and messy and we want a nice clean AI which actually is robustly aligned

5. ^

Suppose we model humans as the "inner agent" and evolution as the "outer optimizer"—I think this is, in general, the wrong framing, but let's roll with it for now. I would guess that Eliezer believes that human values are an unpredictable godshatter with respect to the outer criterion of inclusive genetic fitness. This means that if you reroll evolution many times with perturbed initial conditions, you get inner agents with dramatically different values each time—it means that human values are akin to a raindrop which happened to land in some location for no grand reason. I notice that I have medium-strength objections to this claim, but let's just say that he is correct for now.

I think this unpredictability-to-evolution doesn't matter. We aren't going to reroll evolution to get AGI. Thus, for a variety of reasons too expansive for this margin, I am little moved by analogy-based reasoning along the lines of "here's the one time inner alignment was tried in reality, and evolution failed horribly." I think that historical fact is mostly irrelevant, for reasons I will discuss later.

# 53

New Comment

I think a lot of people have thought about how humans end up aligned to each other, and concluded that many of the mechanisms wouldn't generalize. E.g. the fact that different humans have relative similar levels of power to each other seems important; we aren't very aligned to agents much less powerful than us like animals, and I wouldn't expect a human who had been given all the power in the world all their life such that they've learned they can solve any conflict by destroying their opposition to be very aligned.

I think a lot of people have thought about how humans end up aligned to each other, and concluded that many of the mechanisms wouldn't generalize.

I disagree both with this conclusion and the process that most people use to reach it.

The process: I think that, unless you have a truly mechanistic, play-by-play, and predicatively robust understanding of how human values actually form, then you are not in an epistemic position to make strong conclusions about whether or not the underlying mechanisms can generalize to superintelligences.

E.g., there are no birds in the world able to lift even a single ton of weight. Despite this fact, the aerodynamic principles underlying bird flight still ended up allowing for vastly more capable flying machines. Until you understand exactly why (some) humans end up caring about each other and why (some) humans end up caring about animals, you can't say whether a similar process can be adapted to make AIs care about humans.

The conclusion: Humans vary wildly in their degrees of alignment to each other and to less powerful agents. People often take this as a bad thing, that humans aren't "good enough" for us to draw useful insights from. I disagree, and think it's a reason for optimism. If you sample n humans and pick the most "aligned" of the n, what you've done is applied  bits of optimization pressure on the underlying generators of human alignment properties.

The difference in alignment between a median human and a top-1000 most aligned human equates to only 10 bits of optimization pressure towards alignment. If there really was no more room to scale human alignment generators further, then humans would differ very little in their levels of alignment.

We're not trying to mindlessly copy the alignment properties of the median human into a superintelligent AI. We're trying to understand the certain-to-exist generators of those alignment properties well enough that we can scale them to whatever level is needed for superintelligence (if doing so is possible).

I don't think I've ever seen a truly mechanistic, play-by-play and robust explanation of how anything works in human psychology. At least not by how I would label things, but maybe you are using the labels differently; can you give an example?

"Humans are nice because they were selected to be nice" -- non-mechanistic.

"Humans are nice because their contextually activated heuristics were formed by past reinforcement by reward circuits A, B, C; this convergently occurs during childhood because of experiences D, E, F; credit assignment worked appropriately at that time because their abstraction-learning had been mostly taken care of by self-supervised predictive learning, as evidenced by developmental psychology timelines in G, H, I, and also possibly natural abstractions." -- mechanistic (although I can only fill in parts of this story for now)

Although I'm not a widely-read scholar on what theories people have for human values, of those which I have read, most (but not all) are more like the first story than the second.

The principles from the post can still be applied. Some humans do end up aligned to animals - particularly vegans (such as myself!). How does that happen? There empirically are examples of general intelligences with at least some tendency to terminally value entities massively less powerful than themselves; we should be analyzing how this occurs.

Also, remember that the problem is not to align an entire civilization of naturally evolved organisms to weaker entities. The problem is to align exactly one entirely artificial organism to weaker entities. This is much simpler, and as mentioned entirely possible by just figuring out how already existing people of that sort end up that way - but your use of "we" here seems to imply that you think the entirety of human civilization is the thing we ought to be using as inspiration for the AGI, which is not the case.

By the way: at least part of the explanation for why I personally am aligned to animals is that I have a strong tendency to be moved by the Care/Harm moral foundation - see this summary of The Righteous Mind for more details. It is unclear exactly how it is implemented in the brain, but it is suspected to be a generalization of the very old instincts that cause mothers to care about the safety and health of their children. I have literally, regularly told people that I perceive animals as identical in moral relevance to human children, implying that some kind of parental instincts are at work in the intuitions that make me care about their welfare. Even carnists feel this way about their pets, hence calling themselves e.g. "cat moms". So, the main question here for alignment is: how can we reverse engineer parental instincts?

Human beings and other animals have parental instincts (and in general empathy) because they were evolutionary advantageous for the population that developed them.

AGI won't be subjected to the same evolutionary pressures, so every alignment strategy relying on empathy or social reward functions, it is, in my opinion, hopelessly naive.

There must have been some reason(s) why organisms exhibiting empathy were selected for during our evolution. However, evolution did not directly configure our values. Rather, it configured our (individually slightly different) learning processes. Each human’s learning process then builds their different values based on how the human’s learning process interacts with that human’s environment and experiences.

The human learning process (somewhat) consistently converges to empathy. Evolution might have had some weird, inhuman reason for configuring a learning process to converge to empathy, but it still built such a learning process.

It therefore seems very worthwhile to understand what part of the human learning process allows for empathy to emerge in humans. We may not be able to replicate the selection pressures that caused evolution to build an empathy-producing learning process, but it’s not clear we need to. We still have an example of such a learning process to study. The Wright brothers didn't need to re-evolve birds to create their flying machine.

We could study such a learning process, but I am afraid that the lessons learned won't be so useful.

Even among human beings, there is huge variability in how much those emotions arise or if they do, in how much they affect behavior.  Worst, humans tend to hack these feelings (incrementing or decrementing them) to achieve other goals: i.e MDMA to increase love/empathy or drugs for soldiers to make them soulless killers.

An AGI will have a much easier time hacking these pro-social-reward functions.

An AGI will have a much easier time hacking these pro-social-reward functions.

Not sure what you mean by this. If you mean "Pro-social reward is crude and easy to wirehead on", I think this misunderstands the mechanistic function of reward

The "Humans do X because evolution" argument does not actually explain anything about mechanisms. I keep seeing people make this argument, but it's a non sequitur to the points I'm making in this post. You're explaining how the behavior may have gotten there, not how the behavior is implemented. I think that "because selection pressure" is a curiosity-stopper, plain and simple.

AGI won't be subjected to the same evolutionary pressures, so every alignment strategy relying on empathy or social reward functions, it is, in my opinion, hopelessly naive.

This argument proves too much, since it implies that planes can't work because we didn't subject them to evolutionary pressures for flight. It's locally invalid.

The principles from the post can still be applied. Some humans do end up aligned to animals - particularly vegans (such as myself!). How does that happen? There empirically are examples of general intelligences with at least some tendency to terminally value entities massively less powerful than themselves; we should be analyzing how this occurs.

Sure, if you've got some example of a mechanism for this that's likely to scale, it may be worthwhile. I'm just pointing out that a lot of people have already thought about mechanisms and concluded that the mechanisms they could come up with would be unlikely to scale.

By the way: at least part of the explanation for why I personally am aligned to animals is that I have a strong tendency to be moved by the Care/Harm moral foundation - see this summary of The Righteous Mind for more details.

I'm not a big fan of moral foundations theory for explaining individual differences in moral views. I think it lacks evidence.

I'm just pointing out that a lot of people have already thought about mechanisms and concluded that the mechanisms they could come up with would be unlikely to scale.

In my experience, researchers tend to stop at "But humans are hacky kludges" (what do they think they know, and why do they think they know it?). Speaking for myself, I viewed humans as complicated hacks which didn't offer substantial evidence about alignment questions. This "humans as alignment-magic" or "the selection pressure down the street did it" view seems quite common (but not universal).

AFAICT, most researchers do not appreciate the importance of asking questions with guaranteed answers.

AFAICT, most alignment-produced thinking about humans is about their superficial reliability (e.g. will they let an AI out of the box) or the range of situations in which their behavior will make sense (e.g. how hard is it to find adversarial examples which make a perfect imitation of a human). I think these questions are relatively unimportant to alignment.

I think that past investigators didn't have good guesses of what the mechanisms are. Most reasoning about human values seems to be of the sort "look at how contextually dependent these 'values' things are, and the biases are also a huge mess, I doubt there are simple generators of these preferences", or "Evolution caused human values in an unpredictable way, and that doesn't help us figure out alignment."

E.g. the fact that different humans have relative similar levels of power to each other seems important; we aren't very aligned to agents much less powerful than us like animals, and I wouldn't expect a human who had been given all the power in the world all their life such that they've learned they can solve any conflict by destroying their opposition to be very aligned.

This reasoning is not about mechanisms. It is analogical. You might still believe the reasoning, and I think it's at least an a priori relevant observation, but let's call a spade a spade. This is analogical reasoning to AGI by drawing inferences from select observations (some humans don't care about less powerful entities) and then inferring that AGI will behave similarly.

(Edited this comment to reduce unintended sharpness)

To summarize your argument: people are not aligned w/ others who are less powerful than them, so this will not generalize to AGI that is much more power than humans.

Parents have way more power than their kids, and there exists some parents that are very loving (ie aligned) towards their kids. There are also many, many people who care about their pets & there exist animal rights advocates.

If we understand the mechanisms behind why some people e.g. terminally value animal happiness and some don't, then we can apply these mechanisms to other learning systems.

I wouldn't expect a human who had been given all the power in the world all their life such that they've learned they can solve any conflict by destroying their opposition to be very aligned.

I agree this is likely.

To summarize your argument: people are not aligned w/ others who are less powerful than them, so this will not generalize to AGI that is much more power than humans.

Parents have way more power than their kids, and there exists some parents that are very loving (ie aligned) towards their kids. There are also many, many people who care about their pets & there exist animal rights advocates.

Well, the power relations thing was one example of one mechanism. There are other mechanisms which influence other things, but I wouldn't necessarily trust them to generalize either.

Ah, yes I recognized I was replying to only an example you gave, and decided to post a separate comment on the more general point:)

There are other mechanisms which influence other things, but I wouldn't necessarily trust them to generalize either.

Could you elaborate?

Could you elaborate?

One factor I think is relevant is:

Suppose you are empowered in some way, e.g. you are healthy and strong. In that case, you could support systems that grant preference to the empowered. But that might not be a good idea, because you could become disempowered, e.g. catch a terrible illness, and in that case the systems would end up screwing you over.

In fact, it is particularly in the case where you become disempowered that you would need the system's help, so you would probably weight this priority more strongly than would be implied by the probability of becoming disempowered.

So people may under some conditions have an incentive to support systems that benefit others. And one such systems could be a general moral agreement that "everyone should be treated as having equal inherent worth, regardless of their power".

Establishing such a norm will then tend to have knock-on effects outside of the original domain of application, e.g. granting support to people who have never been empowered. But the knock-on effects seem potentially highly contingent, and there are many degrees of freedom in how to generalize the norms.

This is not the only factor of course, I'm not claiming to have a comprehensive idea of how morality works.

Oh, you're stating potential mechanisms for human alignment w/ humans that you don't think will generalize to AGI. It would be better for me to provide an informative mechanism that might seem to generalize.

Turntrout's other post claims that the genome likely doesn't directly specify rewards for everything humans end up valuing. People's specific families aren't encoded as circuits in the limbic system, yet downstream of the crude reward system, many people end up valuing their families. There are more details to dig into here, but already it implies that work towards specifying rewards more exactly is not as useful as understanding how crude rewards lead to downstream values.

A related point: humans don't maximize the reward specified by their limbic system, but can instead be modeled as a system of inner-optimizers that value proxies instead (e.g. most people wouldn't push a wirehead button if it killed a loved one). This implies that inner-optimizers that are not optimizing the base objective are good, meaning that inner-alignment & outer-alignment are not the right terms to use.

There are other mechanisms, and I believe it's imperative to dig deeper into them, develop a better theory of how learning systems grow values, and test that theory out on other learning systems.

There are many alignment properties that humans exhibit such as valuing real world objects, being corrigible, not wireheading if given the chance, not suffering ontological crises, and caring about sentient life (not everyone has these values of course). I believe the post's point that studying the mechanisms behind these value formations is more informative than other sources of info. Looking at the post:

the inner workings of those generally intelligent apes is invaluable evidence about the mechanistic within-lifetime process by which those apes form their values, and, more generally, about how intelligent minds can form values at all.

Humans can provide a massive amount of info on how highly intelligent systems value things in the real world. There are guaranteed-to-exist mechanisms behind why humans value real world things and mechanisms behind the variance in human values, and the post argues we should look at these mechanisms first (if we're able to). I predict that a mechanistic understanding will enable the below knowledge:

I aspire for the kind of alignment mastery which lets me build a diamond-producing AI, or if that didn’t suit my fancy, I’d turn around and tweak the process and the AI would press green buttons forever instead, or—if I were playing for real—I’d align that system of mere circuitry with humane purposes.

I think it can be worthwhile to look at those mechanisms, in my original post I'm just pointing out that people might have done so more than you might naively think if you just consider whether their alignment approaches mimic the human mechanisms, because it's quite likely that they've concluded that the mechanisms they've come up with for humans don't work.

Secondly, I think with some of the examples you mention, we do have the core idea of how to robustly handle them. E.g. valuing real-world objects and avoiding wireheading seems to almost come "for free" with model-based agents.

If it turns out to be currently too hard to understand the aligned protein computers, then I want to keep coming back to the problem with each major new insight I gain. When I learned about scaling laws, I should have rethought my picture of human value formation—Did the new insight knock anything loose? I should have checked back in when I heard about mesa optimizers, about the Bitter Lesson, about the feature universality hypothesis for neural networks, about natural abstractions.

Humans do display many many alignment properties, and unlocking that mechanistic understanding is 1,000x more informative than other methods. Though this may not be worth arguing until you read the actual posts showing the mechanistic understandings (the genome post and future ones), and we could argue about specifics then?

If you're convinced by them, then you'll understand the reaction of "Fuck, we've been wasting so much time and studying humans makes so much sense" which is described in this post (e.g. Turntrout's idea on corrigibility and statement "I wrote this post as someone who previously needed to read it."). I'm stating here that me arguing "you should feel this way now before being convinced of specific mechanistic understandings" doesn't make sense when stated this way.

Secondly, I think with some of the examples you mention, we do have the core idea of how to robustly handle them. E.g. valuing real-world objects and avoiding wireheading seems to almost come "for free" with model-based agents.

Link? I don't think we know how to use model-based agents to e.g. tile the world in diamonds even given unlimited compute, but I'm open to being wrong.

Curated. I'm not sure I endorse all the specific examples, but the general principles make sense to me as considerations to help guide alignment research directions.

I don't have anything especially insightful to contribute, but I wanted to thank you (TurnTrout and Quinton) for this post.  I agree with it, and I often find myself thinking things like this when I read alignment posts by others on LW/AF.

When people present frameworks for thinking about AGIs or generic "intelligent agents," I often want to ask them: "are humans expressible in your framework?"  Often it seems like the answer is "no."

And a common symptom of this is that the framework cannot express entities with human-level capabilities that are as well aligned with other such agents are humans are with one another.  Deception, for example, is much less of a problem for humans in practice than it is claimed to be for AGIs in theory.  Yes, we do engage in it sometimes, but we could do it a lot more than (most of us) do.  Since this state of affairs is possible, and since it's desirable, it seems important to know how it can be achieved.

I strongly disagree with your notion of how privileging the hypothesis works. It's not absurd to think that techniques for making AIXI-tl value diamonds despite ontological shifts could be adapted for other architectures. I agree that there are other examples of people working on solving problems within a formalisation that seem rather formalisation specific, but you seem to have cast the net too wide.

My basic point remains. Why is it not absurd to think that, without further evidential justification? By what evidence have you considered the highly specific investigation into AIXI-tl, and located the idea that ontology identification is a useful problem to think about at all (in its form of "detecting a certain concept in the AI")?

I think it's quite clear how shifting ontologies could break a specification of values. And sometimes you just need a formalisation, any formalisation, to play around with. But I suppose it depends more of the specific details of your investigation.

After more discussion with bmk, I appended the following edit:

In this post, I wrote about the Arbital article's unsupported jump from "Build an AI which cares about a simple object like diamonds" to "Let's think about ontology identification for AIXI-tl." The point is not that there is no valid reason to consider the latter, but that the jump, as written, seemed evidence-starved. For separate reasons, I currently think that ontology identification is unattractive in some ways, but this post isn't meant to argue against that framing in general. The main point of the post is that humans provide tons of evidence about alignment, by virtue of containing guaranteed-to-exist mechanisms which produce e.g. their values around diamonds.

It is not that human values are particularly stable. It's that humans themselves are pretty limited. Within that context, we identify the stable parts of ourselves as "our human values".

If we lift that stability - if we allow humans arbitrary self-modification and intelligence increase - the parts of us that are stable will change, and will likely not include much of our current values. New entities, new attractors.

It is not that human values are particularly stable

I might agree or disagree with this statement, depending on what "particularly stable" means. (Also, is there a portion of my post which seems to hinge on "stability"?)

we identify the stable parts of ourselves as "our human values".

I don't see why you think this.

if we allow humans arbitrary self-modification and intelligence increase - the parts of us that are stable will change, and will likely not include much of our current values.

Do you predict that if I had access to a range of pills which changed my values to whatever I wanted, and I could somehow understand the consequences of each pill (the paperclip pill, the yay-killing pill, ...), I would choose a pill such that my new values would be almost completely unaligned with my old values?

Do you predict that if I had access to a range of pills which changed my values to whatever I wanted, and I could somehow understand the consequences of each pill (the paperclip pill, the yay-killing pill, ...), I would choose a pill such that my new values would be almost completely unaligned with my old values?

This is the wrong angle, I feel (though it's the angle I introduced, so apologies!). The following should better articulate my thoughts:

We have an AI-CEO money maximiser, rewarded by the stock price ticker as a reward function. As long as the AI is constrained and weak, it continues to increase the value of the company; when it becomes powerful, it wireheads and takes over the stock price ticker.

Now that wireheading is a perfectly correct extrapolation of its reward function; it hasn't "changed" its reward function, it simply has gained the ability to control its environment well, so that it now can decorrelate the stock ticker from the company value.

Notice the similarity with humans who develop contraception so they can enjoy sex without risking childbirth. Their previous "values" seemed to be a bundle of "have children, enjoy sex" and this has now been wireheaded into "enjoy sex".

Is this a correct extrapolation of prior values? In retrospect, according to our current values, it seems to mainly be the case. But some people strongly disagree even today, and, if you'd done a survey of people before contraception, you'd have got a lot of mixed responses (especially if you'd got effective childbirth medicine long before contraceptives). And if we want to say that the "true" values have been maintained, we'd have to parse the survey data in specific ways, that others may argue with.

So we like to think that we've maintained our "true values" across these various "model splinterings", but it seems more that what we've maintained has been retrospectively designated as "true values". I won't go the whole hog of saying "humans are rationalising beings, rather than rational ones", but there is at least some truth to that, so it's never fully clear what our "true values" really were in the past.

So if you see humans as examples of entities that maintain their values across ontology changes and model splinterings, I would strongly disagree. If you see them as entities that sorta-kinda maintain and adjust their values, preserving something of what happened before, then I agree. That to me is value extrapolation, for which humans have shown a certain skill (and many failings). And I'm very interested in automating that, though I'm sceptical that the purely human version of it can extrapolate all the way up to superintelligence.

Hm, thanks for the additional comment, but I mostly think we are using words and frames differently, and disagree with my understanding of what you think values are.

We have an AI-CEO money maximiser, rewarded by the stock price ticker as a reward function. As long as the AI is constrained and weak, it continues to increase the value of the company; when it becomes powerful, it wireheads and takes over the stock price ticker.

Their previous "values" seemed to be a bundle of "have children, enjoy sex" and this has now been wireheaded into "enjoy sex".

I think this is not what happened. Those desires are likely downstream of past reinforcement of different kinds; I do not think there is a "wireheading" mechanism here. Wireheading is a very specific kind of antecedent-computation-reinforcement chasing behavior, on my ontology.

I'm sceptical that the purely human version of it can extrapolate all the way up to superintelligence.

Not at all what I'm angling at. There's a mechanistic generator for why humans navigate ontology shifts well (on my view). Learn about the generators, don't copy the algorithm.

Not at all what I'm angling at. There's a mechanistic generator for why humans navigate ontology shifts well (on my view). Learn about the generators, don't copy the algorithm.

I agree that humans navigate "model splinterings" quite well. But I actually think the algorithm might be more important than the generators. The generators comes from evolution and human experience in our actual world; this doesn't seem like it would generalise. The algorithm itself, though, may very generalisable (potential analogy: humans have instinctive grasp of all numbers under five, due to various evolutionary pressures, but we produced the addition algorithm that is far more generalisable).

I'm not sure that we disagree much. We may just have different emphases and slightly different takes on the same question?

I'm not sure that we disagree much.

Yes and no. I think most of our disagreements are probably like "what is instinctual?" and "what is the type signature of human values?" etc. And not on "should we understand what people are doing?".

The generators comes from evolution and human experience in our actual world

By "generators", I mean "the principles by which the algorithm operates", which means the generators are found by studying the within-lifetime human learning process.

potential analogy: humans have instinctive grasp of all numbers under five, due to various evolutionary pressures

Dubious to me due to information inaccessibility & random initialization of neocortex (which is a thing I am reasonably confident in). I think it's more likely that our architecture&compute&learning process makes it convergent to learn this quick <= 5 number-sense.

(Transcribed in part from Eleuther discussion and DMs.)

My understanding of the argument here is that you're using the fact that you care about diamonds as evidence that whatever the brain is doing is worth studying, with the hope that it might help us with alignment. I agree with that part. However, I disagree with the part where you claim that things like CIRL and ontology identification aren't as worthy of being elevated to consideration. I think there exist lines of reasoning that these fall naturally out as subproblems, and the fact that they fall out of these other lines of reasoning promotes them to the level of consideration.

I think there are a few potential cruxes of disagreement from reading the posts and our discussion:

• You might be attributing far broader scope to the ontology identification problem than I would; I think of ontology identification as an interesting subproblem that recurs in a lot of different agendas, that we may need to solve in certain worst plausible cases / for robustness against black swans.
• In my mind ontology identification is one of those things where it could be really hard worst case or it could be pretty trivial, depending on other things. I feel like you're pointing at "humans can solve this in practice" and I'm pointing at "yeah but this problem is easy to solve in the best case and really hard to solve in the worst case."
• More broadly, we might disagree on how scalable certain approaches used in humans are, or how surprising it is that humans solve certain problems in practice. I generally don't find arguments about humans implementing a solution to some hard alignment problem compelling, because almost always when we're trying to solve the problem for alignment we're trying to come up with an airtight robust solution, and humans implement the kludgiest, most naive solution that works often enough
• I think you're attributing more importance to the "making it care about things in the real world, as opposed to wireheading" problem than I am. I think of this as one subproblem of embeddedness that might turn out to be difficult, that falls somewhere between 3rd and 10th place on my list of most urgent alignment problems to fix. This applies to shard theory more broadly.

I also think the criticism of invoking things like AIXI-tl is missing the point somewhat. As I understand it, the point that is being made when people think about things like this is that nobody expects AGI to actually look like AIXI-tl or be made of Bayes nets, but this is just a preliminary concretization that lets us think about the problem, and substituting this is fine because this isn't core to the phenomenon we're poking at (and crucially the core of the thing that we're pointing at is something very limited in scope, as I listed in one of the cruxes above). As an analogy, it's like thinking about computational complexity by assuming you have an infinitely large Turing machine and pretending coefficients don't exist or something, even though real computers don't look remotely like that. My model of you is saying "ah, but it is core, because humans don't fit into this framework and they solve the problem, so by restricting yourself to this rigid framework you exclude the one case where it is known to be solved." To which I would point to the other crux and say "au contraire, humans do actually fit into this formalism, it works in humans because humans happen to be the easy case, and this easy solution generalizing to AGI would exactly correspond to scanning AIXI-tl's Turing machines for diamond concepts just working without anything special." (see also: previous comments where I explain my views on ontology identification in humans).

More broadly, we might disagree on how scalable certain approaches used in humans are, or how surprising it is that humans solve certain problems in practice.

I want to understand the generators of human alignment properties, so as to learn about the alignment problem and how it "works" in practice, and then use that knowledge of alignment-generators in the AI case. I'm not trying to make an "amplified" human.

when we're trying to solve the problem for alignment we're trying to come up with an airtight robust solution, and

I personally am unsure whether this is even a useful frame, or an artifact of conditioning on our own confusion about how alignment works.

humans implement the kludgiest, most naive solution that works often enough

How do you know that?

I think of this as one subproblem of embeddedness that might turn out to be difficult, that falls somewhere between 3rd and 10th place on my list of most urgent alignment problems to fix.

"Get the agent to care about some parts of reality" is not high on my list of problems, because I don't think it's a problem, I think it's the default outcome for the agents we will train. (I don't have a stable list right now because my list of alignment subproblems is rapidly refactoring as I understand the problem better.)

"Get the agent to care about specific things in the real world" seems important to me, because it's challenging our ability to map outer supervision signals into internal cognitive structures within the agent. Also, it seems relatively easy to explain, and I also have a good story for why people (and general RL agents) will "bind their values to certain parts of reality" (in a sense which I will later explain).

this is just a preliminary concretization that lets us think about the problem, and substituting this is fine because this isn't core to the phenomenon we're poking at

Disagreeing with the second phrase is one major point of this essay. How do we know that substituting this is fine? By what evidence do we know that the problem is even compactly solvable in the AIXI framing?

My model of you is saying "ah, but it is core, because humans don't fit into this framework and they solve the problem, so by restricting yourself to this rigid framework you exclude the one case where it is known to be solved."

(Thanks for querying your model of me, btw! Pretty nice model, that indeed sounds like something I would say. :) )

This easy solution generalizing to AGI would exactly correspond to scanning AIXI-tl's Turing machines for diamond concepts just working without anything special."

I don't think you think humans care about diamonds because the genome specifies brian-scanning circuitry which rewards diamond-thoughts. Or am I wrong? So, humans caring about diamonds actually wouldn't correspond to the AIXI case? (I also am confused if and why you think that this is how it gets solved for other human motivations...?)

falls somewhere between 3rd and 10th place on my list of most urgent alignment problems to fix

What is your list of problems by urgency, btw?  Would be curious to know.

I find myself confused about what point this post is trying to make even after reading through it twice. Can you summarize your central point in 100 words or less?

If the title is meant to be a summary of the post, I think that would be analogous to someone saying "nuclear forces provide an untapped wealth of energy". It's true, but the reason the energy is untapped is because nobody has come up with a good way of tapping into it. A post which tried to address engineering problems around energy production by "we need to look closely at how to extract energy from the strong interaction and we need to check if we can squeeze anything out of that whenever new physics is discovered" would not be compelling.

If you come up with a strategy for how to do this then I'm much more interested, and that's a big reason why I'm asking for a summary since I think you might have tried to express something like this in the post that I'm missing.

If the title is meant to be a summary of the post, I think that would be analogous to someone saying "nuclear forces provide an untapped wealth of energy". It's true, but the reason the energy is untapped is because nobody has come up with a good way of tapping into it.

The difference is people have been trying hard to harness nuclear forces for energy, while people have not been trying hard to research humans for alignment in the same way. Even relative to the size of the alignment field being far smaller, there hasn't been a real effort as far as I can see. Most people immediately respond with "AGI is different from humans for X,Y,Z reasons" (which are true) and then proceed to throw out the baby with the bathwater by not looking into human value formation at all.

Planes don't fly like birds, but we sure as hell studied birds to make them.

If you come up with a strategy for how to do this then I'm much more interested, and that's a big reason why I'm asking for a summary since I think you might have tried to express something like this in the post that I'm missing.

This is their current research direction, The shard theory of human values which they're currently making posts on.

In an upcoming post, I’ll discuss one particularly rich vein of evidence provided by humans.

so the doc Ulisse provided is a decent write-up about just that, but there are more official posts intended to published.

I am skeptical of your premise. I know of zero humans who terminally value “diamonds” as defined by their chemical constitution.

Indeed, diamonds are widely considered to be a fake scarce good, elevated to their current position by deceptive marketing and monopolistic practices. So this seems more like a case study of how humans’ desires to own scarce symbols of wealth have been manipulated to lead to an outcome that is misaligned with the original objective.

I believe the diamond example is true, but not the best example to use. I bet it was mentioned because of the arbital article linked in the post.

The premise isn't dependent on diamonds being terminal goals; it could easily be about valuing real life people or dogs or nature or real life anything. Writing an unbounded program that values real world objects is an open-problem in alignment; yet humans are a bounded program that values real world objects all of the time, millions of times a day.

The post argues that focusing on the causal explanations behind humans growing values is way more informative than other sources of information, because humans exist in reality and anchoring your thoughts to reality is more informative about reality.

I just introspected. I am weakly attracted to the idea of acquiring diamonds. I therefore know of at least one human who values diamonds.

I never claimed that humans are hardwired to value diamonds. I pointed out that some people do value diamonds, and pointed out that true facts have guaranteed-to-exist explanations. If you're interested in building a mind which values diamonds, first ask why some already-existing minds value diamonds.


text:
# NormalityTest_CramerVonMisesNormal¶

NormalityTest_CramerVonMisesNormal(sample, level=0.05)

Evaluate whether a sample follows a normal distribution.

Available usages:

NormalityTest.CramerVonMisesNormal(sample)

NormalityTest.CramerVonMisesNormal(sample, level)

Parameters: sample : 2-d sequence of float Tested sample. level : positive float Threshold p-value of the test (= first kind risk), it must be , equal to 0.05 by default. testResult : TestResult Structure containing the result of the test.

Notes

The test is used to check whether the sample follows a normal distribution. The test concerns the deviation squared and integrated over the entire variation domain, it often appears to be more robust than the Kolmogorov-Smirnov test.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> sample = distribution.getSample(30)
>>> test_result = ot.NormalityTest.CramerVonMisesNormal(sample)
>>> print(test_result)
class=TestResult name=Unnamed type=CramerVonMisesNormal binaryQualityMeasure=true p-value threshold=0.05 p-value=0.682524 description=[]

format: plain


text:
# Definition:Abundancy Index

## Definition

Let $n$ be a positive integer.

Let $\map \sigma n$ be the sigma function of $n$.

That is, let $\map \sigma n$ be the sum of all positive divisors of $n$.

Then the abundancy index of $n$ is defined as $\dfrac {\map \sigma n} n$.

### Abundant Number

Let $\sigma \left({n}\right)$ be the sigma function of $n$.

$n$ is abundant if and only if $\dfrac {\sigma \left({n}\right)} n > 2$.

### Perfect Number

A perfect number $n$ is a (strictly) positive integer such that:

$\dfrac {\sigma \left({n}\right)} n = 2$

where $\sigma: \Z_{>0} \to \Z_{>0}$ is the sigma function.

### Deficient Number

Let $\sigma \left({n}\right)$ be the sigma function of $n$.

$n$ is deficient if and only if:

$\dfrac {\sigma \left({n}\right)} n < 2$


text:
# Indexing an interval of words on top of every page

Friends, I'm curious on how to do the following in LaTeX:

Dictionaries have two words on the top of each page, meaning the interval of words to be found on that specific page, e.g.,

In the figure, analyst refers to the lower bound (the first word), and ancillary refers to the upper bound (the last word) in this page.

I was wondering of how we could achieve something similar in LaTeX. Let's say we have the following document:

\documentclass{article}
\usepackage{multicol}
\usepackage{enumerate}
\usepackage{lipsum}

\begin{document}
\begin{multicols}{2}
\begin{description}
\end{description}
\end{multicols}
\end{document}

For this page, I expect to see both adequate and adhesive in the top of the page (first and last items on the page, respectively). The same rule applies to the rest of the pages. Update: I should've mentioned that I'm curious of an "automatic" way of choosing which words will be set in the page headers. =)

Any ideas?

-
Section 10 of the fancyhdr documentation shows how to do this. –  Alan Munn Aug 19 '11 at 19:07
@Alan: Interesting, thanks for mentioning. In fact, I was looking for something like an automatic procedure to look which words are the first and last in the current page and then set them in the header. fancyhdr solves the second part (how to put them in there), I wonder how could we solve the first one. =) –  Paulo Cereda Aug 19 '11 at 19:16
It's all in there. See my posted answer. –  Alan Munn Aug 19 '11 at 21:19
@Alan: my bad, I probably misread the documentation. ;-) –  Paulo Cereda Aug 19 '11 at 21:34

Here's a worked up example based on section 10 of the fancyhdr documentation:

\documentclass[twoside]{article}
\usepackage{multicol}
\usepackage{ifthen}
\usepackage{fancyhdr}
\usepackage{enumerate}
\usepackage{lipsum}
% empty \sectionmark
\renewcommand{\sectionmark}[1]{}
% create a command to create marks and collapse them if they are identical
\newcommand{\mymarks}{%
\ifthenelse{\equal{\leftmark}{\rightmark}}
{\rightmark} % if equal
{\rightmark--\leftmark}} % if not equal
% define a wrapper on the description environment to add the marks
% this part is quick and dirty; it would be better to define one's own
% environment to do this, but the basic idea is the same: you need
% to add the \markboth command to each dictionary entry
\def\ditem[#1]{\markboth{#1}{#1}\item[#1]}
\pagestyle{fancy}
\begin{document}
\begin{multicols}{2}
\begin{description}

Absolutely fantastic, Alan! Thanks a million! =) –  Paulo Cereda Aug 19 '11 at 21:31


text:
Bloomberg bond clean price and accrued amount differs from Quantlib

I'm getting the different bond clean price from Bloomberg and from QL but surprisingly Bloomberg price matches with excel price() function

I have the following bond : GETC21117030. The parameters are given below:

Parameter Name Value
Settlment Date 30-12-20
Bond Issue Date 17-Jan-19
Interest Acrual date 17-Jan-19
Maturity Date 17-Jan-21
Last Coupon Date 17-Jul-20
Coupon Rate 7.25%
Coupon Frequency 2
Day Count ACT/ACT
Redemption 100
Yield 7.95%
Calendar NullCalendar
GenRule Backward

if you look at the parameters you'll notice that there is only one payment left on maturity date. If I calculate price and accrued interest in QLXL I'm getting different results from Bloomberg. But surprisingly Bloomberg numbers match if I use excel native price calculation function.

I looked into the excel formula and it looks that the price calculate formula is different when there is only one payment left (see below)

When N > 1 (N is the number of coupons payable between the settlement date and redemption date), PRICE is calculated as follows:

When N = 1 (N is the number of coupons payable between the settlement date and redemption date), PRICE is calculated as follows:

DSR = number of days from settlement to next coupon date.

E = number of days in coupon period in which the settlement date falls.

A = number of days from beginning of coupon period to settlement date.

It seems that for the last payment calculation excel is moving from compounded yield to simple yield.

I calculated the clean price both with compounded yield and with simple yield. While the clean price with simple yield is close to the Bloomberg/Excel price it still does not match.

With 7.95% yield and settlement date 30 Dec 2020:

Bloomberg/Excel clean price is 99.953226, Accrued Amount 3.270380

QLXL(semiannually compounded yield) clean price is 99.95983172, Accrued Amount 3.288251366

QLXL(simple yield) clean price is 99.95278714, Accrued Amount 3.288251366

I'm not C++ specialist but the QL code I've checked does not change the price calculation algorithm when only one payment is left.

The question is: Is it possible with current implementation of QuantLib to match the price and accrued amount for the above mentioned bond (and in general with all coupon bonds when there is only one cashflow is left)?

Several things might be affecting your result. Check if all the conventions are correct, namely the daycount.

Regarding, the compounding on the last period, I can replicate Bloomberg's price for that bond in QuantLib using the SimpleThenCompounded parameter.

import QuantLib as ql

settlementDate = ql.Date(30,12,2020)
issueDate = ql.Date(17,1,2019)
maturityDate = ql.Date(17,1,2021)
coupon = 0.0725
freq = ql.Period('6M')
dayCount = ql.ActualActual(ql.ActualActual.ISMA)
yld = 0.0795

bbgPrice = 99.953226
bond = ql.FixedRateBond(0, ql.TARGET(), 100.0, issueDate, maturityDate, freq, [coupon], dayCount, ql.Unadjusted, ql.Unadjusted)
print(f"BBG Price: {bbgPrice}")

px = bond.cleanPrice(yld, dayCount, ql.SimpleThenCompounded, ql.Annual, settlementDate)
print(f"QuantLib  Price: {px:.6f}\n")

BBG Price: 99.953226
QuantLib Price: 99.953226


text:
# How to relate speed of sound with relative humidity?

I am exploring the idea of measuring the humidity of a space using sound waves, however I am having trouble finding a mathematical relationship between the speed of sound and the humidity level.

$c_{air} = 331.3 \sqrt{1 + \frac{T}{273.15}}$ but this is for dry air (0%RH)

How can I factor the effects of humidity into this relationship?

-

Speed of sound in a gas is given by the equation: $$c = \sqrt{\gamma R T}$$

where $\gamma = c_p/c_v$ ( $c_p$ and $c_v$ are specific heats), $R$ is the gas constant, and $T$ is temperature. The specific heat of a gas changes with humidity, so varying these will vary your calculated speed of sound.

This page has a calculator as well as a great explanation of how their formula works.

Hope this helps!

-

The speed of sound in a gas is:

$$c = \sqrt{\gamma R T}$$

where $\gamma = c_p/c_v$ is the ratio of specific heats, $R$ is the specific gas constant and $T$ is temperature. Both $\gamma$ and $R$ depend on the composition of the gas, which includes humidity in air.

The specific heats are $c_p = 1.005+1.82H$ (see this answer) where $H$ is the absolute humidty and $c_v = c_p - R$. Finally, $R = R_{univ}/M_{gas}$ where $M_{gas}$ is the molecular weight of the gas (which depends on humidity).

To get it all in terms of relative humidity is just an exercise in unit conversion.

-


text:
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## Argument essay template, if anyone wants it

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#### Argument essay template, if anyone wants it

Thu Jun 04, 2009 8:09 pm
Hey guys-

I'm not hugely qualified to give GMAT advice (I'm not an instructor), but I took the GMAT twice and got a 6.0 essay score both times, so I hope someone will find my essay templates/advice useful.

Analysis of Argument
Paragraph 1
I always start begin with a broad statement about the issue at hand. For instance in an argument essay about whether it was necessary to conserve energy, I would begin with:

Energy conservation has become a hot topic in the United States as of late. There are those who debate climate change and those who affirm it, those who assert that humans are depleting the world's natural resources, including fossil fuels, and those who believe that humans are barely making a dent in consuming the resources the earth has to offer.

This sets up a fluid introduction to my essay, and by starting with an introductory sentence, I felt I would set myself apart from the majority of other test takers who begin "I agree" or "I disagree" -- remember, you want to distinguish yourself from other essay writers (in a good way) right from the start.

I always continue by saying, "In the preceding statement, the author claims that (paraphrase of the author's argument)." This shows that I understand the author's argument. I continue with my disagreement (and, as has been often said, ALWAYS disagree with the author's reasoning, and I pretty much always used the same thesis statement, something like:

Though his claim may well have merit, the author presents a poorly reasoned argument, based on several questionable premises and assumptions, and based solely on the evidence the author offers, we cannot accept his argument as valid.

I can use that statement for pretty much any argument essay I encounter. The beginning shows that I see the issue as nuanced, rather than black and white, and I recognize that though the author may have arrived at the correct answer, his reasoning is flawed. I also use "we" but I try to avoid using "I". Take that as you will.

Paragraph 2
For me, paragraph two always attacks the premises of the author's argument. I usually jot down a couple of premises on my board -- these are things that show up in the author's argument, usually without any evidence provided. So 99% of the time, I attack the lack of evidence that the author bases his premises on. I usually begin with some version of:

The primary issue with the author's reasoning lies in his unsubstantiated premises.

I like "primary" and "secondary" as transitional tools because they are more complex than "first" and "second". Throughout the first paragraph, I show flaws in the author's premises by pointing out his lack of evidentiary support (they pretty much always lack evidentiary support) and where they are open to holes or alternate explanations. I usually have two or three, but one would be fine if it it was strong. I generally end with something like:

The author's premises, the basis for his argument, lack any legitimate evidentiary support and render his conclusion unacceptable.

Paragraph 3
In the third paragraph, I always attack the assumptions - again, I jot down a couple assumptions on my notepad while reading the prompt. Generally, the issue with assumptions is that they need to be clearly explicated - the author is asking the reader to make a jump with them, but the reader may well veer off course if the author doesn't explicitly state his arguments. I usually begin with some variation of:

In addition, the author makes several assumptions that remain unproven.

Again, I begin with a transitional phrase that the e-grader can pick up on. As with the premises, I spend this paragraph attacking a couple of the author's assumptions. The easiest way to do this is to find an alternate explanation -- ie, what if the assumption wasn't true? I usually have two or three, again. My assumption paragraph ends with something like:

The author weakens his argument by making assumptions and failing to provide explication of the links between X and Y he assumes exists.

Paragraph 4
Paragraph 4 is where I talk about how the author could strengthen his argument -- that is, I go back to my claim that his argument could have some validity, but not as it stands. I usually begin this paragraph with something like:

While the author does have several key issues in his argument's premises and assumptions, that is not to say that the entire argument is without base.

Then I provide some concrete ways the author could strengthen his argument. The easiest way to do this is to give examples of what kind of evidence the author could provide, and discuss how he can fill the holes in his assumptions. I generally end with something like:

Though there are several issues with the author's reasoning at present, with research and clarification, he could improve his argument significantly.

Paragraph 5
This is my conclusion paragraph. I pretty much always conclude with the same sentence:

In sum, the author's illogical argument is based on unsupported premises and unsubstantiated assumptions that render his conclusion invalid.

I usually use "in sum" because it's considered better stylistically than "in conclusion" but signals to the e-grader that you're at your conclusion. I usually add a couple sentences of fluff in between and then I end with:

If the author truly hopes to change his readers' minds on the issue, he would have to largely restructure his argument, fix the flaws in his logic, clearly explicate his assumptions, and provide evidentiary support. Without these things, his poorly reasoned argument will likely convince few people.

...And that's pretty much it.

So the cliff notes:

P1- Intro with generic thesis statement that works for 99.9% of argument essays.

P2 - Attack the premises of the argument.

P3 - Attack the assumptions of the argument.

P4 - Discuss what type of evidence or reasoning would strengthen the argument.

P5 - Conclusion.

Hope that helps someone out there and good luck on your essays!

vaishalijain7 Master | Next Rank: 500 Posts
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Fri Jun 05, 2009 8:22 am
Thanks for the awesome post. It's really helpful and clearly states what is measured in 'Analysis of argument' questions. Any views on 'Analysis of issue'?

Tweetyspeaks Newbie | Next Rank: 10 Posts
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Sat Aug 01, 2009 6:43 am
Thanks a lot for your wonderful template. This is so far the best I have seen. It would be very helpful to us if you could please post us your issue template too.

myohmy wrote:
Hey guys-

I'm not hugely qualified to give GMAT advice (I'm not an instructor), but I took the GMAT twice and got a 6.0 essay score both times, so I hope someone will find my essay templates/advice useful.

Analysis of Argument
Paragraph 1
I always start begin with a broad statement about the issue at hand. For instance in an argument essay about whether it was necessary to conserve energy, I would begin with:

Energy conservation has become a hot topic in the United States as of late. There are those who debate climate change and those who affirm it, those who assert that humans are depleting the world's natural resources, including fossil fuels, and those who believe that humans are barely making a dent in consuming the resources the earth has to offer.

This sets up a fluid introduction to my essay, and by starting with an introductory sentence, I felt I would set myself apart from the majority of other test takers who begin "I agree" or "I disagree" -- remember, you want to distinguish yourself from other essay writers (in a good way) right from the start.

I always continue by saying, "In the preceding statement, the author claims that (paraphrase of the author's argument)." This shows that I understand the author's argument. I continue with my disagreement (and, as has been often said, ALWAYS disagree with the author's reasoning, and I pretty much always used the same thesis statement, something like:

Though his claim may well have merit, the author presents a poorly reasoned argument, based on several questionable premises and assumptions, and based solely on the evidence the author offers, we cannot accept his argument as valid.

I can use that statement for pretty much any argument essay I encounter. The beginning shows that I see the issue as nuanced, rather than black and white, and I recognize that though the author may have arrived at the correct answer, his reasoning is flawed. I also use "we" but I try to avoid using "I". Take that as you will.

Paragraph 2
For me, paragraph two always attacks the premises of the author's argument. I usually jot down a couple of premises on my board -- these are things that show up in the author's argument, usually without any evidence provided. So 99% of the time, I attack the lack of evidence that the author bases his premises on. I usually begin with some version of:

The primary issue with the author's reasoning lies in his unsubstantiated premises.

I like "primary" and "secondary" as transitional tools because they are more complex than "first" and "second". Throughout the first paragraph, I show flaws in the author's premises by pointing out his lack of evidentiary support (they pretty much always lack evidentiary support) and where they are open to holes or alternate explanations. I usually have two or three, but one would be fine if it it was strong. I generally end with something like:

The author's premises, the basis for his argument, lack any legitimate evidentiary support and render his conclusion unacceptable.

Paragraph 3
In the third paragraph, I always attack the assumptions - again, I jot down a couple assumptions on my notepad while reading the prompt. Generally, the issue with assumptions is that they need to be clearly explicated - the author is asking the reader to make a jump with them, but the reader may well veer off course if the author doesn't explicitly state his arguments. I usually begin with some variation of:

In addition, the author makes several assumptions that remain unproven.

Again, I begin with a transitional phrase that the e-grader can pick up on. As with the premises, I spend this paragraph attacking a couple of the author's assumptions. The easiest way to do this is to find an alternate explanation -- ie, what if the assumption wasn't true? I usually have two or three, again. My assumption paragraph ends with something like:

The author weakens his argument by making assumptions and failing to provide explication of the links between X and Y he assumes exists.

Paragraph 4
Paragraph 4 is where I talk about how the author could strengthen his argument -- that is, I go back to my claim that his argument could have some validity, but not as it stands. I usually begin this paragraph with something like:

While the author does have several key issues in his argument's premises and assumptions, that is not to say that the entire argument is without base.

Then I provide some concrete ways the author could strengthen his argument. The easiest way to do this is to give examples of what kind of evidence the author could provide, and discuss how he can fill the holes in his assumptions. I generally end with something like:

Though there are several issues with the author's reasoning at present, with research and clarification, he could improve his argument significantly.

Paragraph 5
This is my conclusion paragraph. I pretty much always conclude with the same sentence:

In sum, the author's illogical argument is based on unsupported premises and unsubstantiated assumptions that render his conclusion invalid.

I usually use "in sum" because it's considered better stylistically than "in conclusion" but signals to the e-grader that you're at your conclusion. I usually add a couple sentences of fluff in between and then I end with:

If the author truly hopes to change his readers' minds on the issue, he would have to largely restructure his argument, fix the flaws in his logic, clearly explicate his assumptions, and provide evidentiary support. Without these things, his poorly reasoned argument will likely convince few people.

...And that's pretty much it.

So the cliff notes:

P1- Intro with generic thesis statement that works for 99.9% of argument essays.

P2 - Attack the premises of the argument.

P3 - Attack the assumptions of the argument.

P4 - Discuss what type of evidence or reasoning would strengthen the argument.

P5 - Conclusion.

Hope that helps someone out there and good luck on your essays!

kyabe Senior | Next Rank: 100 Posts
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Sun Aug 02, 2009 1:46 am
Hi myohmy,

If I use the word "AWESOME" to describe your post it won't be unjustified. This is a brilliant post mate and I reckon will surely help many people.. Now here I am being little greedy here.. Can you please give your insight about Issue Essay.. How to deal with the issue essay if nothing concrete example jumps out to you..

Cheeers Mate ...

myohmy Master | Next Rank: 500 Posts
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GMAT Score:
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Sun Aug 02, 2009 1:42 pm
I'm sorry guys -- I really didn't use a template for issue essays! I did those far more on the fly since those were more question-specific than argument essays.

I guess a general template would be

P1 - Intro and a thesis
P2 - Example 1 (usually in depth)
P3 - Example 2 (in depth)
P4 - Exploring the nuances of the question -- ie, why the opposing position is not entirely wrong. This shows I understand that the issue is not black and white.
P5 - Conclusion

I'm sorry, I really structured issues essays loosely and didn't go as in depth with them as I did with arguments. I've attached an issue essay below and hopefully that might help some of you guys? If you have specific questions let me know.

Question:
"Despite the convenience of distance learning and online educational programs, they will never replace in-class instruction."

Discuss the extent to which you agree or disagree with the position stated above. Support your viewpoint using reasons and examples from your own experience, observations, or reading.

Essay:
With an increasingly globalized world, and the advent of ever-improving technology that allows people to go as far as to project a holograph of themselves sitting in a chair in Tokyo from their office in San Jose, California, we are starting to reexamine the ways we structure learning. Gone are the days on the one-room schoolhouse, where all learning is completed between eight and three p.m. More and more often, schools are utilizing the significant technological tools that have been developed in order to redefine the way we teach and the way we learn. Indeed, we can now learn math from an online recorded voice while we sit on the couch in our pajamas. In the statement above, the author claims that though distance learning and online educational programs offer convenience, in-class instruction is irreplaceable. Though, distance learning and online educational tools can provide fantastic aids to traditional classroom learning and a great deal of benefit to certain students, as the author claims, they cannot entirely take the place of in-class instruction.

The main reason that distance learning cannot take the place of traditional in-class instruction is that the primary benefit that in-class instruction provides is spontaneity. Students can learn from the questions another student asks, which can make them realize that they do not understand a subject as well as they thought they did. In debates with other students surrounding, perhaps, the Cold War, students can learn from each other based on their give-and-take, something impossible to duplicate in online educational programs. Many programs through reputable universities, such as Johns Hopkins' CTY program or Stanford's EPGY program provide distance learning to secondary school students. In such programs, students complete assignments, email them back and forth with their teachers, receiving comments each time, learn primarily from books or prewritten tools, and only hear their teacher speak through phone or web based tools. Studies show that humans communicate over 90% of their emotion through body language, yet this interaction is nonexistent in distance learning. CTY students cannot see the imperceptible body shift or raised eyebrow that let them know they are moving off track. Because they can only communicate with other students (generally) through discussion boards or chat rooms, they are not as spontaneous in their student-to-student interaction. By writing down what they say, they have time to read it over, think about it, before posting it. In a typical classroom, however, students bounce ideas off each other, and often, the exchange of ideas is far more free than if they are given the chance to self-censor. Because distance learning lacks the spontaneity of conversation that in-person teaching provides, by definition, it cannot perform the exact same function.

Another issue with the replacement of in-class instruction with distance/online learning is that the two serve often drastically different populations. In-class instruction generally caters to students in a specific geographical area, whereas distance learning allows for interactions with students around the world. In-class instruction might utilize specific community examples such as a proposed city ordinance to teach a concept, while distance learning, by definition, must include more universal examples that are easily understood by people with a variety of backgrounds. This lack of personalization and tailoring of teaching to specific students makes distance learning fundamentally different than in-class instruction, and therefore, beneficial to different people. MIT recently launched an open courseware system where lecture notes, Power Point slides, essay questions, and assessments are provided to anyone with an Internet connection. Yet the act of attending MIT is substantially different than the act of using the courseware to take the same classes MIT students take. The students one would interact with at MIT are generally at the top of their high school classes, have been preselected by the university as able to do the work, whereas though the MIT courseware allows for online discussion of the material, any person can log in and utilize it - a significantly different population than the population that attends MIT. Because the two modes of teaching by definition must serve different populations, they cannot act (fully) as substitutes for one another.

Though distance/online learning may not replace in-class instruction, we cannot go so far to say it is not valuable or that a student cannot learn a great deal from them. Many colleges, particularly community colleges, have launched distance learning and online educational systems to better serve their largely commuter population. The student who takes, for example, Calculus I through distance learning will likely leave with a similar understanding of the mathematical principles as the student who takes Calculus I through a traditional, in-class teaching system. The key point, however, is that their experiences will not be the same. Distance learning/online education and in-class instructions provide substantially different experiences to the students (and teacher) involved, and different students will prefer different methods of course instruction. Distance learning has value, can teach a student a great deal, but not all students learn best in such an environment. Distance learning will never replace in-class instruction, since many students learn better through in-class instruction than through distance learning (and vice versa), but that is not to say it will not continue to expand and provide value for the students who utilize it.

In sum, distance learning and in class instruction provide different modes of learning, and neither can exist as a substitute for the other. Neither can replicate the other so completely as to say they are the same, and thus, neither can replace the other. While distance learning will likely to continue to expand, better serving populations that likely otherwise would not have access to the types of information the courses disseminate, in-class instruction will remain, primarily because it offers benefits that distance learning does not. Distance learning provides convenience and an ever wider net of people willing to be educated, but in-class instruction provides a spontaneity of interaction that distance learning cannot duplicate. Therefore, distance learning will never truly replace in-class instruction worldwide, though it will surely continue as a supplement to such instruction and beneficial program on its own merit.

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Mon Dec 14, 2009 8:03 pm
This is so fantastic, thanks myohmy! I'm going to add this to our GMAT Resource Directory

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myohmy Master | Next Rank: 500 Posts
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Tue Dec 22, 2009 9:31 pm
Thanks so much, Eric, that means a lot!

becnil MBA Student
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Thu Jan 14, 2010 1:13 pm
Thank You, the template is very nice. I would like to try it out.

becnil MBA Student
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Thu Jan 14, 2010 1:15 pm
Thank You, the template is very nice. I would like to try it out.

punksareforever Newbie | Next Rank: 10 Posts
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Sun Jan 31, 2010 4:50 am
Excellent template..what I like about the template is that it has lot of meat, the template itself covers 3-4 lines,irrespective of the topic, i think this would save me quite some time on the Exam..cheers!

valleeny Senior | Next Rank: 100 Posts
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Sat Feb 06, 2010 1:06 am
I scored a 6.0 using myohmy's template. I was taken in for a shock. Thanks myohmy! I suggest people take this template and build their own statements and styles surrounding the way the intro was made and how the points were structured. Thanks once again.

punksareforever Newbie | Next Rank: 10 Posts
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Fri Feb 12, 2010 5:42 am
Scored a 6.0 with this template...
@myohmy : Thanks a ton..

mjp9483 Newbie | Next Rank: 10 Posts
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Thu Apr 22, 2010 2:35 pm
This really is a great template! I hadn't practiced any AWA until I found this post about 5 days before my test. With minimal effort and practice I was able to apply this template to the actual GMAT and received a 6.0. Thanks myohmy for your post!

greentealeaf Senior | Next Rank: 100 Posts
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Thu Apr 29, 2010 7:46 am
the best i ve even seen. thanks!

gmatguy7 Newbie | Next Rank: 10 Posts
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Sat May 08, 2010 4:43 am
It is THE best template I have come across. Thanks for sharing!

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text:
Selecting only one transcript in BiomartGeneRegionTrack
1
0
Entering edit mode
klim314 • 0
@klim314-13119
Last seen 4.4 years ago

Hi, I've been having an issue with rendering the tracks when selecting a single transcript. When rendering without from and to fields, the annotation track renders properly, showing only one transcript.

However, when adding to and from to the plotTracks field, this appears to override the filter of the annotation field

How would I be able to both add from and to arguments while maintaining the filters?

Code:

library("data.table")
library("biomaRt")
library("Gviz")

data_dir = "~/work/data/bamsets/igv_b2"
plot_type = "histogram"
from = 96648967
to = 96670936

ensembl = useMart("ensembl", dataset = "mmusculus_gene_ensembl")
biomTrack_hmgcr <- BiomartGeneRegionTrack(genome="GRCm38.p5",
symbol = "HMGCR",
name="Hmgcr\nstructure",
biomart = ensembl, stacking = "squish",
filters = list(ensembl_transcript_id = "ENSMUST00000022176",
start = from,
end = to),
#transcriptAnnotation = "transcript"
)

hmgcr_sko_table = fread(file.path(data_dir, "hmgcr2", "summarized_bedgraphs", "sko.bedgraph"),
col.names = c('chromosome', 'start', 'end', 's1', "s2", "s3"))

hmg_sko = DataTrack(range = hmgcr_sko_table,
genome="GRCm38.p5",
name="test",
biomart = ensembl,
type = plot_type,
ylim = c(0, 135),
col.histogram = "#000000")

plotTracks(list(biomTrack_hmgcr,  hmg_sko), aggregation = "mean", from = from, to = to)
plotTracks(list(biomTrack_hmgcr,  hmg_sko), aggregation = "mean")
gviz gviz-package R • 889 views
1
Entering edit mode
Jeremy Ng ▴ 180
@jeremy-ng-5464
Last seen 6.4 years ago
Singapore
A very quick workaround is to simply subset on the BiomartGeneRegionTrack to contain feature information only on the specific transcript of interest prior to plotting. This can be done by modifying the data directly as such: biomTrack_hmgcr@range = biomTrack_hmgcr@range[biomTrack_hmgcr@range \$transcript%in%"ENSMUST00000022176"] This workaround just works around the issue of why specifying the range in your plotTracks ignores the filter in your BiomartGeneRegionTrack, but does not address it. I'm sure someone else will be in a better position to address why the filter was ignored. J On Fri, May 26, 2017 at 5:53 PM, klim314 [bioc] <noreply@bioconductor.org> wrote: > Activity on a post you are following on support.bioconductor.org > > User klim314 <https: support.bioconductor.org="" u="" 13119=""/> wrote Question: > Selecting only one transcript in BiomartGeneRegionTrack > <https: support.bioconductor.org="" p="" 96318=""/>: > > Hi, I've been having an issue with rendering the tracks when selecting a single transcript. When rendering without from and to fields, the annotation track renders properly, showing only one transcript. > > However, when adding to and from to the plotTracks field, this appears to > override the filter of the annotation field > > How would I be able to both add from and to arguments while maintaining > the filters? > > *Code:* > > > library("data.table") > library("biomaRt") > library("Gviz") > > data_dir = "~/work/data/bamsets/igv_b2" > plot_type = "histogram" > from = 96648967 > to = 96670936 > > ensembl = useMart("ensembl", dataset = "mmusculus_gene_ensembl") > biomTrack_hmgcr <- BiomartGeneRegionTrack(genome="GRCm38.p5", > symbol = "HMGCR", > name="Hmgcr\nstructure", > biomart = ensembl, stacking = "squish", > filters = list(ensembl_transcript_id = "ENSMUST00000022176", > start = from, > end = to), > #transcriptAnnotation = "transcript" > ) > > > hmgcr_sko_table = fread(file.path(data_dir, "hmgcr2", "summarized_bedgraphs", "sko.bedgraph"), > col.names = c('chromosome', 'start', 'end', 's1', "s2", "s3")) > > hmg_sko = DataTrack(range = hmgcr_sko_table, > genome="GRCm38.p5", > name="test", > biomart = ensembl, > type = plot_type, > ylim = c(0, 135), > col.histogram = "#000000") > > plotTracks(list(biomTrack_hmgcr, hmg_sko), aggregation = "mean", from = from, to = to) > plotTracks(list(biomTrack_hmgcr, hmg_sko), aggregation = "mean") > > ------------------------------ > > Post tags: gviz, gviz-package, R > > You may reply via email or visit Selecting only one transcript in BiomartGeneRegionTrack >


text:
# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
$q$-extensions of Genocchi numbers. (English) Zbl 1129.11008

The classical Genocchi numbers, ${G}_{n}$ are defined by means of the following generating function: $\left(\left(2t\right)/\left({e}^{t}+1\right)\right)={\sigma }_{n=0}^{\infty }{G}_{n}\left(\left({t}^{n}\right)/\left(n!\right)\right)$, where ${G}_{1}=1,{G}_{3}={G}_{5}={G}_{7}=\cdots =0$. Relations between Genocchi numbers, Bernoulli numbers and Euler polynomials are given by ${G}_{n}=\left(2-{2}^{n+1}\right){B}_{n}=2n{E}_{2n-1}\left(0\right)$. Genocchi numbers and polynomials are very important not only in Number Theory but also in the other areas in Mathematics and Mathematical Physics. The authors define $q$-Genocchi numbers and polynomials by means of the following generating functions, respectively:

${F}_{q}^{\left(G\right)}\left(t\right)=q\left(1+q\right)t{\sigma }_{n=0}^{\infty }{\left(-1\right)}^{n}{q}^{n}{e}^{\left[n\right]t}={\sigma }_{n=0}^{\infty }{G}_{n}\left(q\right)\left(\left({t}^{n}\right)/\left(n!\right)\right),$

and

${F}_{q}^{\left(G\right)}\left(t\right)={F}_{q}^{\left(G\right)}\left({q}^{x}t\right){e}^{\left[x\right]t}={\sigma }_{n=0}^{\infty }{G}_{n}\left(x,q\right)\left(\left({t}^{n}\right)/\left(n!\right)\right),$

where $\left[x\right]=\left(\left(1-{q}^{x}\right)/\left(1-q\right)\right)$ and $q\in C$ with $|q|<1$. The authors give interpolations functions of these numbers and polynomials at negative integers. They define $p$-adic $q$-$l$-function which interpolate $q$-Genocchi numbers at negative integers. They also give congruences for $q$-Genocchi numbers.

##### MSC:
 11B68 Bernoulli and Euler numbers and polynomials 11S80 Other analytic theory of local fields