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Stupid Questions February 2017

4 Post author: Erfeyah 08 February 2017 07:51PM

 

This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.

Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.

To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.

Comments (103)

Comment author: Erfeyah 08 February 2017 08:33:55PM *  2 points [-]

I am getting to grips with the basics of Bayesian rationality and there is something I would like to clarify. For this comment please assume that whenever I use the word 'rationality' I mean 'Bayesian rationality'.

I feel there is too strong a dependency between rationality and available data. If current understanding is close to the truth then using rational assessment will be effective. But in any complex subject the data is so inconclusive that the possibility that we can not even conceive the right hypothesis, to rationally choose it from its alternatives, is quite high. No? I will give a simplified example.

In this post it is said:

Suppose you are a doctor, and a patient comes to you, complaining about a headache. Further suppose that there are two reasons for why people get headaches: they might have a brain tumor, or they might have a cold. A brain tumor always causes a headache, but exceedingly few people have a brain tumor. In contrast, a headache is rarely a symptom for cold, but most people manage to catch a cold every single year. Given no other information, do you think it more likely that the headache is caused by a tumor, or by a cold?

It then goes on to explain how we rationally choose between the options. That is all good. Let's suppose though that the actual cause of the headache is psychosomatic. And let us also suppose that the culture in which the experiment is taking place does not have a concept of psychosomatic causes. They just always think it is either cancer or a cold. And most of the times it is. Is it not true that a rational assessment of the situation will fail? How would someone with a sound rational mind approach that situation (in the world of the thought experiment)?

This is dealt with in science by not accepting explanations as truths until they are confirmed experimentally (Well.. in an ideal science cause in reality scientists jump into philosophical speculation all too often). But rationality can only be effective if we assume that we are quite close to an accurate understanding of nature. And I hope you will agree that the evidence does not indicate that at all.

Am I missing something here?

Comment author: moridinamael 08 February 2017 09:37:00PM *  5 points [-]

I try to always include an extra option which is just "everything I haven't thought of yet", and the prior for that option reflects how confident you feel about your mastery of the domain. Even a medical expert must always admit some small likelihood that the true cause is neither a tumor nor a cold, because medical experts know that medical science evolves over time.

Comment author: Erfeyah 08 February 2017 10:24:08PM *  1 point [-]

That is good. But how would you assign the probability of 'everything you haven't thought of yet' in a problem? You would have to base it again on data; which takes us back to the same question. Data can of course be sufficient for fields that are advanced to a point of overwhelming clarity. But when we get into sufficiently complex subjects the rational approach would be to say that my 'everything I haven't thought of yet' prior is so large that the only rational answer is "I don't know". Would you agree?

Comment author: moridinamael 08 February 2017 11:00:42PM 2 points [-]

Yes, you can't get away from data. And in fact it is often rational to put a dominant prior on "whatever the explanation is, it probably isn't one of the ones that I've managed to come up with". There's nothing magic about Bayes theorem, it can't create new information, but when properly used it helps avoid overconfidence and underconfidence.

Comment author: Erfeyah 08 February 2017 11:16:23PM 1 point [-]

Yes, this is clear, thank you. I recall rational discussions in LW with expositions on ontology, cosmology, sociology, the arts etc. in which probabilities are thrown around as if we know a lot, which makes me think that this point has not been fully understood. On the other hand whenever I talk to people on a one to one bases (like in this comment thread) people seem lucid about it. Will have to address it where I see it. Thanks for your input! :)

Comment author: ChristianKl 09 February 2017 10:49:20AM *  0 points [-]

"I don't know" means "I can't predict the outcome better than a dart throwing monkey". Doctors usually know more than that.

You seem to have a lot of black and white terms like "right hypothesis", "accepting explanations as truths" and "I don't know" in your thinking.

In the Bayesian perspective 0 and 1 aren't probabilities.

Comment author: Erfeyah 09 February 2017 11:25:14AM *  0 points [-]

"I don't know" means "I can't predict the outcome better than a dart throwing monkey". Doctors usually know more than that.

The example I chose is a bit misleading. I am just using it to indicate the problem though. You are thinking of 'doctors' as the doctors in our culture but I was hypothesising a situation in which the field is much more primitive. It is interesting to me to see how rationality is applied to a field where data is unavailable, scarce or inconclusive.

You seem to have a lot of black and white terms like "right hypothesis", "accepting explanations as truths" and "I don't know" in your thinking.

I don't see the problem of saying 'I don't know' when the data is obviously insufficient for me to judge. I would actually consider it counter productive to give a probability in this case, as it might create the illusion that I know more than I actually do. In this sense my 'I don't know' is not a value of 0 but admitting that there is no reason to use rational jargon at all.

The terms 'right hypothesis' and 'truth' are used, in the above comment, in the context of what is considered a good enough truth in science. You are right that this can be confusing if we get into the epistemological details though I thought it was sufficient for the purpose of communicating in this thread. I can change it to 'scientific fact' and we should be ok?

Does that make sense?

Comment author: ChristianKl 09 February 2017 11:42:59AM 0 points [-]

After Popper science isn't about establishing truth or the right hypothesis.

I would actually consider it counter productive to give a probability in this case, as it might create the illusion that I know more than I actually do.

If you can do better than a random guess (the dart throwing monkey) than you have knowledge in the Bayesian sense.

There could be situations where you really don't know more than the dart throwing monkey and were it thus doesn't make sense to speak about probability but in most cases we know at least a little bit.

Comment author: Erfeyah 09 February 2017 12:09:47PM 0 points [-]

After Popper science isn't about establishing truth or the right hypothesis.

I am not familiar with Popper but I would agree anyway. I will be more careful with my terms. Would 'scientific fact' work though? I think it does but I am open to being corrected.

If you can do better than a random guess (the dart throwing monkey) than you have knowledge in the Bayesian sense.

[1] What if a rational assessment of inconclusive data weighs you towards the wrong direction. Wouldn't you then start doing worse than the dart throwing monkey?

There could be situations where you really don't know more than the dart throwing monkey and were it thus doesn't make sense to speak about probability but in most cases we know at least a little bit.

I would challenge your 'in most cases' statement. I would also challenge the contention that a little bit is better than nothing according to [1].

Comment author: ChristianKl 10 February 2017 09:02:45AM 0 points [-]

Would 'scientific fact' work though?

No. Everything in science is falsifiable and open to challenge.

[1] What if a rational assessment of inconclusive data weighs you towards the wrong direction.

It's certainly possible to be completely deceived by reality.

Whenever you act where an outcome matters to you, you will take the expected outcomes into account. Even if you say "I don't know" you still have to make decisions about what you do about an issue.

Maybe http://slatestarcodex.com/2013/08/06/on-first-looking-into-chapmans-pop-bayesianism/ is worth reading for you. The kind of "I don't know that you advocate is what Scott calls Anton-Wilsonism.

I would challenge your 'in most cases' statement.

When doing credence calibration I don't get result that indicate that I should label all claims 50/50.

Comment author: Erfeyah 10 February 2017 12:34:13PM *  0 points [-]

No. Everything in science is falsifiable and open to challenge.

I understand and agree with that. I am just trying to find the term I can use when discussing scientific results. I thought 'scientific fact' was ok cause it includes 'scientific' which implies all the rest. But yes the word 'fact' is misleading. Should we just call it 'scientific result'? What do you recommend?

Maybe http://slatestarcodex.com/2013/08/06/on-first-looking-into-chapmans-pop-bayesianism/ is worth reading for you.

I can't stress enough how useful that link is to me as a new LW user. My criticisms are quite close to what David Chapman is saying and it is really nice to see how someone representative of LW responds to this.

The kind of "I don't know that you advocate is what Scott calls Anton-Wilsonism.

Discussing in LW is giving me the impression at the moment that I have to learn to talk in a new language. I have to admit that at the moment all the corrections you guys have indicated are an improvement on my previous way of expressing. Very exciting!

But this is a great opportunity to deepen my understanding of the language by practising it. Let me try to reformulate my 'I don't know' in the Bayesian language. So, what I mean by 'I don't know' is that you should use a uniform distribution. For example, you have attached the label of 'Anton-Wilsonism' to me according to what I have currently expressed. I could assume, if you are literally using this way of thinking, that you went through the process of considering a weight for the probability that I am an exact match of what Scott is describing and decided that based on your current evidence I am. This also implies that you have, now or in the past, assigned ratings for all the assumptions and conclusions made in Scott's two paragraphs (there are quite a few) and you are applying all these to my model. So:

  1. Did you really quantify all that or were these labels applied, as it commonly happens in humans, automatically?
  2. Do you think that my recommendation of creating your model using uniform distributions would be useful as we are going through the process of getting more evidence about each other.

It is a trivial, but indicative of an attitude, example that using my approach your action could change from writing (but most importantly thinking):

"The kind of 'I don't know' that you advocate is what Scott calls Anton-Wilsonism."

to

"Is the kind of 'I don't know' you advocate what Scott calls Anton-Wilsonism?"

When doing credence calibration I don't get result that indicate that I should label all claims 50/50.

I just learned (see comments bellow) that "I don't know" is not 50/50 but a uniform distribution. Could you give me a few examples of credence calibration as it happens from your perspective?

Whenever you act where an outcome matters to you, you will take the expected outcomes into account. Even if you say "I don't know" you still have to make decisions about what you do about an issue.

Indeed. This is practical. All I am saying is that we shouldn't confuse the fact that we need to decide when we need to decide with the belief that our ratings express truth. I think it perfectly possible to be forced by circumstances into making an action related decision but return the conceptualisation of the underlying assumptions to a uniform distribution for the purpose of further exploration. It is just being aware that you have a belief system, that you need it, but not fully believe in it.

Comment author: ChristianKl 10 February 2017 02:06:42PM 0 points [-]

My criticisms are quite close to what David Chapman is saying and it is really nice to see how someone representative of LW responds to this.

No, I don't think what you are saying is close to what Chapman is arguing. Chapman doesn't argue that we should say "I don't know" instead of pinning probability on statements where we have little knowledge.

I understand and agree with that. I am just trying to find the term I can use when discussing scientific results. I thought 'scientific fact' was ok cause it includes 'scientific' which implies all the rest.

There are enough people who use terms like "scientific fact" without thinking in terms of falsificationism that it's not clear what's implied.

All I am saying is that we shouldn't confuse the fact that we need to decide when we need to decide with the belief that our ratings express truth.

To me your sentence sounds like you have a naive idea of what the word "truth" is supposed to mean. A meaning that you learned as child.

There are some intuitions that come with that view of the world. Some of those intuitions will come into conflict if you come into contact with more refined ideas of what truth happens to be and how epistemology should work. There are various philosophers like Popper who have put forward more refined concepts. Eliezer Yudkowsky has put forward his own concepts on lesswrong.

I just learned (see comments bellow) that "I don't know" is not 50/50 but a uniform distribution. Could you give me a few examples of credence calibration as it happens from your perspective?

For binary yes/no predictions the uniform distribution leads to 50/50. https://www.metaculus.com, http://predictionbook.com/ and https://www.gjopen.com/ do have plenty of examples.

Comment author: gjm 09 February 2017 01:51:07PM 0 points [-]

What if a rational assessment of inconclusive data weighs you towards the wrong direction. Wouldn't you then start doing worse than the dart throwing monkey?

Sure. In other words, if you get fed bad enough data then you have (so to speak) anti-knowledge. Surely this isn't surprising?

Comment author: Erfeyah 09 February 2017 02:17:23PM *  0 points [-]

No, not really surprising.

I would just clarify though, that the data does not need to be 'bad' in the sense that it is false. We might have data that are accurate but misinterpret them by generalising to the larger context or mistakenly transposing them to a different one.

Comment author: MrMind 09 February 2017 09:37:39AM 2 points [-]

I don't think you're missing anything. Bayesian reasoning allows you to treat your data without introducing errors, but the results you come up with are a product of the available data and the prior model.
This is a point that is often overlooked: if you start with a completely false model, even with Bayesian reasoning the data will get you further away from the truth (case in point: someone who believes in an invisible dragon which has to invent more and more complicated explanation for the lack of evidence). Bayesian probability is just the way of reasoning that introduces the least amount of error.
To counter at least partially our fallibility, it's considered good practice to:

  • never put any assumption at precisely 0 or 1 probability;
  • leave always a reservoir of probability mass in your model to unknown unknows.

Other than that, findind the truth is a quest that needs creativity, ingenuity and a good dose of luck.

Comment author: Douglas_Knight 09 February 2017 02:04:07AM 1 point [-]

This is dealt with in science by not accepting explanations as truths until they are confirmed experimentally

A lot of people say that and go on to give a specific example, that Science did not accept general relativity on the basis that it explained the precession of Mercury, but rather on the novel prediction of solar lensing. But this is historically false. Scientists were much more impressed with the precession than the eclipse (even leaving aside Eddington's reliability).

Comment author: Vaniver 09 February 2017 08:14:19PM 0 points [-]

Note that experimental confirmation isn't really the thing here; experiments just give you data and the problem here is conceptual (the actual truth isn't in the hypothesis space).

Most Bayes is "small world" Bayes, where you have conceptual and logical omniscience, which is possible only because of how small the problem is. "Big world" Bayes has universal priors that give you that conceptual omniscience.

In order to make a real agent, you need a language of conceptual uncertainty, logical uncertainty, and naturalization. (Most of these frameworks are dualistic, in that they have a principled separation between agent and environment, but in fact real agents exist in their environments and use those environments to run themselves.)

Comment author: Erfeyah 09 February 2017 08:33:12PM 0 points [-]

"Big world" Bayes has universal priors that give you that conceptual omniscience.

I assume you are talking hypothetically and not really saying that we, in reality, have these priors? Is there an article about this 'small world' 'big world' distinction?

In order to make a real agent, you need a language of conceptual uncertainty, logical uncertainty, and naturalization. (Most of these frameworks are dualistic, in that they have a principled separation between agent and environment, but in fact real agents exist in their environments and use those environments to run themselves.)

This went completely over my head. Why did you bring agents in the conversation?

Comment author: Vaniver 09 February 2017 10:08:02PM 0 points [-]

I assume you are talking hypothetically and not really saying that we, in reality, have these priors?

I had in mind Solomonoff Induction.

Is there an article about this 'small world' 'big world' distinction?

Here's the last time that came up; I think it's mostly in margins rather than an article on its own.

This went completely over my head. Why did you bring agents in the conversation?

Ah, because when talking about the how to model problems (which I think Bayesian rationality is an example of), agents are the things that do that.

Comment author: Erfeyah 09 February 2017 11:40:18PM *  0 points [-]

Ok that makes sense. These approaches are trying to add considerations such as mine into the model. Not sure I see how that can solve the issue of "the truth missing from the hypothesis space". Or how accurate modelling of the agents can be achieved at our current level of understanding. Examples of real world applications instead of abstract formulations would be really helpful but I will study the article on Solomonoff induction.

Comment author: Vaniver 10 February 2017 12:10:45AM *  0 points [-]

Not sure I see how that can solve the issue of "the truth missing from the hypothesis space".

Solomonoff Induction contains every possible (computable) hypothesis; so long as you're in a computable universe (and have logical omniscience), the truth is in your hypothesis space.

But this is sort of the trivial solution, because while it's guaranteed to have the right answer it had to bring in a truly staggering number of wrong answers to get it. It looks like what people do is notice when their models are being surprisingly bad, and then explicitly attempt to generate alternative models to expand their hypothesis space.

(You can actually do this in a principled statistical way; you can track, for example, whether or not you would have converged to the right answer by now if the true answer were in your hypothesis space, and call for a halt when it becomes sufficiently unlikely.)

Most of the immediate examples that jump to mind are mathematical, but that probably doesn't count as concrete. If you have a doctor trying to treat patients, they might suspect that if they actually had the right set of possible conditions, they would be able to apply a short flowchart to determine the correct treatment, apply it, and then the issues would be resolved. And so when building that flowchart (i.e. the hypothesis space of what conditions the patient might have), they'll notice when they find too many patients who aren't getting better, or when it's surprisingly difficult to classify patients.

If people with disease A cough and don't have headaches, and people with disease B have headaches and don't cough, on observing a patient who both coughs and has a headache the doctor might think "hmm, I probably need to make a new cluster" instead of "Ah, someone with both A and B."

Comment author: Erfeyah 10 February 2017 01:08:47AM 0 points [-]

I read the article and I have to say that the approach is fascinating in its scale and vision. And I can see how it might lead to interesting applications in computer science. But, in its current state, as an algorithm for a human mind.. I have to admit that I can not justify investing the time for even attempting to apply it.

Thank you for all the info! :)

Comment author: MaryCh 09 February 2017 10:20:04AM 0 points [-]

Seems like under that system, some headaches would just go away on their own, without symptoms of cold appearing later, which would mean the probability of cancer goes up. The patient panics, gets checked for cancer (since a recurring headache would hardly be the only symptom), no such disease is found, so there apparently has to be a new category for non-cancer, non-cold headaches.

So usually, the evidence soup has pieces that don't conform to a theory, and if the stakes are high enough, people will go looking for them and maybe use the BR for it.

Comment author: Erfeyah 09 February 2017 11:30:18AM 0 points [-]

Yes, the example is a bit misleading. My purpose is to observe rationality in a field where data is unavailable, scarce or inconclusive. So use the example as a loose analogy for the purpose of communicating the point.

Comment author: MaryCh 09 February 2017 01:30:14PM 1 point [-]

[I think that] where data are unavailable, you cannot really constrain your expectations of them. You can build models, even, perhaps, assign weights within them, but there is no basis to choose between one model and another, and every number of models you find 'satisfying' remains arbitrary.

(This is why I don't argue about religion, for example.)

Comment author: AmagicalFishy 08 February 2017 09:08:17PM *  0 points [-]

I don't think you're missing anything, no.

Comment author: MaryCh 11 February 2017 04:38:51PM 1 point [-]

There are fields of science where different research teams use not-quite-the-same units of measurement. For example, in phytohormonology, the amount of a hormone in plant tissue can be expressed in (nano)grams per grams of dry weight or fresh weight, and people who compare values expressed in different ways cringe because they understand how inexact it really is. There simply is no reliable scale that would allow recalculation, especially for different species etc. (not to mention all the other ways in which drawing conclusions from only the amount of such a substance somewhere in the organism is - hard.) Yet in other fields, people negotiate a common measure, and get more 'research cohesion' as a result.

Has there been any research into how using a common measure allows for more united science? I don't mean miles versus kilometres, I mean cases where there is no coefficient between two valid units. And then there are cases like the coastline paradox (there is a coefficient, but the end results differ.) And cases like the "huge differences in the amount of infection, depending on how you stain your samples, and yes, different people stain them differently and nobody thinks it a problem" (but unlike the phytohormonology example, the coefficient could be found and it would be of some use). And maybe other kinds of cases, of which I haven't thought - enough to build a rough classification.

I think it must be a large topic, but I can't think of how to Google it. Something about 'measure'?.. Can anybody help? Thank you.

Comment author: ChristianKl 12 February 2017 10:07:39AM 0 points [-]

Standardization is the core word. Institutions like ISO exist to create common standards. Jounals can then force scientists to actually follow standards.

Controlled vocabularies and applied ontology seem other key words.

How useful standardization happens to be depends a lot on the quality of the standard. The DSM-V for example seems to be a standard that holds science back and as a result there are calls for funding research that tries to use new standards.

Comment author: MaryCh 12 February 2017 02:47:48PM *  0 points [-]

Thank you! I'll look at/read "Applied ontology: an introduction" (ed. by Munn and Smith) - the results are rather varied and have their own developed terminology, and this one looks as good place to start as any.

Edit to add: tentatively, the "automated information systems" angle might not be what I'm looking for:(

Comment author: ChristianKl 12 February 2017 11:04:39PM 0 points [-]

Automated information system require fixed vocabulary.

If people who observe rats have a different idea about what a leg happens to be then the people who study humans (the leg is the part between the foot and the knee) there are problems with translating knowledge.

Humans might be smart enough to do the translation but computers won't. As a result there's interest in standardization. Bioinformatics needs the standardization and that's where Barry Smith comes from. Bioinformatics has the interests in standardization because automated information systems don't work without it.


I remember a story, which I think cames from People Works (a book about Google's HR department). It made the point that it's not trivial to have a charged definition in a company of what it means to have 10 employees. The people who pay the wages might count 6 full time employees plus 4 half-time employees as 8 employees. When it comes to paying health insurance, it's 10 employees.

The HR department might count prospective employees as an employee the moment the employee signs the offer while another department waits till their starting date.

The fact that Google has a charged definition of employee allowed them to do much better statistics.

Comment author: MaryCh 13 February 2017 06:17:44AM 0 points [-]

Yes, I appreciate the effect of automation on standardization, it is really a great thing. I just have the impression that differences stemming from the deep, very much method-shaped variability of research - like 'radiation' in the evolutionary sense - might be only superficially addressed using only the standardization-as-I-have-read-of-it. (I'm still reading, and expect this to change.)

I'm starting with an image of 'variable and its measure can be only tenuously linked (like 'length' and 'meter) to pretty much baked together (like the phytohormone example)'. This image might itself be just wrong.

Comment author: ChristianKl 13 February 2017 09:41:42AM 0 points [-]

Meter is not our only measure of length. We also have astronomical units to measure length. In school they taught us that they were different units and that we can speak with more precision about the distance between two stars if we talk in astronomical units.

For a long time there were also a bunch of interesting questions such as whether it makes sense to say that the norm meter in Paris is 1-meter long and whether it stays exactly 1-meter long is it's surface oxidates a bit.

Metal changes it's length at different temperature. That means you need a definition of temperature to define the length of the meter if you define it over the norm meter.

Newton thought that there's was a fixed "temperature of blood". Fahrenheit used "body temperature" as a measuring stick for a specific temperature.

It took a lot of science to find the freezing point and the boiling point of water as the perfect way to norm temperature. If you shape the vessel the right way, it's possible to boil water at 102 degree C, so they needed to specify the right conditions.

Comment author: MaryCh 13 February 2017 10:19:24AM 0 points [-]

I either didn't know or hadn't thought in the context about most of what you say here, thank you.

Yet this (the exact length of a meter) is more-or-less settled, in the sense that very many people use it without significant loss of what they want to convey. This is kind of exactly the thing I'd like to learn about - how unit-variable relationships evolve and come to some 'resting position'. How people first come to think about the matter of a subject, than about the ways to describe it, and finally about the number of a common 'piece' used to measure it.

Comment author: ChristianKl 13 February 2017 11:18:02AM 0 points [-]

I think the Applied Ontology book is worth reading as it touches a lot of the practical concerns that come with the need for standardization due to automated knowledge processing. Even if you aren't interested in automated knowledge processing it still useful.

Inventing Temperature: Measurement and Scientific Progress by Hasok Chang is a good case study for how our measure of temperature evolved. Temperature is a good example because conceptualizing it is harder than conceptualizing length. In the middle ages people had their measures for length but they didn't have one for temperature.

The definition of the meter over the wavelength of light instead of over the norm meter was settled in 1960 but the amount of people for whom there were practical concerns was relatively little. Interestingly we have at the moment a proposed change to the SI system that redefines the kilogram: https://en.wikipedia.org/wiki/Proposed_redefinition_of_SI_base_units

It changes the uncertainity that we have over a few constants. Beforehand we had an exact definition of the kilogram and afterwards we only know 8 digits of accuracy. On the other hand we get more accuracy for a bunch of other measurements. It might be worth reading a bit into the debate if you care about how standards are set.

Comment author: Pimgd 10 February 2017 01:54:49PM *  1 point [-]

How does a rational actor resolve the emperor's clothes?

Story link: http://www.andersen.sdu.dk/vaerk/hersholt/TheEmperorsNewClothes_e.html

Specifically, insert ourselves into every step of the process.

1) You're the emperor. Two tailors come to you saying they can make you a suit that cannot be seen by those that are stupid and/or unfit for their current position.

Answer to this, I think, is: You don't believe this magical stuff, see it for the scam that it is and tell them to bugger off.


2) You as the emperor, somehow agree to this. They take your measurements and start weaving, then start demanding all sorts of resources (cloth and silks).

Answer to this is probably: You give them this, because as the story goes, you really want fancy clothes. ... Besides, if you say no, they'll say they can't make clothes without cloth. Now what? It's not an unreasonable request. Maybe you can complain about the quantities, ask for an itemized invoice, but, eh.


3) You've sent your minister, which you trust dearly, has been at your side for years, real standup guy, and he says they're making the most beautiful clothing. You've sent another official, and he says it's absolutely magnificent. You go and visit in person, and they point at empty looms, whilst saying "see, aren't these the most beautiful clothes ever?" Your guards stay silent.

So here's one of the places where I'm interested in the answer, because this is the point of personal doubt as the emperor. You can either, as in the story, say "Oh yes, such wonderful clothes!" and internally go "oh crap am I unfit", or I think you could go "What clothes are you talking about, those are empty looms!" But the evidence you have is, there's 2 people who you don't know that are saying "the clothes exist and they have a property that if you cannot see them you are dumb and/or unfit", and there's 2 people who you really really trust that are saying "look at these fine fine clothes, they really do exist".

My answer in this case would be to station the guards in the room, leave the room with the ministers, and ask them individually "Okay, now let's be honest. Did you really see those clothes?" If any of them say no, I'd have the "tailors" executed. But if they both say yes and start expressing worry for me and all that then I don't know what to believe.


4) You're a citizen of the country. The emperor is having a parade to showcase his new clothes! They're supposedly magical clothes, which cannot be seen by those who are unfit and/or dumb. It's a bit chilly. Everyone's talking about the fancy clothes, and when the emperor comes around the corner, you can see him: He's naked, but otherwise fine. Behind him are several noblemen, pretending to hold the drape of the clothes. Your friend looks at you and says, "Look, aren't those the most fancy clothes?"

This case too, is hard for me. I mean, it depends on your standing in society for how much you stand to lose, but in a medieval society, if you're a farmhand? I'd say "but he's naked!". Farmhands aren't particularily clever (I might be misguided), but they haven't got a whole lot to lose. But if you're a craftsman, somehow who has a shop? Yeah, that'd be a big reputation hit, if the whole town thought you were unfit to make the things you make.


My question, for each case - what's the rational belief to hold? The main beliefs you can hold that I can see are "The clothes do not exist, but everyone is faking it, and it should stop", "The clothes do not exist, but everyone is faking it, and I should fake it too" and "I am unfit and/or dumb and I better fake seeing those clothes lest I lose my station".

My other question - As the emperor, you could go all science on the clothes. "I can see the clothes just fine, but why do they not cast shadows?" "These clothes are very light", in fact, when weighed, they don't weigh anything, they don't create shadows, they let heat through, they don't hold water (it seeps straight through as if the clothes weren't there)... That'd be one way to quickly gather evidence. I'd also express worry - if someone can't see the clothes, won't they see me naked?

Anyway, my other question - how would you gather extra evidence as a citizen?

Comment author: Viliam 10 February 2017 03:19:43PM 2 points [-]

But the evidence you have is, there's 2 people who you don't know that are saying "the clothes exist and they have a property that if you cannot see them you are dumb and/or unfit", and there's 2 people who you really really trust that are saying "look at these fine fine clothes, they really do exist".

Collect more evidence.

If possible, find a person who never heard about the supposed properties of the clothes, and ask them to describe them to you. If they can't, maybe they are stupid, but then find another one and... uhm, if everyone who didn't hear about the supposed properties of the clothes is stupid, that's suspicious.

Unexpectedly invite a few painters, put them in different corners of the room, and ask them to paint you in the clothes.

Alternatively, test your ministers. First, meet them with the clothes; next, without them. If they see the clothes both times...

Put the clothes in a bag. Add a few empty bags. Ask your ministers which bag contains the clothes. If all of them failed, ask the tailors.

Comment author: MockTurtle 14 February 2017 04:43:46PM 1 point [-]

Interesting questions to think about. Seeing if everyone independently describes the clothes the same way (as suggested by others) might work, unless the information is leaked. Personally, my mind went straight to the physics of the thing, 'going all science on it' as you say - as emperor, I'd claim that the clothes should have some minimum strength, lest I rip them the moment I put them on. If a piece of the fabric, stretched by the two tailors, can at least support the weight of my hand (or some other light object if you're not too paranoid about the tailor's abilities as illusionists), then it should be suitable.

Then, when your hand (or whatever) goes straight through, either they'll admit that the clothes aren't real, or they'll come up with some excuse about the cloth being so fine that it ripped or things go straight through, at which point you can say that these clothes are useless to you if they'll rip at the slightest movement or somehow phase through flesh, etc.

Incidentally, that's one of my approaches to other things invisible to me that others believe in. Does it have practical uses or create a physical effect in the world? If not, then even if it's really there, there's not much point in acknowledging it...

Comment author: ChristianKl 10 February 2017 02:35:59PM *  0 points [-]

The irony of the situation is that some fancy closes that are today worn in Milan leave a large part of the person naked.

Anyway, my other question - how would you gather extra evidence as a citizen?

As different people for the color of the clothes and for more details. If the people really can see the clothes they should be able to describe the clothes in the same way.

If there already common knowledge about the color of the clothes or details then it would be required to see the clothes in a new context. How do the clothes look like when they get wet? If two people agree how the clothes look under a completely new context it's more likely that they don't just tell you the answer they learned by heart.

Comment author: hodgestar 09 February 2017 07:04:55PM *  1 point [-]

Less Wrong has a number of participants who endorse the idea of assigning probability values to beliefs. Less Wrong also seems to have a number of participants who broadly fall into the "New Atheist" group, many of the members of which insist that there is an important semantic distinction to be made between "lack of belief in God" and "belief that God does not exist."

I'm not sure how to translate this distinction into probabilistic terms, assuming it is possible to do so-- it is a basic theorem in standard probability theory (e.g. starting from the Kolmogorov axioms) that P(X) + P(not(X)) = 1 for any event X. In particular, if you take "lack of belief in God" to mean that you assign a value very close to 0 for P("God exists"), then you must assign a value very close to 1 for P(not("God exists")). I would have thought (perhaps naively) that not("God exists") and "God does not exist" are equivalent, and that what it means to say that you believe in some proposition X is that you assign it a probability that is close to 1 (though not exactly 1, if you're following the advice to never assign probabilities of exactly 0 or 1 to anything). This would imply that that a lack of belief in God implies a belief that God does not exist.

Am I misunderstanding something about translating these statements into probabilistic language? Or am I just wrong to think that there are people who simultaneously endorse both assigning probabilities to beliefs and the distinction between "lack of belief that God exists" and "belief that God does not exist?"

Comment author: Erfeyah 09 February 2017 08:46:46PM *  2 points [-]

Shouldn't a lack of belief in god imply:

P(not("God exists")) = 0.5

P("God exists") = 0.5

(I am completely ignoring the very important part of defining God in the sentence as I take the question to be asking of a way to express 'not knowing' in probabilistic terms. This can be applied to any subject really.)

Comment author: hairyfigment 09 February 2017 11:06:10PM 0 points [-]

I am completely ignoring the very important part of defining God

That is indeed the chief problem here. I'm assuming you're talking about the prior probability which we have before looking at the evidence.

Comment author: Lumifer 09 February 2017 08:58:27PM 0 points [-]

Shouldn't a lack of belief in god imply

No. Why would it?

"I don't know" is a perfectly valid answer. Sometimes it's called Knightian uncertainty or Rumsfeldian "unknown unknowns".

Comment author: Erfeyah 09 February 2017 09:08:20PM *  1 point [-]

I agree that "I don't know" is a better answer as there is no reason to talk in rational jargon in a case like this. Especially when we haven't even defined our terms. But could you explain to me why assigning 0.5 probabilities in the two opposites (assuming the question is clear and binary) does not make sense for expressing ignorance?

Comment author: Lumifer 09 February 2017 09:19:46PM *  0 points [-]

why assigning 0.5 probabilities in the two opposites (assuming the question is clear and binary) does not make sense for expressing ignorance?

Because you lose the capability to distinguish between the "I know the probabilities involved and they are 50% for X and 50% for Y" and "I don't know".

Look at the distributions of your probability estimates. For the "I don't know" case it's a uniform distribution on the 0 to 1 range. For the "I know it's 50%" it's a narrow spike at 0.5. These are very different things.

Comment author: Erfeyah 10 February 2017 12:03:09AM 0 points [-]

Ahhh, this is confusing me. I intuitively feel a 50-50 chance implies a uniform distribution. But what you are saying about the distribution being a spike for 0.5 makes total sense. Well, I guess I have a bit of studying to do...

Comment author: gjm 10 February 2017 12:57:57AM 2 points [-]

Being a full-on Bayesian means not only having probability assignments for every proposition, but also having the conditional probabilities that will allow you to make appropriate updates to your probability assignments when new information comes in.

The difference between "The probability of X is definitely 0.5" and "The probability of X is somewhere between 0 and 1, and I have no idea at all where" lies in how you will adjust your estimates for Pr(X) as new information comes in. If your estimate is based on a lot of strong evidence, then your conditional probabilities for X given modest quantities of new evidence will still be close to 0.5. If your estimate is a mere seat-of-the-pants guess, then your conditional probabilities for X given modest quantities of new evidence will be all over the place.

Sometimes this is described in terms of your probability estimates for your probability estimates. That's appropriate when, e.g., what you know about X is that it is governed by some sort of random process that makes X happen with a particular probability (a coin toss, say) but you are uncertain about the details of that random process (e.g., does something about the coin or how it's tossed mean that Pr(heads) is far from 0.5?). But similar issues arise in different cases where there's nothing going on that could reasonably be called a random process but your degree of knowledge is greater or less, and I'm not sure the "probabilities of probabilities" perspective is particularly helpful there.

Comment author: Erfeyah 10 February 2017 10:06:37AM 0 points [-]

Thanks for the detailed explanation. It helps!

Comment author: Lumifer 10 February 2017 03:34:16AM 0 points [-]

I intuitively feel a 50-50 chance implies a uniform distribution

Well, imagine a bet on a fair coin flip. That's a 50-50 chance, right? And yet there is no uniform distribution in sight.

Comment author: niceguyanon 10 February 2017 07:20:22PM 0 points [-]

So if we can distinguish between

"I know the probabilities involved and they are 50% for X and 50% for Y" and "I don't know".

Could we further distinguish between

a uniform distribution on the 0 to 1 range and "I don't know"?

Let's say a biased coin with unknown probability of landing heads is tossed, p is uniform on (0,1) and "I don't know" means you can't predict better than randomly guessing. So saying p is 50% doesn't matter because it doesn't beat random.

But what if we tossed the coin twice, and I had you guess twice, before the tosses. If you get at least one guess correct then you get to keep your life. Assuming you want to play to keep your life, then how would you play? Coin is still p uniform on (0,1), but it seems like "I don't know" doesn't mean the same thing anymore, because you can play in a way that can better predict the outcome of keeping your life.

You would guess (H,T) or (T,H) but avoid randomly guessing because it would produce things like (H,H) which is really bad because if p is uniform on (0,1), then probability of heads is 90% is just as likely as probability of heads is 10%, but heads at 10% is really bad for (H,H), so bad that even 90% heads doesn't really help that much more.

If p is 90% or 10%, guessing (H,T) or (T,H) would result in the same small probability of dying at 9%. But (H,H) would result in at best 1% or 81% chance of dying. Saying I don't know in this scenario doesn't feel the same as I don't know in the first scenario. I am probably confused.

Comment author: Lumifer 10 February 2017 09:48:27PM 0 points [-]

but it seems like "I don't know" doesn't mean the same thing anymore, because you can play in a way that can better predict the outcome of keeping your life.

But you've changed things :-) In your situation you know a very important thing: that the probability p is the same for both throws. That is useful information which allows you to do some probability math (specifically compare 1 - p(1-p) and 1 - p^2).

But let's say you don't toss the same coin twice, but you toss two different coins. Does guessing (H,T) help now?

Comment author: Erfeyah 10 February 2017 10:03:28AM 0 points [-]

You are obviously right! This is helpful :)

Now, just to make sure I got it, does this make sense: the question of gods existence (assuming the term was perfectly defined) is a yes/no question but you are conceptualising the probability that a yes or a no is true. That is why you are using a uniform distribution in a question with a binary answer. It is not representing the answer but your current confidence. Right?

Comment author: Lumifer 10 February 2017 03:53:19PM *  1 point [-]

Skipping a complicated discussion about many meanings of "probability", yes.

Think about it this way. Someone gives you a box and says that if you press a button, the box will show you either a dragon head or a dragon tail. That's all the information you have.

What's the probability of the box showing you a head if you press the button? You don't know. This means you need an estimate. If you're forced to produce a single-number estimate (a "point estimate") it will be 50%. However if you can produce this estimate as a distribution, it will be uniform from 0 to 1. Basically, you are very unsure about your estimate.

Now, let's say you had this box for a while and pressed the button a couple thousands of times. Your tally is 1017 heads and 983 tails. What is your point estimate now? More or less the same, rounding to 50%. But the distribution is very different now. You are much more confident about your estimate.

Your probability estimate is basically a forecast of what do you think will happen when you press the button. Like with any forecast, there is a confidence interval around it. It can be wide or it can be narrow.

Comment author: Vaniver 09 February 2017 08:00:58PM 1 point [-]

You're right about the probabilistic statements, with a potentially tangential elaboration. There are nonsense sentences--not contradictions ("A and not A") but things that fail to parse ("A and")--and it doesn't make sense to assign probabilities to those. One might claim that "God exists" is a nonsense sentence in that way, but I think most New Atheists don't take that approach.

The distinction that people are drawing is basically which framing should have the benefit of the doubt, since not believing a new statement is the default. This is much more important for social rationality / human psychology than it is for Bayesianism, where you just assign a prior and then start calculating likelihood ratios.

Comment author: ChristianKl 10 February 2017 03:13:32PM *  0 points [-]

From my perspective, a belief needs to be about empiric facts to have a probability attached to it. I need to be able to clearly describe how the belief could be tested in principle.

In addition to beliefs about empiric facts there are also beliefs like "Nobody loves me." that aren't about specific empiric facts but that still matter a great deal.

Comment author: MrMind 10 February 2017 09:32:50AM 0 points [-]

I cannot speak for other atheists, but as far as I'm concerned I agree with you.
Since we have a hard time defining even a human being, I accept that "God" cannot be clearly defined in any model, but I accept that there are narrations that points to some being of divine nature, and I accept that as a valid 'reference' to God(s). To those, I give a very low probability, with very little Knightian uncertainty (meaning that I also give very little probability to future evidence that would raise this probability, and high probability to evidence that will lower this value). For that account of the divine, I consider myself a full fledged atheist.
There are other narrations though, and I've heard of definitions that basically reduce to "the law of physics", to which I give obviously very high probability with very high meta-certainty.
There might be definitions or narrations that are in the middle, though. On that account, I cannot say precisely what my probabilities are, and thus would be appropriate to say that I lack a belief in this kind of god, more than a definite belief in the non-existence.

Comment author: gjm 09 February 2017 08:40:06PM 0 points [-]

It seems to me that someone could quite consistently hold the following position:

"Atheist" means "lacking positive belief in any god or gods". You can be an atheist without thinking the existence of gods is vanishingly improbable, or indeed without giving any thought at all to probabilities. I, as it happens, do prefer to think in probabilities when possible. Exactly what I think about the existence of God depends a great deal on how you define God, and it might be anywhere from "vanishingly unlikely" to "somewhat unlikely", or in many cases "I can't answer that question because it's not clear enough what it means". But, whatever way you pose the question, I don't positively believe in any sort of god, and it's therefore appropriate to call me an atheist.

Comment author: madhatter 09 February 2017 01:35:21AM 1 point [-]

Thanks for this topic! Stupid questions are my specialty, for better or worse.

1) Isn't cryonics extremely selfish? I mean, couldn't the money spent on cryopreserving oneself be better spend on, say, AI safety research?

2) Would the human race be eradicated if there is a worst-possible-scenario nuclear incident? Or merely a lot of people?

3) Is the study linking nut consumption to longevity found in the link below convincing?

http://jamanetwork.com/journals/jamainternalmedicine/fullarticle/2173094

And if so, is it worth a lot of effort promoting nut consumption in moderation?

Comment author: Thomas 09 February 2017 08:45:48AM 1 point [-]

couldn't the money spent on cryopreserving oneself be better spend on, say, AI safety research?

Here comes another "stupid question" from this one.

Couldn't the money spent on AI safety research be better spend on, say, AI research?

Comment author: Vaniver 09 February 2017 08:07:17PM 3 points [-]

Couldn't the money spent on AI safety research be better spend on, say, AI research?

There's something like 100 times as much funding for AI research as there is for AI safety research. In general, it seems like it would be weird to have only 1% of the effort in a project spent on making sure the project is doing the thing that it should be doing.

For this specific question, I like Stuart Russell's approach:

My proposal is that we should stop doing AI in its simple definition of just improving the decision-making capabilities of systems. […] With civil engineering, we don’t call it “building bridges that don’t fall down” — we just call it “building bridges.” Of course we don’t want them to fall down. And we should think the same way about AI: of course AI systems should be designed so that their actions are well-aligned with what human beings want. But it’s a difficult unsolved problem that hasn’t been part of the research agenda up to now.

Comment author: MrMind 09 February 2017 09:26:14AM 1 point [-]

Well, the whole point of this forum is to convince someone that the answer is most definitely not.

Comment author: gjm 09 February 2017 11:58:53AM 2 points [-]

the whole point of this forum

It really isn't. One of the reasons for the founding of this forum, yes. But what this forum is meant to be for is advancing the art of human rationality. If compelling evidence comes along that AI safety research is useless and AI research is vanishingly unlikely to have the sort of terrible consequences feared by the likes of MIRI, then "this forum" should be very much in the business of advocating against AI safety research.

Comment author: VincentYu 09 February 2017 02:03:18PM *  1 point [-]

In support of your point, MIRI itself changed (in the opposite direction) from its former stance on AI research.

You've been around long enough to know this, but for others: The former ambition of MIRI in the early 2000s—back when it was called the SIAI—was to create artificial superintelligence, but that ambition changed to ensuring AI friendliness after considering the "terrible consequences [now] feared by the likes of MIRI".

In the words of Zack_M_Davis 6 years ago:

(Disclaimer: I don't speak for SingInst, nor am I presently affiliated with them.)

But recall that the old name was "Singularity Institute for Artificial Intelligence," chosen before the inherent dangers of AI were understood. The unambiguous for is no longer appropriate, and "Singularity Institute about Artificial Intelligence" might seem awkward.

I seem to remember someone saying back in 2008 that the organization should rebrand as the "Singularity Institute For or Against Artificial Intelligence Depending on Which Seems to Be a Better Idea Upon Due Consideration," but obviously that was only a joke.

I've always thought it's a shame they picked the name MIRI over SIFAAIDWSBBIUDC.

Comment author: Lumifer 09 February 2017 03:39:24PM 1 point [-]

<cynical hat>Or maybe because SIAI realized their ability to actually create an AI is non-existent</cynical hat>

Comment author: MrMind 10 February 2017 09:21:19AM *  0 points [-]

</cynical hat>

Ha! It's wonderful news that you can take it off!
For me you're the closest human (?) correlate to the man with the hat from XKCD, and I mean that as a compliment.

Comment author: Lumifer 10 February 2017 03:42:40PM 0 points [-]

I take it as such :-)

You do mean the black hat guy, right? (there is also a white hat guy who doesn't pop up as frequently).

Comment author: MrMind 10 February 2017 05:16:22PM 0 points [-]

Yes, the black hatter. I totally forgot about the white hat guy...

Comment author: MrMind 10 February 2017 09:16:00AM 0 points [-]

You're right, but.
The whole story goes like this: Eliezer founded this forum to advancing the art of human rationality, so that people would stop making silly objections to the issue of AI safety like "intelligence would surely bring about morality" and things like that.
The focus of LW is human rationality and of MIRI is AI safety, but as far as I can tell, we still haven't found any valid objections to the orthogonality thesis. On the contrary, the issue of autonomous agents safety is gaining traction and recognition.
I do agree that if we found a strong objections we should change perspective, but we still haven't and indeed we are seeing more and more worrisome examples.

Comment author: Thomas 09 February 2017 09:33:26AM 0 points [-]

I know that. But the whole point of this thread is to ask stupid questions, isn't it?

And sometimes apparently the stupidest question, isn't stupid after all.

Comment author: Lumifer 09 February 2017 03:37:49PM 0 points [-]

Yes.

Comment author: Viliam 09 February 2017 10:14:26AM 0 points [-]

Isn't cryonics extremely selfish?

If we are talking about "extremes", what is the base set here: people's usual spending habits? Because I don't think cryonics is more selfish than e.g. buying an expensive car.

Comment author: MrMind 09 February 2017 09:23:52AM *  0 points [-]

I mean, couldn't the money spent on cryopreserving oneself be better spend on, say, AI safety research?

Well, 'better' here does all the work. It depends on your model and ethics: for example if you think that resuscitation is probably nearer then full AGI, then it's better to be frozen.

2) Would the human race be eradicated if there is a worst-possible-scenario nuclear incident? Or merely a lot of people?

This question I couldn't parse correctly. A nuclear war is improbable to wipe out humanity in its entirety, whereby a lot of people is th exact opposite of extinction, so...?

3) Is the study linking nut consumption to longevity found in the link below convincing?

This is far from a stupid question. The sample sizes are at least large, but it has the usual problem of using p-values, which are notoriously very fragile. It would require someone acquainted with statistics to judge better the thing, if it can be done at all.

Comment author: Bound_up 13 February 2017 11:52:49PM 0 points [-]

I'm looking for a link I saw on Slate Star Codex. It was poetry written by a woman who took drugs every day for a year (something like that). Anyone know where I might find it?

Comment author: ChristianKl 12 February 2017 10:51:48AM 0 points [-]

How many jobs that were done 50 years ago still exist in roughly the same form?

Comment author: VincentYu 10 February 2017 06:25:09AM 0 points [-]

Why is downvoting disabled, for how long has it been like this, and when will it be back?

Comment author: Viliam 10 February 2017 10:53:49AM 6 points [-]

The original purpose of downvoting was to allow community moderation. Here, "moderation" means two things: (1) Giving higher visibility to high-quality content. This functionality we still have, it's the upvotes. (2) Removing low-quality content. Comments with karma below -5 and their whole subthreads are collapsed by default. This is especially important when some newcomers start spamming LW with a lot of low-quality comments. It happened more frequently in the past when LW was more popular.

And the "community" aspect means that these decisions about what to show prominently and what to hide are done by the local "hive mind", i.e. everyone, more precisely anyone above some amount of karma. This is good for several reasons: "wisdom of the crowds", preventing a few people from getting disproportional power, but most practically because moderators are busy and unable to review everything.

Why was it disabled:

The previous political debates on LW attracted one very persistent and very "mind-killed" person, known as Eugine. This guy made it his personal mission to promote neoreactionary politics on LW, and to harass away everyone who disagrees (because people who disagree with him or with neoreaction are by definition irrational people and don't belong here). To achieve this, he abused the downvoting system.

The first form of abuse was punishing everyone who disagreed with him by going through their comment history and downvoting all their previous comments. That means, one day you wrote a comment he didn't like, and the next day you lost hundreds of karma points. And afterwards, any comment you wrote, immediately had one downvote.

This was against how the karma system was supposed to be used (you were supposed to vote on specific comments, not users), and pretty much ruined our important feedback system. Eugine was asked to stop doing this, he didn't give a fuck. So his account was banned, but he created another one, and then another. So it became a game of whack-a-mole, where Eugine created hundreds of accounts, and moderators tried to find and remove them. Even worse, with multiple accounts Eugine started multiple voting, which means that if he disliked a comment, he downvoted it from dozen accounts, immeditely moving its karma into negative numbers. He typically downvoted all comments that disagreed with neoreactionary politics, or which mentioned Eugine.

LessWrong code is a clone of Reddit; it is not an elegant code, and the database is even less elegant. A few professional web developers tried to implement a few changes; most of them left crying, and the few changes that were successfully implemented took a lot of time. Fighting with Eugine was a huge drain of resources, and one of the main reasons why currently LW is "dead".

What now:

The short-term solution was to disable downvotes, thus removing from Eugine his ability to censor comments he doesn't like. Yeah, it has a few negative side-effects.

A long-term solution is to move the whole website to a completely different codebase, which will be easier to maintain. This is a work in progress. Respectful of the planning fallacy I will not give any estimates, except "it will be done when it will be done". On the new software, downvoting (or some other method of removing low-quality content) will presumably exist.

Comment author: VincentYu 10 February 2017 03:05:06PM 1 point [-]

Thanks for writing such a comprehensive explanation!

Comment author: Erfeyah 10 February 2017 10:10:14AM 0 points [-]

I am very new here but my impression from reading around is that people were taking advantage of the system by creating multiple accounts and downvoting comments that opposed them in order to appear to be right. I am not sure though.

Comment author: Viliam 10 February 2017 03:21:14PM 0 points [-]

Correct, with the addition that it was only one person. Very persistent, though... keeps doing this for years.

Comment author: James_Miller 09 February 2017 11:49:44PM 0 points [-]

If I email someone non-famous to be on my podcast and they don't respond should I take that as a "no" or as a "didn't get the message try again".

Comment author: gjm 10 February 2017 12:49:04AM 3 points [-]

I make no claim to know what you should do, but what I would do in that situation is: wait at least a month; then email them again saying: no obligation to reply or anything, just wanted to make sure emails aren't going astray. If still no reply, assume that either they aren't interested or they're spam-binning your emails and you'll never reach them by email anyway.