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Alejandro130

The question is analogous to the Grim Reaper Paradox, described by Chalmers here:

A slightly better example of prima facie without ideal positive conceivability may be the Grim Reaper paradox (Benardete 1964; Hawthorne 2000). There are countably many grim reapers, one for every positive integer. Grim reaper 1 is disposed to kill you with a scythe at 1pm, if and only if you are still alive then (otherwise his scythe remains immobile throughout), taking 30 minutes about it. Grim reaper 2 is disposed to kill you with a scythe at 12:30 pm, if and only if you are still alive then, taking 15 minutes about it. Grim reaper 3 is disposed to kill you with a scythe at 12:15 pm, and so on. You are still alive just before 12pm, you can only die through the motion of a grim reaper's scythe, and once dead you stay dead. On the face of it, this situation seems conceivable — each reaper seems conceivable individually and intrinsically, and it seems reasonable to combine distinct individuals with distinct intrinsic properties into one situation. But a little reflection reveals that the situation as described is contradictory. I cannot survive to any moment past 12pm (a grim reaper would get me first), but I cannot be killed (for grim reaper n to kill me, I must have survived grim reaper n+1, which is impossible). So the description D of the situation is prima facie positively conceivable but not ideally positively conceivable.

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Thomas20

You are right. This is actually the same problem. The problem of the (math) infinity magic itself.

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See in context
by pepe_prime
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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.

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Stupid Questions December 2016
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[-]Beluga110

Dear Americans,

While spending a holiday in the New Orleans and Mississippi region, I was baffled by the typical temperatures in air-conditioned rooms. The point of air conditioning is to make people feel comfortable, right? It is obviously very bad at achieving this. I saw shivering girls with blue lips waiting in the airport. I saw ladies wearing a jacket with them which they put on as soon as they entered an air-conditioned room. The rooms were often so cold that I felt relieved the moment I left them and went back into the heat. Cooling down less than to the optimally comfortable temperature would make some economical and ecological sense, and would make the transition between outside and inside less brutal. Cooling down more seems patently absurd.

What is going on here? Some possible explanations that come to mind:

  • Employees who have to wear suits and ties prefer lower temperatures than tourists in shorts and T-shirts.
  • Overweight people prefer lower temperatures than skinny girls, and the high obesity rates in America are well-known.
  • Some places (like airports) may intentionally want to prevent people from hanging around for too long without a good reason.

Still, the above points seem nowhere near sufficient to explain the phenomenon. The temperatures seem uncomfortably low even for people wearing a suit with a tie. Places like cinemas clearly want their customers to feel comfortable, and their employees don't wear suits.

Thanks for clarifying.

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4moridinamael
First, the temperature will be uneven throughout any given building. In order to ensure that the outskirts of a large building are adequately cooled, the interior may end up frigid. This effect is more pronounced with larger buildings. Please complain to your nearest HVAC contractor, not to us poor Texans. Second, people who are just coming in from 115 F outdoor temperatures actually tend to want it to be nice and cold inside. Believe me. Third, the outdoor temperature varies over the course of a day. A thermostat setting that resulting in an acceptable actual indoor temperature at noon might be causing very cold indoor temperatures at 6 PM, even though nobody touched the thermostat. Fourth, colder air is drier, which causes sweat to evaporate faster. So there's a sweat-evaporating benefit along with the rapid cooling benefit, which is very beneficial and widely appreciated when every single person entering a building is drenched in sweat. The best way to learn these lessons is to simply live in Texas and observe your own behavior vis-a-vis air conditioning preferences.
2Good_Burning_Plastic
No, it does not work that way. Artificially cooling air without taking water out of it decreases its equilibrium vapor pressure while keeping its absolute humidity constant, thereby increasing its relative humidity and making it worse at drying things. (Conversely, artificially heating air without adding water to it makes it better at drying things.)
0moridinamael
As Lumifer said, air conditioners extract water from the air. Then the air warms up again slightly as it percolates through the building. The net effect is enhanced drying.
0Douglas_Knight
The more powerful the AC, the less it dehumidifies. How about you talk to an HVAC contractor.
0moridinamael
Not sure what "powerful" means in this context. I have a degree in chemical engineering so I'm moderately confident that I understand compression and saturation pressure. Saturation pressure of water in air declines with temperature. Making the air colder reduces the humidity of the air, and this is true all the way down to the freezing point of water. In a large building, you will have a pump outlet temperature much lower than the thermostat setpoint. For example, the coils themselves may be operating at 25-45 F, even though the air in in the building at large may be 75 F. The consequence of this is that the percent saturation ("humidity") of the air will be significantly lower than the outdoor humidity. The net effect will be perceptible drying.
0Lumifer
Yeah, but that's not what air conditioners do. They do take water out of the air via condensation on the coils.
4Viliam
Some form of signalling? Air-conditioning is higher status than no air-conditioning. Higher-status people are more likely to live with air-conditioning; lower-status people are more likely to live without it. Lower-status people will feel more inconvenienced by too much air-conditioning, because it is a greater shock for them. Complaining about too much air-conditioning is an evidence of lower status. People who want to seem higher-status will avoid complaining about air-conditioning (and maybe just dress warmer). If all high-status people agree that the air-conditioning is okay as it is, it will remain as it is, because higher-status people make the decisions.
4shev
I think you get more of that in Texas and the southeast. It (by my observation - very much a stereotype) correlates with driving big trucks, eating big meals, liking steak dinners and soda and big desserts, obesity, not caring about the environment, and taking strong unwavering opinions on things. And with conservatism, but not exclusively. I distinctly remember driving in my high school band director's car once, maybe a decade ago, and he was blasting the AC at max when it maybe needed to be on the lowest setting, tops -- it seemed to reflect a mindset that "I want to get cold NOW" when it's hot, to the point of overreaction. Maybe a mindset that - if the sun is bright and on my face, I need a lot of cold air, even if the rest of me doesn't need it? Or maybe, 'it feels hot in the world so I want a lot of cold air'. Certainly there was no realization that it was excessive, and he didn't seem bothered by the unnecessary use of resources. I've noticed this same mindset a lot ever since, and I still don't understand it.
0Osho
The optimal AC setting in terms of comfort is subjective. I don't see any reason to speculate beyond the simple fact that he was hot. I don't think anyone should care about "unnecessary uses of resources"- that's why we have markets.
2Good_Burning_Plastic
That would apply if there were no such things as subsidies or negative externalities -- if all of the costs associated with cooling a room to a given temperature were always paid by the person who decided the temperature.
0Osho
Well that's why we have governments...
0Good_Burning_Plastic
Yeah, but I don't think they're anywhere near reliable enough that no-one "should care about unnecessary uses of resources"...
0shev
No, markets only work for services whose costs are high enough to participants to care and model their behavior accordingly. In my observation, specifically, these people behave this way for reasons other than their personal comfort, and the costs aren't high enough (or they're not aware that they're high enough) to influence their behavior. The 'reason to speculate' is that it's interesting to talk about it. That's all.
3bogus
There is no "optimally-comfortable temperature" - different folks want different temps! The optimum choice is in fact to have two rooms/environments, one of which cools down a bit more, the other less (or not at all). If you feel cold, just spend some time in the warmer room.
1Richard Korzekwa
Yeah, this is a thing, and I hear plenty of Americans make baffled complaints about it as well. I don't know the answer, but this is my guess. A while back, there was a flurry of news sites talking about air conditioning being "sexist". The short version is that standards for climate control were all written when offices were full of men in suits. Times have changed, in terms of who's wearing what in which buildings, but things like building codes and temperature guidelines haven't caught up.
[-]shev50

Is there an index of everything I ought to read to be 'up-to-date' in the rationalist community? I keep finding new stuff: new ancient LW posts, new bloggers, etc. There's also this on the Wiki, which is useful (but is curiously not what you find when you click on 'all pages' on the wiki; that instead gets a page with 3 articles on it?). But I think that list is probably more than I want - a lot of it is filler/fluff (though I plan to at least skim everything, if I don't burn out).

I just want to be able to make sure, if I try to post something I think is new on here, that it hasn't been talked to death about already.

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5NancyLebovitz
I think you're better off raising your topics in open threads, and see whether people tell you a topic's already been covered.
2MrMind
No, there's no index. The rationalist community is a disapora of people in which everyone keeps producing its own content. It's basically impossible to read everything and be on-par with everyone. I suggest you select a couple of forum (the obvious choices are LW and SSC) and read a bunch of things from there (again, "AI to Zombie" strikes me as the obvious choice).
[-]Erfeyah40

I am seeing an 'epistemic status' descriptor used in some posts. If I want to use it does the community have a standard vocabulary described in a post somewhere or is it up to the author to use it as they like?

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4tut
I don't think there's any standardization. People just make it up as they go. Scott often uses the phrase epistemic status at slatestarcodex, I think that's where it come from.
4Good_Burning_Plastic
I think he got the idea from Muflax's blog.
[-]Erfeyah30

Does the community do anything different when discussing?

I am going through the site and exploring some of the writings. I am also listening to the Bayesian conspiracy podcast. It is all very interesting but I can not see a change in the method of discussion. Techniques such as Bayes theorem etc. do not seem to be used when the subjects are of some complexity (which all interesting subjects are). It all seems to me that it is just a nice, civilised conversation with awareness of biases and the need to keep emotion on hold, as well as, examine assumptions.

Is there a discussion in video/audio/writing that you can point me to which demonstrates a different methodology of argumentation?

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5MrMind
That might not seem to amount to much, but it's an extremely high bar, compared to the average discussion even in rationality hub like SSC.
5Erfeyah
Good point. On reflection, I think my question is trying to project a criticism of mine regarding the community. Apologies for trying to sneak it in as a question. I seem to have the impression that the community is projecting an image of effective rationality when I can not see practical applications and sometimes I see mistakes of overconfidence towards conclusions. That is what made me think that the community thinks it has found some methodology that is more robust than the usual ones. Actually getting involved and starting commenting is giving me a better view of what is actually going on. I think I will have to take some time to get a feel of the situation before I voice criticisms. Thanks!
2tog
That plus it's a more intelligent than average community with shared knowledge and norms of rationality. This is why I personally value LessWrong and am glad it's making something of a comeback.
0ChristianKl
http://lesswrong.com/lw/o6p/double_crux_a_strategy_for_resolving_disagreement/ is a well specific methodology.
0Erfeyah
This is very interesting and seems to have potential. Thanks for pointing me to the article! The important thing though would be to see the technique in action. Is there a thread were the community is experimenting with the application of the methodology?
0ChristianKl
Specific applications of the framework that I have seen in practice were always offline discussions. Most online discussions are unstructured and people don't follow an explicit framework. As far as structured goes, there's http://predictionbook.com/ and http://www.metaculus.com
[-]Richard Korzekwa 20

Is there a good way to find out what's common knowledge?

I feel like it would be handy to have a repository of things that, for example, a typical high school or college graduate knows. I think this would be useful for explaining things or writing about topics where you have too much domain knowledge to remember what it's like to be outside the field, and also for finding out if there are topics where you're lacking. Another case where I found myself wanting such a tool was when I recently got in a disagreement about whether a particular word was a niche t... (read more)

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2Strangeattractor
It varies a lot from culture to culture. That's part of what a culture is, what is thought of as default or background knowledge, or something people will know. So...who is your audience? What cultures or sub-cultures are they from? It's not going to be the same from country to country, or different regions within a country, or rural vs. urban, or age group or educational background. When authors write books about a culture they are unfamiliar with, sometimes they hire someone from that culture to read over the book, and give feedback about what they could do better. For example Mary Robinette Kowal did this for her novel Of Noble Family. http://maryrobinettekowal.com/journal/im-spending-today-swapping-dialect-novel/ I don't think there is a one-size-fits-all answer for a "general audience" that would apply to all people around the world. It might be helpful to be more specific about what you think a general audience means. People of a certain educational background within a particular region of a particular country who speak a specific language? There are few events aimed at a world audience - the Olympics, some United Nations events, so you could study some of those and see what they assume of people. For specific words, a rough approach might be to google that word and look at the number of results, and see the relative popularity of them. For example "onion" has 148 million results, "carrot" has 90 million results, "artichoke" has 20 million results, so that might be an indication of how popular those vegetables are, relative to each other.
0Richard Korzekwa
This is why I specified by education level (and I thought I'd specified Americans or Europeans, but apparently not), though I'll admit that I'd been thinking primarily in terms of English-speaking people (though this is an English forum, and I'm not likely to be writing for a non-English-speaking audience). I also didn't specify that I'm not really talking about cultural common knowledge; I'm not expecting a typical Londoner to have the same culinary knowledge as a typical person from Nashville. However, the kinds of things that I think are generally regarded as common knowledge are also relatively culturally insensitive, and I do expect that the typical college graduate from London and the typical college graduate from Nashville have quite a lot of overlap in their secondary education curricula. When I say 'quite a lot', I just mean that, if you have a good understanding of one group's common common knowledge, you'll be able to use that with the other group, at least for things that are generally made for a "general audience". The main reason I think this is true is that watching British TV and watching American TV isn't any different, in terms of what I'm expected to know, apart from cultural references. Similarly, as an American, I've never really run into problems related to assumed knowledge while talking to non-Americans. (The main exception here might be history education.) Then again, a majority of the non-Americans that I talk to I meet either through either the rationalist community or academia, so there may be some selection bias. Also, it's possible that the wide proliferation of American media gives non-Americans a good sense of what they can assume Americans know. Am I wrong? Are American and European audiences sufficiently different that they usually require different accommodations? I like this idea, though I'm unsure how to find media that isn't written mainly for a particular nationality, and that assumes anything apart from English literacy. (Th
2Viliam
In theory, one of the goals of general education is to define what is supposed to be common knowledge, and to make it so. But clearly people forget many things they learned at school, and learn many things from media or internet. Maybe there are some standardized exams where you could look at the results, if they are published in details, to see what students actually learned. But I suspect that whatever method you use, at the end there will be a scale... some things generally known by 99% of your target population, some known by 90%, 80%, 50%, 20%, 10%, 1%, 0.1% etc. I guess a typical solution is to have your text read by a few people, and hope they are a representative sample. Or just hope that you are lucky and got it right.
[-]Richard Korzekwa 10

I recently had a dream in which an unspecified organization was anticipating trouble from an unspecified group of people. One member of the organization remarked that, should things get bad, they had seven gay 400 lb game theorists that could be called in on a moment's notice.

What sort of problem is solved by the deployment of unusually heavy game theorists? Does it matter that they are gay? What kind of organization would have such resources at its disposal?

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3Lumifer
The alt-right homophobic sumo wrestlers are invading via multiple lanes.
[-]Thomas10

This is my stupid question:

https://protokol2020.wordpress.com/2016/12/14/geometry-problem/

Do not hesitate to patronize me, or whatever does it take, I'd really like to have an answer.

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3Alejandro1
The question is analogous to the Grim Reaper Paradox, described by Chalmers here:
2Thomas
You are right. This is actually the same problem. The problem of the (math) infinity magic itself.
2NoSuchPlace
As you point out later in the thread the light can never touch any given sphere, since no matter which one you pick there will always be another sphere in front of it to block the light. At the same time the light beam must eventually hit something because the centre sphere is in its way. So your light beam must both eventually hit a sphere and never hit a sphere so your system is contradictory and thus ill defined. You could make the question answerable by instead asking for the limit of the light beam as number of steps of packing done goes to infinity in which case the light reflects back at 180°, since it does that in every step of the packing. Alternately you could ask what happens to the light beam if it is reflected of a shape which is the limit of the packing you described, in which case it will split in three since the shape produced is a cube (since it will have no empty spaces). (Edit:no it doesn't the answer to this question is again undefined via the argument in the first paragraph, since the matter it bounced of of had to belong to some sphere)
1Thomas
It's not a cube. The corner points for example, are NOT covered by any sphere. Its a cube MINUS infinitely many points. On the edges, for example, only aleph zero points are covered and aleph one many - aren't. The limit technique you employ here, does not apply at all.
0NoSuchPlace
Thank you I fixed it. I think the same argument shows that that question is also undefined. I think the real takeaway is that physics doesn't deal well with some infinities.
0Thomas
The question may be flawed in a way that I don't see it. Or the question may be flawed not by my mistake, but by a mistake already built in R^3 or R^4 math. I think, it's the later.
1LawrenceC
Maybe think about the problem this way: Suppose there was some small ball inside of your super-packed structure that isn't filled. Then we can fill this ball, and so the structure isn't super-packed. It follows that the volume of the empty space inside of your structure has to be 0. Now, what does your super-packed structure look like, given that it's a empty cube that's been filled? EDIT: Nevermind, just saw that Villiam gave a similar answer.
0Richard Korzekwa
The answer "cubes with no empty space are filled cubes" was perfectly decent, as was the verbal argument about limits that Viliam provided. But in case those weren't satisfying, I've written a more explicit version of the proof* that the ray travels zero distance between reaching the cube and reaching a sphere. It utilizes the solution to the geometric sum, which is proved using limits: https://en.wikipedia.org/wiki/Geometric_series The proof (derivation?) is here: http://imgur.com/vSfABHk I think you can just argue by symmetry that the ray must retro-reflect. *At least, it looks like a proof to a physicist. It may not meet the standards of a proof to a mathematician.
0Thomas
By the symmetry you can argue that the ray hasn't reach the sphere. Lumifer suggested something very similar as you, but this retro-reflection is equally possible as the retro-shadowing. Which do you prefer and why? Can't be both.
0Richard Korzekwa
Can you explain?
0Lumifer
My intuition says the ray should bounce back immediately. The reason is how the spheres are packed in the cube: if you look along the main diagonal, there is the largest one in the center, and then there is a sequence of smaller spheres which are all aligned along the main diagonal. The ray shot into the cube along that diagonal would thus be aimed at the center of the corner-most sphere and so should just reflect at 180 degrees.
0Thomas
You are 100% right about that. That one doesn't exist. It's always at least one still closer to the corner.
0Lumifer
I didn't say any particular one. The reasoning applies to all of them so it doesn't matter.
0Thomas
You are suggesting a kind of Einstein-Bose condensate, where a collective of particles becomes one. An interesting idea, but ... I doubt it's correct way of thinking about this.
1Lumifer
Not at all. I'm just saying that you have an infinite sequence of spheres with the property X. You're saying that because the sequence is infinite I can't point to the last sphere and therefore can't say anything about it. I'm saying that because all spheres in this sequence have the property X, it doesn't matter that the sequence is infinite.
4LawrenceC
This isn't true in general. Each natural number is finite, but the limit of the natural numbers is infinite. Just because each of the intermediate shapes has property doesn't mean the limiting shape has property X. Notably, in this case each of the intermediate shapes has a non-zero amount of empty space, but the limiting shape has no empty space.
2Thomas
That no ray can come to them from that direction, since it's eclipsed by the smaller ball toward the corner? If this is the property X, then all those spheres have it, yes!
1Lumifer
Oh, dear. So all the spheres are shadowed, meaning the ray cannot reach any of them, so it just passes through the cube without even noticing it was there. Fee-fi-fo-fum, I smell Zeno!
0Thomas
So it's looks like. This does not follow at all. You should rather smell Yablo.
0Lumifer
I didn't specifically mean the paradoxes, I meant Zeno as the first guy who said "Let's throw some infinities into a physical-world scenario and see how many amphoras of wine do we need until it starts to make sense..."
0Thomas
Oh, I see. I strongly suspect, that the abstract world of pure mathematics doesn't handle infinities any better than the real world does. It's a fundamentally broken. I mean the infinity is a fundamentally broken concept. Well, I don't even believe in mathematics outside the physical world. It's just a game of particles in Zeno's head. Or Cantor's or any other human's head. Okay, heads, papers, blackboards, computers etc. Mathematics lives inside of physics only.
0Lumifer
I don't know about that. It's a model. "All models are wrong, but some are useful" -- George Box On the other hand: "God created the integers and the rest is the work of man" :-/
0Richard Korzekwa
This sounds familiar. Since every point between your nose and your computer monitor has the property X, that there exists another point between it and your computer monitor, no matter how many points you move your nose through, there's always more points it must go through before reaching the computer monitor. This is why, no matter how you try, you can never touch your nose to a computer monitor.
0Thomas
It's not a Zeno's paradox. You CAN touch the screen, if there is no obstacle between. But here it's a different story. Every sphere is shadowed, has an obstacle between itself and the incoming ray. The finite amount of obstacles where there is then the outer obstacle - and everything is fine. Ray bounces back of this outer/unshadowed reflective sphere. Pretty much like the Yablo's list. If there is the last member of the list, everything is just fine.
2Richard Korzekwa
There is no last point between your nose and your monitor. Let me pose a different problem, to demonstrate what I think is wrong with your argument. You start with a reflective square slab that is half as thick as it is wide. You place another slab, which is half as thick as the first on top, then another half as thick as that. You continue doing this until your stack of slabs is as tall as it is wide. If you direct an ideal ray at this slab, along the symmetry axis of the stack, what does the ray do? This situation is, once constructed, identical to the first ray described in your problem (the one that hits the face of the cube), but your argument would imply that the ray won't reflect back, because whichever slab it would reflect from has another slab shadowing it.
0Thomas
Look! Need not to be the last point. Zeno is resolved by infinite sums, which can give us finite numbers. Yablo isn't resolved and this is related to Yablo, not to Zeno paradox.
0Viliam
Taken literally, this means there is an infinite amount of spheres, some of them (actually, the vast majority of them) smaller than the size of an atom. What are they made of? The machine that simulates our universe will crash with an "out of memory" error, because this would require the simulator to spawn infinitely many small spheres at the corner of the cube when trying to determine which sphere will the photons hit first. If the ray is supposed to be just an infinitely small line, the question is somewhat similar to asking "how much is zero divided by zero?" -- there are multiple different answers that can be defended by approaching the problem from a different point of view. In general, the answer is undefined because the question is... wrong. With real photons, there is the additional question of how they would interact with the hypothetical objects of extremely small size. Maybe they would just skip the first few "too small" spheres, and only interact with the first one larger than Plack size? I give up here, because I am not sufficiently familiar with physics to answer this.
0Thomas
We are talking about mathematics here, an abstract (unreal) world. Not about physics. It's geometry in the sense of Euclides. It's not everything "division by zero error". Still, it's a nice try, thank you.
6Viliam
In mathematics we deal with infinities by using limits -- essentially by definiting a sequence of finite scenarios that gradually approach the desired situation, and observe how the answer develops for these finite scenarios. So, by gradually adding the reflective spheres we find that: 1) the diagonal ray bounces back; 2) from a place that becomes nearer and nearer the corner as we keep adding the spheres. The answer is that limit of the ray behavior is the ray bouncing back from the corner of the cube. However, the answer depends on how the sequence of the scenarios was constructed; namely that we keep adding the spherese, but the ray already aims to the diagonal perfectly. Small changes, such as assuming that the ray is also getting gradually more precise as we keep adding the spheres (becoming perfectly precise only at the time all the spheres are added), could justify reflection in any angle. Or bouncing between the spheres.
0Thomas
They are tightly packed. How could they "bounce between spheres"?
0Thomas
Really? What is the diameter of the sphere, which reflected the ray back? And how come, that a smaller sphere didn't shadow this ray?
5Viliam
Okay, I'll try to be more explicit about this: Infinity doesn't exist. Some people say there is a difference between a "potential infinity" and "actual infinity", but that seems like a wrong way to use language; it would be more precise to say that we can imagine processes that continue indefinitely -- ignoring the technical details of running out of resources, heat death of the universe, etc. -- but nothing can be infinite here and now. Or, to put it shortly, "infinite" only exists as an adjective describing processes, but never as a noun. (Historical trivia: I found this argument in Alfred Korzybski's Science and Sanity. That's the "the map is not the territory" guy.) There are also mathematicians that pretend otherwise and talk about various infinities, effectively extending their maps beyond the territory. But magic always comes with a price, and in this case the price is that there are multiple possible maps (which all fit the territory, and only disagree about the things happening outside of it) and then the mathematicians start arguing about which one should they use, because there is no way to choose the "true" one (by abandoning the territory, all we can talk about is self-consistence, and you can have multiple different self-consistent maps), so instead they try to choose the most "elegant" one, which is kinda subjective, because even when someone finds weird things happening on a map, the owner of the map will proudly proclaim that this is not a bug, but a feature. -- This leads to a lot of confusion even among people who study mathematics, probably because the few people who understand what this is all about find it too obvious to mention. Uhm, back to the point: infinity doesn't exist. If we want to debate something meaningful, we can only debate properties of some indefinite process. For example, a process of "adding more small spheres inside the cube, while a ray shines at it diagonally". But it is a process without an end. There will never be a m
0Thomas
I agree, that this is the solution. I completely and absolutely agree with you. It's a false (mad if you wish) construction. But tell this to the 99% of the top mathematicians! For them all those infinities - infinite multitude of them - exist. What I don't agree with you, is: It cannot continue "indefinitely" - it will stop rather soon. But yes ... I gave this solution as the possibility number 6. 6. This is an illegal or ill defined question You have answered correctly at the bottom line, Viliam. By my judgement. But that's just my judgement, of course. I disagree with your reasoning above the bottom line, but that's not that important as your (and mine) final answer.
0Viliam
Okay, I am happy we came to an agreement, but... ...I wonder whether this is true. I mean, as long as someone knows that you can have multiple mutually incompatible systems of axioms, then they should on some level realize that the choice of a specific system is arbitrary. I mean, I haven't realized this for a long time simply because I read have some popular books about infinities probably already at elementary school age, and they didn't start with a big red warning "everything you will read in this book is merely a consequence of an arbitrarily selected set of axioms; other sets of axioms could lead to completely different outcomes; and the choice of the axioms is arbitrary because nothing of this is real, mwa-ha-ha-ha!" So, I naively assumed it was just business as usual. If I didn't suspect books about prime numbers or complex numbers, why should I suspect the books about infinities? And when I later heard something about the axioms, the idea of the "one true system of aleph-zero, aleph-one, etc." was already firmly stuck in my head. So even while I was reading about how different axioms are possible, I still on some level assumed that the ones I was already familiar with are -- in some sense -- the correct ones (without asking myself what exactly the word "correct" could even possibly mean in this context). Only a few years later I have finally connected the dots in my head. It was while thinking about natural numbers, the fifth Peano's axiom, how without it we could have different models of natural numbers, and what exactly that means. And a few years later, my friend complained about the axiom of choice, and suddenly something clicked in my head, and I was like "wait, isn't that the same thing as with the fifth Peano's axiom? like you can have different models that all satisfy the same set of axioms, but they still differ at some underspecified places, and you need an extra axiom to distinguish between them?" Because at that moment I already had an under
0Thomas
I think you underestimate the zel of the 1000 top mathematicians about this infinity business. Perhaps there is about 10 dissidents among them, who are finitists. But for all the others, the concept of infinity is a fundamental one. It's easier to find a Catholic bishop who doesn't care about God or Trinity, than a top mathematician who doesn't believe and love infinity. The infinity mythology is quite a rich one. Surprisingly rich, indeed. First, we have the countable infinity - like all the natural numbers, or all the rational numbers. Aleph 0 is the cardinal of those. Then, we have 2^aleph0 or aleph1. The number of all real numbers. Between those two, you are free to postulate some greater then aleph0 and smaller than aleph1. You are also free to postulate that there is no cardinal between aleph zero and aleph one. It's the Cohen's solution of the so called Continuum problem. You have more alephs above aleph 1. One aleph for every natural number. And you are free to postulate (or not) cardinal numbers between each two. Then you have trans aleph big cardinal numbers. Then you have non-constructible big infinite cardinals. And then you have a lot of ordinals. And then you have the Axiom of Choice. You can accept it or not. But it is proven, that if the whole structure of infinity is broken. then is broken with or without the Axiom of Choice. I suspect Terence Tao has no strong opinion about ZF or ZFC system. He loves prime numbers and all the natural and real numbers and so on. But I don't think he is in Set Theory very much.
[-]sone3d00

I would like to know what do you think it is the probability that we are living in a simulation.

Personally, my guess is that the posibility that we are living in a base reality is only 1 in (Very big number with lot of zeroes).

Reply
2Dagon
This depends a lot on where you draw the line between "simulation" and "universe". We definitely seem to be in a mathematically-describable finite (or finitely-perceivable) system. If it could be simulated so completely that we can't tell, then it may as well be simulated.
1ChristianKl
That question is in our yearly census. http://lesswrong.com/r/lesswrong/lw/nkw/2016_lesswrong_diaspora_survey_results/ brings you to the latest census.
0Erfeyah
This is related to the (unsolved) question of what consciousness is. Briefly the currently conceived possibilities: * [A] Consciousness is an algorithm. * [B] Consciousness is a fundamental property of nature that emerges from certain structures of integrated information. * [C] Consciousness is a fundamental property of nature. * [D] Consciousness does not exist. We do not have an internal experience of anything. About [A]: Neuroscientists are trying to find the locus of consciousness in the brain but they haven’t managed yet. Even more important, there is a conceptual gap about the possibility of information encoding subjective experience. The very influential Chinese room thought experiment of John Searle is an extremely strong argument against the possibility of filling the information/meaning gap. About [B]: This is an interesting theory. It is not the same as [A]. I recommend Tononi's book Phi if you want to learn more about it. It is not easy to digest but a really fascinating possibility. He proposes (and has a mathematical model for it), that certain configurations of matters with certain properties give rise to consciousness depending on their integration of information. It has not been experimentally proven or strongly indicated. It implies Panpsychism (see [C]). About [C]: In philosophy this is labelled as Panpsychism. It is a view that seems to be implied in the writings of all the major mystical traditions. About [D]: This is Daniel Dennett’s position. The proposition that our internal experience. The one we are having right now. Does not exist. ---------------------------------------- To my understanding, the simulation hypothesis is only valid if [A] or [D] is true.
[-]cousin_it00

I'd be very curious to hear any creativity tips that have worked for LWers in any fields (writing, drawing, music, etc.)

Reply
6Elo
Every day. Do it every day. This is the number one piece of advice for writers, artists. Every day. (An hour every day, less if you can't handle that, and maybe start smaller like 5mins). Every day. There will be days when your grandma dies, days when it's been raining for 3 days straight, Days where you might have to tie yourself to the desk, days when people are literally dragging you away. Things will happen, you will go on holidays, WRITE EVERY DAY. Every day. Every day. Every day. Feel uncreative? Do it anyway. You can still produce great work by generating what you think creativity would look like. Every day! Every day. Cannot emphasise enough - every day. (And yes this works for me) Other than that - have a workspace (future article of mine one day) - a setup that is designed to enable you to work. If this means a bottle of water nearby - that. If it means headphones, extra lighting, 16 pencils all lined up square. A pentagram with candles at the corners. Whatever it is; work out what's stopping you from working, and remove those things. Then work out what's enabling you to work and increase them until you have the most fruitful workspace possible. I can't tell you all the answers to how to make a perfect workspace, but if you sit down with a pen and paper and work through whatever you can think of this should take you well on your way. Once you are on your way, notice things that distract you and later come back and remove them. Keep tab-closing habits, phone on the other side of the room habits, cup-of-tea-making habits, whatever it takes. Make a good system and a good workspace, then repeat. And write every day. (probably in the morning is better, probably first thing is better)
0Viliam
It's similar for exercise. And probably any other activity you deeply care about.
0Risto_Saarelma
Cal Newport on "Write Every Day". If it's not your main job, you're going to end up having no write days, and if you're committed to a hard schedule a missed day is going to translate into "welp, couldn't make the cut then, better quit for good".
4Elo
Disagree with his opinion. He suggests the biggest problem with write every day is: Yea, and? That doesn't have to cause failure. We know things like You don't have to fail with abandon.. Also iteration cycles He also says: Which is fine. That's his experience. You can listen to him and his experience or you can not. Anecdata is anecdata. There's a reason why every list of writing advice and every famous writer says to write every day. If you only ever do that; you will be doing yourself a disservice. You don't need to know the full plan before setting off. And it's often a waste of time to not start and pivot. Imagine having to know every word of a book before you start writing it down on paper. That's a ridiculous concept. ---------------------------------------- in counter point - if you set out to write every day - yes you will fail. That doesn't mean you can't try to do it, and do really really well in the process. If you fail you don't have to quit for good. If you iterate and try again you can diagnose that failure mode and try again. Try harder. Try smarter.
0RomeoStevens
This has hugely impacted my whole life https://vimeo.com/89936101
[-][anonymous]00

I read this post named Flinching away from truth is often about protecting the epistemology. The post reminds me of familiar psychological biases such as catastrophic thinking. In catastrophic thinking individual events are seen as having further, ill nature consequences than they de facto usually have. I see these two approaches (the bucket error and the catastrophic thinking) have qualitatively different approaches to the same thing. The kid in the story is engaging in catastrophic thinking when they equate the writing mistake with not being allowed to b... (read more)

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