Stupid Questions February 2015

The current definition of the gravitational constant maximizes the simplicity of Newton's law F = Gmm'/r^2. Adding a 4π to its definition would maximize the simplicity of the Poisson equation that Metus wrote. Adding instead 8π, on the other hand, would maximize the simplicity of Einstein's field equations. No matter what you do, some equation will look a bit more complicated.

I'd like to put in a word for sine:

sin(0) = 0
sin(x) ≈ x

These are highly useful properties in some contexts. That said, cos(0) being the unit prior to any rotation is also nice. (But the definition of a rotation in Cartesian coordinates contains exactly as many sines as cosines; and that generalizes to 3 dimensions where complex numbers do not.)

What is your complaint about Zeta? That it is the sum of n^-s, rather than the sum of n^s? It's the one that converges. Or are you bothered that zeta(-3) is rational, while zeta(3) is irrational?

A function that fills in the gaps between factorials seems useful.

Maybe useful for some purposes. Maybe that would be a good function to have when defining the Beta distribution, though there are other reasons for the normalization there.

But in the context of the Riemann Zeta function (which is the context you have suggested), that is not at all the purpose of the Gamma function. Its role is as the Mellin transform of the exponential function. The Zeta function itself is a Mellin tranform and two interact well because of their common origin. Of course, that pushes back the question to why the Mellin tranform has a -1. What it really has is a dx/x. This measure is invariant under scaling, just as dx is invariant under translation. Indeed, the measures correspond under the exponential change of variables.

(In fact, that is closely related to a justification for the normalization of the Beta distribution. B(0,0) is the measure invariant under logistic transformations; B(p,q) is the posterior after seeing p,q observations.)

I have been pissed off for years at the existance of h-bar and h as separate constants, where almost everywhere h-bar should be the basic constant. IIRC, this is just because the first time either was derived, it happened to be h, so that got called the quantum mechanical constant.

The Gamma function has this -1 I don't understand

Yeah, this is completely historical. Edwards in his book on the Riemann zeta function tries to go back to using Gamma normalized in the obvious way so it agrees with factorial but that's never caught on.

In the case of the Riemann zeta function the key issue is that it is seen as more natural to have a plane of convegence for positive values of s. Moreover, writing it in that way, the values at positive integers are then natural and easy series.

cosine seems more primitive than sine

Can you expand on this one?

In my opinion the gamma function is by far the stupidest. IME, the off-by-one literally never makes equations clearer; it only obfuscates the relationship between continuous and discrete things (etc.) by adding in an annoying extra step that trips up your intuition. Seems like simple coordination failure.

I used to think that the way mathematicians did things was forced to be the best way we could do because of the requirements to do things properly in order to advance in maths. But then the Tau Manifesto showed me I was wrong.

I think you're right about cosine. I think sine seemed simpler when it was named back in classical times, but then when complex numbers were discovered and their relationships to the trigonometric functions was discovered, cosine turned out to be simpler.

Here's one I come across as a programmer: which number is better for starting indexing and counting things with? Zero or one? Zero is so much better for calculating with relative indexes, you have less off-by-one errors. In maths, the default convention is to number things starting at one. But when working with serieses (arithmetic series, discrete fourier transforms, maclaurin series e.g. the polynomial that equals e) the convention is to start at zero.

Can you elaborate on the Gamma function thing?

(I am currently conceptually wrestling with the Gamma function myself, and your question either has an obvious superficial answer, or I've misunderstood it. Probably the latter.)

π seems like half the size it should be

That one you found out already, it would make it much more consistent with how similar constants are used.

The gravitational constant looks like off by a factor of 4π

Not sure what you mean. Do you mean when comparing the equation for gravitational force to the electric force? Or do you mean when looking at the 'intuitive' way of writing the differential equation

?

In either case it seems that the choice of 4π is arbitrary on one equation or the other. For example choosing Gaussian units introduces a 4π in the electrical equation and makes it look more like the gravitational equation.

cosine seems more primitive than sine

They seem equally primitive by

and

%20=%20cos(x%20-%20\pi/2))

The Riemann Zeta function ζ(s) negates s for reasons beyond me

It doesn't according to Wikipedia

The Gamma function has this -1 I don't understand

I haven't read up on that so I don't really know. Seems arbitrary to me too.

Moreover, which vaccines are worth getting? For example, is it worth getting a meningococcal vaccine if you're not in any of the major risk groups?

Many universities strongly encourage their students to get the meningococcal vaccine (as sleeping in rubbish communal bedding is a risk factor), but for something really rare, even the risk involved in traveling to the clinic to get vaccinated could have more disutility than the protection the vaccine might provide would be worth.

The meningococcal vaccine causes a fever 3% of the time, and a few days of mild to moderate discomfort 60% of the time. If it causes any other problems in healthy people, the CDC hasn't documented it.

Outside of major risk groups, this vaccine decreases your chances of getting meningococcal disease by some low amount, less than one in a million annually. If you get the disease, there's a 10% chance of dying and a further 10% chance of being permanently disabled in some severe way. This is less than a tenth of a micromort.

The bacteria that causes meningoccoal disease is ubiquitous (10% of people are carriers), so other benefits of vaccines, such as herd immunity, would require extreme measures to obtain.

Driving causes about 1.5 fatalities per 100 million miles traveled, according to FARS, so this particular vaccine actively averts about as much risk as is involved in driving ten miles a year, which may or may not be worthwhile, but it certainly isn't a low-hanging fruit in terms of risk aversion.

Anyway, let's tally it all up:

Meningococcal vaccine utility:

• 0.00001% lower individual chance of getting meningococcal disease per year (minus 0.1 micromorts/year = at best a few minutes more of expected healthy lifespan, unless we solve the aging problem)

• increased herd immunity (negligible due to the nature of this particular disease)

Meningococcal vaccine disutility:

• mild discomfort

• 3 to 5% chance of fever

• whatever risk is involved in traveling to the clinic (could be several minutes less of expected healthy lifespan)

• whatever time it takes to get the vaccine (a few minutes to over an hour) could be spent doing something else

• any undocumented risks that the vaccine itself might have (What are these?)

• risk of physician error (What is this for a simple injection?)

Obviously, a lot of this will vary depending on the vaccine and the disease it's meant to prevent. Some diseases pose higher risk, as do some vaccines. I didn't get all of the standard vaccinations as a child because I was too severely allergic to some of them.

It might be helpful to do this sort of calculation for every available vaccine, but it's a bit tedious. I haven't found anywhere that lists the necessary information in anything resembling a convenient format.

Not currently relevant, but an example of balancing risk and benefit and deciding to stop vaccinating against smallpox. Wikipedia

There are side effects and risks associated with the smallpox vaccine. In the past, about 1 out of 1,000 people vaccinated for the first time experienced serious, but non-life-threatening, reactions, including toxic or allergic reaction at the site of the vaccination (erythema multiforme), spread of the vaccinia virus to other parts of the body, and to other individuals. Potentially life-threatening reactions occurred in 14 to 500 people out of every 1 million people vaccinated for the first time. Based on past experience, it is estimated that 1 or 2 people in 1 million (0.000198 percent) who receive the vaccine may die as a result, most often the result of postvaccinial encephalitis or severe necrosis in the area of vaccination (called progressive vaccinia).[38]

Given these risks, as smallpox became effectively eradicated and the number of naturally occurring cases fell below the number of vaccine-induced illnesses and deaths, routine childhood vaccination was discontinued in the United States in 1972, and was abandoned in most European countries in the early 1970s.[5][40] Routine vaccination of health care workers was discontinued in the U.S. in 1976, and among military recruits in 1990 (although military personnel deploying to the Middle East and Korea still receive the vaccination.[41]) By 1986, routine vaccination had ceased in all countries.[5] It is now primarily recommended for laboratory workers at risk for occupational exposure.[20]

I'm 30 years old and almost entirely unvaccinated.

I've always had poor health, I had lymphoma at age 27, type 1 Diabetes since age 13, all of which suggests poor immune system performance. And anecdotally, when I get sick with common cold etc, I seem to stay sick longer than other people. So I don't expect my body to be good at fighting off really dangerous disease.

Which vaccines should I get? Most resources either target or assume vaccination of children on a regular schedule.

Cost-Benefit analysis of a flu shot

This is not my area of epidemiology, so take this with a grain of salt, but my best guess is that the impact is negligible, for the following reasons

(1) Mutations that confer resistance are specific for classes of antibiotics. A mutation that provides resistance to Doxycycline will not help the bug against Penicillins.

(2) If I understand correctly, the reason tetracyclines are approved for acne is that they are no longer the first line choice for empirical treatment of any serious infections. This is because tetracycline resistance is already widespread. In other words, the FDA have allowed Doxycycline to be used with this indication specifically because they are not worried about increasing the prevalence of resistance.

(3) If you are taking these drugs while you are healthy, there are no pathogens that are subjected to adaptive pressure by your use. Of course, you will have commensals that are subjected to this evolutionary pressure, but I think the risk that these bacteria acquire pathogenicity and escape to start an epidemic is minimal.

I also want to note that, based on anecdotal experience and conversations with dermatologists, my impression is that long term treatment with doxycycline is probably not the most effective way to treat acne. By far the most effective treatments are variations of retinoic acid. If you have serious ongoing acne, Isotretonoin (Accutane) is the only thing that will really help. If you have less serious acne or want maintenance treatment after taking a course of Accutane, topical medications which contain variations of the same active ingredients (retinoids) are very effective. Your alternatives are creams that only include retinoids (Such as Adapelene), which tend to be cheap; or you can take a cream that also benzoyl peroxide (such as Epiduo). The second option is more effective, but also more expensive, and if you get it on your clothes they may get bleached from the peroxide.

Probably not as much harm as the factory farms that give antibiotics to all of their animals.

People have strong anti-market biases. It has been said that if there was not a market in sandwiches, and one was suggested, people would recoil in horror. "Only the rich will be able to buy sandwiches." "Sandwiches will be filled with rat poison and feces." "It's just wrong! People should feed each other out of kindness, not greed." Even "Many people only sell sandwiches because they need money. It's exploitation."

Taboo tradeoffs. Probably most readers are too young (as am I) to remember when life insurance was considered immoral. How can you put a price on life?

Political incentives. Why should any one voter demand change? Why should any one politician? Or any one judge? Collective action problems are hard.

The concern is exploitation of poor people. (And no, I agree that that reasoning doesn't make much sense).

Probably because the poor would have a lot of trouble getting organ transplants. Under the current system, you're put on a waiting list until your number is called. If others can bid more money on organs, you're out of luck. I can't imagine insurance companies being overly keen on bidding for organs.

I really don't want to think about issues arising from people selling off their organs to make ends meet (or to settle gambling debts). And let's not forget human trafficking. Instead of just forcing people into prostitution, you could also harvest their organs.

I think there are several thorny problems and issues of consent that complicate this matter. Losing an organ is permanent.

It is legal to sell kidneys in Iran. As a result, Iran has no waiting lists for kidney transplantation. You can read an interesting study of the situation here. TLDR: it works well, but everything has tradeoffs.

Why do we not allow people to sell organs?

The top-level answer is because people do not own them. As far as I remember, in the US people do NOT have property rights in their organs and tissues (yes, there were court cases).

Digging deeper, allowing people to own their organs and tissues would make life more complicated and expensive for the medical establishment and it doesn't like that.

The concern is that we don't want poor people forced to sell parts of themselves to pay off their debts - it's a bit too Merchant of Venice. (I think it'd still be good policy, because I don't see how them not having the choice is any better, but that's the common concern)

There exists a mild market in organs. I can donate a kidney in exchange for a loved one getting a kidney. I also can donate my body to science, in exchange the institution - at least in Germany - pays for some kind of burial.

Immediate edit: Actually, since there exists a black market in organs we could make some estimates about prices and conditions on a legalised market in organs.

I suggest that allowing people to sell something where the market price of the item is much less than the price that most people would name if they were asked how much they would accept to sell it but were not in immediate need of money, is generally a bad idea.

This includes organs, prostitution, and signing away your house for a glass of water if you're dying of thirst in the desert and someone offers to give you water in exchange for your house.

For the same reason tribes living near the edge of starvation have especially strong cannibalism taboos.

• Cancerous cells multiply incontrollably until they form their little own neighborhood, called tumor, which slowly and ruthlessly pushes everything else out of its way. In the case of lung cancer, the obvious consequence is that there's less space available for the healthy lung to do its job.
• Cancerous cells are ravenous consumers of resources, and compete with the host body for them. You slowly become emaciated and malnourished as your cancer steals your food from you.
• Tumors arising in glands may result in the dangerous overproduction of certain hormones.

Cancers can cause death in more than one way. So there is no single answer to this question. It really depends on the type of cancer you have and which parts of your body are affected.

Other people have covered the effects of solid tumors quite well.

Blood tumors often do not form solid masses. They are the result of stem cells in the bone marrow (or occasionally actual immune system cells) becoming cancerous. These cells are highly mobile and usually do not embed themselves in solid tissue (except for lymphomas). What they do is outcompete your normal bone marrow and blood cells, preventing your immune system from working and your red blood cells from regenerating and your platelets from clotting your blood. I've read reports from autopsies in the 1800s of people who died from (what we would call untreated) leukemia that their blood resembled pus more than blood due to the paucity of normal red blood cells and huge level of abnormal nonfunctional white blood cells.

I'm not particularly knowledgeable about cancer but I can give you the simplified version:

few additional cells

I think this is at the root of your misconception. It starts out as a few additional cells rapidly dividing, but the end-stage typically involves macroscopic-level changes, like this Here.

Sometimes it's the sheer bulk of cells that kills in the same way a rock in your brain might, other times it's the gradual replacement of working cells with non-functional cells, and other times it messes up sophisticated signalling stuff. (For example, the cancer cells might be putting out large amounts of hormones, or diverting blood flow).

primary cancer seldom kills ; most of the time the metastasic-induced does. Why ?

Metastatis means little cancer "seed" cells are floating around all over your bloodstream, right? This means that at any random time, a cancerous growth can suddenly pop up in any random region with no warning. Some of these growths will be benign, and others deadly. You have to obsessively scan the body for new growths from then on if you want to protect yourself.

With primary cancers at least you can sometimes just cut them or irradiate them or shrink them, or just work around them (like with lung cancer, just give them an oxygen tank to make up for the reduced efficiency).

I read somewhere that a primary cancer seldom kills ; most of the time the metastasic-induced does. Why ? There should be far more "bad" cells in the primary site, doesn’t it ?

In the West you can often operate the primary site away.

I read somewhere that a primary cancer seldom kills ; most of the time the metastasic-induced does. Why ? There should be far more "bad" cells in the primary site, doesn’t it ?

The most anatomical origins for cancers (skin, breast and prostate) are not vital organs, so a cancer in one of those places won't kill you if it stays in place. The danger is if it metastasizes to a vital organ (most commonly the lungs or liver) and interferes with its function. If a cancer starts in a vital organ, it's more likely to kill you through its effects on that organ, not by spreading elsewhere.

To throw another reference into the discussion, section 1.8 of McKinnell et al.'s The Biological Basis of Cancer spends a few pages on this. Summary: cancers can cause organ failure, but because the body has "an enormous reserve of normal tissue plus a built-in mechanism to regenerate more" organ failure is not usually the proximate cause of (edit: non-leukaemia) cancer death; the most common cause of death is instead cachexia (wasting) and hence infection.

Don't tell yourself that you're half-cleaning the house. Tell yourself that you're fully cleaning those rooms(which happen to be half the house). That way, you're actually completing something.

If you cleaned really frequently in small bursts (say, for 20 minutes a day, almost every day?), starting from your "satisfactory" point, would that be enough to maintain the satisfactory point more or less continuously? Then each 20-minute burst of work would come with the "satisfactory state" reward.

An update:

I decided to test the "not fun" part of the cost, by doing some cleaning and really asking myself how I felt while I was doing it. The answer was "not bad, almost relaxing". So I will try to update my model.

Presumably there is some reason you want a cleaner house, e.g. it will be easier to find stuff. If you spend 90 minutes cleaning, that will get you half as much gain in terms of making it easier to find stuff. So it's still worth doing in its own right. (Similarly, every marginal minute of exercise buys you 3-7 marginal minutes of life (within reason). Etc. This doesn't work for everything but it works for some things.)

One of the most popular LW posts ever is on this topic:

http://lesswrong.com/lw/3w3/how_to_beat_procrastination/

The Ultra-Orthodox as they stand are a relatively modern thing. The charedi movement arose as a reaction to the rise of the Reform movements and the enlightenment. None of the current movements in Judaism really do a good job of mimicking what Ashkenazi Jews were like in the 1700 or 1800s because the forced ghettoization and constant fear of pogroms was such a major aspect in so much of Europe.

It is worth noting in this context that many "fundamentalist" (for lack of a better term) religions are similar in this regard: they are modern reactions which have only a romantic connection to the past.

Like people said, also a few centuries ago welfare programs did not exist.

The idea of a large subculture of nonworking religious scholars, supported by state welfare, appears to be relatively novel and limited —

Two factors have contributed to the increasing impoverishment of the ḥaredim in Israel: the mushrooming of the nonworking yeshivah population, which embraced some 80,000 men in the early 2000s, about half of them married, and the drastic cutback in welfare spending by the Israeli government in the face of the deep recession brought on by the second intifada and global factors. The system of army deferment and state support for "professional yeshivah scholars" has a long history in Israel. Originally the number of such scholars qualifying for support in the new state was just 400, earmarked to revive the lost yeshivah world of Europe. In 1968 their number was doubled. In 1977, as part of Menahem Begin's coalition agreement with the religious political parties, the quota was abolished and virtually all ḥaredi men who wished to do so could engage in protracted full-time yeshivah study. The inducements to remain in the yeshivah were great: a government stipend and perpetual draft deferment. In the United States, where such inducements did not exist, a different kind of yeshivah world had evolved. Ḥasidim, who lacked a strong scholarly tradition, would leave the yeshivah at around the age of 21 and enter the labor market, usually in low-paying, unskilled jobs, which indeed caused many with their large families to subsist beneath the poverty line. However, the "Lithuanian" ḥaredim, while prolonging their studies in a flourishing yeshivah world, though rarely beyond the age of 30, often combined vocational and even academic studies in suitable frameworks, like the *Touro college system , with yeshivah study, and consequently were able to get well-paid jobs in high-tech industries and other professions.

— Encyclopædia Judaica

Possibly. You can send information through power lines for example. There are consumer devices that use it for like local internet connections, and I think power companies have started using something like it to replace meter readers.

There are multiple ways to transmit radio frequencies through computer monitors (e.g. this), and communication via ultrasonic sound which we can't hear.

See a recent MIRI paper.

A narrow AI, "tasked with designing an oscillating circuit, re-purposed the circuit tracks on its motherboard to use as a radio which amplified oscillating signals from nearby computers."

One of those things we can't know for sure, because there could hypothetically exist a new physical law we don't know yet. The AI could somehow learn about this law -- even if it cannot do experiments, it could somehow derive it from the first principles... ahem, Solomonoff priors.

But I guess that is rather unlikely.

Then, there is the possibility of using the familiar laws of physics and the existing hardware (which is what you asked). Seems to me that this kind of output would be too noisy. I can imagine the AI using the fans to create some resonation and maybe literally break the box... but since the AI is at that moment not a physical entity but only a pattern existing in the computer memory, that would be equivalent to suicide.

Okay, with a really insane computing power the AI could hypothetically measure the positions of particles in the air, and use the fans to manipulate them... now this would depend on whether the AI can gather the information about the particles in its environment faster than the information is lost because of e.g. ventilation in the room which keeps bringing new particles with unpredictable positions and speeds. At some moment the AI would be limited by the fact that it does not have literally infinite computing power.

(AI with literally infinite computing power and infinite computing speed could probably do almost anything. It could use Solomonoff priors to model all possible universes, use all its data to select the most likely one, and for any possible action X it could make, it could calculate whether its desired goal is more likely to happen if it does X or if it does non-X. Thus the probability of the goal would keep increasing; the question is how fast, and whether that growth would have a limit lower than 100%. Maybe the AI would require millenia to strategically modify the particles in the air to bring the desired outcome through e.g. a series of almost invisible social changes; but maybe it will be disassembled sooner so it cannot complete its plans. But literally infinite computing power and speed is physically impossible... according to our knowledge of the laws of physics.)

I don't understand the details, so this is all just guessing... but seems to me it's something about induction and infinity. How, if you are not careful enough, you could use induction to prove something that is not true. Something like: "There is a natural number greater than 1. If there is a natural number greater than N, there is also a natural number greater than N+1. Therefore, there is a natural number greater than any natural number." but more complicated.

The procrastination paradox seems to have a form of: "To believe that I will clean my room some day, it is not necessary to clean it today. I just have to know that starting tomorrow, I will clean it in a finite time." Which seems reasonable, but then tomorrow, you will use the very same reasoning for postponing the cleaning yet another day. Et cetera, forever.

In the context of self-modifying agents, imagine that you are trying to build a room-cleaning AI. Is it okay to accept as a "provably room-cleaning AI" one that does not clean the room today, but tomorrow it self-modifies to a provably room-cleaning AI? If you say yes, you may build a machine that will never actually clean the room. But it is difficult to explain why "no" is the correct answer, because it seems completely harmless.

tl;dr: Don't use infinite induction to prove that something will happen in a "finite but unspecified time", because the limit of "finite but unspecified time" could easily be "never".

Presumably the counterstrategy is to just shut it off as soon as it makes the threat. It can't simulate anything if it isn't running.

Destroying the AI would also reduce the suffering the AI causes.

But even assuming that for some reason the humans can't destroy the AI, the humans can precommit to not unboxing AIs that simulate lots of suffering. Like many precommitments, this would be disadvantageous to the human if the human has to abide by it (since the AI would not be unboxed, and would simulate lots of suffering), but it would decrease the likelihood of such a situation happening in the first place (since, knowing that humans could make this precommitment, the AI would know its own precommitment would not be useful, and would probably not make it).

Note that human "irrationality" (such as wanting to hurt enemies even when it brings you no personal gain and may even hurt yourself too) can serve as a precommitment.

Also, the humans could solve this by precommitting to never treat simulations of humans as people or as equivalent to themselves except in a few narrow situations. Again, 1) this would be harmful when it comes to having to do it (since lots of simulations will get dehumanized), but lead to fewer situations where this happens, and 2) is a case where (if you go by LW dogma that simulations are people and equivalent to you) actual human beings' irrationality serves as a beneficial precommitment.

Or you just be the type of person that would tell it to go fuck itself, try to destroy it, and leave it boxed or maximally constrain it if you can't destroy it. If you cannot credibly commit to this or a similar threat resistant variant, no one should ever let you near a boxed AI and you should never want to go near one as you will likely be using a suboptimal strategy.

This sort of thing has happened to me before, and typically it has come with an unstated, "No, we're just kidding about accepting lower-quality work for your old job. Suck it up and don't bother asking for overtime pay."

I hope your managerial culture is different.

I just read a description of that lottery. I see its expected value is a divergent series. If both games you compare have their expected values defined this way then I think you can subtract one series from the other. i think this is the approach you mentioned, and I would do it.

Also, I'm not an expert on infinity, but I think there are different kinds of infinity. If one game gives you, on average, a dollar for each natural number, and one gives you, on average, one dollar for each pair of natural numbers that exists, then the second game gives you infinitely as much expected value as the first one.

By the way, sometimes "fear of Death" is actually a fear of not living your life the way you would like to.

To avoid misunderstanding, Death is bad. But that's too abstract, and people usually don't react emotionally to this kind of abstract things. (Unless something threatens to kill you right now. Or someone you love. Or someone you love has died recently.) More often there are other problems that make us sad, and instead of facing them directly, it is easier to complain about Death in abstract.

When you say "Death is bad", if you explore your feelings, sometimes there will be a more specific emotion, such as "Death is bad because I will lose eternal time I could spend doing X which I want to do". Now the real source the emotional reaction may be that you would actually want to do X right now, but for some reason you don't. Maybe you are afraid to take the necessary risk or pay the necessary price. Instead you just dream that maybe one day in the unspecified future you will be able to do X without the sacrifice. And then Death reminds you that your time is actually not infinite, and that procrastination may actually mean you will never do X. And then you feel bad.

Again, to avoid misunderstanding, Death is bad. If there is something you want to do to prevent Death, do it. But in addition to that, you could also think about the possible X and face it directly.

Interesting idea. I have a strong fear of death and also despite my best effort, I am prone to procrastination.

But my procrastination diverts my attention from the things I really want to be doing. So it wastes my time more than anything.

Does this help explain why I spend so much time browsing reddit instead of doing the slightly more fun (but also more effort) thing of learning how to program?

Or to put it differently, I don't think it is since I don't think anyone values their "browsing tumblr" state of mind more than their "learn something useful" state.

I could divert my attention to useful things, too. For example, instead of reading the web, I could be programming computer games. But I am reading the web instead.

But when certain level of fear is already there, it can be difficult to focus on anything productive, because it is too complicated for the moment.

I suspect that the stock of stupid questions doesn't regenerate fast enough for a monthly thread, and every three or four months would be better.

Jung didn't really play the science game, and Jungians continue not to play the science game, but if we squint a little, we can see that some of his ideas have been vindicated by science.

The term ‘archetype’ is often misunderstood as meaning certain definite mythological images or motifs. ... The archetype is a tendency to form such representations of a motif. ... My critics have incorrectly assumed that I am dealing with "inherited representations"

From Jung's Approaches to the unconscious (1964), quoted in Jones, Mixed Metaphors and Narrative Shifts (2003).

In this narrow sense, Jung's archetypes are uncontroversial: Much reasoning in humans is framed in cognitive science as proceeding by a mechanism of counter-factual simulation called manipulation of mental imagery. Kosslyn, for example, was a pioneer of studies of (visual modality) mental imagery manipulation. The knowledge used in this reasoning, stored in neural degrees of freedom, such as firing biases or synaptic connectivity, may be called abstract, semantic, or conceptual when it is generalized from across many episodic contexts and when its access does not strongly evoke vivid, specific memories of the experiences from which it was generalized (i.e. so much as you can reason about dogs without thinking of the last dog you saw, your dog knowledge may be called semantic rather than episodic). Features of concepts which are typical or discriminative of instances of those concepts are sometimes called prototypical, stereotypical, or (occasionally) archetypal. For science here, the study of cognitive biases relating to typical and discriminative features of conceptual reasoning were pioneered by Rosch. In addition to cached knowledge which is source-situated (exemplar knowledge from episodic memories of individual entities), there may be cached abstract knowledge, such as a mental image of a bird which takes its character from typical or discriminative features of the concept (perhaps specified randomly or unspecified in regard to features which have wide variance across birds), rather than as a cut-and-past mixture of bird-instance parts.

This is all pretty strongly based on visual-modality knowledge of physical objects, and it doesn't always generalize exceptionally well to other modalities. Like Ullman does nice research on how the declarative / procedural division of memory types maps well onto a lexical / grammatical division of language capacities; a lexicon, Ullman says, is cached linguistic knowledge, and certainly I can recall cached lexical entities, like idioms, which are not episodically situated ("sick as a dog" without thinking of anyone saying that phrase"), yet my introspection suggests that when I think about idioms generally, I'm not usually looking to "sick as a dog" to guide my reasoning. And it's much harder to find a reasonable interpretation wherein "sick as a dog" is a conjunction of discriminative features of idioms, than it is to understand how a mental image of a bird could have typical features of birds and yet not be identifiable as belonging to a recognized genus.

Other parts of the Jungian archetype construct than "capacity to reason with non-situated mental images having discriminative features" probably haven't been borne out so well by scientific inquiry.

Seems to have a similar structure to Chicken (i.e. two cars drive straight at each other and the "chicken" is the one to turn away first). Mutual cooperation is okay, but each player would prefer that he defect while the other cooperates. Mutual defection (a head-on collision) is the worst option by far. You get two Nash equilibria, where one player defects and the other cooperates.

This mostly reminds me of the "tragedy of the commons", where everyone benefits when an action is taken (like irrigating land, picking up litter, etc.), but it costs some small amount to one who takes the action, such that everyone agrees that action should be taken, but nobody wants to do it themselves.

There is also the related concept of "not in my back yard" (NIMBY), where everyone agrees that some 'necessary evil' be done, like creating a new landfill site or nuclear power plant, but nobody wants to take the sacrifice themselves (ie. have it "in their back yard").

Some real-life examples of this effect http://www.dummies.com/how-to/content/ten-reallife-examples-of-the-tragedy-of-the-common.html

I think calling it "stupid questions" is intended to make it more inclusive -- the idea being that you shouldn't feel embarrassed to post a stupid question here because that's what it's for, and that you should see other people being unembarrassed to post stupid questions here.

Why not both?

Does anyone know why the statistics field settled on k = 1/n?

I am guessing that this is the default assumption of equal weighting or equal scaling of the variances that you are pooling. If you want to assign non-equal weights you should have some specific reason to do so.

I don't think it's "superior", it's just the simplest default in the absence of any additional information.

Where are people blaming atheism for religious killings?